%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP767-1 : 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 : n026.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 07:21:56 AM UTC 2026
% Result : Unsatisfiable 26.30s 7.20s
% Output : Refutation 26.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 21
% Syntax : Number of formulae : 109 ( 74 unt; 0 typ; 0 def)
% Number of atoms : 157 ( 156 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 780 ( 78 ~; 48 |; 0 &; 654 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 140 ( 0 ^; 140 !; 0 ?; 140 :)
% Comments :
%------------------------------------------------------------------------------
thf(product_decl,type,
product: $i > $i > $i ).
thf(j_decl,type,
j: $i > $i ).
thf(x0_decl,type,
x0: $i ).
thf(x1_decl,type,
x1: $i ).
thf(i_decl,type,
i: $i > $i ).
thf(difference_decl,type,
difference: $i > $i > $i ).
thf(one_decl,type,
one: $i ).
thf(l_decl,type,
l: $i > $i > $i > $i ).
thf(eta_decl,type,
eta: $i > $i ).
thf(t_decl,type,
t: $i > $i > $i ).
thf(quotient_decl,type,
quotient: $i > $i > $i ).
thf(15,axiom,
! [A: $i] :
( ( A @ j )
= ( A @ ( one @ quotient ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos10) ).
thf(51,plain,
! [A: $i] :
( ( A @ j )
= ( A @ ( one @ quotient ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(52,plain,
! [A: $i] :
( ( A @ ( one @ quotient ) )
= ( A @ j ) ),
inference(lifteq,[status(thm)],[51]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ ( one @ product ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos02) ).
thf(29,plain,
! [A: $i] :
( ( A @ ( one @ product ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(30,plain,
! [A: $i] :
( ( A @ ( one @ product ) )
= A ),
inference(lifteq,[status(thm)],[29]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ i @ i @ product ) )
= ( B @ ( A @ product ) @ ( A @ eta @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos13) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ i @ i @ product ) )
= ( B @ ( A @ product ) @ ( A @ eta @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ product ) @ ( A @ eta @ product ) )
= ( B @ ( A @ i @ i @ product ) ) ),
inference(lifteq,[status(thm)],[33]) ).
thf(354,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( one @ product ) )
!= ( C @ ( B @ product ) ) )
| ( ( A @ ( B @ eta @ product ) )
= ( C @ ( B @ i @ i @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[30,34]) ).
thf(355,plain,
! [A: $i] :
( ( A @ ( one @ eta @ product ) )
= ( A @ ( one @ i @ i @ product ) ) ),
inference(pattern_uni,[status(thm)],[354:[bind(A,$thf( A )),bind(B,$thf( one )),bind(C,$thf( A ))]]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ eta )
= ( A @ ( A @ i @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos12) ).
thf(63,plain,
! [A: $i] :
( ( A @ eta )
= ( A @ ( A @ i @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(64,plain,
! [A: $i] :
( ( A @ ( A @ i @ product ) )
= ( A @ eta ) ),
inference(lifteq,[status(thm)],[63]) ).
thf(14,axiom,
! [A: $i] :
( ( one @ ( A @ product ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos01) ).
thf(49,plain,
! [A: $i] :
( ( one @ ( A @ product ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(50,plain,
! [A: $i] :
( ( one @ ( A @ product ) )
= A ),
inference(lifteq,[status(thm)],[49]) ).
thf(97,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ i @ product ) )
!= ( one @ ( B @ product ) ) )
| ( ( A @ eta )
= B ) ),
inference(paramod_ordered,[status(thm)],[64,50]) ).
thf(98,plain,
( ( one @ eta )
= ( one @ i ) ),
inference(pattern_uni,[status(thm)],[97:[bind(A,$thf( one )),bind(B,$thf( one @ i ))]]) ).
thf(389,plain,
! [A: $i] :
( ( A @ ( one @ i @ i @ product ) )
= ( A @ ( one @ i @ product ) ) ),
inference(rewrite,[status(thm)],[355,98]) ).
thf(393,plain,
! [B: $i,A: $i] :
( ( ( A @ ( one @ i @ i @ product ) )
!= ( one @ ( B @ product ) ) )
| ( ( A @ ( one @ i @ product ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[389,50]) ).
thf(394,plain,
( ( one @ ( one @ i @ product ) )
= ( one @ i @ i ) ),
inference(pattern_uni,[status(thm)],[393:[bind(A,$thf( one )),bind(B,$thf( one @ i @ i ))]]) ).
thf(444,plain,
( ( one @ eta )
= ( one @ i @ i ) ),
inference(rewrite,[status(thm)],[394,64]) ).
thf(445,plain,
( ( one @ i @ i )
= ( one @ i ) ),
inference(rewrite,[status(thm)],[98,444]) ).
thf(456,plain,
( ( one @ eta )
= ( one @ i ) ),
inference(rewrite,[status(thm)],[444,445]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ product ) @ ( A @ eta @ t ) )
= ( C @ ( A @ eta @ t ) @ ( B @ ( A @ eta @ t ) @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos20) ).
thf(53,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ product ) @ ( A @ eta @ t ) )
= ( C @ ( A @ eta @ t ) @ ( B @ ( A @ eta @ t ) @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1,negated_conjecture,
( ( x0 @ ( x1 @ product ) @ j @ ( x0 @ j @ j @ product ) )
!= ( x1 @ j ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(22,plain,
( ( x0 @ ( x1 @ product ) @ j @ ( x0 @ j @ j @ product ) )
!= ( x1 @ j ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(23,plain,
( ( x0 @ ( x1 @ product ) @ j @ ( x0 @ j @ j @ product ) )
!= ( x1 @ j ) ),
inference(polarity_switch,[status(thm)],[22]) ).
thf(24,plain,
( ( x0 @ ( x1 @ product ) @ j @ ( x0 @ j @ j @ product ) )
!= ( x1 @ j ) ),
inference(lifteq,[status(thm)],[23]) ).
thf(71,plain,
! [A: $i] :
( ( ( A @ ( one @ product ) )
!= ( x0 @ ( x1 @ product ) @ j @ ( x0 @ j @ j @ product ) ) )
| ( A
!= ( x1 @ j ) ) ),
inference(paramod_ordered,[status(thm)],[30,24]) ).
thf(77,plain,
( ( ( x0 @ ( x1 @ product ) @ j )
!= ( x1 @ j ) )
| ( ( x0 @ j @ j )
!= one ) ),
inference(simp,[status(thm)],[71]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ product ) @ ( A @ difference ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos04) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ product ) @ ( A @ difference ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ product ) @ quotient ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos05) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ product ) @ quotient ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ product ) @ quotient ) )
= A ),
inference(lifteq,[status(thm)],[39]) ).
thf(133,plain,
! [C: $i,B: $i,A: $i] :
( ( ( one @ ( A @ product ) )
!= ( C @ ( B @ product ) ) )
| ( ( C @ ( A @ quotient ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[50,40]) ).
thf(134,plain,
! [A: $i] :
( ( one @ ( A @ quotient ) )
= A ),
inference(pattern_uni,[status(thm)],[133:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( one ))]]) ).
thf(135,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( one @ product ) )
!= ( C @ ( B @ product ) ) )
| ( ( C @ ( A @ quotient ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[30,40]) ).
thf(136,plain,
! [A: $i] :
( ( A @ ( A @ quotient ) )
= one ),
inference(pattern_uni,[status(thm)],[135:[bind(A,$thf( A )),bind(B,$thf( one )),bind(C,$thf( A ))]]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ difference ) @ ( A @ product ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos03) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ difference ) @ ( A @ product ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ product ) @ ( A @ product ) @ ( B @ ( A @ product ) @ difference ) )
= ( A @ ( B @ ( B @ ( A @ product ) @ ( C @ product ) @ quotient ) @ quotient ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos08) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ product ) @ ( A @ product ) @ ( B @ ( A @ product ) @ difference ) )
= ( A @ ( B @ ( B @ ( A @ product ) @ ( C @ product ) @ quotient ) @ quotient ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(2,axiom,
! [A: $i] :
( ( A @ i )
= ( one @ ( A @ difference ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos09) ).
thf(25,plain,
! [A: $i] :
( ( A @ i )
= ( one @ ( A @ difference ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(220,plain,
! [B: $i,A: $i] :
( ( ( one @ ( A @ quotient ) )
!= ( B @ ( one @ quotient ) ) )
| ( A
= ( B @ j ) ) ),
inference(paramod_ordered,[status(thm)],[134,52]) ).
thf(221,plain,
( ( one @ j )
= one ),
inference(pattern_uni,[status(thm)],[220:[bind(A,$thf( one )),bind(B,$thf( one ))]]) ).
thf(237,plain,
( ( ( x0 @ j @ j )
!= ( one @ j ) )
| ( ( x0 @ ( x1 @ product ) @ j )
!= ( x1 @ j ) )
| ( one != one ) ),
inference(paramod_ordered,[status(thm)],[221,77]) ).
thf(238,plain,
( ( ( x0 @ j @ j )
!= ( one @ j ) )
| ( ( x0 @ ( x1 @ product ) @ j )
!= ( x1 @ j ) ) ),
inference(simp,[status(thm)],[237]) ).
thf(257,plain,
( ( ( x0 @ j )
!= one )
| ( ( x0 @ ( x1 @ product ) )
!= x1 ) ),
inference(simp,[status(thm)],[238]) ).
thf(69,plain,
! [A: $i] :
( ( ( one @ ( A @ product ) )
!= ( x0 @ ( x1 @ product ) @ j @ ( x0 @ j @ j @ product ) ) )
| ( A
!= ( x1 @ j ) ) ),
inference(paramod_ordered,[status(thm)],[50,24]) ).
thf(74,plain,
( ( ( x0 @ ( x1 @ product ) @ j )
!= one )
| ( ( x0 @ j @ j )
!= ( x1 @ j ) ) ),
inference(simp,[status(thm)],[69]) ).
thf(83,plain,
! [A: $i] :
( ( ( A @ ( one @ product ) )
!= ( x0 @ ( x1 @ product ) ) )
| ( ( A @ j )
!= one )
| ( ( x0 @ j @ j )
!= ( x1 @ j ) ) ),
inference(paramod_ordered,[status(thm)],[30,74]) ).
thf(89,plain,
! [A: $i] :
( ( A != x0 )
| ( one != x1 )
| ( ( A @ j )
!= one )
| ( ( x0 @ j )
!= x1 ) ),
inference(simp,[status(thm)],[83]) ).
thf(93,plain,
( ( one != x1 )
| ( ( x0 @ j )
!= one )
| ( ( x0 @ j )
!= x1 ) ),
inference(simp,[status(thm)],[89]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ ( A @ i @ product ) )
= ( A @ j @ ( A @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos11) ).
thf(57,plain,
! [A: $i] :
( ( A @ ( A @ i @ product ) )
= ( A @ j @ ( A @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ quotient ) @ product ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos06) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ quotient ) @ product ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ l ) ) )
= ( C @ ( B @ product ) @ ( A @ product ) @ ( B @ ( A @ product ) @ difference ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos17) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ l ) ) )
= ( C @ ( B @ product ) @ ( A @ product ) @ ( B @ ( A @ product ) @ difference ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ l ) ) )
= ( C @ ( B @ product ) @ ( A @ product ) @ ( B @ ( A @ product ) @ difference ) ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( A @ product ) @ ( C @ product ) @ quotient ) @ quotient ) )
= ( C @ ( B @ product ) @ ( A @ product ) @ ( B @ ( A @ product ) @ difference ) ) ),
inference(lifteq,[status(thm)],[37]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( A @ eta @ ( B @ product ) @ ( A @ product ) )
= ( A @ eta @ ( B @ ( A @ product ) @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos15) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( A @ eta @ ( B @ product ) @ ( A @ product ) )
= ( A @ eta @ ( B @ ( A @ product ) @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ product ) @ ( A @ eta @ product ) )
= ( C @ ( B @ ( A @ eta @ product ) @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos16) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ product ) @ ( A @ eta @ product ) )
= ( C @ ( B @ ( A @ eta @ product ) @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ eta @ product ) @ product ) )
= ( C @ ( B @ product ) @ ( A @ eta @ product ) ) ),
inference(lifteq,[status(thm)],[31]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ product ) @ product ) @ ( A @ difference ) )
= ( A @ ( A @ ( C @ product ) @ ( B @ product ) @ quotient ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos07) ).
thf(59,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ product ) @ product ) @ ( A @ difference ) )
= ( A @ ( A @ ( C @ product ) @ ( B @ product ) @ quotient ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(81,plain,
( ( ( x0 @ ( x1 @ product ) @ j )
!= one )
| ( ( x0 @ j )
!= x1 ) ),
inference(simp,[status(thm)],[74]) ).
thf(398,plain,
! [B: $i,A: $i] :
( ( ( A @ ( one @ i @ i @ product ) )
!= ( B @ ( B @ i @ product ) ) )
| ( ( A @ ( one @ i @ product ) )
= ( B @ eta ) ) ),
inference(paramod_ordered,[status(thm)],[389,64]) ).
thf(399,plain,
( ( one @ i @ ( one @ i @ product ) )
= ( one @ i @ eta ) ),
inference(pattern_uni,[status(thm)],[398:[bind(A,$thf( one @ i )),bind(B,$thf( one @ i ))]]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ t ) )
= ( A @ ( B @ ( A @ product ) @ quotient ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos19) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ t ) )
= ( A @ ( B @ ( A @ product ) @ quotient ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ product ) @ quotient ) )
= ( B @ ( A @ t ) ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(524,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( one @ product ) )
!= ( C @ ( B @ product ) ) )
| ( ( B @ ( A @ quotient ) )
= ( C @ ( B @ t ) ) ) ),
inference(paramod_ordered,[status(thm)],[30,36]) ).
thf(525,plain,
! [A: $i] :
( ( one @ ( A @ quotient ) )
= ( A @ ( one @ t ) ) ),
inference(pattern_uni,[status(thm)],[524:[bind(A,$thf( A )),bind(B,$thf( one )),bind(C,$thf( A ))]]) ).
thf(705,plain,
! [A: $i] :
( ( A @ ( one @ t ) )
= A ),
inference(rewrite,[status(thm)],[525,134]) ).
thf(490,plain,
! [A: $i] :
( ( ( A @ ( one @ product ) )
!= ( x0 @ ( x1 @ product ) ) )
| ( ( x0 @ j )
!= one )
| ( A != x1 ) ),
inference(paramod_ordered,[status(thm)],[30,257]) ).
thf(497,plain,
( ( x1 != x0 )
| ( one != x1 )
| ( ( x0 @ j )
!= one ) ),
inference(simp,[status(thm)],[490]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ product ) @ ( A @ ( A @ l ) ) )
= ( C @ ( A @ ( A @ l ) ) @ ( B @ ( A @ ( A @ l ) ) @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos18) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ product ) @ ( A @ ( A @ l ) ) )
= ( C @ ( A @ ( A @ l ) ) @ ( B @ ( A @ ( A @ l ) ) @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(26,plain,
! [A: $i] :
( ( one @ ( A @ difference ) )
= ( A @ i ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ eta @ product ) @ ( A @ product ) )
= ( B @ ( A @ j @ j @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos14) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ eta @ product ) @ ( A @ product ) )
= ( B @ ( A @ j @ j @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(131,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ i @ product ) )
!= ( C @ ( B @ product ) ) )
| ( ( C @ ( A @ eta @ quotient ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[64,40]) ).
thf(132,plain,
! [A: $i] :
( ( A @ ( A @ eta @ quotient ) )
= ( A @ i ) ),
inference(pattern_uni,[status(thm)],[131:[bind(A,$thf( D )),bind(B,$thf( D @ i )),bind(C,$thf( D ))]]) ).
thf(139,plain,
! [A: $i] :
( ( A @ ( A @ eta @ quotient ) )
= ( A @ i ) ),
inference(simp,[status(thm)],[132]) ).
thf(144,plain,
! [A: $i] :
( ( ( one @ ( A @ product ) )
!= ( x0 @ ( x1 @ product ) ) )
| ( ( A @ j )
!= ( x1 @ j ) )
| ( ( x0 @ j @ j )
!= one ) ),
inference(paramod_ordered,[status(thm)],[50,77]) ).
thf(151,plain,
! [A: $i] :
( ( one != x0 )
| ( A != x1 )
| ( A != x1 )
| ( ( x0 @ j @ j )
!= one ) ),
inference(simp,[status(thm)],[144]) ).
thf(159,plain,
( ( one != x0 )
| ( ( x0 @ j @ j )
!= one ) ),
inference(simp,[status(thm)],[151]) ).
thf(291,plain,
( ( ( x0 @ j @ j )
!= ( one @ j ) )
| ( one != x0 )
| ( one != one ) ),
inference(paramod_ordered,[status(thm)],[221,159]) ).
thf(292,plain,
( ( ( x0 @ j @ j )
!= ( one @ j ) )
| ( one != x0 ) ),
inference(simp,[status(thm)],[291]) ).
thf(294,plain,
( ( ( x0 @ j )
!= one )
| ( one != x0 ) ),
inference(simp,[status(thm)],[292]) ).
thf(297,plain,
( ( ( one @ j )
!= ( x0 @ j ) )
| ( one != one )
| ( one != x0 ) ),
inference(paramod_ordered,[status(thm)],[221,294]) ).
thf(298,plain,
( ( ( one @ j )
!= ( x0 @ j ) )
| ( one != x0 ) ),
inference(simp,[status(thm)],[297]) ).
thf(299,plain,
( ( one != x0 )
| ( one != x0 ) ),
inference(simp,[status(thm)],[298]) ).
thf(300,plain,
one != x0,
inference(simp,[status(thm)],[299]) ).
thf(246,plain,
( ( ( x0 @ ( x1 @ product ) @ j )
!= ( one @ j ) )
| ( one != one )
| ( ( x0 @ j @ j )
!= ( x1 @ j ) ) ),
inference(paramod_ordered,[status(thm)],[221,74]) ).
thf(247,plain,
( ( ( x0 @ ( x1 @ product ) @ j )
!= ( one @ j ) )
| ( ( x0 @ j @ j )
!= ( x1 @ j ) ) ),
inference(simp,[status(thm)],[246]) ).
thf(254,plain,
( ( ( x0 @ ( x1 @ product ) )
!= one )
| ( ( x0 @ j )
!= x1 ) ),
inference(simp,[status(thm)],[247]) ).
thf(570,plain,
! [B: $i,A: $i] :
( ( ( one @ i @ ( one @ i @ product ) )
!= ( B @ ( A @ product ) ) )
| ( ( A @ ( one @ i @ eta @ quotient ) )
= ( B @ ( A @ t ) ) ) ),
inference(paramod_ordered,[status(thm)],[399,36]) ).
thf(571,plain,
( ( one @ i @ ( one @ i @ eta @ quotient ) )
= ( one @ i @ ( one @ i @ t ) ) ),
inference(pattern_uni,[status(thm)],[570:[bind(A,$thf( one @ i )),bind(B,$thf( one @ i ))]]) ).
thf(708,plain,
( ( one @ i @ ( one @ i @ t ) )
= ( one @ i @ i ) ),
inference(rewrite,[status(thm)],[571,139]) ).
thf(3811,plain,
$false,
inference(e,[status(thm)],[52,456,53,77,41,134,136,47,24,37,25,257,93,57,29,61,221,74,33,28,38,45,64,32,34,22,59,27,445,49,81,39,399,35,63,705,50,31,497,43,40,26,55,139,300,36,30,51,254,708]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP767-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % 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 : n026.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 15:47:54 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 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
% 1.18/1.06 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.54/1.21 % [INFO] Parsing done (139ms).
% 1.54/1.22 % [INFO] Running in sequential loop mode.
% 2.12/1.58 % [INFO] eprover registered as external prover.
% 2.12/1.58 % [INFO] Scanning for conjecture ...
% 2.38/1.66 % [INFO] Found a conjecture (or negated_conjecture) and 20 axioms. Running axiom selection ...
% 2.58/1.72 % [INFO] Axiom selection finished. Selected 20 axioms (removed 0 axioms).
% 2.58/1.75 % [INFO] Problem is propositional (TPTP CNF).
% 2.58/1.76 % [INFO] Type checking passed.
% 2.58/1.77 % [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 ...
% 30.84/7.19 % External prover 'e' found a proof!
% 30.84/7.19 % [INFO] Killing All external provers ...
% 30.84/7.20 % Time passed: 6587ms (effective reasoning time: 5972ms)
% 26.30/7.20 % Axioms used in derivation (20): sos14, sos20, sos06, sos13, sos10, sos09, sos02, sos11, sos19, sos08, sos12, sos04, sos15, sos17, sos03, sos16, sos05, sos07, sos01, sos18
% 26.30/7.20 % No. of inferences in proof: 109
% 26.30/7.20 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6587 ms resp. 5972 ms w/o parsing
% 26.30/7.27 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 26.30/7.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------