%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP777-10 : TPTP v9.3.1. Released v8.1.0.
% 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 07:21:57 AM UTC 2026
% Result : Unsatisfiable 27.98s 10.98s
% Output : Refutation 23.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 93 ( 54 unt; 0 typ; 0 def)
% Number of atoms : 157 ( 156 equ; 0 cnn)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 967 ( 78 ~; 64 |; 0 &; 825 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 125 ( 0 ^; 125 !; 0 ?; 125 :)
% Comments :
%------------------------------------------------------------------------------
thf(bigC_decl,type,
bigC: $i > $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(x0_decl,type,
x0: $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(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ quotient ) @ product ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ quotient ) @ product ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ quotient ) @ product ) )
= A ),
inference(lifteq,[status(thm)],[20]) ).
thf(1,negated_conjecture,
( ( x0 @ ( b @ ( a @ bigC ) ) )
!= ( x0 @ ( c @ ( c @ bigC ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
thf(11,plain,
( ( x0 @ ( b @ ( a @ bigC ) ) )
!= ( x0 @ ( c @ ( c @ bigC ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(12,plain,
( ( x0 @ ( b @ ( a @ bigC ) ) )
!= ( x0 @ ( c @ ( c @ bigC ) ) ) ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(13,plain,
( ( x0 @ ( c @ ( c @ bigC ) ) )
!= ( x0 @ ( b @ ( a @ bigC ) ) ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ bigC ) ) )
= ( A @ ( C @ product ) @ ( B @ ( A @ product ) @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos08) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ bigC ) ) )
= ( A @ ( C @ product ) @ ( B @ ( A @ product ) @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ bigC ) ) )
= ( A @ ( C @ product ) @ ( B @ ( A @ product ) @ product ) ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(3815,plain,
( ( c @ ( x0 @ product ) @ ( c @ ( c @ product ) @ product ) )
!= ( a @ ( x0 @ product ) @ ( b @ ( a @ product ) @ product ) ) ),
inference(rewrite,[status(thm)],[13,29]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ ( A @ product ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).
thf(24,plain,
! [A: $i] :
( ( A @ ( A @ product ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(25,plain,
! [A: $i] :
( ( A @ ( A @ product ) )
= A ),
inference(lifteq,[status(thm)],[24]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ product ) @ ( B @ ( A @ product ) @ product ) )
= ( D @ ( B @ product ) @ ( C @ ( A @ product ) @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).
thf(22,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ product ) @ ( B @ ( A @ product ) @ product ) )
= ( D @ ( B @ product ) @ ( C @ ( A @ product ) @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(23,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ product ) @ ( B @ ( A @ product ) @ product ) )
= ( D @ ( B @ product ) @ ( C @ ( A @ product ) @ product ) ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(672,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ product ) @ ( B @ ( A @ product ) @ product ) )
!= ( E @ ( E @ product ) ) )
| ( ( D @ ( B @ product ) @ ( C @ ( A @ product ) @ product ) )
= E ) ),
inference(paramod_ordered,[status(thm)],[23,25]) ).
thf(673,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ product ) @ ( A @ ( A @ product ) @ product ) )
= ( B @ ( A @ product ) ) ),
inference(pattern_uni,[status(thm)],[672:[bind(A,$thf( C )),bind(B,$thf( D )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( D @ ( C @ product ) ))]]) ).
thf(890,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ product ) @ ( A @ ( A @ product ) @ product ) )
= ( B @ ( A @ product ) ) ),
inference(simp,[status(thm)],[673]) ).
thf(993,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ product ) )
!= ( C @ ( C @ product ) ) )
| ( ( A @ ( B @ ( B @ product ) @ product ) )
= ( C @ ( B @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[25,890]) ).
thf(994,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ product ) @ product ) )
= ( A @ ( B @ product ) ) ),
inference(pattern_uni,[status(thm)],[993:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(3818,plain,
( ( a @ ( x0 @ product ) @ ( b @ ( a @ product ) @ product ) )
!= ( c @ ( x0 @ product ) @ ( c @ product ) ) ),
inference(rewrite,[status(thm)],[3815,994]) ).
thf(3854,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ quotient ) @ product ) )
!= ( a @ ( x0 @ product ) @ ( b @ ( a @ product ) @ product ) ) )
| ( A
!= ( c @ ( x0 @ product ) @ ( c @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,3818]) ).
thf(3907,plain,
! [A: $i] :
( ( A
!= ( a @ ( x0 @ product ) ) )
| ( ( A @ ( c @ ( x0 @ product ) @ ( c @ product ) @ quotient ) )
!= ( b @ ( a @ product ) ) ) ),
inference(simp,[status(thm)],[3854]) ).
thf(4015,plain,
( ( a @ ( x0 @ product ) @ ( c @ ( x0 @ product ) @ ( c @ product ) @ quotient ) )
!= ( b @ ( a @ product ) ) ),
inference(simp,[status(thm)],[3907]) ).
thf(10,axiom,
( ( b @ ( c @ product ) @ ( c @ ( a @ product ) @ product ) )
= ( b @ ( a @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos09) ).
thf(30,plain,
( ( b @ ( c @ product ) @ ( c @ ( a @ product ) @ product ) )
= ( b @ ( a @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(31,plain,
( ( b @ ( c @ product ) @ ( c @ ( a @ product ) @ product ) )
= ( b @ ( a @ product ) ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ product ) @ ( A @ difference ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).
thf(14,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ product ) @ ( A @ difference ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ product ) @ ( A @ difference ) )
= B ),
inference(lifteq,[status(thm)],[14]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( ( b @ ( c @ product ) @ ( c @ ( a @ product ) @ product ) )
!= ( B @ ( A @ product ) ) )
| ( ( b @ ( a @ product ) @ ( A @ difference ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[31,15]) ).
thf(53,plain,
( ( b @ ( c @ product ) )
= ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) ) ),
inference(pattern_uni,[status(thm)],[52:[bind(A,$thf( c @ ( a @ product ) )),bind(B,$thf( b @ ( c @ product ) ))]]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ product ) @ ( B @ product ) @ ( B @ ( B @ ( A @ product ) @ product ) @ product ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos07) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ product ) @ ( B @ product ) @ ( B @ ( B @ ( A @ product ) @ product ) @ product ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ product ) @ ( B @ product ) @ ( B @ ( B @ ( A @ product ) @ product ) @ product ) )
= B ),
inference(lifteq,[status(thm)],[26]) ).
thf(2172,plain,
! [B: $i,A: $i] :
( ( ( b @ ( c @ product ) )
!= ( A @ ( B @ product ) ) )
| ( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) @ ( B @ product ) @ ( B @ ( B @ ( A @ product ) @ product ) @ product ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[53,27]) ).
thf(2173,plain,
( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) @ ( c @ product ) @ ( c @ ( c @ ( b @ product ) @ product ) @ product ) )
= c ),
inference(pattern_uni,[status(thm)],[2172:[bind(A,$thf( b )),bind(B,$thf( c ))]]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ product ) @ quotient ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ product ) @ quotient ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ product ) @ quotient ) )
= A ),
inference(lifteq,[status(thm)],[18]) ).
thf(2579,plain,
! [B: $i,A: $i] :
( ( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) @ ( c @ product ) @ ( c @ ( c @ ( b @ product ) @ product ) @ product ) )
!= ( B @ ( A @ product ) ) )
| ( ( B @ ( c @ quotient ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[2173,19]) ).
thf(2580,plain,
( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) @ ( c @ product ) @ ( c @ quotient ) )
= ( c @ ( c @ ( b @ product ) @ product ) ) ),
inference(pattern_uni,[status(thm)],[2579:[bind(A,$thf( c @ ( c @ ( b @ product ) @ product ) )),bind(B,$thf( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) @ ( c @ product ) ))]]) ).
thf(110,plain,
! [A: $i] :
( ( ( b @ ( c @ product ) )
!= ( A @ ( A @ product ) ) )
| ( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[53,25]) ).
thf(114,plain,
! [A: $i] :
( ( b != A )
| ( c != A )
| ( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) )
= A ) ),
inference(simp,[status(thm)],[110]) ).
thf(116,plain,
( ( c != b )
| ( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) )
= c ) ),
inference(simp,[status(thm)],[114]) ).
thf(40,plain,
! [A: $i] :
( ( ( A @ ( A @ product ) )
!= ( c @ ( a @ product ) ) )
| ( ( b @ ( c @ product ) @ ( A @ product ) )
= ( b @ ( a @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[25,31]) ).
thf(44,plain,
! [A: $i] :
( ( A != c )
| ( A != a )
| ( ( b @ ( c @ product ) @ ( A @ product ) )
= ( b @ ( a @ product ) ) ) ),
inference(simp,[status(thm)],[40]) ).
thf(48,plain,
( ( c != a )
| ( ( b @ ( c @ product ) @ ( a @ product ) )
= ( b @ ( a @ product ) ) ) ),
inference(simp,[status(thm)],[44]) ).
thf(546,plain,
( ( c != a )
| ( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) @ ( a @ product ) )
= ( b @ ( a @ product ) ) ) ),
inference(rewrite,[status(thm)],[48,53]) ).
thf(406,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ quotient ) @ product ) )
!= ( D @ ( C @ product ) ) )
| ( ( A @ ( C @ difference ) )
= D ) ),
inference(paramod_ordered,[status(thm)],[21,15]) ).
thf(407,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ quotient ) @ difference ) )
= B ),
inference(pattern_uni,[status(thm)],[406:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ quotient ) )),bind(D,$thf( F ))]]) ).
thf(435,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ quotient ) @ difference ) )
= B ),
inference(simp,[status(thm)],[407]) ).
thf(112,plain,
! [B: $i,A: $i] :
( ( ( b @ ( c @ product ) )
!= ( B @ ( A @ product ) ) )
| ( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) @ ( A @ difference ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[53,15]) ).
thf(113,plain,
( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) @ ( c @ difference ) )
= b ),
inference(pattern_uni,[status(thm)],[112:[bind(A,$thf( c )),bind(B,$thf( b ))]]) ).
thf(144,plain,
! [B: $i,A: $i] :
( ( ( b @ ( c @ product ) )
!= ( B @ ( A @ product ) ) )
| ( ( B @ ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) @ quotient ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[53,19]) ).
thf(145,plain,
( ( b @ ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) @ quotient ) )
= c ),
inference(pattern_uni,[status(thm)],[144:[bind(A,$thf( c )),bind(B,$thf( b ))]]) ).
thf(2589,plain,
! [B: $i,A: $i] :
( ( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) @ ( c @ product ) @ ( c @ ( c @ ( b @ product ) @ product ) @ product ) )
!= ( B @ ( A @ product ) ) )
| ( ( c @ ( A @ difference ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[2173,15]) ).
thf(2590,plain,
( ( c @ ( c @ ( c @ ( b @ product ) @ product ) @ difference ) )
= ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) @ ( c @ product ) ) ),
inference(pattern_uni,[status(thm)],[2589:[bind(A,$thf( c @ ( c @ ( b @ product ) @ product ) )),bind(B,$thf( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) @ ( c @ product ) ))]]) ).
thf(34,plain,
( ( ( b @ ( c @ product ) @ ( c @ ( a @ product ) @ product ) )
!= ( b @ ( c @ product ) ) )
| ( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ product ) )
= ( b @ ( a @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,31]) ).
thf(36,plain,
( ( ( b @ ( c @ product ) )
!= b )
| ( ( c @ ( a @ product ) )
!= c )
| ( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ product ) )
= ( b @ ( a @ product ) ) ) ),
inference(simp,[status(thm)],[34]) ).
thf(63,plain,
( ( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ product ) )
!= ( c @ ( a @ product ) ) )
| ( ( b @ ( c @ product ) @ ( b @ ( a @ product ) @ product ) )
= ( b @ ( a @ product ) ) )
| ( ( b @ ( c @ product ) )
!= b )
| ( ( c @ ( a @ product ) )
!= c ) ),
inference(paramod_ordered,[status(thm)],[36,31]) ).
thf(89,plain,
( ( ( b @ ( a @ product ) )
!= c )
| ( ( c @ ( a @ product ) )
!= a )
| ( ( b @ ( c @ product ) )
!= b )
| ( ( c @ ( a @ product ) )
!= c )
| ( ( b @ ( c @ product ) @ ( b @ ( a @ product ) @ product ) )
= ( b @ ( a @ product ) ) ) ),
inference(simp,[status(thm)],[63]) ).
thf(235,plain,
( ( ( b @ ( a @ product ) )
!= c )
| ( ( c @ ( a @ product ) )
!= a )
| ( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) )
!= b )
| ( ( c @ ( a @ product ) )
!= c )
| ( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) @ ( b @ ( a @ product ) @ product ) )
= ( b @ ( a @ product ) ) ) ),
inference(rewrite,[status(thm)],[89,53]) ).
thf(39,plain,
! [A: $i] :
( ( ( A @ ( A @ product ) )
!= ( b @ ( c @ product ) ) )
| ( ( A @ ( c @ ( a @ product ) @ product ) )
= ( b @ ( a @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[25,31]) ).
thf(43,plain,
! [A: $i] :
( ( A != b )
| ( A != c )
| ( ( A @ ( c @ ( a @ product ) @ product ) )
= ( b @ ( a @ product ) ) ) ),
inference(simp,[status(thm)],[39]) ).
thf(47,plain,
( ( c != b )
| ( ( c @ ( c @ ( a @ product ) @ product ) )
= ( b @ ( a @ product ) ) ) ),
inference(simp,[status(thm)],[43]) ).
thf(485,plain,
( ( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) @ ( b @ ( a @ product ) @ product ) )
!= ( c @ ( a @ product ) ) )
| ( c != b )
| ( ( c @ ( b @ ( a @ product ) @ product ) )
= ( b @ ( a @ product ) ) )
| ( ( b @ ( a @ product ) )
!= c )
| ( ( c @ ( a @ product ) )
!= a )
| ( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) )
!= b )
| ( ( c @ ( a @ product ) )
!= c ) ),
inference(paramod_ordered,[status(thm)],[235,47]) ).
thf(504,plain,
( ( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) )
!= c )
| ( ( b @ ( a @ product ) )
!= a )
| ( c != b )
| ( ( b @ ( a @ product ) )
!= c )
| ( ( c @ ( a @ product ) )
!= a )
| ( ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) )
!= b )
| ( ( c @ ( a @ product ) )
!= c )
| ( ( c @ ( b @ ( a @ product ) @ product ) )
= ( b @ ( a @ product ) ) ) ),
inference(simp,[status(thm)],[485]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ difference ) @ ( A @ product ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos02) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ difference ) @ ( A @ product ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ difference ) @ ( A @ product ) )
= B ),
inference(lifteq,[status(thm)],[16]) ).
thf(3863,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ difference ) @ ( A @ product ) )
!= ( a @ ( x0 @ product ) @ ( b @ ( a @ product ) @ product ) ) )
| ( B
!= ( c @ ( x0 @ product ) @ ( c @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,3818]) ).
thf(3909,plain,
! [A: $i] :
( ( ( c @ ( x0 @ product ) @ ( c @ product ) @ ( A @ difference ) )
!= ( a @ ( x0 @ product ) ) )
| ( A
!= ( b @ ( a @ product ) ) ) ),
inference(simp,[status(thm)],[3863]) ).
thf(4016,plain,
( ( c @ ( x0 @ product ) @ ( c @ product ) @ ( b @ ( a @ product ) @ difference ) )
!= ( a @ ( x0 @ product ) ) ),
inference(simp,[status(thm)],[3909]) ).
thf(32,plain,
( ( x0 != x0 )
| ( c != b )
| ( c != a ) ),
inference(simp,[status(thm)],[13]) ).
thf(33,plain,
( ( c != b )
| ( c != a ) ),
inference(simp,[status(thm)],[32]) ).
thf(997,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ product ) )
!= ( B @ ( B @ product ) ) )
| ( ( C @ ( C @ product ) @ ( A @ product ) )
= ( C @ ( B @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[25,890]) ).
thf(998,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ product ) @ ( A @ product ) )
= ( B @ ( A @ product ) ) ),
inference(pattern_uni,[status(thm)],[997:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(1135,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ product ) @ ( A @ product ) )
= ( B @ ( A @ product ) ) ),
inference(simp,[status(thm)],[998]) ).
thf(2175,plain,
! [B: $i,A: $i] :
( ( ( b @ ( c @ product ) )
!= ( B @ ( A @ product ) ) )
| ( ( A @ ( B @ product ) @ ( B @ product ) @ ( B @ ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) @ product ) @ product ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[53,27]) ).
thf(2176,plain,
( ( c @ ( b @ product ) @ ( b @ product ) @ ( b @ ( b @ ( a @ product ) @ ( c @ ( a @ product ) @ difference ) @ product ) @ product ) )
= b ),
inference(pattern_uni,[status(thm)],[2175:[bind(A,$thf( c )),bind(B,$thf( b ))]]) ).
thf(146,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ difference ) @ ( A @ product ) )
!= ( D @ ( C @ product ) ) )
| ( ( D @ ( B @ quotient ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[17,19]) ).
thf(147,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ difference ) @ ( B @ quotient ) )
= A ),
inference(pattern_uni,[status(thm)],[146:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ difference ) ))]]) ).
thf(148,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ difference ) @ ( B @ quotient ) )
= A ),
inference(simp,[status(thm)],[147]) ).
thf(142,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ product ) )
!= ( C @ ( B @ product ) ) )
| ( ( C @ ( A @ quotient ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[25,19]) ).
thf(143,plain,
! [A: $i] :
( ( A @ ( A @ quotient ) )
= A ),
inference(pattern_uni,[status(thm)],[142:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(2035,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)],[116,145]) ).
thf(2036,plain,
( ( ( b @ ( c @ quotient ) )
= c )
| ( c != b ) ),
inference(pattern_uni,[status(thm)],[2035:[]]) ).
thf(50,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ product ) )
!= ( C @ ( B @ product ) ) )
| ( ( A @ ( B @ difference ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[25,15]) ).
thf(51,plain,
! [A: $i] :
( ( A @ ( A @ difference ) )
= A ),
inference(pattern_uni,[status(thm)],[50:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(7890,plain,
$false,
inference(e,[status(thm)],[4015,2580,116,546,435,53,113,890,145,18,994,2590,24,2173,25,14,504,20,29,4016,28,21,33,1135,2176,148,17,22,27,3818,16,11,143,26,23,235,2036,30,51,19,47,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP777-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.09 % 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
% 0.12/0.47 % Computer : n016.cluster.edu
% 0.12/0.47 % Model : x86_64 x86_64
% 0.12/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.47 % Memory : 8046.5625MB
% 0.12/0.47 % OS : Linux 6.8.0-71-generic
% 0.12/0.47 % CPULimit : 300
% 0.12/0.47 % WCLimit : 300
% 0.12/0.47 % DateTime : Fri Sep 25 15:51:29 UTC 2026
% 0.12/0.47 % CPUTime :
% 0.12/0.47 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
% 0.86/1.19 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/1.40 % [INFO] Parsing done (213ms).
% 1.20/1.42 % [INFO] Running in sequential loop mode.
% 1.84/1.92 % [INFO] eprover registered as external prover.
% 1.84/1.93 % [INFO] Scanning for conjecture ...
% 1.99/2.05 % [INFO] Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ...
% 1.99/2.08 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 1.99/2.09 % [INFO] Problem is propositional (TPTP CNF).
% 1.99/2.09 % [INFO] Type checking passed.
% 1.99/2.10 % [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 ...
% 27.98/10.96 % External prover 'e' found a proof!
% 27.98/10.97 % [INFO] Killing All external provers ...
% 27.98/10.98 % Time passed: 10287ms (effective reasoning time: 9543ms)
% 27.98/10.98 % Axioms used in derivation (9): sos06, sos03, sos09, sos02, sos05, sos08, sos04, sos07, sos01
% 27.98/10.98 % No. of inferences in proof: 93
% 27.98/10.98 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 10287 ms resp. 9543 ms w/o parsing
% 23.29/11.11 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 23.29/11.11 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------