## TSTP Solution File: GRP125-1.003 by SPASS---3.9

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP125-1.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n012.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  : 600s
% DateTime : Sat Jul 16 11:45:34 EDT 2022

% Result   : Unsatisfiable 0.18s 0.41s
% Output   : Refutation 0.18s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   11
% Syntax   : Number of clauses     :   28 (  11 unt;   9 nHn;  28 RR)
%            Number of literals    :   68 (   0 equ;  25 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   7 con; 0-0 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
group_element(e_1),
file('GRP125-1.003.p',unknown),
[] ).

cnf(2,axiom,
group_element(e_2),
file('GRP125-1.003.p',unknown),
[] ).

cnf(4,axiom,
~ equalish(e_1,e_2),
file('GRP125-1.003.p',unknown),
[] ).

cnf(6,axiom,
~ equalish(e_2,e_1),
file('GRP125-1.003.p',unknown),
[] ).

cnf(7,axiom,
~ equalish(e_2,e_3),
file('GRP125-1.003.p',unknown),
[] ).

cnf(10,axiom,
( ~ group_element(u)
| ~ group_element(v)
| product(v,u,e_3)
| product(v,u,e_2)
| product(v,u,e_1) ),
file('GRP125-1.003.p',unknown),
[] ).

cnf(11,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equalish(x,w) ),
file('GRP125-1.003.p',unknown),
[] ).

cnf(12,axiom,
( ~ product(u,v,w)
| ~ product(u,x,w)
| equalish(x,v) ),
file('GRP125-1.003.p',unknown),
[] ).

cnf(13,axiom,
( ~ product(u,v,w)
| ~ product(x,v,w)
| equalish(x,u) ),
file('GRP125-1.003.p',unknown),
[] ).

cnf(14,axiom,
product(u,u,u),
file('GRP125-1.003.p',unknown),
[] ).

cnf(15,axiom,
( ~ product(u,v,w)
| ~ product(v,u,x)
| product(x,w,v) ),
file('GRP125-1.003.p',unknown),
[] ).

cnf(23,plain,
( ~ product(u,v,v)
| equalish(u,v) ),
inference(res,[status(thm),theory(equality)],[14,13]),
[iquote('0:Res:14.0,13.0')] ).

cnf(25,plain,
( ~ product(u,v,u)
| equalish(v,u) ),
inference(res,[status(thm),theory(equality)],[14,12]),
[iquote('0:Res:14.0,12.0')] ).

cnf(27,plain,
( ~ product(u,u,v)
| equalish(v,u) ),
inference(res,[status(thm),theory(equality)],[14,11]),
[iquote('0:Res:14.0,11.0')] ).

cnf(33,plain,
( ~ group_element(u)
| ~ group_element(e_1)
| product(e_1,u,e_3)
| product(e_1,u,e_2)
| equalish(u,e_1) ),
inference(res,[status(thm),theory(equality)],[10,25]),
[iquote('0:Res:10.4,25.0')] ).

cnf(38,plain,
( ~ group_element(e_1)
| ~ group_element(u)
| product(u,e_1,e_3)
| product(u,e_1,e_2)
| equalish(u,e_1) ),
inference(res,[status(thm),theory(equality)],[10,23]),
[iquote('0:Res:10.4,23.0')] ).

cnf(40,plain,
( ~ group_element(u)
| product(e_1,u,e_3)
| product(e_1,u,e_2)
| equalish(u,e_1) ),
inference(ssi,[status(thm)],[33,1]),
[iquote('0:SSi:33.1,1.0')] ).

cnf(41,plain,
( ~ group_element(u)
| product(u,e_1,e_3)
| product(u,e_1,e_2)
| equalish(u,e_1) ),
inference(ssi,[status(thm)],[38,1]),
[iquote('0:SSi:38.0,1.0')] ).

cnf(51,plain,
( ~ group_element(e_2)
| product(e_1,e_2,e_3)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(res,[status(thm),theory(equality)],[40,23]),
[iquote('0:Res:40.2,23.0')] ).

cnf(52,plain,
( product(e_1,e_2,e_3)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(ssi,[status(thm)],[51,2]),
[iquote('0:SSi:51.0,2.0')] ).

cnf(53,plain,
product(e_1,e_2,e_3),
inference(mrr,[status(thm)],[52,6,4]),
[iquote('0:MRR:52.1,52.2,6.0,4.0')] ).

cnf(54,plain,
( ~ product(e_2,e_1,u)
| product(u,e_3,e_2) ),
inference(res,[status(thm),theory(equality)],[53,15]),
[iquote('0:Res:53.0,15.0')] ).

cnf(80,plain,
( ~ group_element(e_2)
| product(e_2,e_1,e_3)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(res,[status(thm),theory(equality)],[41,25]),
[iquote('0:Res:41.2,25.0')] ).

cnf(86,plain,
( product(e_2,e_1,e_3)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(ssi,[status(thm)],[80,2]),
[iquote('0:SSi:80.0,2.0')] ).

cnf(87,plain,
product(e_2,e_1,e_3),
inference(mrr,[status(thm)],[86,6,4]),
[iquote('0:MRR:86.1,86.2,6.0,4.0')] ).

cnf(92,plain,
product(e_3,e_3,e_2),
inference(res,[status(thm),theory(equality)],[87,54]),
[iquote('0:Res:87.0,54.0')] ).

cnf(93,plain,
equalish(e_2,e_3),
inference(res,[status(thm),theory(equality)],[92,27]),
[iquote('0:Res:92.0,27.0')] ).

cnf(100,plain,
\$false,
inference(mrr,[status(thm)],[93,7]),
[iquote('0:MRR:93.0,7.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : GRP125-1.003 : TPTP v8.1.0. Released v1.2.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n012.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Mon Jun 13 23:15:10 EDT 2022
% 0.12/0.33  % CPUTime  :
% 0.18/0.41
% 0.18/0.41  SPASS V 3.9
% 0.18/0.41  SPASS beiseite: Proof found.
% 0.18/0.41  % SZS status Theorem
% 0.18/0.41  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.41  SPASS derived 67 clauses, backtracked 0 clauses, performed 0 splits and kept 65 clauses.
% 0.18/0.41  SPASS allocated 75670 KBytes.
% 0.18/0.41  SPASS spent	0:00:00.06 on the problem.
% 0.18/0.41  		0:00:00.03 for the input.
% 0.18/0.41  		0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.41  		0:00:00.00 for inferences.
% 0.18/0.41  		0:00:00.00 for the backtracking.
% 0.18/0.41  		0:00:00.01 for the reduction.
% 0.18/0.41
% 0.18/0.41
% 0.18/0.41  Here is a proof with depth 6, length 28 :
% 0.18/0.41  % SZS output start Refutation
% See solution above
% 0.18/0.41  Formulae used in the proof : element_1 element_2 e_1_is_not_e_2 e_2_is_not_e_1 e_2_is_not_e_3 product_total_function1 product_total_function2 product_right_cancellation product_left_cancellation product_idempotence qg3
% 0.18/0.41
%------------------------------------------------------------------------------
```