%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP571-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:21:17 AM UTC 2026
% Result : Unsatisfiable 15.65s 5.04s
% Output : Refutation 17.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 93 ( 41 unt; 0 typ; 0 def)
% Number of atoms : 185 ( 184 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 936 ( 152 ~; 92 |; 0 &; 692 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 98 ( 0 ^; 98 !; 0 ?; 98 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(a3_decl,type,
a3: $i ).
thf(b3_decl,type,
b3: $i ).
thf(c3_decl,type,
c3: $i ).
thf(double_divide_decl,type,
double_divide: $i > $i > $i ).
thf(identity_decl,type,
identity: $i ).
thf(inverse_decl,type,
inverse: $i > $i ).
thf(4,axiom,
! [A: $i] :
( ( A @ inverse )
= ( identity @ ( A @ double_divide ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
thf(13,plain,
! [A: $i] :
( ( A @ inverse )
= ( identity @ ( A @ double_divide ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,plain,
! [A: $i] :
( ( identity @ ( A @ double_divide ) )
= ( A @ inverse ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) )
= ( identity @ ( A @ ( B @ double_divide ) @ double_divide ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
thf(11,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) )
= ( identity @ ( A @ ( B @ double_divide ) @ double_divide ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,plain,
! [B: $i,A: $i] :
( ( identity @ ( A @ ( B @ double_divide ) @ double_divide ) )
= ( B @ ( A @ multiply ) ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ double_divide ) @ inverse )
= ( B @ ( A @ multiply ) ) ),
inference(rewrite,[status(thm)],[12,14]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( ( identity @ ( A @ double_divide ) )
!= ( B @ ( C @ double_divide ) ) )
| ( ( A @ inverse @ inverse )
= ( C @ ( B @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,24]) ).
thf(34,plain,
! [A: $i] :
( ( A @ ( identity @ multiply ) )
= ( A @ inverse @ inverse ) ),
inference(pattern_uni,[status(thm)],[33:[bind(A,$thf( A )),bind(B,$thf( identity )),bind(C,$thf( A ))]]) ).
thf(1,negated_conjecture,
( ( c3 @ ( b3 @ ( a3 @ multiply ) @ multiply ) )
!= ( c3 @ ( b3 @ multiply ) @ ( a3 @ multiply ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_3) ).
thf(6,plain,
( ( c3 @ ( b3 @ ( a3 @ multiply ) @ multiply ) )
!= ( c3 @ ( b3 @ multiply ) @ ( a3 @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,plain,
( ( c3 @ ( b3 @ ( a3 @ multiply ) @ multiply ) )
!= ( c3 @ ( b3 @ multiply ) @ ( a3 @ multiply ) ) ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( c3 @ ( b3 @ ( a3 @ multiply ) @ multiply ) )
!= ( c3 @ ( b3 @ multiply ) @ ( a3 @ multiply ) ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(58,plain,
! [A: $i] :
( ( ( A @ ( identity @ multiply ) )
!= ( c3 @ ( b3 @ ( a3 @ multiply ) @ multiply ) ) )
| ( ( A @ inverse @ inverse )
!= ( c3 @ ( b3 @ multiply ) @ ( a3 @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[34,8]) ).
thf(66,plain,
! [A: $i] :
( ( A != c3 )
| ( ( b3 @ ( a3 @ multiply ) )
!= identity )
| ( ( A @ inverse @ inverse )
!= ( c3 @ ( b3 @ multiply ) @ ( a3 @ multiply ) ) ) ),
inference(simp,[status(thm)],[58]) ).
thf(69,plain,
( ( ( b3 @ ( a3 @ multiply ) )
!= identity )
| ( ( c3 @ ( b3 @ multiply ) @ ( a3 @ multiply ) )
!= ( c3 @ inverse @ inverse ) ) ),
inference(simp,[status(thm)],[66]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) )
!= ( c3 @ ( b3 @ ( a3 @ multiply ) @ multiply ) ) )
| ( ( A @ ( B @ double_divide ) @ inverse )
!= ( c3 @ ( b3 @ multiply ) @ ( a3 @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,8]) ).
thf(30,plain,
( ( b3 @ ( a3 @ multiply ) @ ( c3 @ double_divide ) @ inverse )
!= ( c3 @ ( b3 @ multiply ) @ ( a3 @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[29:[bind(A,$thf( b3 @ ( a3 @ multiply ) )),bind(B,$thf( c3 ))]]) ).
thf(209,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) )
!= ( c3 @ ( b3 @ multiply ) ) )
| ( ( A @ ( B @ double_divide ) @ inverse @ ( a3 @ multiply ) )
!= ( b3 @ ( a3 @ multiply ) @ ( c3 @ double_divide ) @ inverse ) ) ),
inference(paramod_ordered,[status(thm)],[24,30]) ).
thf(210,plain,
( ( b3 @ ( c3 @ double_divide ) @ inverse @ ( a3 @ multiply ) )
!= ( b3 @ ( a3 @ multiply ) @ ( c3 @ double_divide ) @ inverse ) ),
inference(pattern_uni,[status(thm)],[209:[bind(A,$thf( b3 )),bind(B,$thf( c3 ))]]) ).
thf(756,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ double_divide ) @ inverse )
!= ( b3 @ ( a3 @ multiply ) @ ( c3 @ double_divide ) @ inverse ) )
| ( ( B @ ( A @ multiply ) )
!= ( b3 @ ( c3 @ double_divide ) @ inverse @ ( a3 @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,210]) ).
thf(757,plain,
( ( c3 @ ( b3 @ ( a3 @ multiply ) @ multiply ) )
!= ( b3 @ ( c3 @ double_divide ) @ inverse @ ( a3 @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[756:[bind(A,$thf( b3 @ ( a3 @ multiply ) )),bind(B,$thf( c3 ))]]) ).
thf(813,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) )
!= ( b3 @ ( a3 @ multiply ) ) )
| ( ( c3 @ ( A @ ( B @ double_divide ) @ inverse @ multiply ) )
!= ( b3 @ ( c3 @ double_divide ) @ inverse @ ( a3 @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,757]) ).
thf(814,plain,
( ( c3 @ ( a3 @ ( b3 @ double_divide ) @ inverse @ multiply ) )
!= ( b3 @ ( c3 @ double_divide ) @ inverse @ ( a3 @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[813:[bind(A,$thf( a3 )),bind(B,$thf( b3 ))]]) ).
thf(205,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) )
!= ( b3 @ ( a3 @ multiply ) ) )
| ( ( A @ ( B @ double_divide ) @ inverse @ ( c3 @ double_divide ) @ inverse )
!= ( c3 @ ( b3 @ multiply ) @ ( a3 @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,30]) ).
thf(206,plain,
( ( a3 @ ( b3 @ double_divide ) @ inverse @ ( c3 @ double_divide ) @ inverse )
!= ( c3 @ ( b3 @ multiply ) @ ( a3 @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[205:[bind(A,$thf( a3 )),bind(B,$thf( b3 ))]]) ).
thf(23,plain,
( ( ( c3 @ ( b3 @ multiply ) )
!= c3 )
| ( ( b3 @ ( a3 @ multiply ) )
!= a3 ) ),
inference(simp,[status(thm)],[8]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) )
!= ( b3 @ ( a3 @ multiply ) ) )
| ( ( c3 @ ( b3 @ multiply ) )
!= c3 )
| ( ( A @ ( B @ double_divide ) @ inverse )
!= a3 ) ),
inference(paramod_ordered,[status(thm)],[24,23]) ).
thf(38,plain,
( ( ( c3 @ ( b3 @ multiply ) )
!= c3 )
| ( ( a3 @ ( b3 @ double_divide ) @ inverse )
!= a3 ) ),
inference(pattern_uni,[status(thm)],[37:[bind(A,$thf( a3 )),bind(B,$thf( b3 ))]]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( identity @ ( identity @ double_divide ) @ ( identity @ ( C @ double_divide ) @ ( C @ ( A @ double_divide ) @ ( B @ double_divide ) @ double_divide ) @ ( A @ double_divide ) @ double_divide ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
thf(9,plain,
! [C: $i,B: $i,A: $i] :
( ( identity @ ( identity @ double_divide ) @ ( identity @ ( C @ double_divide ) @ ( C @ ( A @ double_divide ) @ ( B @ double_divide ) @ double_divide ) @ ( A @ double_divide ) @ double_divide ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) )
!= ( c3 @ ( b3 @ multiply ) ) )
| ( ( A @ ( B @ double_divide ) @ inverse )
!= c3 )
| ( ( a3 @ ( b3 @ double_divide ) @ inverse )
!= a3 ) ),
inference(paramod_ordered,[status(thm)],[24,38]) ).
thf(44,plain,
( ( ( b3 @ ( c3 @ double_divide ) @ inverse )
!= c3 )
| ( ( a3 @ ( b3 @ double_divide ) @ inverse )
!= a3 ) ),
inference(pattern_uni,[status(thm)],[43:[bind(A,$thf( b3 )),bind(B,$thf( c3 ))]]) ).
thf(5,axiom,
! [A: $i] :
( identity
= ( A @ inverse @ ( A @ double_divide ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
thf(15,plain,
! [A: $i] :
( identity
= ( A @ inverse @ ( A @ double_divide ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,plain,
! [A: $i] :
( ( A @ inverse @ ( A @ double_divide ) )
= identity ),
inference(lifteq,[status(thm)],[15]) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ double_divide ) @ inverse )
!= ( C @ inverse ) )
| ( ( B @ ( A @ multiply ) @ ( C @ double_divide ) )
= identity ) ),
inference(paramod_ordered,[status(thm)],[24,16]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ multiply ) @ ( B @ ( A @ double_divide ) @ double_divide ) )
= identity ),
inference(pattern_uni,[status(thm)],[25:[bind(A,$thf( E )),bind(B,$thf( D )),bind(C,$thf( E @ ( D @ double_divide ) ))]]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ multiply ) @ ( B @ ( A @ double_divide ) @ double_divide ) )
= identity ),
inference(simp,[status(thm)],[26]) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ inverse @ ( A @ double_divide ) )
!= ( B @ ( C @ double_divide ) ) )
| ( ( C @ ( B @ multiply ) )
= ( identity @ inverse ) ) ),
inference(paramod_ordered,[status(thm)],[16,24]) ).
thf(28,plain,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= ( identity @ inverse ) ),
inference(pattern_uni,[status(thm)],[27:[bind(A,$thf( D )),bind(B,$thf( D @ inverse )),bind(C,$thf( D ))]]) ).
thf(36,plain,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= ( identity @ inverse ) ),
inference(simp,[status(thm)],[28]) ).
thf(330,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ inverse @ multiply ) )
!= ( B @ ( C @ multiply ) ) )
| ( ( identity @ inverse @ ( C @ ( B @ double_divide ) @ double_divide ) )
= identity ) ),
inference(paramod_ordered,[status(thm)],[36,35]) ).
thf(331,plain,
! [A: $i] :
( ( identity @ inverse @ ( A @ inverse @ ( A @ double_divide ) @ double_divide ) )
= identity ),
inference(pattern_uni,[status(thm)],[330:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ inverse ))]]) ).
thf(349,plain,
! [A: $i] :
( ( identity @ inverse @ ( A @ inverse @ ( A @ double_divide ) @ double_divide ) )
= identity ),
inference(simp,[status(thm)],[331]) ).
thf(966,plain,
( ( identity @ inverse @ ( identity @ double_divide ) )
= identity ),
inference(rewrite,[status(thm)],[349,16]) ).
thf(55,plain,
! [A: $i] :
( ( ( A @ ( identity @ multiply ) )
!= ( c3 @ ( b3 @ multiply ) ) )
| ( ( A @ inverse @ inverse )
!= c3 )
| ( ( a3 @ ( b3 @ double_divide ) @ inverse )
!= a3 ) ),
inference(paramod_ordered,[status(thm)],[34,38]) ).
thf(65,plain,
! [A: $i] :
( ( A != c3 )
| ( identity != b3 )
| ( ( A @ inverse @ inverse )
!= c3 )
| ( ( a3 @ ( b3 @ double_divide ) @ inverse )
!= a3 ) ),
inference(simp,[status(thm)],[55]) ).
thf(68,plain,
( ( identity != b3 )
| ( ( c3 @ inverse @ inverse )
!= c3 )
| ( ( a3 @ ( b3 @ double_divide ) @ inverse )
!= a3 ) ),
inference(simp,[status(thm)],[65]) ).
thf(995,plain,
( ( ( identity @ inverse @ ( identity @ double_divide ) )
!= ( a3 @ ( b3 @ double_divide ) ) )
| ( identity != b3 )
| ( ( c3 @ inverse @ inverse )
!= c3 )
| ( ( identity @ inverse )
!= a3 ) ),
inference(paramod_ordered,[status(thm)],[966,68]) ).
thf(1026,plain,
( ( ( identity @ inverse )
!= a3 )
| ( identity != b3 )
| ( identity != b3 )
| ( ( c3 @ inverse @ inverse )
!= c3 )
| ( ( identity @ inverse )
!= a3 ) ),
inference(simp,[status(thm)],[995]) ).
thf(1059,plain,
( ( identity != b3 )
| ( ( c3 @ inverse @ inverse )
!= c3 )
| ( ( identity @ inverse )
!= a3 ) ),
inference(simp,[status(thm)],[1026]) ).
thf(325,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ inverse @ ( A @ double_divide ) )
!= ( C @ ( B @ double_divide ) ) )
| ( ( B @ ( C @ multiply ) @ ( identity @ double_divide ) )
= identity ) ),
inference(paramod_ordered,[status(thm)],[16,35]) ).
thf(326,plain,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) @ ( identity @ double_divide ) )
= identity ),
inference(pattern_uni,[status(thm)],[325:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ inverse ))]]) ).
thf(348,plain,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) @ ( identity @ double_divide ) )
= identity ),
inference(simp,[status(thm)],[326]) ).
thf(59,plain,
! [A: $i] :
( ( ( A @ ( identity @ multiply ) )
!= ( b3 @ ( a3 @ multiply ) ) )
| ( ( c3 @ ( A @ inverse @ inverse @ multiply ) )
!= ( c3 @ ( b3 @ multiply ) @ ( a3 @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[34,8]) ).
thf(62,plain,
! [A: $i] :
( ( ( A @ ( identity @ multiply ) )
!= ( b3 @ ( a3 @ multiply ) ) )
| ( ( c3 @ ( b3 @ multiply ) )
!= c3 )
| ( ( A @ inverse @ inverse )
!= a3 ) ),
inference(simp,[status(thm)],[59]) ).
thf(512,plain,
! [A: $i] :
( ( ( A @ inverse @ inverse )
!= ( b3 @ ( a3 @ multiply ) ) )
| ( ( c3 @ ( b3 @ multiply ) )
!= c3 )
| ( ( A @ inverse @ inverse )
!= a3 ) ),
inference(rewrite,[status(thm)],[62,34]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) )
!= ( c3 @ ( b3 @ multiply ) ) )
| ( ( A @ ( B @ double_divide ) @ inverse )
!= c3 )
| ( ( b3 @ ( a3 @ multiply ) )
!= a3 ) ),
inference(paramod_ordered,[status(thm)],[24,23]) ).
thf(40,plain,
( ( ( b3 @ ( c3 @ double_divide ) @ inverse )
!= c3 )
| ( ( b3 @ ( a3 @ multiply ) )
!= a3 ) ),
inference(pattern_uni,[status(thm)],[39:[bind(A,$thf( b3 )),bind(B,$thf( c3 ))]]) ).
thf(80,plain,
! [A: $i] :
( ( ( A @ inverse @ ( A @ double_divide ) )
!= ( b3 @ ( c3 @ double_divide ) ) )
| ( ( identity @ inverse )
!= c3 )
| ( ( b3 @ ( a3 @ multiply ) )
!= a3 ) ),
inference(paramod_ordered,[status(thm)],[16,40]) ).
thf(82,plain,
! [A: $i] :
( ( ( A @ inverse )
!= b3 )
| ( A != c3 )
| ( ( identity @ inverse )
!= c3 )
| ( ( b3 @ ( a3 @ multiply ) )
!= a3 ) ),
inference(simp,[status(thm)],[80]) ).
thf(85,plain,
( ( ( c3 @ inverse )
!= b3 )
| ( ( identity @ inverse )
!= c3 )
| ( ( b3 @ ( a3 @ multiply ) )
!= a3 ) ),
inference(simp,[status(thm)],[82]) ).
thf(207,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) )
!= ( c3 @ ( b3 @ multiply ) @ ( a3 @ multiply ) ) )
| ( ( A @ ( B @ double_divide ) @ inverse )
!= ( b3 @ ( a3 @ multiply ) @ ( c3 @ double_divide ) @ inverse ) ) ),
inference(paramod_ordered,[status(thm)],[24,30]) ).
thf(208,plain,
( ( a3 @ ( c3 @ ( b3 @ multiply ) @ double_divide ) @ inverse )
!= ( b3 @ ( a3 @ multiply ) @ ( c3 @ double_divide ) @ inverse ) ),
inference(pattern_uni,[status(thm)],[207:[bind(A,$thf( a3 )),bind(B,$thf( c3 @ ( b3 @ multiply ) ))]]) ).
thf(605,plain,
( ( a3 @ ( c3 @ ( b3 @ multiply ) @ double_divide ) )
!= ( b3 @ ( a3 @ multiply ) @ ( c3 @ double_divide ) ) ),
inference(simp,[status(thm)],[208]) ).
thf(653,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) )
!= ( c3 @ ( b3 @ multiply ) ) )
| ( ( a3 @ ( A @ ( B @ double_divide ) @ inverse @ double_divide ) )
!= ( b3 @ ( a3 @ multiply ) @ ( c3 @ double_divide ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,605]) ).
thf(654,plain,
( ( a3 @ ( b3 @ ( c3 @ double_divide ) @ inverse @ double_divide ) )
!= ( b3 @ ( a3 @ multiply ) @ ( c3 @ double_divide ) ) ),
inference(pattern_uni,[status(thm)],[653:[bind(A,$thf( b3 )),bind(B,$thf( c3 ))]]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) )
!= ( b3 @ ( a3 @ multiply ) ) )
| ( ( c3 @ ( A @ ( B @ double_divide ) @ inverse @ multiply ) )
!= ( c3 @ ( b3 @ multiply ) @ ( a3 @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,8]) ).
thf(32,plain,
( ( c3 @ ( a3 @ ( b3 @ double_divide ) @ inverse @ multiply ) )
!= ( c3 @ ( b3 @ multiply ) @ ( a3 @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[31:[bind(A,$thf( a3 )),bind(B,$thf( b3 ))]]) ).
thf(976,plain,
( ( ( identity @ inverse @ ( identity @ double_divide ) )
!= ( a3 @ ( b3 @ double_divide ) ) )
| ( ( c3 @ ( b3 @ multiply ) )
!= c3 )
| ( ( identity @ inverse )
!= a3 ) ),
inference(paramod_ordered,[status(thm)],[966,38]) ).
thf(1025,plain,
( ( ( identity @ inverse )
!= a3 )
| ( identity != b3 )
| ( ( c3 @ ( b3 @ multiply ) )
!= c3 )
| ( ( identity @ inverse )
!= a3 ) ),
inference(simp,[status(thm)],[976]) ).
thf(1058,plain,
( ( identity != b3 )
| ( ( c3 @ ( b3 @ multiply ) )
!= c3 )
| ( ( identity @ inverse )
!= a3 ) ),
inference(simp,[status(thm)],[1025]) ).
thf(46,plain,
! [A: $i] :
( ( ( A @ inverse @ ( A @ double_divide ) )
!= ( a3 @ ( b3 @ double_divide ) ) )
| ( ( c3 @ ( b3 @ multiply ) )
!= c3 )
| ( ( identity @ inverse )
!= a3 ) ),
inference(paramod_ordered,[status(thm)],[16,38]) ).
thf(48,plain,
! [A: $i] :
( ( ( A @ inverse )
!= a3 )
| ( A != b3 )
| ( ( c3 @ ( b3 @ multiply ) )
!= c3 )
| ( ( identity @ inverse )
!= a3 ) ),
inference(simp,[status(thm)],[46]) ).
thf(49,plain,
( ( ( b3 @ inverse )
!= a3 )
| ( ( c3 @ ( b3 @ multiply ) )
!= c3 )
| ( ( identity @ inverse )
!= a3 ) ),
inference(simp,[status(thm)],[48]) ).
thf(79,plain,
! [A: $i] :
( ( ( A @ ( identity @ multiply ) )
!= ( b3 @ ( a3 @ multiply ) ) )
| ( ( b3 @ ( c3 @ double_divide ) @ inverse )
!= c3 )
| ( ( A @ inverse @ inverse )
!= a3 ) ),
inference(paramod_ordered,[status(thm)],[34,40]) ).
thf(83,plain,
! [A: $i] :
( ( A != b3 )
| ( identity != a3 )
| ( ( b3 @ ( c3 @ double_divide ) @ inverse )
!= c3 )
| ( ( A @ inverse @ inverse )
!= a3 ) ),
inference(simp,[status(thm)],[79]) ).
thf(86,plain,
( ( identity != a3 )
| ( ( b3 @ ( c3 @ double_divide ) @ inverse )
!= c3 )
| ( ( b3 @ inverse @ inverse )
!= a3 ) ),
inference(simp,[status(thm)],[83]) ).
thf(303,plain,
! [C: $i,B: $i,A: $i] :
( ( ( identity @ ( A @ double_divide ) )
!= ( C @ ( B @ double_divide ) ) )
| ( ( B @ ( C @ multiply ) @ ( A @ inverse @ double_divide ) )
= identity ) ),
inference(paramod_ordered,[status(thm)],[14,35]) ).
thf(304,plain,
! [A: $i] :
( ( A @ ( identity @ multiply ) @ ( A @ inverse @ double_divide ) )
= identity ),
inference(pattern_uni,[status(thm)],[303:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( identity ))]]) ).
thf(362,plain,
! [A: $i] :
( ( A @ inverse @ inverse @ ( A @ inverse @ double_divide ) )
= identity ),
inference(rewrite,[status(thm)],[304,34]) ).
thf(815,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) )
!= ( b3 @ ( c3 @ double_divide ) @ inverse @ ( a3 @ multiply ) ) )
| ( ( A @ ( B @ double_divide ) @ inverse )
!= ( c3 @ ( b3 @ ( a3 @ multiply ) @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,757]) ).
thf(816,plain,
( ( a3 @ ( b3 @ ( c3 @ double_divide ) @ inverse @ double_divide ) @ inverse )
!= ( c3 @ ( b3 @ ( a3 @ multiply ) @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[815:[bind(A,$thf( a3 )),bind(B,$thf( b3 @ ( c3 @ double_divide ) @ inverse ))]]) ).
thf(10,plain,
! [C: $i,B: $i,A: $i] :
( ( identity @ ( identity @ double_divide ) @ ( identity @ ( C @ double_divide ) @ ( C @ ( A @ double_divide ) @ ( B @ double_divide ) @ double_divide ) @ ( A @ double_divide ) @ double_divide ) )
= B ),
inference(lifteq,[status(thm)],[9]) ).
thf(103,plain,
! [C: $i,B: $i,A: $i] :
( ( identity @ inverse @ ( C @ inverse @ ( C @ ( A @ double_divide ) @ ( B @ double_divide ) @ double_divide ) @ ( A @ double_divide ) @ double_divide ) )
= B ),
inference(rewrite,[status(thm)],[10,14]) ).
thf(45,plain,
! [A: $i] :
( ( ( identity @ ( A @ double_divide ) )
!= ( a3 @ ( b3 @ double_divide ) ) )
| ( ( c3 @ ( b3 @ multiply ) )
!= c3 )
| ( ( A @ inverse @ inverse )
!= a3 ) ),
inference(paramod_ordered,[status(thm)],[14,38]) ).
thf(47,plain,
! [A: $i] :
( ( identity != a3 )
| ( A != b3 )
| ( ( c3 @ ( b3 @ multiply ) )
!= c3 )
| ( ( A @ inverse @ inverse )
!= a3 ) ),
inference(simp,[status(thm)],[45]) ).
thf(50,plain,
( ( identity != a3 )
| ( ( c3 @ ( b3 @ multiply ) )
!= c3 )
| ( ( b3 @ inverse @ inverse )
!= a3 ) ),
inference(simp,[status(thm)],[47]) ).
thf(57,plain,
! [A: $i] :
( ( ( A @ ( identity @ multiply ) )
!= ( c3 @ ( b3 @ multiply ) ) )
| ( ( A @ inverse @ inverse )
!= c3 )
| ( ( b3 @ ( a3 @ multiply ) )
!= a3 ) ),
inference(paramod_ordered,[status(thm)],[34,23]) ).
thf(61,plain,
! [A: $i] :
( ( A != c3 )
| ( identity != b3 )
| ( ( A @ inverse @ inverse )
!= c3 )
| ( ( b3 @ ( a3 @ multiply ) )
!= a3 ) ),
inference(simp,[status(thm)],[57]) ).
thf(72,plain,
( ( identity != b3 )
| ( ( c3 @ inverse @ inverse )
!= c3 )
| ( ( b3 @ ( a3 @ multiply ) )
!= a3 ) ),
inference(simp,[status(thm)],[61]) ).
thf(1658,plain,
$false,
inference(e,[status(thm)],[69,814,24,206,38,757,9,44,35,8,210,14,1059,348,966,6,512,85,654,13,605,32,34,1058,49,86,362,208,816,103,50,16,11,72,40,23,36,30,15,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP571-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.23/0.48 % Computer : n016.cluster.edu
% 0.23/0.48 % Model : x86_64 x86_64
% 0.23/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.48 % Memory : 8046.5625MB
% 0.23/0.48 % OS : Linux 6.8.0-71-generic
% 0.23/0.48 % CPULimit : 300
% 0.23/0.48 % WCLimit : 300
% 0.23/0.48 % DateTime : Fri Sep 25 15:05:29 UTC 2026
% 0.23/0.49 % CPUTime :
% 0.23/0.49 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.29/1.20 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.61/1.47 % [INFO] Parsing done (263ms).
% 1.61/1.49 % [INFO] Running in sequential loop mode.
% 2.60/2.06 % [INFO] eprover registered as external prover.
% 2.60/2.07 % [INFO] Scanning for conjecture ...
% 2.60/2.13 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.84/2.16 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.84/2.17 % [INFO] Problem is propositional (TPTP CNF).
% 2.84/2.18 % [INFO] Type checking passed.
% 2.84/2.18 % [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 ...
% 15.65/5.03 % External prover 'e' found a proof!
% 15.65/5.03 % [INFO] Killing All external provers ...
% 15.65/5.04 % Time passed: 4335ms (effective reasoning time: 3534ms)
% 15.65/5.04 % Axioms used in derivation (4): inverse, multiply, single_axiom, identity
% 15.65/5.04 % No. of inferences in proof: 93
% 15.65/5.04 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 4335 ms resp. 3534 ms w/o parsing
% 17.16/5.11 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 17.16/5.11 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------