%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP777+1 : TPTP v9.3.1. Released v4.1.0.
% 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 : n017.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 07:21:57 AM UTC 2026
% Result : Theorem 39.88s 10.08s
% Output : Refutation 33.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 102 ( 62 unt; 0 typ; 1 def)
% Number of atoms : 167 ( 166 equ; 0 cnn)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 978 ( 82 ~; 64 |; 0 &; 832 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 140 ( 0 ^; 139 !; 0 ?; 140 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(bigC_decl,type,
bigC: $i > $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(difference_decl,type,
difference: $i > $i > $i ).
thf(product_decl,type,
product: $i > $i > $i ).
thf(quotient_decl,type,
quotient: $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
( ( A @ ( b @ ( a @ bigC ) ) )
!= ( A @ ( c @ ( c @ bigC ) ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ ( b @ ( a @ bigC ) ) )
= ( A @ ( c @ ( c @ bigC ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ ( b @ ( a @ bigC ) ) )
= ( A @ ( c @ ( c @ bigC ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(12,plain,
~ ! [A: $i] :
( ( A @ ( b @ ( a @ bigC ) ) )
= ( A @ ( c @ ( c @ bigC ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,plain,
( ( sk1 @ ( b @ ( a @ bigC ) ) )
!= ( sk1 @ ( c @ ( c @ bigC ) ) ) ),
inference(cnf,[status(esa)],[12]) ).
thf(14,plain,
( ( sk1 @ ( c @ ( c @ bigC ) ) )
!= ( sk1 @ ( b @ ( a @ bigC ) ) ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ bigC ) ) )
= ( C @ ( A @ product ) @ ( B @ ( C @ product ) @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos08) ).
thf(36,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ bigC ) ) )
= ( C @ ( A @ product ) @ ( B @ ( C @ product ) @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ bigC ) ) )
= ( C @ ( A @ product ) @ ( B @ ( C @ product ) @ product ) ) ),
inference(cnf,[status(esa)],[36]) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ bigC ) ) )
= ( C @ ( A @ product ) @ ( B @ ( C @ product ) @ product ) ) ),
inference(lifteq,[status(thm)],[37]) ).
thf(2710,plain,
( ( c @ ( sk1 @ product ) @ ( c @ ( c @ product ) @ product ) )
!= ( a @ ( sk1 @ product ) @ ( b @ ( a @ product ) @ product ) ) ),
inference(rewrite,[status(thm)],[14,38]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ ( A @ product ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos06) ).
thf(30,plain,
! [A: $i] :
( ( A @ ( A @ product ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(31,plain,
! [A: $i] :
( ( A @ ( A @ product ) )
= A ),
inference(cnf,[status(esa)],[30]) ).
thf(32,plain,
! [A: $i] :
( ( A @ ( A @ product ) )
= A ),
inference(lifteq,[status(thm)],[31]) ).
thf(2711,plain,
( ( a @ ( sk1 @ product ) @ ( b @ ( a @ product ) @ product ) )
!= ( c @ ( sk1 @ product ) @ ( c @ product ) ) ),
inference(rewrite,[status(thm)],[2710,32]) ).
thf(2712,plain,
( ( ( c @ ( sk1 @ product ) )
!= ( a @ ( sk1 @ product ) ) )
| ( ( b @ ( a @ product ) )
!= c ) ),
inference(simp,[status(thm)],[2711]) ).
thf(11,axiom,
( ( b @ ( c @ product ) @ ( c @ ( a @ product ) @ product ) )
= ( b @ ( a @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos09) ).
thf(39,plain,
( ( b @ ( c @ product ) @ ( c @ ( a @ product ) @ product ) )
= ( b @ ( a @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(40,plain,
( ( b @ ( c @ product ) @ ( c @ ( a @ product ) @ product ) )
= ( b @ ( a @ product ) ) ),
inference(lifteq,[status(thm)],[39]) ).
thf(48,plain,
! [A: $i] :
( ( ( A @ ( A @ product ) )
!= ( c @ ( a @ product ) ) )
| ( ( b @ ( c @ product ) @ ( A @ product ) )
= ( b @ ( a @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,40]) ).
thf(52,plain,
! [A: $i] :
( ( A != c )
| ( A != a )
| ( ( b @ ( c @ product ) @ ( A @ product ) )
= ( b @ ( a @ product ) ) ) ),
inference(simp,[status(thm)],[48]) ).
thf(56,plain,
( ( c != a )
| ( ( b @ ( c @ product ) @ ( a @ product ) )
= ( b @ ( a @ product ) ) ) ),
inference(simp,[status(thm)],[52]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ product ) @ ( B @ difference ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos01) ).
thf(15,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ product ) @ ( B @ difference ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ product ) @ ( B @ difference ) )
= A ),
inference(cnf,[status(esa)],[15]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ product ) @ ( B @ difference ) )
= A ),
inference(lifteq,[status(thm)],[16]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( ( b @ ( c @ product ) @ ( c @ ( a @ product ) @ product ) )
!= ( A @ ( B @ product ) ) )
| ( ( b @ ( a @ product ) @ ( B @ difference ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[40,17]) ).
thf(62,plain,
( ( b @ ( c @ product ) )
= ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) ) ),
inference(pattern_uni,[status(thm)],[61:[bind(A,$thf( b @ ( c @ product ) )),bind(B,$thf( c @ ( a @ product ) ))]]) ).
thf(734,plain,
( ( c != a )
| ( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) @ ( a @ product ) )
= ( b @ ( a @ product ) ) ) ),
inference(rewrite,[status(thm)],[56,62]) ).
thf(59,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ product ) )
!= ( B @ ( C @ product ) ) )
| ( ( A @ ( C @ difference ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[32,17]) ).
thf(60,plain,
! [A: $i] :
( ( A @ ( A @ difference ) )
= A ),
inference(pattern_uni,[status(thm)],[59:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ product ) @ quotient ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos03) ).
thf(21,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ product ) @ quotient ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ product ) @ quotient ) )
= B ),
inference(cnf,[status(esa)],[21]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ product ) @ quotient ) )
= B ),
inference(lifteq,[status(thm)],[22]) ).
thf(155,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ product ) )
!= ( B @ ( C @ product ) ) )
| ( ( B @ ( A @ quotient ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[32,23]) ).
thf(156,plain,
! [A: $i] :
( ( A @ ( A @ quotient ) )
= A ),
inference(pattern_uni,[status(thm)],[155:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ difference ) @ ( B @ product ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos02) ).
thf(18,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ difference ) @ ( B @ product ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ difference ) @ ( B @ product ) )
= A ),
inference(cnf,[status(esa)],[18]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ difference ) @ ( B @ product ) )
= A ),
inference(lifteq,[status(thm)],[19]) ).
thf(2722,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ difference ) @ ( B @ product ) )
!= ( a @ ( sk1 @ product ) @ ( b @ ( a @ product ) @ product ) ) )
| ( A
!= ( c @ ( sk1 @ product ) @ ( c @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[20,2711]) ).
thf(2778,plain,
! [A: $i] :
( ( ( c @ ( sk1 @ product ) @ ( c @ product ) @ ( A @ difference ) )
!= ( a @ ( sk1 @ product ) ) )
| ( A
!= ( b @ ( a @ product ) ) ) ),
inference(simp,[status(thm)],[2722]) ).
thf(2899,plain,
( ( c @ ( sk1 @ product ) @ ( c @ product ) @ ( b @ ( a @ product ) @ difference ) )
!= ( a @ ( sk1 @ product ) ) ),
inference(simp,[status(thm)],[2778]) ).
thf(121,plain,
! [B: $i,A: $i] :
( ( ( b @ ( c @ product ) )
!= ( A @ ( B @ product ) ) )
| ( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) @ ( B @ difference ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[62,17]) ).
thf(122,plain,
( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) @ ( c @ difference ) )
= b ),
inference(pattern_uni,[status(thm)],[121:[bind(A,$thf( b )),bind(B,$thf( c ))]]) ).
thf(41,plain,
( ( sk1 != sk1 )
| ( c != b )
| ( c != a ) ),
inference(simp,[status(thm)],[14]) ).
thf(42,plain,
( ( c != b )
| ( c != a ) ),
inference(simp,[status(thm)],[41]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ quotient ) @ product ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos04) ).
thf(24,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ quotient ) @ product ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(120,plain,
! [A: $i] :
( ( ( A @ ( A @ product ) )
!= ( b @ ( c @ product ) ) )
| ( A
= ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,62]) ).
thf(123,plain,
! [A: $i] :
( ( A != b )
| ( A != c )
| ( A
= ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) ) ) ),
inference(simp,[status(thm)],[120]) ).
thf(125,plain,
( ( c != b )
| ( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) )
= c ) ),
inference(simp,[status(thm)],[123]) ).
thf(153,plain,
! [B: $i,A: $i] :
( ( ( b @ ( c @ product ) )
!= ( A @ ( B @ product ) ) )
| ( ( A @ ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) @ quotient ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[62,23]) ).
thf(154,plain,
( ( b @ ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) @ quotient ) )
= c ),
inference(pattern_uni,[status(thm)],[153:[bind(A,$thf( b )),bind(B,$thf( c ))]]) ).
thf(1481,plain,
( ( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) )
!= ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) ) )
| ( ( b @ ( c @ quotient ) )
= c )
| ( c != b ) ),
inference(paramod_ordered,[status(thm)],[125,154]) ).
thf(1482,plain,
( ( ( b @ ( c @ quotient ) )
= c )
| ( c != b ) ),
inference(pattern_uni,[status(thm)],[1481:[]]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ quotient ) @ product ) )
= B ),
inference(cnf,[status(esa)],[24]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ quotient ) @ product ) )
= B ),
inference(lifteq,[status(thm)],[25]) ).
thf(660,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ quotient ) @ product ) )
!= ( C @ ( D @ product ) ) )
| ( ( B @ ( D @ difference ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[26,17]) ).
thf(661,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ quotient ) @ difference ) )
= B ),
inference(pattern_uni,[status(thm)],[660:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( F @ ( E @ quotient ) ))]]) ).
thf(702,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ quotient ) @ difference ) )
= B ),
inference(simp,[status(thm)],[661]) ).
thf(151,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ difference ) @ ( B @ product ) )
!= ( C @ ( D @ product ) ) )
| ( ( C @ ( A @ quotient ) )
= D ) ),
inference(paramod_ordered,[status(thm)],[20,23]) ).
thf(152,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ difference ) @ ( B @ quotient ) )
= A ),
inference(pattern_uni,[status(thm)],[151:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F @ ( E @ difference ) )),bind(D,$thf( E ))]]) ).
thf(157,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ difference ) @ ( B @ quotient ) )
= A ),
inference(simp,[status(thm)],[152]) ).
thf(49,plain,
! [A: $i] :
( ( ( A @ ( A @ product ) )
!= ( b @ ( c @ product ) ) )
| ( ( A @ ( c @ ( a @ product ) @ product ) )
= ( b @ ( a @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,40]) ).
thf(53,plain,
! [A: $i] :
( ( A != b )
| ( A != c )
| ( ( A @ ( c @ ( a @ product ) @ product ) )
= ( b @ ( a @ product ) ) ) ),
inference(simp,[status(thm)],[49]) ).
thf(57,plain,
( ( c != b )
| ( ( c @ ( c @ ( a @ product ) @ product ) )
= ( b @ ( a @ product ) ) ) ),
inference(simp,[status(thm)],[53]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ product ) @ ( C @ ( D @ product ) @ product ) )
= ( A @ ( C @ product ) @ ( B @ ( D @ product ) @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos05) ).
thf(27,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ product ) @ ( C @ ( D @ product ) @ product ) )
= ( A @ ( C @ product ) @ ( B @ ( D @ product ) @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(28,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ product ) @ ( C @ ( D @ product ) @ product ) )
= ( A @ ( C @ product ) @ ( B @ ( D @ product ) @ product ) ) ),
inference(cnf,[status(esa)],[27]) ).
thf(29,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ product ) @ ( C @ ( D @ product ) @ product ) )
= ( A @ ( C @ product ) @ ( B @ ( D @ product ) @ product ) ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ product ) @ ( A @ product ) @ ( A @ ( A @ ( B @ product ) @ product ) @ product ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos07) ).
thf(33,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ product ) @ ( A @ product ) @ ( A @ ( A @ ( B @ product ) @ product ) @ product ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1373,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ quotient ) @ difference ) )
!= ( C @ ( D @ difference ) ) )
| ( ( B @ ( D @ product ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[702,20]) ).
thf(1374,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ quotient ) @ product ) )
= A ),
inference(pattern_uni,[status(thm)],[1373:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ quotient ) ))]]) ).
thf(1410,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ quotient ) @ product ) )
= A ),
inference(simp,[status(thm)],[1374]) ).
thf(2752,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ quotient ) @ product ) )
!= ( a @ ( sk1 @ product ) @ ( b @ ( a @ product ) @ product ) ) )
| ( A
!= ( c @ ( sk1 @ product ) @ ( c @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[1410,2711]) ).
thf(2842,plain,
! [A: $i] :
( ( A
!= ( a @ ( sk1 @ product ) ) )
| ( ( A @ ( c @ ( sk1 @ product ) @ ( c @ product ) @ quotient ) )
!= ( b @ ( a @ product ) ) ) ),
inference(simp,[status(thm)],[2752]) ).
thf(2873,plain,
( ( a @ ( sk1 @ product ) @ ( c @ ( sk1 @ product ) @ ( c @ product ) @ quotient ) )
!= ( b @ ( a @ product ) ) ),
inference(simp,[status(thm)],[2842]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ product ) @ ( A @ product ) @ ( A @ ( A @ ( B @ product ) @ product ) @ product ) )
= A ),
inference(cnf,[status(esa)],[33]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ product ) @ ( A @ product ) @ ( A @ ( A @ ( B @ product ) @ product ) @ product ) )
= A ),
inference(lifteq,[status(thm)],[34]) ).
thf(1633,plain,
! [B: $i,A: $i] :
( ( ( b @ ( c @ product ) )
!= ( B @ ( A @ product ) ) )
| ( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) @ ( A @ product ) @ ( A @ ( A @ ( B @ product ) @ product ) @ product ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[62,35]) ).
thf(1634,plain,
( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) @ ( c @ product ) @ ( c @ ( c @ ( b @ product ) @ product ) @ product ) )
= c ),
inference(pattern_uni,[status(thm)],[1633:[bind(A,$thf( c )),bind(B,$thf( b ))]]) ).
thf(1630,plain,
! [B: $i,A: $i] :
( ( ( b @ ( c @ product ) )
!= ( A @ ( B @ product ) ) )
| ( ( B @ ( A @ product ) @ ( A @ product ) @ ( A @ ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) @ product ) @ product ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[62,35]) ).
thf(1631,plain,
( ( c @ ( b @ product ) @ ( b @ product ) @ ( b @ ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) @ product ) @ product ) )
= b ),
inference(pattern_uni,[status(thm)],[1630:[bind(A,$thf( b )),bind(B,$thf( c ))]]) ).
thf(3207,plain,
( ( c != a )
| ( sk1 != sk1 )
| ( ( b @ ( a @ product ) )
!= c ) ),
inference(simp,[status(thm)],[2712]) ).
thf(3319,plain,
( ( c != a )
| ( ( b @ ( a @ product ) )
!= c ) ),
inference(simp,[status(thm)],[3207]) ).
thf(43,plain,
( ( ( b @ ( c @ product ) @ ( c @ ( a @ product ) @ product ) )
!= ( c @ ( a @ product ) ) )
| ( ( b @ ( c @ product ) @ ( b @ ( a @ product ) @ product ) )
= ( b @ ( a @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[40,40]) ).
thf(45,plain,
( ( ( b @ ( c @ product ) )
!= c )
| ( ( c @ ( a @ product ) )
!= a )
| ( ( b @ ( c @ product ) @ ( b @ ( a @ product ) @ product ) )
= ( b @ ( a @ product ) ) ) ),
inference(simp,[status(thm)],[43]) ).
thf(66,plain,
( ( ( b @ ( c @ product ) @ ( b @ ( a @ product ) @ product ) )
!= ( b @ ( c @ product ) ) )
| ( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ product ) )
= ( b @ ( a @ product ) ) )
| ( ( b @ ( c @ product ) )
!= c )
| ( ( c @ ( a @ product ) )
!= a ) ),
inference(paramod_ordered,[status(thm)],[45,40]) ).
thf(99,plain,
( ( ( b @ ( c @ product ) )
!= b )
| ( ( b @ ( a @ product ) )
!= c )
| ( ( b @ ( c @ product ) )
!= c )
| ( ( c @ ( a @ product ) )
!= a )
| ( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ product ) )
= ( b @ ( a @ product ) ) ) ),
inference(simp,[status(thm)],[66]) ).
thf(242,plain,
( ( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) )
!= b )
| ( ( b @ ( a @ product ) )
!= c )
| ( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) )
!= c )
| ( ( c @ ( a @ product ) )
!= a )
| ( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ product ) )
= ( b @ ( a @ product ) ) ) ),
inference(rewrite,[status(thm)],[99,62]) ).
thf(288,plain,
( ( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) @ ( c @ difference ) )
!= ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) ) )
| ( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) )
!= b )
| ( ( b @ ( a @ product ) )
!= c )
| ( c != b )
| ( ( c @ ( a @ product ) )
!= a )
| ( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ product ) )
= ( b @ ( a @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[122,242]) ).
thf(306,plain,
( ( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) )
!= ( b @ ( a @ product ) ) )
| ( ( c @ ( a @ product ) )
!= c )
| ( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) )
!= b )
| ( ( b @ ( a @ product ) )
!= c )
| ( c != b )
| ( ( c @ ( a @ product ) )
!= a )
| ( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ product ) )
= ( b @ ( a @ product ) ) ) ),
inference(simp,[status(thm)],[288]) ).
thf(1334,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ product ) @ ( B @ difference ) )
!= ( D @ ( C @ difference ) ) )
| ( ( A @ ( D @ quotient ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[17,157]) ).
thf(1335,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ product ) @ quotient ) )
= A ),
inference(pattern_uni,[status(thm)],[1334:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ product ) ))]]) ).
thf(1348,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ product ) @ quotient ) )
= A ),
inference(simp,[status(thm)],[1335]) ).
thf(2062,plain,
! [B: $i,A: $i] :
( ( ( c @ ( b @ product ) @ ( b @ product ) @ ( b @ ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) @ product ) @ product ) )
!= ( B @ ( A @ product ) ) )
| ( ( B @ ( b @ quotient ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[1631,1348]) ).
thf(2063,plain,
( ( c @ ( b @ product ) @ ( b @ product ) @ ( b @ quotient ) )
= ( b @ ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) @ product ) ) ),
inference(pattern_uni,[status(thm)],[2062:[bind(A,$thf( b @ ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) @ product ) )),bind(B,$thf( c @ ( b @ product ) @ ( b @ product ) ))]]) ).
thf(6293,plain,
$false,
inference(e,[status(thm)],[2712,734,60,156,12,39,2899,18,122,42,24,1482,702,125,157,20,57,29,38,21,33,2873,1634,32,17,1631,3319,27,306,35,154,2711,26,23,1348,36,30,242,1410,2063,15,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP777+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.11 % 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
% 0.22/0.49 % Computer : n017.cluster.edu
% 0.22/0.49 % Model : x86_64 x86_64
% 0.22/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.49 % Memory : 8046.5625MB
% 0.22/0.49 % OS : Linux 6.8.0-71-generic
% 0.22/0.49 % CPULimit : 300
% 0.22/0.49 % WCLimit : 300
% 0.22/0.49 % DateTime : Fri Sep 25 15:42:02 UTC 2026
% 0.22/0.49 % CPUTime :
% 0.22/0.49 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
% 1.43/1.34 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.96/1.62 % [INFO] Parsing done (270ms).
% 1.96/1.64 % [INFO] Running in sequential loop mode.
% 2.88/2.24 % [INFO] eprover registered as external prover.
% 2.88/2.26 % [INFO] Scanning for conjecture ...
% 3.07/2.39 % [INFO] Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ...
% 3.23/2.44 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 3.23/2.48 % [INFO] Problem is first-order (TPTP FOF).
% 3.23/2.49 % [INFO] Type checking passed.
% 3.23/2.49 % [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 ...
% 39.88/10.07 % External prover 'e' found a proof!
% 39.88/10.08 % [INFO] Killing All external provers ...
% 39.88/10.08 % Time passed: 9370ms (effective reasoning time: 8429ms)
% 39.88/10.08 % 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)>
% 39.88/10.08 % Axioms used in derivation (9): sos06, sos03, sos09, sos02, sos05, sos08, sos04, sos07, sos01
% 39.88/10.08 % No. of inferences in proof: 101
% 39.88/10.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 9370 ms resp. 8429 ms w/o parsing
% 33.53/10.16 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 33.53/10.16 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------