%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP751-1 : TPTP v9.3.1. Released v4.0.0.
% 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 : n015.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 07:21:54 AM UTC 2026
% Result : Unsatisfiable 28.26s 11.71s
% Output : Refutation 28.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 97 ( 52 unt; 0 typ; 0 def)
% Number of atoms : 158 ( 157 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 1270 ( 121 ~; 61 |; 0 &;1088 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 174 ( 0 ^; 174 !; 0 ?; 174 :)
% Comments :
%------------------------------------------------------------------------------
thf(mult_decl,type,
mult: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(rd_decl,type,
rd: $i > $i > $i ).
thf(ld_decl,type,
ld: $i > $i > $i ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ mult ) @ ( A @ ld ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
thf(14,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ mult ) @ ( A @ ld ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ld ) @ ( A @ mult ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
thf(12,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ld ) @ ( A @ mult ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ld ) @ ( A @ mult ) )
= B ),
inference(lifteq,[status(thm)],[12]) ).
thf(1,negated_conjecture,
( ( c @ ( b @ mult ) @ ( a @ mult ) )
!= ( c @ ( a @ mult ) @ ( b @ ( a @ ( a @ rd ) @ mult ) @ mult ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(9,plain,
( ( c @ ( b @ mult ) @ ( a @ mult ) )
!= ( c @ ( a @ mult ) @ ( b @ ( a @ ( a @ rd ) @ mult ) @ mult ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(10,plain,
( ( c @ ( b @ mult ) @ ( a @ mult ) )
!= ( c @ ( a @ mult ) @ ( b @ ( a @ ( a @ rd ) @ mult ) @ mult ) ) ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(11,plain,
( ( c @ ( a @ mult ) @ ( b @ ( a @ ( a @ rd ) @ mult ) @ mult ) )
!= ( c @ ( b @ mult ) @ ( a @ mult ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(26,plain,
( ( ( c @ ( b @ mult ) )
!= ( c @ ( a @ mult ) ) )
| ( ( b @ ( a @ ( a @ rd ) @ mult ) )
!= a ) ),
inference(simp,[status(thm)],[11]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( c @ ( b @ mult ) ) )
| ( B
!= ( c @ ( a @ mult ) ) )
| ( ( b @ ( a @ ( a @ rd ) @ mult ) )
!= a ) ),
inference(paramod_ordered,[status(thm)],[13,26]) ).
thf(70,plain,
! [A: $i] :
( ( ( c @ ( a @ mult ) @ ( A @ ld ) )
!= c )
| ( A != b )
| ( ( b @ ( a @ ( a @ rd ) @ mult ) )
!= a ) ),
inference(simp,[status(thm)],[64]) ).
thf(74,plain,
( ( ( c @ ( a @ mult ) @ ( b @ ld ) )
!= c )
| ( ( b @ ( a @ ( a @ rd ) @ mult ) )
!= a ) ),
inference(simp,[status(thm)],[70]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ rd ) @ mult ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ rd ) @ mult ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ rd ) @ mult ) )
= A ),
inference(lifteq,[status(thm)],[16]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ mult ) @ ( A @ ld ) )
= B ),
inference(lifteq,[status(thm)],[14]) ).
thf(90,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( D @ ( C @ mult ) ) )
| ( ( A @ ( C @ ld ) )
= D ) ),
inference(paramod_ordered,[status(thm)],[17,15]) ).
thf(91,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ rd ) @ ld ) )
= B ),
inference(pattern_uni,[status(thm)],[90:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ rd ) )),bind(D,$thf( F ))]]) ).
thf(126,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ rd ) @ ld ) )
= B ),
inference(simp,[status(thm)],[91]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( c @ ( a @ mult ) @ ( b @ ( a @ ( a @ rd ) @ mult ) @ mult ) ) )
| ( B
!= ( c @ ( b @ mult ) @ ( a @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,11]) ).
thf(37,plain,
! [A: $i] :
( ( ( c @ ( b @ mult ) @ ( a @ mult ) @ ( A @ ld ) )
!= ( c @ ( a @ mult ) ) )
| ( A
!= ( b @ ( a @ ( a @ rd ) @ mult ) ) ) ),
inference(simp,[status(thm)],[29]) ).
thf(42,plain,
( ( c @ ( b @ mult ) @ ( a @ mult ) @ ( b @ ( a @ ( a @ rd ) @ mult ) @ ld ) )
!= ( c @ ( a @ mult ) ) ),
inference(simp,[status(thm)],[37]) ).
thf(194,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ rd ) @ ld ) )
!= ( c @ ( b @ mult ) @ ( a @ mult ) @ ( b @ ( a @ ( a @ rd ) @ mult ) @ ld ) ) )
| ( B
!= ( c @ ( a @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[126,42]) ).
thf(201,plain,
! [A: $i] :
( ( A @ ( c @ ( a @ mult ) @ ( A @ rd ) @ ld ) )
!= ( c @ ( b @ mult ) @ ( a @ mult ) @ ( b @ ( a @ ( a @ rd ) @ mult ) @ ld ) ) ),
inference(simp,[status(thm)],[194]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ mult ) @ ( A @ ( A @ mult ) @ mult ) )
= ( C @ ( A @ mult ) @ ( B @ ( A @ mult ) @ mult ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ mult ) @ ( A @ ( A @ mult ) @ mult ) )
= ( C @ ( A @ mult ) @ ( B @ ( A @ mult ) @ mult ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ mult ) @ ( A @ ( A @ mult ) @ mult ) )
= ( C @ ( A @ mult ) @ ( B @ ( A @ mult ) @ mult ) ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(257,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( E @ ( D @ mult ) ) )
| ( ( B @ ( C @ ( C @ mult ) @ mult ) )
= ( E @ ( C @ mult ) @ ( D @ ( C @ mult ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,23]) ).
thf(258,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ mult ) @ mult ) )
= ( C @ ( B @ ld ) @ ( A @ mult ) @ ( B @ ( A @ mult ) @ mult ) ) ),
inference(pattern_uni,[status(thm)],[257:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( F )),bind(E,$thf( G @ ( F @ ld ) ))]]) ).
thf(367,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ mult ) @ mult ) )
= ( C @ ( B @ ld ) @ ( A @ mult ) @ ( B @ ( A @ mult ) @ mult ) ) ),
inference(simp,[status(thm)],[258]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ mult ) @ rd ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ mult ) @ rd ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(260,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( E @ ( C @ mult ) ) )
| ( ( B @ ( D @ ( C @ mult ) @ mult ) )
= ( E @ ( D @ mult ) @ ( C @ ( C @ mult ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,23]) ).
thf(261,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ mult ) @ mult ) )
= ( C @ ( B @ ld ) @ ( A @ mult ) @ ( B @ ( B @ mult ) @ mult ) ) ),
inference(pattern_uni,[status(thm)],[260:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( D )),bind(E,$thf( G @ ( F @ ld ) ))]]) ).
thf(368,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ mult ) @ mult ) )
= ( C @ ( B @ ld ) @ ( A @ mult ) @ ( B @ ( B @ mult ) @ mult ) ) ),
inference(simp,[status(thm)],[261]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ mult ) @ rd ) )
= A ),
inference(lifteq,[status(thm)],[18]) ).
thf(87,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( c @ ( a @ mult ) @ ( b @ ( a @ ( a @ rd ) @ mult ) @ mult ) ) )
| ( A
!= ( c @ ( b @ mult ) @ ( a @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,11]) ).
thf(107,plain,
! [A: $i] :
( ( A @ ( A @ ( c @ ( b @ mult ) @ ( a @ mult ) @ rd ) @ mult ) )
!= ( c @ ( a @ mult ) @ ( b @ ( a @ ( a @ rd ) @ mult ) @ mult ) ) ),
inference(simp,[status(thm)],[87]) ).
thf(122,plain,
! [A: $i] :
( ( A @ ( A @ ( c @ ( b @ mult ) @ ( a @ mult ) @ rd ) @ mult ) )
!= ( c @ ( a @ mult ) @ ( b @ ( a @ ( a @ rd ) @ mult ) @ mult ) ) ),
inference(simp,[status(thm)],[107]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ mult ) @ ( B @ ( A @ mult ) @ mult ) )
= ( C @ ( B @ mult ) @ ( C @ ( A @ mult ) @ mult ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ mult ) @ ( B @ ( A @ mult ) @ mult ) )
= ( C @ ( B @ mult ) @ ( C @ ( A @ mult ) @ mult ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ mult ) @ ( B @ ( A @ mult ) @ mult ) )
= ( C @ ( B @ mult ) @ ( C @ ( A @ mult ) @ mult ) ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(108,plain,
! [A: $i] :
( ( A
!= ( c @ ( a @ mult ) ) )
| ( ( A @ ( c @ ( b @ mult ) @ ( a @ mult ) @ rd ) )
!= ( b @ ( a @ ( a @ rd ) @ mult ) ) ) ),
inference(simp,[status(thm)],[87]) ).
thf(123,plain,
( ( c @ ( a @ mult ) @ ( c @ ( b @ mult ) @ ( a @ mult ) @ rd ) )
!= ( b @ ( a @ ( a @ rd ) @ mult ) ) ),
inference(simp,[status(thm)],[108]) ).
thf(175,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ mult ) @ rd ) )
!= ( c @ ( a @ mult ) @ ( c @ ( b @ mult ) @ ( a @ mult ) @ rd ) ) )
| ( A
!= ( b @ ( a @ ( a @ rd ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,123]) ).
thf(181,plain,
! [A: $i] :
( ( A @ ( A @ ( b @ ( a @ ( a @ rd ) @ mult ) @ mult ) @ rd ) )
!= ( c @ ( a @ mult ) @ ( c @ ( b @ mult ) @ ( a @ mult ) @ rd ) ) ),
inference(simp,[status(thm)],[175]) ).
thf(189,plain,
! [A: $i] :
( ( A @ ( A @ ( b @ ( a @ ( a @ rd ) @ mult ) @ mult ) @ rd ) )
!= ( c @ ( a @ mult ) @ ( c @ ( b @ mult ) @ ( a @ mult ) @ rd ) ) ),
inference(simp,[status(thm)],[181]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ mult ) @ ( A @ ( A @ mult ) @ ( A @ mult ) @ mult ) )
= ( C @ ( A @ ( A @ mult ) @ mult ) @ ( B @ ( A @ mult ) @ mult ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ mult ) @ ( A @ ( A @ mult ) @ ( A @ mult ) @ mult ) )
= ( C @ ( A @ ( A @ mult ) @ mult ) @ ( B @ ( A @ mult ) @ mult ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(692,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( C @ ( C @ ( c @ ( b @ mult ) @ ( a @ mult ) @ rd ) @ mult ) ) )
| ( B
!= ( c @ ( a @ mult ) @ ( b @ ( a @ ( a @ rd ) @ mult ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,122]) ).
thf(720,plain,
! [B: $i,A: $i] :
( ( ( c @ ( a @ mult ) @ ( b @ ( a @ ( a @ rd ) @ mult ) @ mult ) @ ( A @ ld ) )
!= B )
| ( A
!= ( B @ ( c @ ( b @ mult ) @ ( a @ mult ) @ rd ) ) ) ),
inference(simp,[status(thm)],[692]) ).
thf(770,plain,
! [A: $i] :
( ( c @ ( a @ mult ) @ ( b @ ( a @ ( a @ rd ) @ mult ) @ mult ) @ ( A @ ( c @ ( b @ mult ) @ ( a @ mult ) @ rd ) @ ld ) )
!= A ),
inference(simp,[status(thm)],[720]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( c @ ( a @ mult ) ) )
| ( ( B @ ( b @ ( a @ ( a @ rd ) @ mult ) @ mult ) )
!= ( c @ ( b @ mult ) @ ( a @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,11]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) )
!= c )
| ( A != a )
| ( B
!= ( c @ ( b @ mult ) ) )
| ( ( b @ ( a @ ( a @ rd ) @ mult ) )
!= a ) ),
inference(simp,[status(thm)],[27]) ).
thf(38,plain,
( ( ( c @ ( b @ mult ) @ ( a @ ld ) )
!= c )
| ( ( b @ ( a @ ( a @ rd ) @ mult ) )
!= a ) ),
inference(simp,[status(thm)],[32]) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ mult ) @ ( A @ ( A @ mult ) @ ( A @ mult ) @ mult ) )
= ( C @ ( A @ ( A @ mult ) @ mult ) @ ( B @ ( A @ mult ) @ mult ) ) ),
inference(lifteq,[status(thm)],[20]) ).
thf(141,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( D @ ( C @ mult ) ) )
| ( ( D @ ( B @ rd ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[13,19]) ).
thf(142,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ld ) @ ( B @ rd ) )
= A ),
inference(pattern_uni,[status(thm)],[141:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ ld ) ))]]) ).
thf(166,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ld ) @ ( B @ rd ) )
= A ),
inference(simp,[status(thm)],[142]) ).
thf(814,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( B @ rd ) )
!= ( C @ ( C @ ( b @ ( a @ ( a @ rd ) @ mult ) @ mult ) @ rd ) ) )
| ( A
!= ( c @ ( a @ mult ) @ ( c @ ( b @ mult ) @ ( a @ mult ) @ rd ) ) ) ),
inference(paramod_ordered,[status(thm)],[166,189]) ).
thf(826,plain,
! [B: $i,A: $i] :
( ( ( A @ ( c @ ( a @ mult ) @ ( c @ ( b @ mult ) @ ( a @ mult ) @ rd ) @ ld ) )
!= B )
| ( A
!= ( B @ ( b @ ( a @ ( a @ rd ) @ mult ) @ mult ) ) ) ),
inference(simp,[status(thm)],[814]) ).
thf(884,plain,
! [A: $i] :
( ( A @ ( b @ ( a @ ( a @ rd ) @ mult ) @ mult ) @ ( c @ ( a @ mult ) @ ( c @ ( b @ mult ) @ ( a @ mult ) @ rd ) @ ld ) )
!= A ),
inference(simp,[status(thm)],[826]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( b @ ( a @ ( a @ rd ) @ mult ) ) )
| ( ( c @ ( b @ mult ) )
!= ( c @ ( a @ mult ) ) )
| ( B != a ) ),
inference(paramod_ordered,[status(thm)],[13,26]) ).
thf(68,plain,
! [A: $i] :
( ( ( a @ ( A @ ld ) )
!= b )
| ( A
!= ( a @ ( a @ rd ) ) )
| ( c != c )
| ( b != a ) ),
inference(simp,[status(thm)],[63]) ).
thf(73,plain,
( ( ( a @ ( a @ ( a @ rd ) @ ld ) )
!= b )
| ( b != a ) ),
inference(simp,[status(thm)],[68]) ).
thf(192,plain,
( ( b != a )
| ( b != a ) ),
inference(rewrite,[status(thm)],[73,126]) ).
thf(193,plain,
b != a,
inference(simp,[status(thm)],[192]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) )
!= c )
| ( A != a )
| ( ( B @ ( b @ ( a @ ( a @ rd ) @ mult ) @ mult ) )
!= ( c @ ( b @ mult ) @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[27]) ).
thf(44,plain,
! [A: $i] :
( ( ( A @ ( a @ ld ) )
!= c )
| ( ( A @ ( b @ ( a @ ( a @ rd ) @ mult ) @ mult ) )
!= ( c @ ( b @ mult ) @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[31]) ).
thf(4680,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( C @ ( b @ ( a @ ( a @ rd ) @ mult ) @ mult ) ) )
| ( ( C @ ( a @ ld ) )
!= c )
| ( B
!= ( c @ ( b @ mult ) @ ( a @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,44]) ).
thf(4681,plain,
! [A: $i] :
( ( ( A @ ( b @ ( a @ ( a @ rd ) @ mult ) @ ld ) @ ( a @ ld ) )
!= c )
| ( A
!= ( c @ ( b @ mult ) @ ( a @ mult ) ) ) ),
inference(pattern_uni,[status(thm)],[4680:[bind(A,$thf( b @ ( a @ ( a @ rd ) @ mult ) )),bind(B,$thf( I )),bind(C,$thf( I @ ( b @ ( a @ ( a @ rd ) @ mult ) @ ld ) ))]]) ).
thf(4829,plain,
( ( c @ ( b @ mult ) @ ( a @ mult ) @ ( b @ ( a @ ( a @ rd ) @ mult ) @ ld ) @ ( a @ ld ) )
!= c ),
inference(simp,[status(thm)],[4681]) ).
thf(2700,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ mult ) @ rd ) )
!= ( C @ ( c @ ( b @ mult ) @ ( a @ mult ) @ rd ) ) )
| ( ( c @ ( a @ mult ) @ ( b @ ( a @ ( a @ rd ) @ mult ) @ mult ) @ ( A @ ld ) )
!= C ) ),
inference(paramod_ordered,[status(thm)],[19,770]) ).
thf(2701,plain,
( ( c @ ( a @ mult ) @ ( b @ ( a @ ( a @ rd ) @ mult ) @ mult ) @ ( a @ ld ) )
!= ( c @ ( b @ mult ) ) ),
inference(pattern_uni,[status(thm)],[2700:[bind(A,$thf( a )),bind(B,$thf( c @ ( b @ mult ) )),bind(C,$thf( c @ ( b @ mult ) ))]]) ).
thf(2831,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ rd ) @ ld ) )
!= ( c @ ( a @ mult ) @ ( b @ ( a @ ( a @ rd ) @ mult ) @ mult ) @ ( a @ ld ) ) )
| ( B
!= ( c @ ( b @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[126,2701]) ).
thf(2882,plain,
! [A: $i] :
( ( A
!= ( c @ ( a @ mult ) @ ( b @ ( a @ ( a @ rd ) @ mult ) @ mult ) ) )
| ( ( c @ ( b @ mult ) @ ( A @ rd ) )
!= a ) ),
inference(simp,[status(thm)],[2831]) ).
thf(2891,plain,
( ( c @ ( b @ mult ) @ ( c @ ( a @ mult ) @ ( b @ ( a @ ( a @ rd ) @ mult ) @ mult ) @ rd ) )
!= a ),
inference(simp,[status(thm)],[2882]) ).
thf(1303,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( b @ ( a @ ( a @ rd ) @ mult ) ) )
| ( ( c @ ( b @ mult ) @ ( a @ mult ) @ ( B @ ld ) )
!= ( C @ ( c @ ( a @ mult ) @ ( C @ rd ) @ ld ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,201]) ).
thf(1362,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ld ) )
!= b )
| ( A
!= ( a @ ( a @ rd ) ) )
| ( ( c @ ( b @ mult ) @ ( a @ mult ) )
!= C )
| ( B
!= ( c @ ( a @ mult ) @ ( C @ rd ) ) ) ),
inference(simp,[status(thm)],[1303]) ).
thf(1472,plain,
( ( c @ ( a @ mult ) @ ( c @ ( b @ mult ) @ ( a @ mult ) @ rd ) @ ( a @ ( a @ rd ) @ ld ) )
!= b ),
inference(simp,[status(thm)],[1362]) ).
thf(1333,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( b @ ( a @ ( a @ rd ) @ mult ) ) )
| ( ( c @ ( b @ mult ) @ ( a @ mult ) @ ( A @ ld ) )
!= ( C @ ( c @ ( a @ mult ) @ ( C @ rd ) @ ld ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,201]) ).
thf(1402,plain,
! [C: $i,B: $i,A: $i] :
( ( B != b )
| ( ( B @ ( A @ rd ) )
!= ( a @ ( a @ rd ) ) )
| ( ( c @ ( b @ mult ) @ ( a @ mult ) )
!= C )
| ( A
!= ( c @ ( a @ mult ) @ ( C @ rd ) ) ) ),
inference(simp,[status(thm)],[1333]) ).
thf(1504,plain,
( ( b @ ( c @ ( a @ mult ) @ ( c @ ( b @ mult ) @ ( a @ mult ) @ rd ) @ rd ) )
!= ( a @ ( a @ rd ) ) ),
inference(simp,[status(thm)],[1402]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( b @ ( a @ ( a @ rd ) @ mult ) ) )
| ( ( c @ ( a @ mult ) @ ( B @ mult ) )
!= ( c @ ( b @ mult ) @ ( a @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,11]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) )
!= b )
| ( A
!= ( a @ ( a @ rd ) ) )
| ( ( c @ ( a @ mult ) @ ( B @ mult ) )
!= ( c @ ( b @ mult ) @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[28]) ).
thf(40,plain,
! [A: $i] :
( ( ( A @ ( a @ ( a @ rd ) @ ld ) )
!= b )
| ( ( c @ ( a @ mult ) @ ( A @ mult ) )
!= ( c @ ( b @ mult ) @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[34]) ).
thf(86,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( b @ ( a @ ( a @ rd ) @ mult ) ) )
| ( ( c @ ( a @ mult ) @ ( A @ mult ) )
!= ( c @ ( b @ mult ) @ ( a @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,11]) ).
thf(104,plain,
! [B: $i,A: $i] :
( ( B != b )
| ( ( B @ ( A @ rd ) )
!= ( a @ ( a @ rd ) ) )
| ( ( c @ ( b @ mult ) )
!= ( c @ ( a @ mult ) ) )
| ( A != a ) ),
inference(simp,[status(thm)],[86]) ).
thf(119,plain,
( ( ( b @ ( a @ rd ) )
!= ( a @ ( a @ rd ) ) )
| ( ( c @ ( b @ mult ) )
!= ( c @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[104]) ).
thf(4865,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ rd ) @ ld ) )
!= ( c @ ( b @ mult ) @ ( a @ mult ) @ ( b @ ( a @ ( a @ rd ) @ mult ) @ ld ) @ ( a @ ld ) ) )
| ( B != c ) ),
inference(paramod_ordered,[status(thm)],[126,4829]) ).
thf(4944,plain,
! [A: $i] :
( ( A
!= ( c @ ( b @ mult ) @ ( a @ mult ) @ ( b @ ( a @ ( a @ rd ) @ mult ) @ ld ) ) )
| ( ( c @ ( A @ rd ) )
!= a ) ),
inference(simp,[status(thm)],[4865]) ).
thf(4964,plain,
( ( c @ ( c @ ( b @ mult ) @ ( a @ mult ) @ ( b @ ( a @ ( a @ rd ) @ mult ) @ ld ) @ rd ) )
!= a ),
inference(simp,[status(thm)],[4944]) ).
thf(262,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( D @ ( C @ mult ) ) )
| ( ( E @ ( C @ mult ) @ ( B @ mult ) )
= ( E @ ( D @ mult ) @ ( C @ ( C @ mult ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,23]) ).
thf(263,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ mult ) @ ( C @ mult ) )
= ( A @ ( C @ ( B @ ld ) @ mult ) @ ( B @ ( B @ mult ) @ mult ) ) ),
inference(pattern_uni,[status(thm)],[262:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( G @ ( F @ ld ) ))]]) ).
thf(369,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ mult ) @ ( C @ mult ) )
= ( A @ ( C @ ( B @ ld ) @ mult ) @ ( B @ ( B @ mult ) @ mult ) ) ),
inference(simp,[status(thm)],[263]) ).
thf(6952,plain,
$false,
inference(e,[status(thm)],[14,74,201,9,367,18,368,19,126,122,42,24,25,189,20,770,38,21,884,193,4829,13,166,17,22,44,12,2891,123,1472,16,2701,11,1504,40,26,23,119,4964,15,369]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP751-1 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.14/0.52 % Computer : n015.cluster.edu
% 0.14/0.52 % Model : x86_64 x86_64
% 0.14/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.52 % Memory : 8046.5625MB
% 0.14/0.52 % OS : Linux 6.8.0-71-generic
% 0.14/0.52 % CPULimit : 300
% 0.14/0.52 % WCLimit : 300
% 0.14/0.52 % DateTime : Fri Sep 25 15:47:27 UTC 2026
% 0.14/0.53 % CPUTime :
% 0.14/0.53 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
% 0.91/1.36 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.17/1.58 % [INFO] Parsing done (217ms).
% 1.17/1.59 % [INFO] Running in sequential loop mode.
% 1.85/2.07 % [INFO] eprover registered as external prover.
% 1.85/2.08 % [INFO] Scanning for conjecture ...
% 2.07/2.21 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 2.07/2.26 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 2.07/2.28 % [INFO] Problem is propositional (TPTP CNF).
% 2.07/2.28 % [INFO] Type checking passed.
% 2.07/2.29 % [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 ...
% 28.03/11.70 % External prover 'e' found a proof!
% 28.03/11.70 % [INFO] Killing All external provers ...
% 28.26/11.70 % Time passed: 10923ms (effective reasoning time: 10098ms)
% 28.26/11.70 % Axioms used in derivation (7): f03, f02, f07, f06, f05, f04, f01
% 28.26/11.71 % No. of inferences in proof: 97
% 28.26/11.71 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 10923 ms resp. 10098 ms w/o parsing
% 28.26/11.79 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 28.26/11.79 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------