TSTP Solution File: GRP125-1.003 by Leo-III---1.7.0

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : Leo-III---1.7.0
% Problem  : GRP125-1.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n006.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri Sep 16 21:45:22 EDT 2022

% Result   : Unsatisfiable 2.60s 1.55s
% Output   : Refutation 2.79s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   37 (  21 unt;   6 typ;   0 def)
%            Number of atoms       :   55 (   0 equ;   0 cnn)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :  180 (  32   ~;  24   |;   0   &; 124   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   6 usr;   4 con; 0-3 aty)
%            Number of variables   :   38 (   0   ^  38   !;   0   ?;  38   :)

%------------------------------------------------------------------------------
thf(product_type,type,
product: \$i > \$i > \$i > \$o ).

thf(group_element_type,type,
group_element: \$i > \$o ).

thf(e_1_type,type,
e_1: \$i ).

thf(e_2_type,type,
e_2: \$i ).

thf(e_3_type,type,
e_3: \$i ).

thf(equalish_type,type,
equalish: \$i > \$i > \$o ).

thf(15,axiom,
! [A: \$i] : ( product @ A @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).

thf(41,plain,
! [A: \$i] : ( product @ A @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(8,axiom,
~ ( equalish @ e_2 @ e_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).

thf(27,plain,
~ ( equalish @ e_2 @ e_3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(14,axiom,
! [D: \$i,C: \$i,B: \$i,A: \$i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ D @ B @ C )
| ( equalish @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).

thf(39,plain,
! [D: \$i,C: \$i,B: \$i,A: \$i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ D @ B @ C )
| ( equalish @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(12,axiom,
! [D: \$i,C: \$i,B: \$i,A: \$i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ B @ D )
| ( equalish @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).

thf(35,plain,
! [D: \$i,C: \$i,B: \$i,A: \$i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ B @ D )
| ( equalish @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(2,axiom,
group_element @ e_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).

thf(18,plain,
group_element @ e_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(6,axiom,
~ ( equalish @ e_1 @ e_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).

thf(23,plain,
~ ( equalish @ e_1 @ e_3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(3,axiom,
group_element @ e_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).

thf(19,plain,
group_element @ e_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(13,axiom,
! [D: \$i,C: \$i,B: \$i,A: \$i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ D @ C )
| ( equalish @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).

thf(37,plain,
! [D: \$i,C: \$i,B: \$i,A: \$i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ D @ C )
| ( equalish @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(7,axiom,
~ ( equalish @ e_2 @ e_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).

thf(25,plain,
~ ( equalish @ e_2 @ e_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(4,axiom,
group_element @ e_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).

thf(20,plain,
group_element @ e_3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(9,axiom,
~ ( equalish @ e_3 @ e_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).

thf(29,plain,
~ ( equalish @ e_3 @ e_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(5,axiom,
~ ( equalish @ e_1 @ e_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).

thf(21,plain,
~ ( equalish @ e_1 @ e_2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(11,axiom,
! [B: \$i,A: \$i] :
( ~ ( group_element @ A )
| ~ ( group_element @ B )
| ( product @ A @ B @ e_1 )
| ( product @ A @ B @ e_2 )
| ( product @ A @ B @ e_3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).

thf(33,plain,
! [B: \$i,A: \$i] :
( ~ ( group_element @ A )
| ~ ( group_element @ B )
| ( product @ A @ B @ e_1 )
| ( product @ A @ B @ e_2 )
| ( product @ A @ B @ e_3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(1,negated_conjecture,
! [D: \$i,C: \$i,B: \$i,A: \$i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ B @ A @ D )
| ( product @ C @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).

thf(16,plain,
! [D: \$i,C: \$i,B: \$i,A: \$i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ B @ A @ D )
| ( product @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(10,axiom,
~ ( equalish @ e_3 @ e_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).

thf(31,plain,
~ ( equalish @ e_3 @ e_2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(42,plain,
\$false,
inference(e,[status(thm)],[41,27,39,35,18,23,19,37,25,20,29,21,33,16,31]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP125-1.003 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n006.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Wed Aug 31 14:55:39 EDT 2022
% 0.15/0.36  % CPUTime  :
% 0.97/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.16/0.97  % [INFO] 	 Parsing done (117ms).
% 1.16/0.97  % [INFO] 	 Running in sequential loop mode.
% 1.53/1.16  % [INFO] 	 eprover registered as external prover.
% 1.62/1.17  % [INFO] 	 cvc4 registered as external prover.
% 1.62/1.17  % [INFO] 	 Scanning for conjecture ...
% 1.62/1.22  % [INFO] 	 Found a conjecture and 14 axioms. Running axiom selection ...
% 1.80/1.24  % [INFO] 	 Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 1.80/1.26  % [INFO] 	 Problem is propositional (TPTP CNF).
% 1.80/1.26  % [INFO] 	 Type checking passed.
% 1.80/1.26  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ...
% 2.60/1.55  % External prover 'e' found a proof!
% 2.60/1.55  % [INFO] 	 Killing All external provers ...
% 2.60/1.55  % Time passed: 1039ms (effective reasoning time: 570ms)
% 2.60/1.55  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 2.60/1.55  % Axioms used in derivation (14): e_3_is_not_e_2, element_2, product_right_cancellation, product_total_function1, e_1_is_not_e_2, e_2_is_not_e_1, element_1, e_1_is_not_e_3, e_3_is_not_e_1, product_left_cancellation, e_2_is_not_e_3, element_3, product_total_function2, product_idempotence
% 2.60/1.55  % No. of inferences in proof: 31
% 2.60/1.55  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1039 ms resp. 570 ms w/o parsing
% 2.79/1.58  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.79/1.58  % [INFO] 	 Killing All external provers ...
%------------------------------------------------------------------------------
```