%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP754-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n004.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 07:21:55 AM UTC 2026
% Result : Unsatisfiable 20.91s 5.88s
% Output : Refutation 17.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 99 ( 52 unt; 0 typ; 0 def)
% Number of atoms : 157 ( 156 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 1330 ( 124 ~; 58 |; 0 &;1148 @)
% ( 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 : 168 ( 0 ^; 168 !; 0 ?; 168 :)
% 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(ld_decl,type,
ld: $i > $i > $i ).
thf(rd_decl,type,
rd: $i > $i > $i ).
thf(1,negated_conjecture,
( ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) )
!= ( c @ ( a @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(8,plain,
( ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) )
!= ( c @ ( a @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(9,plain,
( ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) )
!= ( c @ ( a @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(10,plain,
( ( c @ ( a @ mult ) @ ( b @ ( a @ mult ) @ mult ) )
!= ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ mult ) @ ( A @ ld ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
thf(13,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ mult ) @ ( A @ ld ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ mult ) @ ( A @ ld ) )
= B ),
inference(lifteq,[status(thm)],[13]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ rd ) @ mult ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ rd ) @ mult ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ rd ) @ mult ) )
= A ),
inference(lifteq,[status(thm)],[15]) ).
thf(115,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)],[16,14]) ).
thf(116,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ rd ) @ ld ) )
= B ),
inference(pattern_uni,[status(thm)],[115:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ rd ) )),bind(D,$thf( F ))]]) ).
thf(166,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ rd ) @ ld ) )
= B ),
inference(simp,[status(thm)],[116]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ mult ) @ rd ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ mult ) @ rd ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ mult ) @ rd ) )
= A ),
inference(lifteq,[status(thm)],[17]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ld ) @ ( A @ mult ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
thf(11,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ld ) @ ( A @ mult ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ld ) @ ( A @ mult ) )
= B ),
inference(lifteq,[status(thm)],[11]) ).
thf(112,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( c @ ( a @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) )
| ( A
!= ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[16,10]) ).
thf(141,plain,
! [A: $i] :
( ( A @ ( A @ ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ rd ) @ mult ) )
!= ( c @ ( a @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ),
inference(simp,[status(thm)],[112]) ).
thf(160,plain,
! [A: $i] :
( ( A @ ( A @ ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ rd ) @ mult ) )
!= ( c @ ( a @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ),
inference(simp,[status(thm)],[141]) ).
thf(580,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( C @ ( C @ ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ rd ) @ mult ) ) )
| ( B
!= ( c @ ( a @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,160]) ).
thf(612,plain,
! [B: $i,A: $i] :
( ( ( c @ ( a @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ ( A @ ld ) )
!= B )
| ( A
!= ( B @ ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ rd ) ) ) ),
inference(simp,[status(thm)],[580]) ).
thf(675,plain,
! [A: $i] :
( ( c @ ( a @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ ( A @ ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ rd ) @ ld ) )
!= A ),
inference(simp,[status(thm)],[612]) ).
thf(1240,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ mult ) @ rd ) )
!= ( C @ ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ rd ) ) )
| ( ( c @ ( a @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ ( A @ ld ) )
!= C ) ),
inference(paramod_ordered,[status(thm)],[18,675]) ).
thf(1241,plain,
( ( c @ ( a @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ ( a @ ( a @ mult ) @ ld ) )
!= ( c @ ( b @ mult ) ) ),
inference(pattern_uni,[status(thm)],[1240:[bind(A,$thf( a @ ( a @ mult ) )),bind(B,$thf( c @ ( b @ mult ) )),bind(C,$thf( c @ ( b @ mult ) ))]]) ).
thf(1361,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ rd ) @ ld ) )
!= ( c @ ( a @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ ( a @ ( a @ mult ) @ ld ) ) )
| ( B
!= ( c @ ( b @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[166,1241]) ).
thf(1373,plain,
! [A: $i] :
( ( A
!= ( c @ ( a @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) )
| ( ( c @ ( b @ mult ) @ ( A @ rd ) )
!= ( a @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[1361]) ).
thf(1402,plain,
( ( c @ ( b @ mult ) @ ( c @ ( a @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ rd ) )
!= ( a @ ( a @ mult ) ) ),
inference(simp,[status(thm)],[1373]) ).
thf(23,plain,
( ( ( c @ ( b @ mult ) )
!= ( c @ ( a @ mult ) ) )
| ( ( b @ ( a @ mult ) )
!= ( a @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[10]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( c @ ( b @ mult ) ) )
| ( B
!= ( c @ ( a @ mult ) ) )
| ( ( b @ ( a @ mult ) )
!= ( a @ ( a @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,23]) ).
thf(75,plain,
! [A: $i] :
( ( ( c @ ( a @ mult ) @ ( A @ ld ) )
!= c )
| ( A != b )
| ( ( b @ ( a @ mult ) )
!= ( a @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[66]) ).
thf(96,plain,
( ( ( c @ ( a @ mult ) @ ( b @ ld ) )
!= c )
| ( ( b @ ( a @ mult ) )
!= ( a @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[75]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ mult ) @ ( A @ mult ) )
= ( C @ ( A @ mult ) @ ( B @ ( A @ ( A @ rd ) @ mult ) @ mult ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ mult ) @ ( A @ mult ) )
= ( C @ ( A @ mult ) @ ( B @ ( A @ ( A @ rd ) @ mult ) @ mult ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ mult ) @ ( B @ ( A @ ( A @ rd ) @ mult ) @ mult ) )
= ( C @ ( B @ mult ) @ ( A @ mult ) ) ),
inference(lifteq,[status(thm)],[19]) ).
thf(260,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( E @ ( C @ mult ) ) )
| ( ( B @ ( D @ ( C @ ( C @ rd ) @ mult ) @ mult ) )
= ( E @ ( D @ mult ) @ ( C @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,20]) ).
thf(261,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ ( B @ rd ) @ mult ) @ mult ) )
= ( C @ ( B @ ld ) @ ( A @ mult ) @ ( B @ mult ) ) ),
inference(pattern_uni,[status(thm)],[260:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( D )),bind(E,$thf( G @ ( F @ ld ) ))]]) ).
thf(318,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ ( B @ rd ) @ mult ) @ mult ) )
= ( C @ ( B @ ld ) @ ( A @ mult ) @ ( B @ mult ) ) ),
inference(simp,[status(thm)],[261]) ).
thf(64,plain,
( ( c != c )
| ( b != a )
| ( b != a )
| ( a != a ) ),
inference(simp,[status(thm)],[23]) ).
thf(91,plain,
b != a,
inference(simp,[status(thm)],[64]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( c @ ( a @ mult ) ) )
| ( ( B @ ( b @ ( a @ mult ) @ mult ) )
!= ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,10]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) )
!= c )
| ( A != a )
| ( ( B @ ( b @ ( a @ mult ) @ mult ) )
!= ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) ) ) ),
inference(simp,[status(thm)],[26]) ).
thf(36,plain,
! [A: $i] :
( ( ( A @ ( a @ ld ) )
!= c )
| ( ( A @ ( b @ ( a @ mult ) @ mult ) )
!= ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(1679,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( C @ ( b @ ( a @ mult ) @ mult ) ) )
| ( ( C @ ( a @ ld ) )
!= c )
| ( B
!= ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,36]) ).
thf(1680,plain,
! [A: $i] :
( ( ( A @ ( b @ ( a @ mult ) @ ld ) @ ( a @ ld ) )
!= c )
| ( A
!= ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) ) ) ),
inference(pattern_uni,[status(thm)],[1679:[bind(A,$thf( b @ ( a @ mult ) )),bind(B,$thf( G )),bind(C,$thf( G @ ( b @ ( a @ mult ) @ ld ) ))]]) ).
thf(1746,plain,
( ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ ( b @ ( a @ mult ) @ ld ) @ ( a @ ld ) )
!= c ),
inference(simp,[status(thm)],[1680]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) )
!= c )
| ( A != a )
| ( B
!= ( c @ ( b @ mult ) ) )
| ( ( b @ ( a @ mult ) )
!= ( a @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[26]) ).
thf(37,plain,
( ( ( c @ ( b @ mult ) @ ( a @ ld ) )
!= c )
| ( ( b @ ( a @ mult ) )
!= ( a @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[34]) ).
thf(1898,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ rd ) @ ld ) )
!= ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ ( b @ ( a @ mult ) @ ld ) @ ( a @ ld ) ) )
| ( B != c ) ),
inference(paramod_ordered,[status(thm)],[166,1746]) ).
thf(1940,plain,
! [A: $i] :
( ( A
!= ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ ( b @ ( a @ mult ) @ ld ) ) )
| ( ( c @ ( A @ rd ) )
!= a ) ),
inference(simp,[status(thm)],[1898]) ).
thf(1963,plain,
( ( c @ ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ ( b @ ( a @ mult ) @ ld ) @ rd ) )
!= a ),
inference(simp,[status(thm)],[1940]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( c @ ( a @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) )
| ( B
!= ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,10]) ).
thf(28,plain,
! [A: $i] :
( ( ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ ( A @ ld ) )
!= ( c @ ( a @ mult ) ) )
| ( A
!= ( b @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[24]) ).
thf(38,plain,
( ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ ( b @ ( a @ mult ) @ ld ) )
!= ( c @ ( a @ mult ) ) ),
inference(simp,[status(thm)],[28]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ mult ) @ mult ) )
= ( C @ ( C @ ld ) @ ( B @ mult ) @ ( C @ ( A @ mult ) @ mult ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f06) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ mult ) @ mult ) )
= ( C @ ( C @ ld ) @ ( B @ mult ) @ ( C @ ( A @ mult ) @ mult ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1248,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ rd ) @ ld ) )
!= ( c @ ( a @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ ( C @ ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ rd ) @ ld ) ) )
| ( B != C ) ),
inference(paramod_ordered,[status(thm)],[166,675]) ).
thf(1304,plain,
! [B: $i,A: $i] :
( ( A
!= ( c @ ( a @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) )
| ( ( B @ ( A @ rd ) )
!= ( B @ ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ rd ) ) ) ),
inference(simp,[status(thm)],[1248]) ).
thf(1324,plain,
! [A: $i] :
( ( A @ ( c @ ( a @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ rd ) )
!= ( A @ ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ rd ) ) ),
inference(simp,[status(thm)],[1304]) ).
thf(855,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( E @ ( D @ ld ) @ ( C @ mult ) ) )
| ( ( B @ ( D @ mult ) )
= ( E @ ( C @ ( D @ ( D @ rd ) @ mult ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,318]) ).
thf(856,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ ( A @ rd ) @ mult ) @ mult ) )
= ( B @ ( A @ mult ) ) ),
inference(pattern_uni,[status(thm)],[855:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(142,plain,
! [A: $i] :
( ( A
!= ( c @ ( a @ mult ) ) )
| ( ( A @ ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ rd ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[112]) ).
thf(161,plain,
( ( c @ ( a @ mult ) @ ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ rd ) )
!= ( b @ ( a @ mult ) ) ),
inference(simp,[status(thm)],[142]) ).
thf(170,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)],[12,18]) ).
thf(171,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ld ) @ ( B @ rd ) )
= A ),
inference(pattern_uni,[status(thm)],[170:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ ld ) ))]]) ).
thf(176,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ld ) @ ( B @ rd ) )
= A ),
inference(simp,[status(thm)],[171]) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ mult ) @ mult ) )
= ( C @ ( C @ ld ) @ ( B @ mult ) @ ( C @ ( A @ mult ) @ mult ) ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(181,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ mult ) @ rd ) )
!= ( c @ ( a @ mult ) @ ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ rd ) ) )
| ( A
!= ( b @ ( a @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,161]) ).
thf(190,plain,
! [A: $i] :
( ( A @ ( A @ ( b @ ( a @ mult ) @ mult ) @ rd ) )
!= ( c @ ( a @ mult ) @ ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ rd ) ) ),
inference(simp,[status(thm)],[181]) ).
thf(204,plain,
! [A: $i] :
( ( A @ ( A @ ( b @ ( a @ mult ) @ mult ) @ rd ) )
!= ( c @ ( a @ mult ) @ ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ rd ) ) ),
inference(simp,[status(thm)],[190]) ).
thf(208,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ rd ) @ ld ) )
!= ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ ( b @ ( a @ mult ) @ ld ) ) )
| ( B
!= ( c @ ( a @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[166,38]) ).
thf(214,plain,
! [A: $i] :
( ( A @ ( c @ ( a @ mult ) @ ( A @ rd ) @ ld ) )
!= ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ ( b @ ( a @ mult ) @ ld ) ) ),
inference(simp,[status(thm)],[208]) ).
thf(766,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ mult ) @ ( A @ ld ) )
!= ( C @ ( c @ ( a @ mult ) @ ( C @ rd ) @ ld ) ) )
| ( B
!= ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ ( b @ ( a @ mult ) @ ld ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,214]) ).
thf(793,plain,
! [B: $i,A: $i] :
( ( ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ ( b @ ( a @ mult ) @ ld ) @ ( A @ mult ) )
!= B )
| ( A
!= ( c @ ( a @ mult ) @ ( B @ rd ) ) ) ),
inference(simp,[status(thm)],[766]) ).
thf(812,plain,
! [A: $i] :
( ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ ( b @ ( a @ mult ) @ ld ) @ ( c @ ( a @ mult ) @ ( A @ rd ) @ mult ) )
!= A ),
inference(simp,[status(thm)],[793]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( b @ ( a @ mult ) ) )
| ( ( c @ ( a @ mult ) @ ( B @ mult ) )
!= ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,10]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) )
!= b )
| ( A != a )
| ( ( c @ ( a @ mult ) @ ( B @ mult ) )
!= ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) ) ) ),
inference(simp,[status(thm)],[25]) ).
thf(40,plain,
! [A: $i] :
( ( ( A @ ( a @ ld ) )
!= b )
| ( ( c @ ( a @ mult ) @ ( A @ mult ) )
!= ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) ) ) ),
inference(simp,[status(thm)],[30]) ).
thf(2499,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( c @ ( a @ mult ) @ ( C @ mult ) ) )
| ( ( C @ ( a @ ld ) )
!= b )
| ( A
!= ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[16,40]) ).
thf(2500,plain,
! [A: $i] :
( ( ( c @ ( a @ mult ) @ ( A @ rd ) @ ( a @ ld ) )
!= b )
| ( A
!= ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) ) ) ),
inference(pattern_uni,[status(thm)],[2499:[bind(A,$thf( D )),bind(B,$thf( c @ ( a @ mult ) )),bind(C,$thf( c @ ( a @ mult ) @ ( D @ rd ) ))]]) ).
thf(2699,plain,
( ( c @ ( a @ mult ) @ ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ rd ) @ ( a @ ld ) )
!= b ),
inference(simp,[status(thm)],[2500]) ).
thf(2755,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ rd ) @ ld ) )
!= ( c @ ( a @ mult ) @ ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ rd ) @ ( a @ ld ) ) )
| ( B != b ) ),
inference(paramod_ordered,[status(thm)],[166,2699]) ).
thf(2783,plain,
! [A: $i] :
( ( A
!= ( c @ ( a @ mult ) @ ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ rd ) ) )
| ( ( b @ ( A @ rd ) )
!= a ) ),
inference(simp,[status(thm)],[2755]) ).
thf(2816,plain,
( ( b @ ( c @ ( a @ mult ) @ ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ rd ) @ rd ) )
!= a ),
inference(simp,[status(thm)],[2783]) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( b @ ( a @ mult ) ) )
| ( ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ ( B @ ld ) )
!= ( c @ ( a @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,38]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) )
!= b )
| ( A != a )
| ( ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ ( B @ ld ) )
!= ( c @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[44]) ).
thf(50,plain,
! [A: $i] :
( ( ( A @ ( a @ ld ) )
!= b )
| ( ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ ( A @ ld ) )
!= ( c @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[48]) ).
thf(1249,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( B @ rd ) )
!= ( C @ ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ rd ) ) )
| ( ( c @ ( a @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ ( A @ ld ) )
!= C ) ),
inference(paramod_ordered,[status(thm)],[176,675]) ).
thf(1250,plain,
! [A: $i] :
( ( c @ ( a @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ ( A @ ld ) )
!= ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ ( A @ ld ) ) ),
inference(pattern_uni,[status(thm)],[1249:[bind(A,$thf( J )),bind(B,$thf( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) )),bind(C,$thf( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ ( J @ ld ) ))]]) ).
thf(1326,plain,
! [A: $i] :
( ( c @ ( a @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ ( A @ ld ) )
!= ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ ( A @ ld ) ) ),
inference(simp,[status(thm)],[1250]) ).
thf(710,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( B @ rd ) )
!= ( C @ ( C @ ( b @ ( a @ mult ) @ mult ) @ rd ) ) )
| ( A
!= ( c @ ( a @ mult ) @ ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ rd ) ) ) ),
inference(paramod_ordered,[status(thm)],[176,204]) ).
thf(727,plain,
! [B: $i,A: $i] :
( ( ( A @ ( c @ ( a @ mult ) @ ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ rd ) @ ld ) )
!= B )
| ( A
!= ( B @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(simp,[status(thm)],[710]) ).
thf(752,plain,
! [A: $i] :
( ( A @ ( b @ ( a @ mult ) @ mult ) @ ( c @ ( a @ mult ) @ ( c @ ( b @ mult ) @ ( a @ ( a @ mult ) @ mult ) @ rd ) @ ld ) )
!= A ),
inference(simp,[status(thm)],[727]) ).
thf(1425,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ ( A @ rd ) @ mult ) @ mult ) )
!= ( D @ ( C @ mult ) ) )
| ( ( B @ ( A @ mult ) @ ( C @ ld ) )
= D ) ),
inference(paramod_ordered,[status(thm)],[856,14]) ).
thf(1426,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ mult ) @ ( B @ ( B @ ( B @ rd ) @ mult ) @ ld ) )
= A ),
inference(pattern_uni,[status(thm)],[1425:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ ( F @ ( F @ rd ) @ mult ) )),bind(D,$thf( B ))]]) ).
thf(1597,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ mult ) @ ( B @ ( B @ ( B @ rd ) @ mult ) @ ld ) )
= A ),
inference(simp,[status(thm)],[1426]) ).
thf(4348,plain,
$false,
inference(e,[status(thm)],[10,14,1402,96,1241,12,318,91,18,11,1746,37,20,1963,38,160,21,1324,13,166,856,161,17,176,22,204,812,675,2816,50,16,1326,40,23,8,214,752,36,19,15,1597,2699]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP754-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.15/0.40 % Computer : n004.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Fri Sep 25 15:43:50 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.87/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/1.16 % [INFO] Parsing done (172ms).
% 1.23/1.17 % [INFO] Running in sequential loop mode.
% 1.73/1.57 % [INFO] eprover registered as external prover.
% 1.73/1.58 % [INFO] Scanning for conjecture ...
% 1.91/1.67 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 2.07/1.72 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 2.07/1.73 % [INFO] Problem is propositional (TPTP CNF).
% 2.07/1.74 % [INFO] Type checking passed.
% 2.07/1.75 % [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 ...
% 20.91/5.88 % External prover 'e' found a proof!
% 20.91/5.88 % [INFO] Killing All external provers ...
% 20.91/5.88 % Time passed: 5336ms (effective reasoning time: 4705ms)
% 20.91/5.88 % Axioms used in derivation (6): f03, f02, f06, f05, f04, f01
% 20.91/5.88 % No. of inferences in proof: 99
% 20.91/5.88 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5336 ms resp. 4705 ms w/o parsing
% 17.73/5.93 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 17.73/5.93 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------