%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG004-1 : TPTP v9.3.1. Released v2.2.0.
% 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 : n011.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 06:45:52 AM UTC 2026
% Result : Unsatisfiable 26.83s 6.67s
% Output : Refutation 22.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 91 ( 39 unt; 0 typ; 2 def)
% Number of atoms : 167 ( 166 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 732 ( 98 ~; 74 |; 0 &; 560 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 102 ( 0 ^; 98 !; 2 ?; 102 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(b_decl,type,
b: $i ).
thf(b0_decl,type,
b0: $i ).
thf(a_decl,type,
a: $i ).
thf(a0_decl,type,
a0: $i ).
thf(d_decl,type,
d: $i ).
thf(c_decl,type,
c: $i ).
thf(d0_decl,type,
d0: $i ).
thf(c0_decl,type,
c0: $i ).
thf(sk1_decl,type,
sk1: $i > $i > $i ).
thf(sk2_decl,type,
sk2: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ multiply ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ multiply ) @ ( B @ A ) )
= C ) ) ) ).
thf(3,negated_conjecture,
( ( d0 @ ( b @ multiply ) )
= ( c0 @ ( a @ multiply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_quotient_condition3) ).
thf(10,plain,
( ( d0 @ ( b @ multiply ) )
= ( c0 @ ( a @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,plain,
( ( c0 @ ( a @ multiply ) )
= ( d0 @ ( b @ multiply ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ multiply ) @ ( B @ ( A @ multiply ) @ multiply ) )
= ( D @ ( B @ multiply ) @ ( C @ ( A @ multiply ) @ multiply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',medial_law) ).
thf(29,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ multiply ) @ ( B @ ( A @ multiply ) @ multiply ) )
= ( D @ ( B @ multiply ) @ ( C @ ( A @ multiply ) @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(30,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ multiply ) @ ( B @ ( A @ multiply ) @ multiply ) )
= ( D @ ( B @ multiply ) @ ( C @ ( A @ multiply ) @ multiply ) ) ),
inference(lifteq,[status(thm)],[29]) ).
thf(240,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c0 @ ( a @ multiply ) )
!= ( D @ ( C @ multiply ) ) )
| ( ( d0 @ ( b @ multiply ) @ ( B @ ( A @ multiply ) @ multiply ) )
= ( D @ ( B @ multiply ) @ ( C @ ( A @ multiply ) @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,30]) ).
thf(241,plain,
! [B: $i,A: $i] :
( ( d0 @ ( b @ multiply ) @ ( B @ ( A @ multiply ) @ multiply ) )
= ( c0 @ ( B @ multiply ) @ ( a @ ( A @ multiply ) @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[240:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( a )),bind(D,$thf( c0 ))]]) ).
thf(399,plain,
! [B: $i,A: $i] :
( ( ( c0 @ ( a @ multiply ) )
!= ( B @ ( A @ multiply ) ) )
| ( ( d0 @ ( b @ multiply ) @ ( d0 @ ( b @ multiply ) @ multiply ) )
= ( c0 @ ( B @ multiply ) @ ( a @ ( A @ multiply ) @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,241]) ).
thf(400,plain,
( ( c0 @ ( c0 @ multiply ) @ ( a @ ( a @ multiply ) @ multiply ) )
= ( d0 @ ( b @ multiply ) @ ( d0 @ ( b @ multiply ) @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[399:[bind(A,$thf( a )),bind(B,$thf( c0 ))]]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( D @ ( A @ multiply ) )
!= C )
| ( ( B @ ( A @ multiply ) )
!= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_cancelaation) ).
thf(23,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( D @ ( A @ multiply ) )
!= C )
| ( ( B @ ( A @ multiply ) )
!= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(24,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( D @ ( A @ multiply ) )
!= C )
| ( ( B @ ( A @ multiply ) )
!= C ) ),
inference(cnf,[status(esa)],[23]) ).
thf(25,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( D @ ( A @ multiply ) )
!= C )
| ( ( B @ ( A @ multiply ) )
!= C ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( C @ ( A @ multiply ) )
!= ( B @ ( A @ multiply ) ) ) ),
inference(simp,[status(thm)],[25]) ).
thf(27,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ multiply ) @ ( B @ A ) )
= C ),
inference(detectInverse,[status(thm)],[26]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) @ ( A @ sk2 ) )
= B ),
inference(cnf,[status(esa)],[27]) ).
thf(140,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) @ ( A @ sk2 ) )
= B ),
inference(lifteq,[status(thm)],[28]) ).
thf(650,plain,
! [B: $i,A: $i] :
( ( ( c0 @ ( c0 @ multiply ) @ ( a @ ( a @ multiply ) @ multiply ) )
!= ( B @ ( A @ multiply ) ) )
| ( ( d0 @ ( b @ multiply ) @ ( d0 @ ( b @ multiply ) @ multiply ) @ ( A @ sk2 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[400,140]) ).
thf(651,plain,
( ( d0 @ ( b @ multiply ) @ ( d0 @ ( b @ multiply ) @ multiply ) @ ( a @ ( a @ multiply ) @ sk2 ) )
= ( c0 @ ( c0 @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[650:[bind(A,$thf( a @ ( a @ multiply ) )),bind(B,$thf( c0 @ ( c0 @ multiply ) ))]]) ).
thf(4,negated_conjecture,
( ( d0 @ ( d @ multiply ) )
!= ( c0 @ ( c @ multiply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_quotient_condition4) ).
thf(11,plain,
( ( d0 @ ( d @ multiply ) )
!= ( c0 @ ( c @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,plain,
( ( d0 @ ( d @ multiply ) )
!= ( c0 @ ( c @ multiply ) ) ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(16,plain,
( ( c0 @ ( c @ multiply ) )
!= ( d0 @ ( d @ multiply ) ) ),
inference(lifteq,[status(thm)],[15]) ).
thf(50,plain,
( ( ( c0 @ ( c @ multiply ) )
!= ( c0 @ ( a @ multiply ) ) )
| ( ( d0 @ ( d @ multiply ) )
!= ( d0 @ ( b @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,16]) ).
thf(59,plain,
( ( c0 != c0 )
| ( c != a )
| ( d0 != d0 )
| ( d != b ) ),
inference(simp,[status(thm)],[50]) ).
thf(65,plain,
( ( c != a )
| ( d != b ) ),
inference(simp,[status(thm)],[59]) ).
thf(2,negated_conjecture,
( ( b0 @ ( d @ multiply ) )
= ( a0 @ ( c @ multiply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_quotient_condition2) ).
thf(9,plain,
( ( b0 @ ( d @ multiply ) )
= ( a0 @ ( c @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,plain,
( ( a0 @ ( c @ multiply ) )
= ( b0 @ ( d @ multiply ) ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(1,negated_conjecture,
( ( b0 @ ( b @ multiply ) )
= ( a0 @ ( a @ multiply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_quotient_condition1) ).
thf(8,plain,
( ( b0 @ ( b @ multiply ) )
= ( a0 @ ( a @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(141,plain,
! [B: $i,A: $i] :
( ( ( c0 @ ( a @ multiply ) )
!= ( B @ ( A @ multiply ) ) )
| ( ( d0 @ ( b @ multiply ) @ ( A @ sk2 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[14,140]) ).
thf(142,plain,
( ( d0 @ ( b @ multiply ) @ ( a @ sk2 ) )
= c0 ),
inference(pattern_uni,[status(thm)],[141:[bind(A,$thf( a )),bind(B,$thf( c0 ))]]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( B @ ( D @ multiply ) )
!= C )
| ( ( B @ ( A @ multiply ) )
!= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_cancellation) ).
thf(17,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( B @ ( D @ multiply ) )
!= C )
| ( ( B @ ( A @ multiply ) )
!= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(18,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( B @ ( D @ multiply ) )
!= C )
| ( ( B @ ( A @ multiply ) )
!= C ) ),
inference(cnf,[status(esa)],[17]) ).
thf(19,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( B @ ( D @ multiply ) )
!= C )
| ( ( B @ ( A @ multiply ) )
!= C ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( C @ multiply ) )
!= ( B @ ( A @ multiply ) ) ) ),
inference(simp,[status(thm)],[19]) ).
thf(57,plain,
( ( ( c0 @ ( c @ multiply ) )
!= ( c0 @ ( a @ multiply ) ) )
| ( d0 != d0 )
| ( d != b ) ),
inference(simp,[status(thm)],[50]) ).
thf(63,plain,
( ( ( c0 @ ( c @ multiply ) )
!= ( c0 @ ( a @ multiply ) ) )
| ( d != b ) ),
inference(simp,[status(thm)],[57]) ).
thf(1376,plain,
( ( ( c0 @ ( c @ multiply ) )
!= ( d0 @ ( b @ multiply ) ) )
| ( d != b ) ),
inference(rewrite,[status(thm)],[63,14]) ).
thf(1377,plain,
( ( c0 != d0 )
| ( c != b )
| ( d != b ) ),
inference(simp,[status(thm)],[1376]) ).
thf(49,plain,
( ( ( c0 @ ( c @ multiply ) )
!= ( a0 @ ( c @ multiply ) ) )
| ( ( d0 @ ( d @ multiply ) )
!= ( b0 @ ( d @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,16]) ).
thf(55,plain,
( ( c0 != a0 )
| ( c != c )
| ( ( d0 @ ( d @ multiply ) )
!= ( b0 @ ( d @ multiply ) ) ) ),
inference(simp,[status(thm)],[49]) ).
thf(61,plain,
( ( c0 != a0 )
| ( ( d0 @ ( d @ multiply ) )
!= ( b0 @ ( d @ multiply ) ) ) ),
inference(simp,[status(thm)],[55]) ).
thf(54,plain,
( ( ( c0 @ ( c @ multiply ) )
!= ( a0 @ ( c @ multiply ) ) )
| ( d0 != b0 )
| ( d != d ) ),
inference(simp,[status(thm)],[49]) ).
thf(60,plain,
( ( ( c0 @ ( c @ multiply ) )
!= ( a0 @ ( c @ multiply ) ) )
| ( d0 != b0 ) ),
inference(simp,[status(thm)],[54]) ).
thf(159,plain,
( ( ( c0 @ ( c @ multiply ) )
!= ( b0 @ ( d @ multiply ) ) )
| ( d0 != b0 ) ),
inference(rewrite,[status(thm)],[60,13]) ).
thf(160,plain,
( ( c0 != b0 )
| ( c != d )
| ( d0 != b0 ) ),
inference(simp,[status(thm)],[159]) ).
thf(21,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ multiply ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[20]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) @ ( B @ sk1 ) )
= A ),
inference(cnf,[status(esa)],[21]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) @ ( B @ sk1 ) )
= A ),
inference(lifteq,[status(thm)],[22]) ).
thf(69,plain,
! [B: $i,A: $i] :
( ( ( a0 @ ( c @ multiply ) )
!= ( B @ ( A @ multiply ) ) )
| ( ( b0 @ ( d @ multiply ) @ ( B @ sk1 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[13,66]) ).
thf(70,plain,
( ( b0 @ ( d @ multiply ) @ ( a0 @ sk1 ) )
= c ),
inference(pattern_uni,[status(thm)],[69:[bind(A,$thf( c )),bind(B,$thf( a0 ))]]) ).
thf(12,plain,
( ( a0 @ ( a @ multiply ) )
= ( b0 @ ( b @ multiply ) ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(37,plain,
( ( ( c0 @ ( a @ multiply ) )
!= ( a0 @ ( a @ multiply ) ) )
| ( ( d0 @ ( b @ multiply ) )
= ( b0 @ ( b @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,12]) ).
thf(41,plain,
( ( c0 != a0 )
| ( a != a )
| ( ( d0 @ ( b @ multiply ) )
= ( b0 @ ( b @ multiply ) ) ) ),
inference(simp,[status(thm)],[37]) ).
thf(45,plain,
( ( c0 != a0 )
| ( ( d0 @ ( b @ multiply ) )
= ( b0 @ ( b @ multiply ) ) ) ),
inference(simp,[status(thm)],[41]) ).
thf(143,plain,
! [B: $i,A: $i] :
( ( ( a0 @ ( c @ multiply ) )
!= ( B @ ( A @ multiply ) ) )
| ( ( b0 @ ( d @ multiply ) @ ( A @ sk2 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[13,140]) ).
thf(144,plain,
( ( b0 @ ( d @ multiply ) @ ( c @ sk2 ) )
= a0 ),
inference(pattern_uni,[status(thm)],[143:[bind(A,$thf( c )),bind(B,$thf( a0 ))]]) ).
thf(450,plain,
! [B: $i,A: $i] :
( ( ( a0 @ ( a @ multiply ) )
!= ( B @ ( A @ multiply ) ) )
| ( ( d0 @ ( b @ multiply ) @ ( b0 @ ( b @ multiply ) @ multiply ) )
= ( c0 @ ( B @ multiply ) @ ( a @ ( A @ multiply ) @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,241]) ).
thf(451,plain,
( ( c0 @ ( a0 @ multiply ) @ ( a @ ( a @ multiply ) @ multiply ) )
= ( d0 @ ( b @ multiply ) @ ( b0 @ ( b @ multiply ) @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[450:[bind(A,$thf( a )),bind(B,$thf( a0 ))]]) ).
thf(417,plain,
! [B: $i,A: $i] :
( ( ( a0 @ ( c @ multiply ) )
!= ( B @ ( A @ multiply ) ) )
| ( ( d0 @ ( b @ multiply ) @ ( b0 @ ( d @ multiply ) @ multiply ) )
= ( c0 @ ( B @ multiply ) @ ( a @ ( A @ multiply ) @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,241]) ).
thf(418,plain,
( ( c0 @ ( a0 @ multiply ) @ ( a @ ( c @ multiply ) @ multiply ) )
= ( d0 @ ( b @ multiply ) @ ( b0 @ ( d @ multiply ) @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[417:[bind(A,$thf( c )),bind(B,$thf( a0 ))]]) ).
thf(768,plain,
! [B: $i,A: $i] :
( ( ( c0 @ ( a0 @ multiply ) @ ( a @ ( c @ multiply ) @ multiply ) )
!= ( B @ ( A @ multiply ) ) )
| ( ( d0 @ ( b @ multiply ) @ ( b0 @ ( d @ multiply ) @ multiply ) @ ( B @ sk1 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[418,66]) ).
thf(769,plain,
( ( d0 @ ( b @ multiply ) @ ( b0 @ ( d @ multiply ) @ multiply ) @ ( c0 @ ( a0 @ multiply ) @ sk1 ) )
= ( a @ ( c @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[768:[bind(A,$thf( a @ ( c @ multiply ) )),bind(B,$thf( c0 @ ( a0 @ multiply ) ))]]) ).
thf(853,plain,
( ( ( a0 @ ( c @ multiply ) )
!= ( d0 @ ( d @ multiply ) ) )
| ( c0 != a0 )
| ( ( b0 @ ( d @ multiply ) )
!= ( b0 @ ( d @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,61]) ).
thf(854,plain,
( ( ( a0 @ ( c @ multiply ) )
!= ( d0 @ ( d @ multiply ) ) )
| ( c0 != a0 ) ),
inference(simp,[status(thm)],[853]) ).
thf(883,plain,
( ( d0 != a0 )
| ( c != d )
| ( c0 != a0 ) ),
inference(simp,[status(thm)],[854]) ).
thf(31,plain,
( ( ( a0 @ ( c @ multiply ) )
!= ( a0 @ ( a @ multiply ) ) )
| ( ( b0 @ ( d @ multiply ) )
= ( b0 @ ( b @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,12]) ).
thf(33,plain,
( ( a0 != a0 )
| ( c != a )
| ( ( b0 @ ( d @ multiply ) )
= ( b0 @ ( b @ multiply ) ) ) ),
inference(simp,[status(thm)],[31]) ).
thf(35,plain,
( ( c != a )
| ( ( b0 @ ( d @ multiply ) )
= ( b0 @ ( b @ multiply ) ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(652,plain,
! [B: $i,A: $i] :
( ( ( c0 @ ( c0 @ multiply ) @ ( a @ ( a @ multiply ) @ multiply ) )
!= ( B @ ( A @ multiply ) ) )
| ( ( d0 @ ( b @ multiply ) @ ( d0 @ ( b @ multiply ) @ multiply ) @ ( B @ sk1 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[400,66]) ).
thf(653,plain,
( ( d0 @ ( b @ multiply ) @ ( d0 @ ( b @ multiply ) @ multiply ) @ ( c0 @ ( c0 @ multiply ) @ sk1 ) )
= ( a @ ( a @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[652:[bind(A,$thf( a @ ( a @ multiply ) )),bind(B,$thf( c0 @ ( c0 @ multiply ) ))]]) ).
thf(71,plain,
! [B: $i,A: $i] :
( ( ( a0 @ ( a @ multiply ) )
!= ( B @ ( A @ multiply ) ) )
| ( ( b0 @ ( b @ multiply ) @ ( B @ sk1 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[12,66]) ).
thf(72,plain,
( ( b0 @ ( b @ multiply ) @ ( a0 @ sk1 ) )
= a ),
inference(pattern_uni,[status(thm)],[71:[bind(A,$thf( a )),bind(B,$thf( a0 ))]]) ).
thf(39,plain,
( ( ( a0 @ ( c @ multiply ) )
!= ( c0 @ ( a @ multiply ) ) )
| ( ( b0 @ ( d @ multiply ) )
= ( d0 @ ( b @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,13]) ).
thf(43,plain,
( ( c0 != a0 )
| ( c != a )
| ( ( b0 @ ( d @ multiply ) )
= ( d0 @ ( b @ multiply ) ) ) ),
inference(simp,[status(thm)],[39]) ).
thf(145,plain,
! [B: $i,A: $i] :
( ( ( a0 @ ( a @ multiply ) )
!= ( B @ ( A @ multiply ) ) )
| ( ( b0 @ ( b @ multiply ) @ ( A @ sk2 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[12,140]) ).
thf(146,plain,
( ( b0 @ ( b @ multiply ) @ ( a @ sk2 ) )
= a0 ),
inference(pattern_uni,[status(thm)],[145:[bind(A,$thf( a )),bind(B,$thf( a0 ))]]) ).
thf(766,plain,
! [B: $i,A: $i] :
( ( ( c0 @ ( a0 @ multiply ) @ ( a @ ( c @ multiply ) @ multiply ) )
!= ( B @ ( A @ multiply ) ) )
| ( ( d0 @ ( b @ multiply ) @ ( b0 @ ( d @ multiply ) @ multiply ) @ ( A @ sk2 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[418,140]) ).
thf(767,plain,
( ( d0 @ ( b @ multiply ) @ ( b0 @ ( d @ multiply ) @ multiply ) @ ( a @ ( c @ multiply ) @ sk2 ) )
= ( c0 @ ( a0 @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[766:[bind(A,$thf( a @ ( c @ multiply ) )),bind(B,$thf( c0 @ ( a0 @ multiply ) ))]]) ).
thf(47,plain,
( ( c0 != d0 )
| ( c != d ) ),
inference(simp,[status(thm)],[16]) ).
thf(67,plain,
! [B: $i,A: $i] :
( ( ( c0 @ ( a @ multiply ) )
!= ( B @ ( A @ multiply ) ) )
| ( ( d0 @ ( b @ multiply ) @ ( B @ sk1 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[14,66]) ).
thf(68,plain,
( ( d0 @ ( b @ multiply ) @ ( c0 @ sk1 ) )
= a ),
inference(pattern_uni,[status(thm)],[67:[bind(A,$thf( a )),bind(B,$thf( c0 ))]]) ).
thf(56,plain,
( ( c0 != a0 )
| ( c != c )
| ( d0 != b0 )
| ( d != d ) ),
inference(simp,[status(thm)],[49]) ).
thf(62,plain,
( ( c0 != a0 )
| ( d0 != b0 ) ),
inference(simp,[status(thm)],[56]) ).
thf(7226,plain,
$false,
inference(e,[status(thm)],[651,14,65,9,13,16,8,10,142,20,29,1377,61,160,70,45,17,12,144,159,451,1376,140,66,769,883,35,241,653,11,72,43,26,418,23,146,30,767,400,47,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG004-1 : TPTP v9.3.1. Released v2.2.0.
% 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
% 0.13/0.39 % Computer : n011.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sat Sep 26 20:57:29 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 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
% 0.89/0.96 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.31/1.14 % [INFO] Parsing done (176ms).
% 1.31/1.16 % [INFO] Running in sequential loop mode.
% 1.82/1.56 % [INFO] eprover registered as external prover.
% 1.82/1.57 % [INFO] Scanning for conjecture ...
% 2.04/1.66 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.04/1.69 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.21/1.70 % [INFO] Problem is propositional (TPTP CNF).
% 2.21/1.71 % [INFO] Type checking passed.
% 2.21/1.71 % [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 ...
% 26.83/6.67 % External prover 'e' found a proof!
% 26.83/6.67 % [INFO] Killing All external provers ...
% 26.83/6.67 % Time passed: 6140ms (effective reasoning time: 5509ms)
% 26.83/6.67 % Axioms used in derivation (3): medial_law, right_cancelaation, left_cancellation
% 26.83/6.67 % No. of inferences in proof: 89
% 26.83/6.67 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6140 ms resp. 5509 ms w/o parsing
% 22.95/6.71 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 22.95/6.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------