TSTP Solution File: GRP667+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP667+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n027.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 May 19 11:15:04 EDT 2023
% Result : Theorem 39.10s 6.95s
% Output : Refutation 39.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 21
% Syntax : Number of formulae : 115 ( 62 unt; 8 typ; 0 def)
% Number of atoms : 177 ( 176 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 936 ( 100 ~; 64 |; 0 &; 766 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 159 ( 0 ^; 159 !; 0 ?; 159 :)
% Comments :
%------------------------------------------------------------------------------
thf(mult_type,type,
mult: $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(c_type,type,
c: $i ).
thf(ld_type,type,
ld: $i > $i > $i ).
thf(rd_type,type,
rd: $i > $i > $i ).
thf(unit_type,type,
unit: $i ).
thf(f_type,type,
f: $i > $i ).
thf(1,conjecture,
( ( mult @ a @ ( mult @ b @ ( mult @ a @ c ) ) )
= ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
( ( mult @ a @ ( mult @ b @ ( mult @ a @ c ) ) )
!= ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ c ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(15,plain,
( ( mult @ a @ ( mult @ b @ ( mult @ a @ c ) ) )
!= ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,plain,
( ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ c )
!= ( mult @ a @ ( mult @ b @ ( mult @ a @ c ) ) ) ),
inference(lifteq,[status(thm)],[15]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( mult @ ( mult @ B @ A ) @ B )
= ( mult @ B @ ( mult @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f08) ).
thf(38,plain,
! [A: $i,B: $i] :
( ( mult @ ( mult @ B @ A ) @ B )
= ( mult @ B @ ( mult @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( mult @ ( mult @ B @ A ) @ B )
= ( mult @ B @ ( mult @ A @ B ) ) ),
inference(cnf,[status(esa)],[38]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( mult @ ( mult @ B @ A ) @ B )
= ( mult @ B @ ( mult @ A @ B ) ) ),
inference(lifteq,[status(thm)],[39]) ).
thf(1173,plain,
( ( mult @ ( mult @ a @ ( mult @ b @ a ) ) @ c )
!= ( mult @ a @ ( mult @ b @ ( mult @ a @ c ) ) ) ),
inference(rewrite,[status(thm)],[16,40]) ).
thf(8,axiom,
! [A: $i] :
( ( mult @ unit @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
thf(32,plain,
! [A: $i] :
( ( mult @ unit @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(33,plain,
! [A: $i] :
( ( mult @ unit @ A )
= A ),
inference(cnf,[status(esa)],[32]) ).
thf(34,plain,
! [A: $i] :
( ( mult @ unit @ A )
= A ),
inference(lifteq,[status(thm)],[33]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( rd @ ( mult @ B @ A ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
thf(26,plain,
! [A: $i,B: $i] :
( ( rd @ ( mult @ B @ A ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( rd @ ( mult @ B @ A ) @ A )
= B ),
inference(cnf,[status(esa)],[26]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( rd @ ( mult @ B @ A ) @ A )
= B ),
inference(lifteq,[status(thm)],[27]) ).
thf(511,plain,
! [C: $i,B: $i,A: $i] :
( ( ( rd @ A @ B )
= C )
| ( ( mult @ unit @ A )
!= ( mult @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[34,28]) ).
thf(512,plain,
! [A: $i] :
( ( rd @ A @ A )
= unit ),
inference(pattern_uni,[status(thm)],[511:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( unit ))]]) ).
thf(11,axiom,
! [A: $i] :
( ( mult @ ( f @ A ) @ ( f @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f09) ).
thf(41,plain,
! [A: $i] :
( ( mult @ ( f @ A ) @ ( f @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(42,plain,
! [A: $i] :
( ( mult @ ( f @ A ) @ ( f @ A ) )
= A ),
inference(cnf,[status(esa)],[41]) ).
thf(43,plain,
! [A: $i] :
( ( mult @ ( f @ A ) @ ( f @ A ) )
= A ),
inference(lifteq,[status(thm)],[42]) ).
thf(7,axiom,
! [A: $i] :
( ( mult @ A @ unit )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
thf(29,plain,
! [A: $i] :
( ( mult @ A @ unit )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(30,plain,
! [A: $i] :
( ( mult @ A @ unit )
= A ),
inference(cnf,[status(esa)],[29]) ).
thf(31,plain,
! [A: $i] :
( ( mult @ A @ unit )
= A ),
inference(lifteq,[status(thm)],[30]) ).
thf(72,plain,
! [A: $i] :
( ( ( mult @ A @ c )
!= ( mult @ a @ ( mult @ b @ ( mult @ a @ c ) ) ) )
| ( ( mult @ unit @ A )
!= ( mult @ ( mult @ a @ b ) @ a ) ) ),
inference(paramod_ordered,[status(thm)],[34,16]) ).
thf(99,plain,
! [A: $i] :
( ( A != a )
| ( ( mult @ b @ ( mult @ a @ c ) )
!= c )
| ( ( mult @ a @ b )
!= unit )
| ( A != a ) ),
inference(simp,[status(thm)],[72]) ).
thf(112,plain,
( ( ( mult @ b @ ( mult @ a @ c ) )
!= c )
| ( ( mult @ a @ b )
!= unit ) ),
inference(simp,[status(thm)],[99]) ).
thf(121,plain,
! [A: $i] :
( ( A != c )
| ( ( mult @ a @ b )
!= unit )
| ( ( mult @ A @ unit )
!= ( mult @ b @ ( mult @ a @ c ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,112]) ).
thf(125,plain,
( ( ( mult @ a @ b )
!= unit )
| ( c != b )
| ( ( mult @ a @ c )
!= unit ) ),
inference(simp,[status(thm)],[121]) ).
thf(147,plain,
( ( ( mult @ a @ b )
!= unit )
| ( c != b )
| ( ( mult @ a @ c )
!= ( mult @ a @ b ) )
| ( unit != unit ) ),
inference(eqfactor_ordered,[status(thm)],[125]) ).
thf(151,plain,
( ( ( mult @ a @ b )
!= unit )
| ( c != b )
| ( a != a )
| ( c != b ) ),
inference(simp,[status(thm)],[147]) ).
thf(162,plain,
( ( ( mult @ a @ b )
!= unit )
| ( c != b ) ),
inference(simp,[status(thm)],[151]) ).
thf(223,plain,
! [A: $i] :
( ( A != unit )
| ( c != b )
| ( ( mult @ ( f @ A ) @ ( f @ A ) )
!= ( mult @ a @ b ) ) ),
inference(paramod_ordered,[status(thm)],[43,162]) ).
thf(229,plain,
( ( c != b )
| ( ( f @ unit )
!= a )
| ( ( f @ unit )
!= b ) ),
inference(simp,[status(thm)],[223]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( mult @ B @ ( ld @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
thf(17,plain,
! [A: $i,B: $i] :
( ( mult @ B @ ( ld @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( mult @ B @ ( ld @ B @ A ) )
= A ),
inference(cnf,[status(esa)],[17]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( mult @ B @ ( ld @ B @ A ) )
= A ),
inference(lifteq,[status(thm)],[18]) ).
thf(516,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( rd @ A @ C )
= D )
| ( ( mult @ B @ ( ld @ B @ A ) )
!= ( mult @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[19,28]) ).
thf(517,plain,
! [B: $i,A: $i] :
( ( rd @ B @ ( ld @ A @ B ) )
= A ),
inference(pattern_uni,[status(thm)],[516:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( ld @ E @ F )),bind(D,$thf( E ))]]) ).
thf(526,plain,
! [B: $i,A: $i] :
( ( rd @ B @ ( ld @ A @ B ) )
= A ),
inference(simp,[status(thm)],[517]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ld @ B @ ( mult @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
thf(20,plain,
! [A: $i,B: $i] :
( ( ld @ B @ ( mult @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( ld @ B @ ( mult @ B @ A ) )
= A ),
inference(cnf,[status(esa)],[20]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( ld @ B @ ( mult @ B @ A ) )
= A ),
inference(lifteq,[status(thm)],[21]) ).
thf(244,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ld @ C @ A )
= B )
| ( ( mult @ A @ unit )
!= ( mult @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[31,22]) ).
thf(245,plain,
! [A: $i] :
( ( ld @ A @ A )
= unit ),
inference(pattern_uni,[status(thm)],[244:[bind(A,$thf( A )),bind(B,$thf( unit )),bind(C,$thf( A ))]]) ).
thf(513,plain,
! [C: $i,B: $i,A: $i] :
( ( ( rd @ A @ B )
= C )
| ( ( mult @ ( f @ A ) @ ( f @ A ) )
!= ( mult @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[43,28]) ).
thf(514,plain,
! [A: $i] :
( ( rd @ A @ ( f @ A ) )
= ( f @ A ) ),
inference(pattern_uni,[status(thm)],[513:[bind(A,$thf( E )),bind(B,$thf( f @ E )),bind(C,$thf( f @ E ))]]) ).
thf(525,plain,
! [A: $i] :
( ( rd @ A @ ( f @ A ) )
= ( f @ A ) ),
inference(simp,[status(thm)],[514]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( mult @ ( rd @ B @ A ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
thf(23,plain,
! [A: $i,B: $i] :
( ( mult @ ( rd @ B @ A ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( mult @ ( rd @ B @ A ) @ A )
= B ),
inference(cnf,[status(esa)],[23]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( mult @ ( rd @ B @ A ) @ A )
= B ),
inference(lifteq,[status(thm)],[24]) ).
thf(315,plain,
! [B: $i,A: $i] :
( ( B != unit )
| ( c != b )
| ( ( mult @ ( rd @ B @ A ) @ A )
!= ( mult @ a @ b ) ) ),
inference(paramod_ordered,[status(thm)],[25,162]) ).
thf(344,plain,
! [A: $i] :
( ( c != b )
| ( ( rd @ unit @ A )
!= a )
| ( A != b ) ),
inference(simp,[status(thm)],[315]) ).
thf(363,plain,
( ( c != b )
| ( ( rd @ unit @ b )
!= a ) ),
inference(simp,[status(thm)],[344]) ).
thf(319,plain,
! [B: $i,A: $i] :
( ( B
!= ( mult @ a @ ( mult @ b @ ( mult @ a @ c ) ) ) )
| ( ( mult @ ( rd @ B @ A ) @ A )
!= ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ c ) ) ),
inference(paramod_ordered,[status(thm)],[25,16]) ).
thf(342,plain,
! [A: $i] :
( ( ( rd @ ( mult @ a @ ( mult @ b @ ( mult @ a @ c ) ) ) @ A )
!= ( mult @ ( mult @ a @ b ) @ a ) )
| ( A != c ) ),
inference(simp,[status(thm)],[319]) ).
thf(362,plain,
( ( rd @ ( mult @ a @ ( mult @ b @ ( mult @ a @ c ) ) ) @ c )
!= ( mult @ ( mult @ a @ b ) @ a ) ),
inference(simp,[status(thm)],[342]) ).
thf(1172,plain,
( ( rd @ ( mult @ a @ ( mult @ b @ ( mult @ a @ c ) ) ) @ c )
!= ( mult @ a @ ( mult @ b @ a ) ) ),
inference(rewrite,[status(thm)],[362,40]) ).
thf(309,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ld @ D @ B )
= C )
| ( ( mult @ ( rd @ B @ A ) @ A )
!= ( mult @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[25,22]) ).
thf(310,plain,
! [B: $i,A: $i] :
( ( ld @ ( rd @ A @ B ) @ A )
= B ),
inference(pattern_uni,[status(thm)],[309:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( rd @ E @ F ))]]) ).
thf(365,plain,
! [B: $i,A: $i] :
( ( ld @ ( rd @ A @ B ) @ A )
= B ),
inference(simp,[status(thm)],[310]) ).
thf(870,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( mult @ D @ B )
= C )
| ( ( ld @ ( rd @ A @ B ) @ A )
!= ( ld @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[365,19]) ).
thf(871,plain,
! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ),
inference(pattern_uni,[status(thm)],[870:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( rd @ E @ F ))]]) ).
thf(892,plain,
! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ),
inference(simp,[status(thm)],[871]) ).
thf(322,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( mult @ ( rd @ B @ A ) @ A )
!= ( mult @ C @ unit ) ) ),
inference(paramod_ordered,[status(thm)],[25,31]) ).
thf(323,plain,
! [A: $i] :
( ( rd @ A @ unit )
= A ),
inference(pattern_uni,[status(thm)],[322:[bind(A,$thf( unit )),bind(B,$thf( D )),bind(C,$thf( rd @ D @ unit ))]]) ).
thf(347,plain,
! [A: $i] :
( ( rd @ A @ unit )
= A ),
inference(simp,[status(thm)],[323]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( mult @ ( mult @ C @ B ) @ ( mult @ ( mult @ A @ B ) @ A ) )
= ( mult @ ( mult @ C @ ( mult @ ( mult @ B @ A ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).
thf(35,plain,
! [A: $i,B: $i,C: $i] :
( ( mult @ ( mult @ C @ B ) @ ( mult @ ( mult @ A @ B ) @ A ) )
= ( mult @ ( mult @ C @ ( mult @ ( mult @ B @ A ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ C @ B ) @ ( mult @ ( mult @ A @ B ) @ A ) )
= ( mult @ ( mult @ C @ ( mult @ ( mult @ B @ A ) @ B ) ) @ A ) ),
inference(cnf,[status(esa)],[35]) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ C @ B ) @ ( mult @ ( mult @ A @ B ) @ A ) )
= ( mult @ ( mult @ C @ ( mult @ ( mult @ B @ A ) @ B ) ) @ A ) ),
inference(lifteq,[status(thm)],[36]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( mult @ A @ ( mult @ B @ ( mult @ C @ B ) ) )
= ( mult @ ( mult @ ( mult @ A @ B ) @ C ) @ B ) )
=> ( ( mult @ B @ ( mult @ A @ ( mult @ B @ C ) ) )
= ( mult @ ( mult @ ( mult @ B @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f10) ).
thf(44,plain,
! [A: $i,B: $i,C: $i] :
( ( ( mult @ A @ ( mult @ B @ ( mult @ C @ B ) ) )
= ( mult @ ( mult @ ( mult @ A @ B ) @ C ) @ B ) )
=> ( ( mult @ B @ ( mult @ A @ ( mult @ B @ C ) ) )
= ( mult @ ( mult @ ( mult @ B @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(45,plain,
! [C: $i,B: $i,A: $i] :
( ( ( mult @ A @ ( mult @ B @ ( mult @ C @ B ) ) )
!= ( mult @ ( mult @ ( mult @ A @ B ) @ C ) @ B ) )
| ( ( mult @ B @ ( mult @ A @ ( mult @ B @ C ) ) )
= ( mult @ ( mult @ ( mult @ B @ A ) @ B ) @ C ) ) ),
inference(cnf,[status(esa)],[44]) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ( ( mult @ ( mult @ ( mult @ A @ B ) @ C ) @ B )
!= ( mult @ A @ ( mult @ B @ ( mult @ C @ B ) ) ) )
| ( ( mult @ ( mult @ ( mult @ B @ A ) @ B ) @ C )
= ( mult @ B @ ( mult @ A @ ( mult @ B @ C ) ) ) ) ),
inference(lifteq,[status(thm)],[45]) ).
thf(165,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( mult @ B @ ( ld @ B @ A ) )
!= ( mult @ unit @ C ) ) ),
inference(paramod_ordered,[status(thm)],[19,34]) ).
thf(166,plain,
! [A: $i] :
( ( ld @ unit @ A )
= A ),
inference(pattern_uni,[status(thm)],[165:[bind(A,$thf( E )),bind(B,$thf( unit )),bind(C,$thf( ld @ unit @ E ))]]) ).
thf(205,plain,
! [A: $i] :
( ( ld @ unit @ A )
= A ),
inference(simp,[status(thm)],[166]) ).
thf(117,plain,
! [A: $i] :
( ( ( mult @ b @ ( mult @ a @ c ) )
!= c )
| ( A != unit )
| ( ( mult @ unit @ A )
!= ( mult @ a @ b ) ) ),
inference(paramod_ordered,[status(thm)],[34,112]) ).
thf(128,plain,
( ( ( mult @ b @ ( mult @ a @ c ) )
!= c )
| ( unit != a )
| ( unit != b ) ),
inference(simp,[status(thm)],[117]) ).
thf(956,plain,
! [A: $i] :
( ( A != c )
| ( unit != a )
| ( unit != b )
| ( ( mult @ unit @ A )
!= ( mult @ b @ ( mult @ a @ c ) ) ) ),
inference(paramod_ordered,[status(thm)],[34,128]) ).
thf(975,plain,
( ( unit != a )
| ( unit != b )
| ( unit != b )
| ( ( mult @ a @ c )
!= c ) ),
inference(simp,[status(thm)],[956]) ).
thf(991,plain,
( ( unit != a )
| ( unit != b )
| ( ( mult @ a @ c )
!= c ) ),
inference(simp,[status(thm)],[975]) ).
thf(1142,plain,
! [A: $i] :
( ( unit != a )
| ( unit != b )
| ( A != c )
| ( ( mult @ unit @ A )
!= ( mult @ a @ c ) ) ),
inference(paramod_ordered,[status(thm)],[34,991]) ).
thf(1151,plain,
( ( unit != a )
| ( unit != b )
| ( unit != a )
| ( c != c ) ),
inference(simp,[status(thm)],[1142]) ).
thf(1170,plain,
( ( unit != a )
| ( unit != b ) ),
inference(simp,[status(thm)],[1151]) ).
thf(174,plain,
! [B: $i,A: $i] :
( ( A
!= ( mult @ a @ ( mult @ b @ ( mult @ a @ c ) ) ) )
| ( ( mult @ B @ ( ld @ B @ A ) )
!= ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ c ) ) ),
inference(paramod_ordered,[status(thm)],[19,16]) ).
thf(181,plain,
! [A: $i] :
( ( A
!= ( mult @ ( mult @ a @ b ) @ a ) )
| ( ( ld @ A @ ( mult @ a @ ( mult @ b @ ( mult @ a @ c ) ) ) )
!= c ) ),
inference(simp,[status(thm)],[174]) ).
thf(211,plain,
( ( ld @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ ( mult @ b @ ( mult @ a @ c ) ) ) )
!= c ),
inference(simp,[status(thm)],[181]) ).
thf(1171,plain,
( ( ld @ ( mult @ a @ ( mult @ b @ a ) ) @ ( mult @ a @ ( mult @ b @ ( mult @ a @ c ) ) ) )
!= c ),
inference(rewrite,[status(thm)],[211,40]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( mult @ ( mult @ A @ B ) @ ( mult @ C @ A ) )
= ( mult @ A @ ( mult @ ( mult @ B @ C ) @ A ) ) )
=> ( ( mult @ A @ ( mult @ B @ ( mult @ A @ C ) ) )
= ( mult @ ( mult @ ( mult @ A @ B ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f12) ).
thf(50,plain,
! [A: $i,B: $i,C: $i] :
( ( ( mult @ ( mult @ A @ B ) @ ( mult @ C @ A ) )
= ( mult @ A @ ( mult @ ( mult @ B @ C ) @ A ) ) )
=> ( ( mult @ A @ ( mult @ B @ ( mult @ A @ C ) ) )
= ( mult @ ( mult @ ( mult @ A @ B ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(224,plain,
! [B: $i,A: $i] :
( ( A != unit )
| ( c != b )
| ( ( mult @ B @ ( ld @ B @ A ) )
!= ( mult @ a @ b ) ) ),
inference(paramod_ordered,[status(thm)],[19,162]) ).
thf(231,plain,
! [A: $i] :
( ( c != b )
| ( A != a )
| ( ( ld @ A @ unit )
!= b ) ),
inference(simp,[status(thm)],[224]) ).
thf(235,plain,
( ( c != b )
| ( ( ld @ a @ unit )
!= b ) ),
inference(simp,[status(thm)],[231]) ).
thf(238,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ld @ C @ A )
= B )
| ( ( mult @ ( f @ A ) @ ( f @ A ) )
!= ( mult @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[43,22]) ).
thf(239,plain,
! [A: $i] :
( ( ld @ ( f @ A ) @ A )
= ( f @ A ) ),
inference(pattern_uni,[status(thm)],[238:[bind(A,$thf( E )),bind(B,$thf( f @ E )),bind(C,$thf( f @ E ))]]) ).
thf(246,plain,
! [A: $i] :
( ( ld @ ( f @ A ) @ A )
= ( f @ A ) ),
inference(simp,[status(thm)],[239]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( mult @ ( mult @ A @ B ) @ ( mult @ C @ A ) )
= ( mult @ ( mult @ A @ ( mult @ B @ C ) ) @ A ) )
=> ( ( mult @ A @ ( mult @ B @ ( mult @ A @ C ) ) )
= ( mult @ ( mult @ ( mult @ A @ B ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f11) ).
thf(47,plain,
! [A: $i,B: $i,C: $i] :
( ( ( mult @ ( mult @ A @ B ) @ ( mult @ C @ A ) )
= ( mult @ ( mult @ A @ ( mult @ B @ C ) ) @ A ) )
=> ( ( mult @ A @ ( mult @ B @ ( mult @ A @ C ) ) )
= ( mult @ ( mult @ ( mult @ A @ B ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(14912,plain,
$false,
inference(e,[status(thm)],[1173,512,229,526,41,245,525,43,363,19,1172,892,365,347,37,25,20,46,29,28,38,205,1170,17,32,34,22,44,1171,35,162,112,50,31,40,26,23,235,246,47,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP667+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n027.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 : Fri May 19 02:04:52 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.85/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.13/0.98 % [INFO] Parsing done (121ms).
% 1.13/0.99 % [INFO] Running in sequential loop mode.
% 1.70/1.19 % [INFO] eprover registered as external prover.
% 1.70/1.19 % [INFO] cvc4 registered as external prover.
% 1.70/1.20 % [INFO] Scanning for conjecture ...
% 1.85/1.25 % [INFO] Found a conjecture and 12 axioms. Running axiom selection ...
% 1.85/1.27 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 1.85/1.30 % [INFO] Problem is first-order (TPTP FOF).
% 1.85/1.30 % [INFO] Type checking passed.
% 1.85/1.30 % [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 ...
% 39.10/6.95 % External prover 'e' found a proof!
% 39.10/6.95 % [INFO] Killing All external provers ...
% 39.10/6.95 % Time passed: 6424ms (effective reasoning time: 5957ms)
% 39.10/6.95 % 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)>
% 39.10/6.95 % Axioms used in derivation (12): f08, f03, f02, f07, f10, f06, f11, f05, f01, f12, f04, f09
% 39.10/6.95 % No. of inferences in proof: 107
% 39.10/6.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6424 ms resp. 5957 ms w/o parsing
% 39.10/6.99 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 39.10/6.99 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------