TSTP Solution File: SYN721+1 by LEO-II---1.7.0

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYN721+1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% 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  : 600s
% DateTime : Thu Jul 21 08:29:21 EDT 2022

% Result   : Theorem 0.21s 0.38s
% Output   : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   34 (  20 unt;   4 typ;   0 def)
%            Number of atoms       :  145 (  37 equ;   0 cnn)
%            Maximal formula atoms :    7 (   4 avg)
%            Number of connectives :  199 (  20   ~;  19   |;  11   &; 138   @)
%                                         (   0 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   4 con; 0-2 aty)
%            Number of variables   :   64 (   0   ^  55   !;   9   ?;  64   :)

%------------------------------------------------------------------------------
thf(tp_a,type,
a: \$i ).

thf(tp_b,type,
b: \$i ).

thf(tp_q,type,
q: \$i > \$i > \$o ).

thf(tp_r,type,
r: \$i > \$i > \$o ).

thf(1,conjecture,
( ( ( r @ a @ b )
& ! [X: \$i] :
( ? [Y: \$i] : ( r @ X @ Y )
=> ( q @ X @ X ) )
& ! [U: \$i,V: \$i] :
( ( q @ U @ V )
=> ! [Z: \$i] : ( r @ Z @ V ) ) )
=> ? [W: \$i] :
( ( r @ b @ W )
& ( q @ W @ a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lx1) ).

thf(2,negated_conjecture,
( ( ( ( r @ a @ b )
& ! [X: \$i] :
( ? [Y: \$i] : ( r @ X @ Y )
=> ( q @ X @ X ) )
& ! [U: \$i,V: \$i] :
( ( q @ U @ V )
=> ! [Z: \$i] : ( r @ Z @ V ) ) )
=> ? [W: \$i] :
( ( r @ b @ W )
& ( q @ W @ a ) ) )
= \$false ),
inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
( ( ( ( r @ a @ b )
& ! [X: \$i] :
( ? [Y: \$i] : ( r @ X @ Y )
=> ( q @ X @ X ) )
& ! [U: \$i,V: \$i] :
( ( q @ U @ V )
=> ! [Z: \$i] : ( r @ Z @ V ) ) )
=> ? [W: \$i] :
( ( r @ b @ W )
& ( q @ W @ a ) ) )
= \$false ),
inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
( ( r @ a @ b )
= \$true ),
inference(standard_cnf,[status(thm)],[3]) ).

thf(5,plain,
( ( ! [X: \$i] :
( ? [Y: \$i] : ( r @ X @ Y )
=> ( q @ X @ X ) ) )
= \$true ),
inference(standard_cnf,[status(thm)],[3]) ).

thf(6,plain,
( ( ! [U: \$i,V: \$i] :
( ( q @ U @ V )
=> ! [Z: \$i] : ( r @ Z @ V ) ) )
= \$true ),
inference(standard_cnf,[status(thm)],[3]) ).

thf(7,plain,
( ( ? [W: \$i] :
( ( r @ b @ W )
& ( q @ W @ a ) ) )
= \$false ),
inference(standard_cnf,[status(thm)],[3]) ).

thf(8,plain,
( ( ~ ? [W: \$i] :
( ( r @ b @ W )
& ( q @ W @ a ) ) )
= \$true ),
inference(polarity_switch,[status(thm)],[7]) ).

thf(9,plain,
( ( ! [W: \$i] :
( ~ ( q @ W @ a )
| ~ ( r @ b @ W ) ) )
= \$true ),
inference(extcnf_combined,[status(esa)],[8]) ).

thf(10,plain,
( ( ! [X: \$i] :
( ! [Y: \$i] :
~ ( r @ X @ Y )
| ( q @ X @ X ) ) )
= \$true ),
inference(extcnf_combined,[status(esa)],[5]) ).

thf(11,plain,
( ( ! [U: \$i,V: \$i] :
( ~ ( q @ U @ V )
| ! [Z: \$i] : ( r @ Z @ V ) ) )
= \$true ),
inference(extcnf_combined,[status(esa)],[6]) ).

thf(12,plain,
( ( ! [U: \$i,V: \$i] :
( ~ ( q @ U @ V )
| ! [Z: \$i] : ( r @ Z @ V ) ) )
= \$true ),
inference(copy,[status(thm)],[11]) ).

thf(13,plain,
( ( ! [X: \$i] :
( ! [Y: \$i] :
~ ( r @ X @ Y )
| ( q @ X @ X ) ) )
= \$true ),
inference(copy,[status(thm)],[10]) ).

thf(14,plain,
( ( r @ a @ b )
= \$true ),
inference(copy,[status(thm)],[4]) ).

thf(15,plain,
( ( ! [W: \$i] :
( ~ ( q @ W @ a )
| ~ ( r @ b @ W ) ) )
= \$true ),
inference(copy,[status(thm)],[9]) ).

thf(16,plain,
! [SV1: \$i] :
( ( ! [SY6: \$i] :
( ~ ( q @ SV1 @ SY6 )
| ! [Z: \$i] : ( r @ Z @ SY6 ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).

thf(17,plain,
! [SV2: \$i] :
( ( ! [SY8: \$i] :
~ ( r @ SV2 @ SY8 )
| ( q @ SV2 @ SV2 ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).

thf(18,plain,
! [SV3: \$i] :
( ( ~ ( q @ SV3 @ a )
| ~ ( r @ b @ SV3 ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).

thf(19,plain,
! [SV4: \$i,SV1: \$i] :
( ( ~ ( q @ SV1 @ SV4 )
| ! [SY9: \$i] : ( r @ SY9 @ SV4 ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).

thf(20,plain,
! [SV2: \$i] :
( ( ( ! [SY8: \$i] :
~ ( r @ SV2 @ SY8 ) )
= \$true )
| ( ( q @ SV2 @ SV2 )
= \$true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).

thf(21,plain,
! [SV3: \$i] :
( ( ( ~ ( q @ SV3 @ a ) )
= \$true )
| ( ( ~ ( r @ b @ SV3 ) )
= \$true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).

thf(22,plain,
! [SV4: \$i,SV1: \$i] :
( ( ( ~ ( q @ SV1 @ SV4 ) )
= \$true )
| ( ( ! [SY9: \$i] : ( r @ SY9 @ SV4 ) )
= \$true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).

thf(23,plain,
! [SV5: \$i,SV2: \$i] :
( ( ( ~ ( r @ SV2 @ SV5 ) )
= \$true )
| ( ( q @ SV2 @ SV2 )
= \$true ) ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(24,plain,
! [SV3: \$i] :
( ( ( q @ SV3 @ a )
= \$false )
| ( ( ~ ( r @ b @ SV3 ) )
= \$true ) ),
inference(extcnf_not_pos,[status(thm)],[21]) ).

thf(25,plain,
! [SV4: \$i,SV1: \$i] :
( ( ( q @ SV1 @ SV4 )
= \$false )
| ( ( ! [SY9: \$i] : ( r @ SY9 @ SV4 ) )
= \$true ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).

thf(26,plain,
! [SV5: \$i,SV2: \$i] :
( ( ( r @ SV2 @ SV5 )
= \$false )
| ( ( q @ SV2 @ SV2 )
= \$true ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).

thf(27,plain,
! [SV3: \$i] :
( ( ( r @ b @ SV3 )
= \$false )
| ( ( q @ SV3 @ a )
= \$false ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).

thf(28,plain,
! [SV1: \$i,SV4: \$i,SV6: \$i] :
( ( ( r @ SV6 @ SV4 )
= \$true )
| ( ( q @ SV1 @ SV4 )
= \$false ) ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).

thf(29,plain,
\$false = \$true,
inference(fo_atp_e,[status(thm)],[14,28,27,26]) ).

thf(30,plain,
\$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[29]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SYN721+1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.35  % Computer : n006.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Mon Jul 11 20:51:05 EDT 2022
% 0.14/0.35  % CPUTime  :
% 0.14/0.35
% 0.14/0.35   No.of.Axioms: 0
% 0.14/0.35
% 0.14/0.35   Length.of.Defs: 0
% 0.14/0.35
% 0.14/0.35   Contains.Choice.Funs: false
% 0.14/0.35  (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.21/0.38
% 0.21/0.38  ********************************
% 0.21/0.38  *   All subproblems solved!    *
% 0.21/0.38  ********************************
% 0.21/0.38  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:29,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.21/0.38
% 0.21/0.38  %**** Beginning of derivation protocol ****
% 0.21/0.38  % SZS output start CNFRefutation
% See solution above
% 0.21/0.38
% 0.21/0.38  %**** End of derivation protocol ****
% 0.21/0.38  %**** no. of clauses in derivation: 30 ****
% 0.21/0.38  %**** clause counter: 29 ****
% 0.21/0.38
% 0.21/0.38  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:29,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------
```