TSTP Solution File: GRP705-1 by Leo-III---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : GRP705-1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n020.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 : Mon Jun 24 07:07:56 EDT 2024
% Result : Unsatisfiable 24.79s 5.60s
% Output : Refutation 24.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of formulae : 106 ( 54 unt; 7 typ; 0 def)
% Number of atoms : 168 ( 167 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 821 ( 104 ~; 69 |; 0 &; 648 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 116 ( 0 ^ 116 !; 0 ?; 116 :)
% Comments :
%------------------------------------------------------------------------------
thf(mult_type,type,
mult: $i > $i > $i ).
thf(op_a_type,type,
op_a: $i ).
thf(op_b_type,type,
op_b: $i ).
thf(a_type,type,
a: $i ).
thf(ld_type,type,
ld: $i > $i > $i ).
thf(rd_type,type,
rd: $i > $i > $i ).
thf(unit_type,type,
unit: $i ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c01) ).
thf(14,plain,
! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c03) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ),
inference(lifteq,[status(thm)],[18]) ).
thf(1,negated_conjecture,
( ( mult @ op_a @ ( mult @ op_b @ a ) )
!= ( mult @ ( mult @ op_a @ op_b ) @ a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(11,plain,
( ( mult @ op_a @ ( mult @ op_b @ a ) )
!= ( mult @ ( mult @ op_a @ op_b ) @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(12,plain,
( ( mult @ op_a @ ( mult @ op_b @ a ) )
!= ( mult @ ( mult @ op_a @ op_b ) @ a ) ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(13,plain,
( ( mult @ ( mult @ op_a @ op_b ) @ a )
!= ( mult @ op_a @ ( mult @ op_b @ a ) ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(390,plain,
! [B: $i,A: $i] :
( ( A
!= ( mult @ op_a @ ( mult @ op_b @ a ) ) )
| ( ( mult @ ( rd @ A @ B ) @ B )
!= ( mult @ ( mult @ op_a @ op_b ) @ a ) ) ),
inference(paramod_ordered,[status(thm)],[19,13]) ).
thf(444,plain,
! [A: $i] :
( ( ( rd @ ( mult @ op_a @ ( mult @ op_b @ a ) ) @ A )
!= ( mult @ op_a @ op_b ) )
| ( A != a ) ),
inference(simp,[status(thm)],[390]) ).
thf(480,plain,
( ( rd @ ( mult @ op_a @ ( mult @ op_b @ a ) ) @ a )
!= ( mult @ op_a @ op_b ) ),
inference(simp,[status(thm)],[444]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c02) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ),
inference(lifteq,[status(thm)],[16]) ).
thf(392,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ld @ C @ A )
= D )
| ( ( mult @ ( rd @ A @ B ) @ B )
!= ( mult @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[19,17]) ).
thf(393,plain,
! [B: $i,A: $i] :
( ( ld @ ( rd @ A @ B ) @ A )
= B ),
inference(pattern_uni,[status(thm)],[392:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( rd @ E @ F )),bind(D,$thf( F ))]]) ).
thf(452,plain,
! [B: $i,A: $i] :
( ( ld @ ( rd @ A @ B ) @ A )
= B ),
inference(simp,[status(thm)],[393]) ).
thf(10,axiom,
( ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ op_b ) ) ) ) ) ) ) )
= unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c09) ).
thf(30,plain,
( ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ op_b ) ) ) ) ) ) ) )
= unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(31,plain,
( ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ op_b ) ) ) ) ) ) ) )
= unit ),
inference(lifteq,[status(thm)],[30]) ).
thf(355,plain,
! [B: $i,A: $i] :
( ( ( ld @ A @ unit )
= B )
| ( ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ op_b ) ) ) ) ) ) ) )
!= ( mult @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[31,17]) ).
thf(356,plain,
( ( ld @ op_b @ unit )
= ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ op_b ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[355:[bind(A,$thf( op_b )),bind(B,$thf( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ op_b ) ) ) ) ) ) ))]]) ).
thf(6,axiom,
! [A: $i] :
( ( mult @ A @ unit )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c05) ).
thf(22,plain,
! [A: $i] :
( ( mult @ A @ unit )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(23,plain,
! [A: $i] :
( ( mult @ A @ unit )
= A ),
inference(lifteq,[status(thm)],[22]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( mult @ A @ ( mult @ B @ ( mult @ B @ C ) ) )
= ( mult @ ( mult @ ( mult @ A @ B ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c07) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( mult @ A @ ( mult @ B @ ( mult @ B @ C ) ) )
= ( mult @ ( mult @ ( mult @ A @ B ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ ( mult @ A @ B ) @ B ) @ C )
= ( mult @ A @ ( mult @ B @ ( mult @ B @ C ) ) ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(921,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( mult @ A @ D )
= ( mult @ B @ ( mult @ C @ ( mult @ C @ D ) ) ) )
| ( ( mult @ A @ unit )
!= ( mult @ ( mult @ B @ C ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[23,27]) ).
thf(922,plain,
! [B: $i,A: $i] :
( ( mult @ ( mult @ B @ unit ) @ A )
= ( mult @ B @ ( mult @ unit @ ( mult @ unit @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[921:[bind(A,$thf( mult @ E @ unit )),bind(B,$thf( E )),bind(C,$thf( unit )),bind(D,$thf( D ))]]) ).
thf(1020,plain,
! [B: $i,A: $i] :
( ( mult @ ( mult @ B @ unit ) @ A )
= ( mult @ B @ ( mult @ unit @ ( mult @ unit @ A ) ) ) ),
inference(simp,[status(thm)],[922]) ).
thf(7,axiom,
! [A: $i] :
( ( mult @ unit @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c06) ).
thf(24,plain,
! [A: $i] :
( ( mult @ unit @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(25,plain,
! [A: $i] :
( ( mult @ unit @ A )
= A ),
inference(lifteq,[status(thm)],[24]) ).
thf(1185,plain,
! [B: $i,A: $i] :
( ( mult @ B @ ( mult @ unit @ A ) )
= ( mult @ B @ A ) ),
inference(rewrite,[status(thm)],[1020,23,25]) ).
thf(9,axiom,
( ( mult @ op_a @ ( mult @ op_a @ ( mult @ op_a @ op_a ) ) )
= unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c08) ).
thf(28,plain,
( ( mult @ op_a @ ( mult @ op_a @ ( mult @ op_a @ op_a ) ) )
= unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(29,plain,
( ( mult @ op_a @ ( mult @ op_a @ ( mult @ op_a @ op_a ) ) )
= unit ),
inference(lifteq,[status(thm)],[28]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c04) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ),
inference(lifteq,[status(thm)],[20]) ).
thf(588,plain,
! [B: $i,A: $i] :
( ( ( rd @ unit @ B )
= A )
| ( ( mult @ op_a @ ( mult @ op_a @ ( mult @ op_a @ op_a ) ) )
!= ( mult @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[29,21]) ).
thf(589,plain,
( ( rd @ unit @ ( mult @ op_a @ ( mult @ op_a @ op_a ) ) )
= op_a ),
inference(pattern_uni,[status(thm)],[588:[bind(A,$thf( op_a )),bind(B,$thf( mult @ op_a @ ( mult @ op_a @ op_a ) ))]]) ).
thf(70,plain,
! [A: $i] :
( ( ( mult @ A @ a )
!= ( mult @ op_a @ ( mult @ op_b @ a ) ) )
| ( ( mult @ unit @ A )
!= ( mult @ op_a @ op_b ) ) ),
inference(paramod_ordered,[status(thm)],[25,13]) ).
thf(77,plain,
! [A: $i] :
( ( A != op_a )
| ( ( mult @ op_b @ a )
!= a )
| ( unit != op_a )
| ( A != op_b ) ),
inference(simp,[status(thm)],[70]) ).
thf(89,plain,
( ( ( mult @ op_b @ a )
!= a )
| ( unit != op_a )
| ( op_b != op_a ) ),
inference(simp,[status(thm)],[77]) ).
thf(373,plain,
! [A: $i] :
( ( A != a )
| ( unit != op_a )
| ( op_b != op_a )
| ( ( mult @ A @ unit )
!= ( mult @ op_b @ a ) ) ),
inference(paramod_ordered,[status(thm)],[23,89]) ).
thf(383,plain,
( ( unit != op_a )
| ( op_b != op_a )
| ( a != op_b )
| ( unit != a ) ),
inference(simp,[status(thm)],[373]) ).
thf(357,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ld @ B @ A )
= C )
| ( ( mult @ A @ unit )
!= ( mult @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[23,17]) ).
thf(358,plain,
! [A: $i] :
( ( ld @ A @ A )
= unit ),
inference(pattern_uni,[status(thm)],[357:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( unit ))]]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ),
inference(lifteq,[status(thm)],[14]) ).
thf(364,plain,
! [B: $i,A: $i] :
( ( ( ld @ A @ unit )
= B )
| ( ( mult @ op_a @ ( mult @ op_a @ ( mult @ op_a @ op_a ) ) )
!= ( mult @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[29,17]) ).
thf(365,plain,
( ( ld @ op_a @ unit )
= ( mult @ op_a @ ( mult @ op_a @ op_a ) ) ),
inference(pattern_uni,[status(thm)],[364:[bind(A,$thf( op_a )),bind(B,$thf( mult @ op_a @ ( mult @ op_a @ op_a ) ))]]) ).
thf(443,plain,
! [A: $i] :
( ( mult @ ( rd @ ( mult @ op_a @ ( mult @ op_b @ a ) ) @ A ) @ A )
!= ( mult @ ( mult @ op_a @ op_b ) @ a ) ),
inference(simp,[status(thm)],[390]) ).
thf(479,plain,
! [A: $i] :
( ( mult @ ( rd @ ( mult @ op_a @ ( mult @ op_b @ a ) ) @ A ) @ A )
!= ( mult @ ( mult @ op_a @ op_b ) @ a ) ),
inference(simp,[status(thm)],[443]) ).
thf(66,plain,
( ( ( mult @ op_a @ op_b )
!= op_a )
| ( ( mult @ op_b @ a )
!= a ) ),
inference(simp,[status(thm)],[13]) ).
thf(251,plain,
! [B: $i,A: $i] :
( ( ( mult @ op_a @ op_b )
!= op_a )
| ( B != a )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ op_b @ a ) ) ),
inference(paramod_ordered,[status(thm)],[15,66]) ).
thf(271,plain,
! [A: $i] :
( ( ( mult @ op_a @ op_b )
!= op_a )
| ( A != op_b )
| ( ( ld @ A @ a )
!= a ) ),
inference(simp,[status(thm)],[251]) ).
thf(288,plain,
( ( ( mult @ op_a @ op_b )
!= op_a )
| ( ( ld @ op_b @ a )
!= a ) ),
inference(simp,[status(thm)],[271]) ).
thf(237,plain,
! [B: $i,A: $i] :
( ( B
!= ( mult @ op_a @ ( mult @ op_b @ a ) ) )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ ( mult @ op_a @ op_b ) @ a ) ) ),
inference(paramod_ordered,[status(thm)],[15,13]) ).
thf(266,plain,
! [A: $i] :
( ( A
!= ( mult @ op_a @ op_b ) )
| ( ( ld @ A @ ( mult @ op_a @ ( mult @ op_b @ a ) ) )
!= a ) ),
inference(simp,[status(thm)],[237]) ).
thf(284,plain,
( ( ld @ ( mult @ op_a @ op_b ) @ ( mult @ op_a @ ( mult @ op_b @ a ) ) )
!= a ),
inference(simp,[status(thm)],[266]) ).
thf(32,plain,
( ( ( mult @ op_a @ unit )
= unit )
| ( ( mult @ op_a @ ( mult @ op_a @ ( mult @ op_a @ op_a ) ) )
!= ( mult @ op_a @ ( mult @ op_a @ op_a ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,29]) ).
thf(34,plain,
( ( ( mult @ op_a @ unit )
= unit )
| ( op_a != op_a )
| ( ( mult @ op_a @ ( mult @ op_a @ op_a ) )
!= ( mult @ op_a @ op_a ) ) ),
inference(simp,[status(thm)],[32]) ).
thf(36,plain,
( ( ( mult @ op_a @ unit )
= unit )
| ( ( mult @ op_a @ ( mult @ op_a @ op_a ) )
!= ( mult @ op_a @ op_a ) ) ),
inference(simp,[status(thm)],[34]) ).
thf(1377,plain,
( ( unit = op_a )
| ( ( mult @ op_a @ ( mult @ op_a @ op_a ) )
!= ( mult @ op_a @ op_a ) ) ),
inference(rewrite,[status(thm)],[36,23]) ).
thf(229,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ unit @ C ) ) ),
inference(paramod_ordered,[status(thm)],[15,25]) ).
thf(230,plain,
! [A: $i] :
( ( ld @ unit @ A )
= A ),
inference(pattern_uni,[status(thm)],[229:[bind(A,$thf( unit )),bind(B,$thf( E )),bind(C,$thf( ld @ unit @ E ))]]) ).
thf(293,plain,
! [A: $i] :
( ( ld @ unit @ A )
= A ),
inference(simp,[status(thm)],[230]) ).
thf(403,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( mult @ ( rd @ A @ B ) @ B )
!= ( mult @ C @ unit ) ) ),
inference(paramod_ordered,[status(thm)],[19,23]) ).
thf(404,plain,
! [A: $i] :
( ( rd @ A @ unit )
= A ),
inference(pattern_uni,[status(thm)],[403:[bind(A,$thf( D )),bind(B,$thf( unit )),bind(C,$thf( rd @ D @ unit ))]]) ).
thf(453,plain,
! [A: $i] :
( ( rd @ A @ unit )
= A ),
inference(simp,[status(thm)],[404]) ).
thf(33,plain,
( ( ( mult @ op_a @ ( mult @ op_a @ unit ) )
= unit )
| ( ( mult @ op_a @ ( mult @ op_a @ ( mult @ op_a @ op_a ) ) )
!= ( mult @ op_a @ op_a ) ) ),
inference(paramod_ordered,[status(thm)],[29,29]) ).
thf(35,plain,
( ( ( mult @ op_a @ ( mult @ op_a @ unit ) )
= unit )
| ( op_a != op_a )
| ( ( mult @ op_a @ ( mult @ op_a @ op_a ) )
!= op_a ) ),
inference(simp,[status(thm)],[33]) ).
thf(37,plain,
( ( ( mult @ op_a @ ( mult @ op_a @ unit ) )
= unit )
| ( ( mult @ op_a @ ( mult @ op_a @ op_a ) )
!= op_a ) ),
inference(simp,[status(thm)],[35]) ).
thf(1525,plain,
( ( ( mult @ op_a @ op_a )
= unit )
| ( ( mult @ op_a @ ( mult @ op_a @ op_a ) )
!= op_a ) ),
inference(rewrite,[status(thm)],[37,23]) ).
thf(576,plain,
! [C: $i,B: $i,A: $i] :
( ( ( rd @ A @ C )
= B )
| ( ( mult @ unit @ A )
!= ( mult @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[25,21]) ).
thf(577,plain,
! [A: $i] :
( ( rd @ A @ A )
= unit ),
inference(pattern_uni,[status(thm)],[576:[bind(A,$thf( A )),bind(B,$thf( unit )),bind(C,$thf( A ))]]) ).
thf(578,plain,
! [B: $i,A: $i] :
( ( ( rd @ unit @ B )
= A )
| ( ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ op_b ) ) ) ) ) ) ) )
!= ( mult @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[31,21]) ).
thf(579,plain,
( ( rd @ unit @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ op_b ) ) ) ) ) ) ) )
= op_b ),
inference(pattern_uni,[status(thm)],[578:[bind(A,$thf( op_b )),bind(B,$thf( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ ( mult @ op_b @ op_b ) ) ) ) ) ) ))]]) ).
thf(374,plain,
! [B: $i,A: $i] :
( ( B != a )
| ( unit != op_a )
| ( op_b != op_a )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ op_b @ a ) ) ),
inference(paramod_ordered,[status(thm)],[15,89]) ).
thf(381,plain,
! [A: $i] :
( ( unit != op_a )
| ( op_b != op_a )
| ( A != op_b )
| ( ( ld @ A @ a )
!= a ) ),
inference(simp,[status(thm)],[374]) ).
thf(387,plain,
( ( unit != op_a )
| ( op_b != op_a )
| ( ( ld @ op_b @ a )
!= a ) ),
inference(simp,[status(thm)],[381]) ).
thf(68,plain,
! [A: $i] :
( ( ( mult @ A @ a )
!= ( mult @ op_a @ ( mult @ op_b @ a ) ) )
| ( ( mult @ A @ unit )
!= ( mult @ op_a @ op_b ) ) ),
inference(paramod_ordered,[status(thm)],[23,13]) ).
thf(86,plain,
! [A: $i] :
( ( A != op_a )
| ( ( mult @ op_b @ a )
!= a )
| ( A != op_a )
| ( unit != op_b ) ),
inference(simp,[status(thm)],[68]) ).
thf(94,plain,
( ( ( mult @ op_b @ a )
!= a )
| ( unit != op_b ) ),
inference(simp,[status(thm)],[86]) ).
thf(95,plain,
! [A: $i] :
( ( A != a )
| ( unit != op_b )
| ( ( mult @ unit @ A )
!= ( mult @ op_b @ a ) ) ),
inference(paramod_ordered,[status(thm)],[25,94]) ).
thf(99,plain,
( ( unit != op_b )
| ( unit != op_b )
| ( a != a ) ),
inference(simp,[status(thm)],[95]) ).
thf(103,plain,
unit != op_b,
inference(simp,[status(thm)],[99]) ).
thf(586,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( rd @ B @ D )
= C )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[15,21]) ).
thf(587,plain,
! [B: $i,A: $i] :
( ( rd @ B @ ( ld @ A @ B ) )
= A ),
inference(pattern_uni,[status(thm)],[586:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( ld @ E @ F ))]]) ).
thf(595,plain,
! [B: $i,A: $i] :
( ( rd @ B @ ( ld @ A @ B ) )
= A ),
inference(simp,[status(thm)],[587]) ).
thf(391,plain,
! [B: $i,A: $i] :
( ( ( mult @ A @ a )
!= ( mult @ op_a @ ( mult @ op_b @ a ) ) )
| ( ( mult @ ( rd @ A @ B ) @ B )
!= ( mult @ op_a @ op_b ) ) ),
inference(paramod_ordered,[status(thm)],[19,13]) ).
thf(429,plain,
! [B: $i,A: $i] :
( ( A != op_a )
| ( ( mult @ op_b @ a )
!= a )
| ( ( rd @ A @ B )
!= op_a )
| ( B != op_b ) ),
inference(simp,[status(thm)],[391]) ).
thf(465,plain,
( ( ( mult @ op_b @ a )
!= a )
| ( ( rd @ op_a @ op_b )
!= op_a ) ),
inference(simp,[status(thm)],[429]) ).
thf(212,plain,
! [A: $i] :
( ( ( mult @ op_a @ op_b )
!= op_a )
| ( A != a )
| ( ( mult @ A @ unit )
!= ( mult @ op_b @ a ) ) ),
inference(paramod_ordered,[status(thm)],[23,66]) ).
thf(218,plain,
( ( ( mult @ op_a @ op_b )
!= op_a )
| ( a != op_b )
| ( unit != a ) ),
inference(simp,[status(thm)],[212]) ).
thf(15853,plain,
$false,
inference(e,[status(thm)],[14,480,452,356,1185,17,589,18,383,358,15,365,479,24,288,25,20,284,29,1377,293,453,89,28,21,13,1525,22,577,579,27,387,103,66,16,31,11,595,465,218,26,23,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP705-1 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n020.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 : 300
% 0.12/0.33 % DateTime : Thu Jun 20 12:52:10 EDT 2024
% 0.12/0.33 % CPUTime :
% 1.05/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.32/1.03 % [INFO] Parsing done (113ms).
% 1.32/1.04 % [INFO] Running in sequential loop mode.
% 1.70/1.25 % [INFO] eprover registered as external prover.
% 1.70/1.26 % [INFO] Scanning for conjecture ...
% 1.70/1.30 % [INFO] Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ...
% 1.70/1.32 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 1.98/1.34 % [INFO] Problem is propositional (TPTP CNF).
% 1.98/1.34 % [INFO] Type checking passed.
% 1.98/1.34 % [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 ...
% 24.79/5.58 % External prover 'e' found a proof!
% 24.79/5.58 % [INFO] Killing All external provers ...
% 24.79/5.58 % Time passed: 5046ms (effective reasoning time: 4539ms)
% 24.79/5.60 % Axioms used in derivation (9): c05, c08, c01, c03, c06, c02, c07, c09, c04
% 24.79/5.60 % No. of inferences in proof: 99
% 24.79/5.60 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 5046 ms resp. 4539 ms w/o parsing
% 24.79/5.65 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 24.79/5.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------