%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP199-1 : TPTP v9.3.1. Released v2.2.0.
% 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 : n003.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 07:20:26 AM UTC 2026
% Result : Unsatisfiable 85.41s 29.90s
% Output : Refutation 78.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 179 ( 82 unt; 0 typ; 2 def)
% Number of atoms : 320 ( 319 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 1874 ( 179 ~; 139 |; 0 &;1556 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 169 ( 0 ^; 165 !; 2 ?; 169 :)
% ( 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(2,negated_conjecture,
( ( b0 @ ( d @ multiply ) )
= ( a0 @ ( c @ multiply ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_quotient2) ).
thf(10,plain,
( ( b0 @ ( d @ multiply ) )
= ( a0 @ ( c @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,negated_conjecture,
( ( d0 @ ( b @ multiply ) )
= ( c0 @ ( a @ multiply ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_quotient3) ).
thf(11,plain,
( ( d0 @ ( b @ multiply ) )
= ( c0 @ ( a @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(15,plain,
( ( c0 @ ( a @ multiply ) )
= ( d0 @ ( b @ multiply ) ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiply ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( A @ multiply ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiply) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiply ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( A @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiply ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( A @ multiply ) ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(102,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c0 @ ( a @ multiply ) )
!= ( B @ ( A @ multiply ) ) )
| ( ( C @ ( d0 @ ( b @ multiply ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( A @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[15,19]) ).
thf(103,plain,
! [A: $i] :
( ( A @ ( d0 @ ( b @ multiply ) @ multiply ) )
= ( A @ ( c0 @ multiply ) @ ( a @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[102:[bind(A,$thf( a )),bind(B,$thf( c0 ))]]) ).
thf(116,plain,
! [A: $i] :
( ( A @ ( d0 @ ( b @ multiply ) @ multiply ) )
= ( A @ ( c0 @ multiply ) @ ( a @ multiply ) ) ),
inference(simp,[status(thm)],[103]) ).
thf(173,plain,
! [A: $i] :
( ( A @ ( d0 @ multiply ) @ ( b @ multiply ) )
= ( A @ ( c0 @ multiply ) @ ( a @ multiply ) ) ),
inference(rewrite,[status(thm)],[116,19]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ multiply ) @ ( C @ multiply ) @ ( B @ multiply ) @ ( A @ multiply ) )
= ( B @ ( A @ multiply ) @ ( C @ multiply ) @ ( A @ multiply ) @ ( B @ multiply ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nilpotency) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ multiply ) @ ( C @ multiply ) @ ( B @ multiply ) @ ( A @ multiply ) )
= ( B @ ( A @ multiply ) @ ( C @ multiply ) @ ( A @ multiply ) @ ( B @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ multiply ) @ ( C @ multiply ) @ ( B @ multiply ) @ ( A @ multiply ) )
= ( B @ ( A @ multiply ) @ ( C @ multiply ) @ ( A @ multiply ) @ ( B @ multiply ) ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(1535,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) @ ( C @ multiply ) @ ( A @ multiply ) @ ( B @ multiply ) )
!= ( D @ ( c0 @ multiply ) @ ( a @ multiply ) ) )
| ( ( A @ ( B @ multiply ) @ ( C @ multiply ) @ ( B @ multiply ) @ ( A @ multiply ) )
= ( D @ ( d0 @ multiply ) @ ( b @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,173]) ).
thf(1536,plain,
! [A: $i] :
( ( c0 @ ( a @ multiply ) @ ( A @ multiply ) @ ( a @ multiply ) @ ( c0 @ multiply ) )
= ( a @ ( c0 @ multiply ) @ ( A @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[1535:[bind(A,$thf( c0 )),bind(B,$thf( a )),bind(C,$thf( E )),bind(D,$thf( a @ ( c0 @ multiply ) @ ( E @ multiply ) ))]]) ).
thf(1795,plain,
! [A: $i] :
( ( c0 @ ( a @ multiply ) @ ( A @ multiply ) @ ( a @ multiply ) @ ( c0 @ multiply ) )
= ( a @ ( c0 @ multiply ) @ ( A @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) ) ),
inference(simp,[status(thm)],[1536]) ).
thf(2623,plain,
! [A: $i] :
( ( d0 @ ( b @ multiply ) @ ( A @ multiply ) @ ( a @ multiply ) @ ( c0 @ multiply ) )
= ( a @ ( c0 @ multiply ) @ ( A @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) ) ),
inference(rewrite,[status(thm)],[1795,15]) ).
thf(2727,plain,
! [B: $i,A: $i] :
( ( ( A @ ( c0 @ multiply ) @ ( a @ multiply ) )
!= ( d0 @ ( b @ multiply ) @ ( B @ multiply ) @ ( a @ multiply ) ) )
| ( ( A @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( c0 @ multiply ) )
= ( a @ ( c0 @ multiply ) @ ( B @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[173,2623]) ).
thf(2728,plain,
( ( d0 @ ( b @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( c0 @ multiply ) )
= ( a @ ( c0 @ multiply ) @ ( c0 @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[2727:[bind(A,$thf( d0 @ ( b @ multiply ) )),bind(B,$thf( c0 ))]]) ).
thf(3285,plain,
! [A: $i] :
( ( ( a @ ( c0 @ multiply ) @ ( c0 @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) )
!= ( a @ ( c0 @ multiply ) @ ( A @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) ) )
| ( ( d0 @ ( b @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( c0 @ multiply ) )
= ( d0 @ ( b @ multiply ) @ ( A @ multiply ) @ ( a @ multiply ) @ ( c0 @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[2728,2623]) ).
thf(3286,plain,
( ( d0 @ ( b @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( c0 @ multiply ) )
= ( d0 @ ( b @ multiply ) @ ( c0 @ multiply ) @ ( a @ multiply ) @ ( c0 @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[3285:[bind(A,$thf( c0 ))]]) ).
thf(14,plain,
( ( a0 @ ( c @ multiply ) )
= ( b0 @ ( d @ multiply ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ multiply ) )
!= ( C @ ( A @ multiply ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_cancellation) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ multiply ) )
!= ( C @ ( A @ multiply ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ multiply ) )
!= ( C @ ( A @ multiply ) ) ) ),
inference(cnf,[status(esa)],[25]) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ multiply ) )
!= ( C @ ( A @ multiply ) ) ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(28,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ multiply ) @ ( B @ A ) )
= C ),
inference(detectInverse,[status(thm)],[27]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) @ ( A @ sk2 ) )
= B ),
inference(cnf,[status(esa)],[28]) ).
thf(1110,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) @ ( A @ sk2 ) )
= B ),
inference(lifteq,[status(thm)],[29]) ).
thf(1111,plain,
! [B: $i,A: $i] :
( ( ( a0 @ ( c @ multiply ) )
!= ( B @ ( A @ multiply ) ) )
| ( ( b0 @ ( d @ multiply ) @ ( A @ sk2 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[14,1110]) ).
thf(1112,plain,
( ( b0 @ ( d @ multiply ) @ ( c @ sk2 ) )
= a0 ),
inference(pattern_uni,[status(thm)],[1111:[bind(A,$thf( c )),bind(B,$thf( a0 ))]]) ).
thf(4,negated_conjecture,
( ( d0 @ ( d @ multiply ) )
!= ( c0 @ ( c @ multiply ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_quotient4) ).
thf(12,plain,
( ( d0 @ ( d @ multiply ) )
!= ( c0 @ ( c @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,plain,
( ( d0 @ ( d @ multiply ) )
!= ( c0 @ ( c @ multiply ) ) ),
inference(polarity_switch,[status(thm)],[12]) ).
thf(17,plain,
( ( c0 @ ( c @ multiply ) )
!= ( d0 @ ( d @ multiply ) ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(51,plain,
( ( ( c0 @ ( c @ multiply ) )
!= ( c0 @ ( a @ multiply ) ) )
| ( ( d0 @ ( d @ multiply ) )
!= ( d0 @ ( b @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[15,17]) ).
thf(59,plain,
( ( c0 != c0 )
| ( c != a )
| ( ( d0 @ ( d @ multiply ) )
!= ( d0 @ ( b @ multiply ) ) ) ),
inference(simp,[status(thm)],[51]) ).
thf(65,plain,
( ( c != a )
| ( ( d0 @ ( d @ multiply ) )
!= ( d0 @ ( b @ multiply ) ) ) ),
inference(simp,[status(thm)],[59]) ).
thf(2361,plain,
( ( ( d0 @ ( d @ multiply ) )
!= ( c0 @ ( a @ multiply ) ) )
| ( c != a )
| ( ( d0 @ ( b @ multiply ) )
!= ( d0 @ ( b @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[15,65]) ).
thf(2362,plain,
( ( ( d0 @ ( d @ multiply ) )
!= ( c0 @ ( a @ multiply ) ) )
| ( c != a ) ),
inference(simp,[status(thm)],[2361]) ).
thf(2390,plain,
( ( c0 != d0 )
| ( d != a )
| ( c != a ) ),
inference(simp,[status(thm)],[2362]) ).
thf(1,negated_conjecture,
( ( b0 @ ( b @ multiply ) )
= ( a0 @ ( a @ multiply ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_quotient1) ).
thf(9,plain,
( ( b0 @ ( b @ multiply ) )
= ( a0 @ ( a @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(13,plain,
( ( a0 @ ( a @ multiply ) )
= ( b0 @ ( b @ multiply ) ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ multiply ) )
!= ( B @ ( C @ multiply ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_cancellation) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ multiply ) )
!= ( B @ ( C @ multiply ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ multiply ) )
!= ( B @ ( C @ multiply ) ) ) ),
inference(cnf,[status(esa)],[20]) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ multiply ) )
!= ( B @ ( C @ multiply ) ) ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(23,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ multiply ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[22]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) @ ( B @ sk1 ) )
= A ),
inference(cnf,[status(esa)],[23]) ).
thf(67,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) @ ( B @ sk1 ) )
= A ),
inference(lifteq,[status(thm)],[24]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ( ( a0 @ ( a @ multiply ) )
!= ( B @ ( A @ multiply ) ) )
| ( ( b0 @ ( b @ multiply ) @ ( B @ sk1 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[13,67]) ).
thf(71,plain,
( ( b0 @ ( b @ multiply ) @ ( a0 @ sk1 ) )
= a ),
inference(pattern_uni,[status(thm)],[70:[bind(A,$thf( a )),bind(B,$thf( a0 ))]]) ).
thf(68,plain,
! [B: $i,A: $i] :
( ( ( a0 @ ( c @ multiply ) )
!= ( B @ ( A @ multiply ) ) )
| ( ( b0 @ ( d @ multiply ) @ ( B @ sk1 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[14,67]) ).
thf(69,plain,
( ( b0 @ ( d @ multiply ) @ ( a0 @ sk1 ) )
= c ),
inference(pattern_uni,[status(thm)],[68:[bind(A,$thf( c )),bind(B,$thf( a0 ))]]) ).
thf(129,plain,
( ( ( b0 @ ( d @ multiply ) @ ( a0 @ sk1 ) )
!= ( b0 @ ( b @ multiply ) @ ( a0 @ sk1 ) ) )
| ( c = a ) ),
inference(paramod_ordered,[status(thm)],[71,69]) ).
thf(137,plain,
( ( ( b0 @ ( d @ multiply ) )
!= ( b0 @ ( b @ multiply ) ) )
| ( a0 != a0 )
| ( c = a ) ),
inference(simp,[status(thm)],[129]) ).
thf(146,plain,
( ( ( b0 @ ( d @ multiply ) )
!= ( b0 @ ( b @ multiply ) ) )
| ( c = a ) ),
inference(simp,[status(thm)],[137]) ).
thf(4666,plain,
( ( ( b0 @ ( d @ multiply ) )
!= ( a0 @ ( a @ multiply ) ) )
| ( ( b0 @ ( b @ multiply ) )
!= ( b0 @ ( b @ multiply ) ) )
| ( c = a ) ),
inference(paramod_ordered,[status(thm)],[13,146]) ).
thf(4667,plain,
( ( ( b0 @ ( d @ multiply ) )
!= ( a0 @ ( a @ multiply ) ) )
| ( c = a ) ),
inference(simp,[status(thm)],[4666]) ).
thf(4695,plain,
( ( a0 != b0 )
| ( d != a )
| ( c = a ) ),
inference(simp,[status(thm)],[4667]) ).
thf(9304,plain,
( ( c != c )
| ( c0 != d0 )
| ( d != a )
| ( a != a )
| ( a0 != b0 )
| ( d != a ) ),
inference(paramod_ordered,[status(thm)],[4695,2390]) ).
thf(9305,plain,
( ( c != c )
| ( c0 != d0 )
| ( a0 != b0 )
| ( d != a ) ),
inference(simp,[status(thm)],[9304]) ).
thf(9306,plain,
( ( c0 != d0 )
| ( a0 != b0 )
| ( d != a ) ),
inference(pattern_uni,[status(thm)],[9305:[]]) ).
thf(32,plain,
( ( ( a0 @ ( c @ multiply ) )
!= ( a0 @ ( a @ multiply ) ) )
| ( ( b0 @ ( d @ multiply ) )
= ( b0 @ ( b @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,13]) ).
thf(34,plain,
( ( a0 != a0 )
| ( c != a )
| ( ( b0 @ ( d @ multiply ) )
= ( b0 @ ( b @ multiply ) ) ) ),
inference(simp,[status(thm)],[32]) ).
thf(36,plain,
( ( c != a )
| ( ( b0 @ ( d @ multiply ) )
= ( b0 @ ( b @ multiply ) ) ) ),
inference(simp,[status(thm)],[34]) ).
thf(2357,plain,
( ( ( d0 @ ( d @ multiply ) )
!= ( b0 @ ( d @ multiply ) ) )
| ( c != a )
| ( ( d0 @ ( b @ multiply ) )
!= ( b0 @ ( b @ multiply ) ) )
| ( c != a ) ),
inference(paramod_ordered,[status(thm)],[36,65]) ).
thf(2358,plain,
( ( ( d0 @ ( d @ multiply ) )
!= ( b0 @ ( d @ multiply ) ) )
| ( ( d0 @ ( b @ multiply ) )
!= ( b0 @ ( b @ multiply ) ) )
| ( c != a ) ),
inference(simp,[status(thm)],[2357]) ).
thf(2380,plain,
( ( d0 != b0 )
| ( d != d )
| ( d0 != b0 )
| ( b != b )
| ( c != a ) ),
inference(simp,[status(thm)],[2358]) ).
thf(2406,plain,
( ( d0 != b0 )
| ( c != a ) ),
inference(simp,[status(thm)],[2380]) ).
thf(93,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a0 @ ( a @ multiply ) )
!= ( B @ ( A @ multiply ) ) )
| ( ( C @ ( b0 @ ( b @ multiply ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( A @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,19]) ).
thf(94,plain,
! [A: $i] :
( ( A @ ( b0 @ ( b @ multiply ) @ multiply ) )
= ( A @ ( a0 @ multiply ) @ ( a @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[93:[bind(A,$thf( a )),bind(B,$thf( a0 ))]]) ).
thf(128,plain,
! [A: $i] :
( ( A @ ( b0 @ ( b @ multiply ) @ multiply ) )
= ( A @ ( a0 @ multiply ) @ ( a @ multiply ) ) ),
inference(simp,[status(thm)],[94]) ).
thf(400,plain,
! [A: $i] :
( ( A @ ( a0 @ multiply ) @ ( a @ multiply ) )
= ( A @ ( b0 @ multiply ) @ ( b @ multiply ) ) ),
inference(rewrite,[status(thm)],[128,19]) ).
thf(432,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( a0 @ multiply ) @ ( a @ multiply ) )
!= ( C @ ( B @ multiply ) ) )
| ( ( A @ ( b0 @ multiply ) @ ( b @ multiply ) @ ( C @ sk1 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[400,67]) ).
thf(433,plain,
! [A: $i] :
( ( A @ ( b0 @ multiply ) @ ( b @ multiply ) @ ( A @ ( a0 @ multiply ) @ sk1 ) )
= a ),
inference(pattern_uni,[status(thm)],[432:[bind(A,$thf( E )),bind(B,$thf( a )),bind(C,$thf( E @ ( a0 @ multiply ) ))]]) ).
thf(481,plain,
! [A: $i] :
( ( A @ ( b0 @ multiply ) @ ( b @ multiply ) @ ( A @ ( a0 @ multiply ) @ sk1 ) )
= a ),
inference(simp,[status(thm)],[433]) ).
thf(3369,plain,
! [A: $i] :
( ( ( a @ ( c0 @ multiply ) @ ( c0 @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) )
!= ( A @ ( d0 @ multiply ) @ ( b @ multiply ) ) )
| ( ( d0 @ ( b @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( c0 @ multiply ) )
= ( A @ ( c0 @ multiply ) @ ( a @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[2728,173]) ).
thf(3370,plain,
( ( d0 @ ( b @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( c0 @ multiply ) )
= ( a @ ( c0 @ multiply ) @ ( c0 @ multiply ) @ ( c0 @ multiply ) @ ( a @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[3369:[bind(A,$thf( a @ ( c0 @ multiply ) @ ( c0 @ multiply ) ))]]) ).
thf(1115,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( d0 @ multiply ) @ ( b @ multiply ) )
!= ( C @ ( B @ multiply ) ) )
| ( ( A @ ( c0 @ multiply ) @ ( a @ multiply ) @ ( B @ sk2 ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[173,1110]) ).
thf(1116,plain,
! [A: $i] :
( ( A @ ( c0 @ multiply ) @ ( a @ multiply ) @ ( b @ sk2 ) )
= ( A @ ( d0 @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[1115:[bind(A,$thf( E )),bind(B,$thf( b )),bind(C,$thf( E @ ( d0 @ multiply ) ))]]) ).
thf(1132,plain,
! [A: $i] :
( ( A @ ( c0 @ multiply ) @ ( a @ multiply ) @ ( b @ sk2 ) )
= ( A @ ( d0 @ multiply ) ) ),
inference(simp,[status(thm)],[1116]) ).
thf(38,plain,
( ( ( c0 @ ( a @ multiply ) )
!= ( a0 @ ( a @ multiply ) ) )
| ( ( d0 @ ( b @ multiply ) )
= ( b0 @ ( b @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[15,13]) ).
thf(42,plain,
( ( c0 != a0 )
| ( a != a )
| ( ( d0 @ ( b @ multiply ) )
= ( b0 @ ( b @ multiply ) ) ) ),
inference(simp,[status(thm)],[38]) ).
thf(46,plain,
( ( c0 != a0 )
| ( ( d0 @ ( b @ multiply ) )
= ( b0 @ ( b @ multiply ) ) ) ),
inference(simp,[status(thm)],[42]) ).
thf(89,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a0 @ ( c @ multiply ) )
!= ( B @ ( A @ multiply ) ) )
| ( ( C @ ( b0 @ ( d @ multiply ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( A @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,19]) ).
thf(90,plain,
! [A: $i] :
( ( A @ ( b0 @ ( d @ multiply ) @ multiply ) )
= ( A @ ( a0 @ multiply ) @ ( c @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[89:[bind(A,$thf( c )),bind(B,$thf( a0 ))]]) ).
thf(127,plain,
! [A: $i] :
( ( A @ ( b0 @ ( d @ multiply ) @ multiply ) )
= ( A @ ( a0 @ multiply ) @ ( c @ multiply ) ) ),
inference(simp,[status(thm)],[90]) ).
thf(284,plain,
! [A: $i] :
( ( A @ ( a0 @ multiply ) @ ( c @ multiply ) )
= ( A @ ( b0 @ multiply ) @ ( d @ multiply ) ) ),
inference(rewrite,[status(thm)],[127,19]) ).
thf(4654,plain,
( ( b0 != b0 )
| ( d != b )
| ( c = a ) ),
inference(simp,[status(thm)],[146]) ).
thf(4726,plain,
( ( d != b )
| ( c = a ) ),
inference(simp,[status(thm)],[4654]) ).
thf(60,plain,
( ( c0 != c0 )
| ( c != a )
| ( d0 != d0 )
| ( d != b ) ),
inference(simp,[status(thm)],[51]) ).
thf(66,plain,
( ( c != a )
| ( d != b ) ),
inference(simp,[status(thm)],[60]) ).
thf(6962,plain,
( ( c != c )
| ( a != a )
| ( d != b )
| ( d != b ) ),
inference(paramod_ordered,[status(thm)],[4726,66]) ).
thf(6963,plain,
( ( c != c )
| ( d != b ) ),
inference(simp,[status(thm)],[6962]) ).
thf(6964,plain,
d != b,
inference(pattern_uni,[status(thm)],[6963:[]]) ).
thf(9307,plain,
( ( c != c )
| ( d0 != b0 )
| ( a != a )
| ( a0 != b0 )
| ( d != a ) ),
inference(paramod_ordered,[status(thm)],[4695,2406]) ).
thf(9308,plain,
( ( c != c )
| ( d0 != b0 )
| ( a0 != b0 )
| ( d != a ) ),
inference(simp,[status(thm)],[9307]) ).
thf(9309,plain,
( ( d0 != b0 )
| ( a0 != b0 )
| ( d != a ) ),
inference(pattern_uni,[status(thm)],[9308:[]]) ).
thf(188,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( d0 @ multiply ) @ ( b @ multiply ) )
!= ( C @ ( B @ multiply ) ) )
| ( ( A @ ( c0 @ multiply ) @ ( a @ multiply ) @ ( C @ sk1 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[173,67]) ).
thf(189,plain,
! [A: $i] :
( ( A @ ( c0 @ multiply ) @ ( a @ multiply ) @ ( A @ ( d0 @ multiply ) @ sk1 ) )
= b ),
inference(pattern_uni,[status(thm)],[188:[bind(A,$thf( E )),bind(B,$thf( b )),bind(C,$thf( E @ ( d0 @ multiply ) ))]]) ).
thf(280,plain,
! [A: $i] :
( ( A @ ( c0 @ multiply ) @ ( a @ multiply ) @ ( A @ ( d0 @ multiply ) @ sk1 ) )
= b ),
inference(simp,[status(thm)],[189]) ).
thf(2731,plain,
! [B: $i,A: $i] :
( ( ( A @ ( c0 @ multiply ) @ ( a @ multiply ) )
!= ( a @ ( c0 @ multiply ) @ ( B @ multiply ) ) )
| ( ( A @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) )
= ( d0 @ ( b @ multiply ) @ ( B @ multiply ) @ ( a @ multiply ) @ ( c0 @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[173,2623]) ).
thf(2732,plain,
( ( d0 @ ( b @ multiply ) @ ( a @ multiply ) @ ( a @ multiply ) @ ( c0 @ multiply ) )
= ( a @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[2731:[bind(A,$thf( a )),bind(B,$thf( a ))]]) ).
thf(3954,plain,
! [B: $i,A: $i] :
( ( ( d0 @ ( b @ multiply ) @ ( a @ multiply ) @ ( a @ multiply ) @ ( c0 @ multiply ) )
!= ( B @ ( A @ multiply ) ) )
| ( ( a @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( A @ sk2 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[2732,1110]) ).
thf(3955,plain,
( ( a @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( c0 @ sk2 ) )
= ( d0 @ ( b @ multiply ) @ ( a @ multiply ) @ ( a @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[3954:[bind(A,$thf( c0 )),bind(B,$thf( d0 @ ( b @ multiply ) @ ( a @ multiply ) @ ( a @ multiply ) ))]]) ).
thf(2872,plain,
! [B: $i,A: $i] :
( ( ( A @ ( a0 @ multiply ) @ ( a @ multiply ) )
!= ( d0 @ ( b @ multiply ) @ ( B @ multiply ) @ ( a @ multiply ) ) )
| ( ( A @ ( b0 @ multiply ) @ ( b @ multiply ) @ ( c0 @ multiply ) )
= ( a @ ( c0 @ multiply ) @ ( B @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[400,2623]) ).
thf(2873,plain,
( ( d0 @ ( b @ multiply ) @ ( b0 @ multiply ) @ ( b @ multiply ) @ ( c0 @ multiply ) )
= ( a @ ( c0 @ multiply ) @ ( a0 @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[2872:[bind(A,$thf( d0 @ ( b @ multiply ) )),bind(B,$thf( a0 ))]]) ).
thf(4850,plain,
! [B: $i,A: $i] :
( ( ( d0 @ ( b @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( c0 @ multiply ) )
!= ( B @ ( A @ multiply ) ) )
| ( ( d0 @ ( b @ multiply ) @ ( c0 @ multiply ) @ ( a @ multiply ) @ ( c0 @ multiply ) @ ( A @ sk2 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[3286,1110]) ).
thf(4851,plain,
( ( d0 @ ( b @ multiply ) @ ( c0 @ multiply ) @ ( a @ multiply ) @ ( c0 @ multiply ) @ ( c0 @ sk2 ) )
= ( d0 @ ( b @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[4850:[bind(A,$thf( c0 )),bind(B,$thf( d0 @ ( b @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) ))]]) ).
thf(12603,plain,
( ( d0 @ ( b @ multiply ) @ ( c0 @ multiply ) @ ( a @ multiply ) )
= ( d0 @ ( b @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) ) ),
inference(rewrite,[status(thm)],[4851,1110]) ).
thf(1127,plain,
! [B: $i,A: $i] :
( ( ( c0 @ ( a @ multiply ) )
!= ( B @ ( A @ multiply ) ) )
| ( ( d0 @ ( b @ multiply ) @ ( A @ sk2 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[15,1110]) ).
thf(1128,plain,
( ( d0 @ ( b @ multiply ) @ ( a @ sk2 ) )
= c0 ),
inference(pattern_uni,[status(thm)],[1127:[bind(A,$thf( a )),bind(B,$thf( c0 ))]]) ).
thf(4315,plain,
! [B: $i,A: $i] :
( ( ( d0 @ ( b @ multiply ) @ ( b0 @ multiply ) @ ( b @ multiply ) @ ( c0 @ multiply ) )
!= ( B @ ( A @ multiply ) ) )
| ( ( a @ ( c0 @ multiply ) @ ( a0 @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( A @ sk2 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[2873,1110]) ).
thf(4316,plain,
( ( a @ ( c0 @ multiply ) @ ( a0 @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( c0 @ sk2 ) )
= ( d0 @ ( b @ multiply ) @ ( b0 @ multiply ) @ ( b @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[4315:[bind(A,$thf( c0 )),bind(B,$thf( d0 @ ( b @ multiply ) @ ( b0 @ multiply ) @ ( b @ multiply ) ))]]) ).
thf(49,plain,
( ( ( c0 @ ( c @ multiply ) )
!= ( a0 @ ( a @ multiply ) ) )
| ( ( d0 @ ( d @ multiply ) )
!= ( b0 @ ( b @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,17]) ).
thf(53,plain,
( ( c0 != a0 )
| ( c != a )
| ( ( d0 @ ( d @ multiply ) )
!= ( b0 @ ( b @ multiply ) ) ) ),
inference(simp,[status(thm)],[49]) ).
thf(3310,plain,
! [B: $i,A: $i] :
( ( ( a @ ( c0 @ multiply ) @ ( c0 @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) )
!= ( B @ ( A @ multiply ) ) )
| ( ( d0 @ ( b @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( c0 @ multiply ) @ ( A @ sk2 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[2728,1110]) ).
thf(3311,plain,
( ( d0 @ ( b @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( c0 @ multiply ) @ ( b @ sk2 ) )
= ( a @ ( c0 @ multiply ) @ ( c0 @ multiply ) @ ( d0 @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[3310:[bind(A,$thf( b )),bind(B,$thf( a @ ( c0 @ multiply ) @ ( c0 @ multiply ) @ ( d0 @ multiply ) ))]]) ).
thf(3440,plain,
! [B: $i,A: $i] :
( ( ( d0 @ ( b @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( c0 @ multiply ) )
!= ( B @ ( A @ multiply ) ) )
| ( ( a @ ( c0 @ multiply ) @ ( c0 @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( B @ sk1 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[2728,67]) ).
thf(3441,plain,
( ( a @ ( c0 @ multiply ) @ ( c0 @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( d0 @ ( b @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) @ sk1 ) )
= c0 ),
inference(pattern_uni,[status(thm)],[3440:[bind(A,$thf( c0 )),bind(B,$thf( d0 @ ( b @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) ))]]) ).
thf(3934,plain,
! [A: $i] :
( ( ( d0 @ ( b @ multiply ) @ ( a @ multiply ) @ ( a @ multiply ) @ ( c0 @ multiply ) )
!= ( d0 @ ( b @ multiply ) @ ( A @ multiply ) @ ( a @ multiply ) @ ( c0 @ multiply ) ) )
| ( ( a @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) )
= ( a @ ( c0 @ multiply ) @ ( A @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[2732,2623]) ).
thf(3935,plain,
( ( a @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) )
= ( a @ ( c0 @ multiply ) @ ( a @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[3934:[bind(A,$thf( a ))]]) ).
thf(1113,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( a0 @ multiply ) @ ( c @ multiply ) )
!= ( C @ ( B @ multiply ) ) )
| ( ( A @ ( b0 @ multiply ) @ ( d @ multiply ) @ ( B @ sk2 ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[284,1110]) ).
thf(1114,plain,
! [A: $i] :
( ( A @ ( b0 @ multiply ) @ ( d @ multiply ) @ ( c @ sk2 ) )
= ( A @ ( a0 @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[1113:[bind(A,$thf( E )),bind(B,$thf( c )),bind(C,$thf( E @ ( a0 @ multiply ) ))]]) ).
thf(1131,plain,
! [A: $i] :
( ( A @ ( b0 @ multiply ) @ ( d @ multiply ) @ ( c @ sk2 ) )
= ( A @ ( a0 @ multiply ) ) ),
inference(simp,[status(thm)],[1114]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ( ( c0 @ ( a @ multiply ) )
!= ( B @ ( A @ multiply ) ) )
| ( ( d0 @ ( b @ multiply ) @ ( B @ sk1 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[15,67]) ).
thf(73,plain,
( ( d0 @ ( b @ multiply ) @ ( c0 @ sk1 ) )
= a ),
inference(pattern_uni,[status(thm)],[72:[bind(A,$thf( a )),bind(B,$thf( c0 ))]]) ).
thf(50,plain,
( ( ( c0 @ ( c @ multiply ) )
!= ( a0 @ ( c @ multiply ) ) )
| ( ( d0 @ ( d @ multiply ) )
!= ( b0 @ ( d @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,17]) ).
thf(55,plain,
( ( ( c0 @ ( c @ multiply ) )
!= ( a0 @ ( c @ multiply ) ) )
| ( d0 != b0 )
| ( d != d ) ),
inference(simp,[status(thm)],[50]) ).
thf(61,plain,
( ( ( c0 @ ( c @ multiply ) )
!= ( a0 @ ( c @ multiply ) ) )
| ( d0 != b0 ) ),
inference(simp,[status(thm)],[55]) ).
thf(359,plain,
( ( ( c0 @ ( c @ multiply ) )
!= ( b0 @ ( d @ multiply ) ) )
| ( d0 != b0 ) ),
inference(rewrite,[status(thm)],[61,14]) ).
thf(360,plain,
( ( c0 != b0 )
| ( c != d )
| ( d0 != b0 ) ),
inference(simp,[status(thm)],[359]) ).
thf(4392,plain,
! [B: $i,A: $i] :
( ( ( d0 @ ( b @ multiply ) @ ( b0 @ multiply ) @ ( b @ multiply ) @ ( c0 @ multiply ) )
!= ( B @ ( A @ multiply ) ) )
| ( ( a @ ( c0 @ multiply ) @ ( a0 @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( B @ sk1 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[2873,67]) ).
thf(4393,plain,
( ( a @ ( c0 @ multiply ) @ ( a0 @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( d0 @ ( b @ multiply ) @ ( b0 @ multiply ) @ ( b @ multiply ) @ sk1 ) )
= c0 ),
inference(pattern_uni,[status(thm)],[4392:[bind(A,$thf( c0 )),bind(B,$thf( d0 @ ( b @ multiply ) @ ( b0 @ multiply ) @ ( b @ multiply ) ))]]) ).
thf(40,plain,
( ( ( a0 @ ( c @ multiply ) )
!= ( c0 @ ( a @ multiply ) ) )
| ( ( b0 @ ( d @ multiply ) )
= ( d0 @ ( b @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[15,14]) ).
thf(44,plain,
( ( c0 != a0 )
| ( c != a )
| ( ( b0 @ ( d @ multiply ) )
= ( d0 @ ( b @ multiply ) ) ) ),
inference(simp,[status(thm)],[40]) ).
thf(48,plain,
( ( c0 != d0 )
| ( c != d ) ),
inference(simp,[status(thm)],[17]) ).
thf(3375,plain,
! [A: $i] :
( ( ( A @ ( d0 @ multiply ) @ ( b @ multiply ) )
!= ( d0 @ ( b @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) ) )
| ( ( A @ ( c0 @ multiply ) @ ( a @ multiply ) @ ( c0 @ multiply ) )
= ( a @ ( c0 @ multiply ) @ ( c0 @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[173,2728]) ).
thf(3376,plain,
( ( d0 @ ( b @ multiply ) @ ( c0 @ multiply ) @ ( a @ multiply ) @ ( c0 @ multiply ) )
= ( a @ ( c0 @ multiply ) @ ( c0 @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[3375:[bind(A,$thf( d0 @ ( b @ multiply ) ))]]) ).
thf(57,plain,
( ( c0 != a0 )
| ( c != c )
| ( d0 != b0 )
| ( d != d ) ),
inference(simp,[status(thm)],[50]) ).
thf(63,plain,
( ( c0 != a0 )
| ( d0 != b0 ) ),
inference(simp,[status(thm)],[57]) ).
thf(190,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( c0 @ multiply ) @ ( a @ multiply ) )
!= ( C @ ( B @ multiply ) ) )
| ( ( A @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( C @ sk1 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[173,67]) ).
thf(191,plain,
! [A: $i] :
( ( A @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( A @ ( c0 @ multiply ) @ sk1 ) )
= a ),
inference(pattern_uni,[status(thm)],[190:[bind(A,$thf( E )),bind(B,$thf( a )),bind(C,$thf( E @ ( c0 @ multiply ) ))]]) ).
thf(282,plain,
! [A: $i] :
( ( A @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( A @ ( c0 @ multiply ) @ sk1 ) )
= a ),
inference(simp,[status(thm)],[191]) ).
thf(1125,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( a0 @ multiply ) @ ( a @ multiply ) )
!= ( C @ ( B @ multiply ) ) )
| ( ( A @ ( b0 @ multiply ) @ ( b @ multiply ) @ ( B @ sk2 ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[400,1110]) ).
thf(1126,plain,
! [A: $i] :
( ( A @ ( b0 @ multiply ) @ ( b @ multiply ) @ ( a @ sk2 ) )
= ( A @ ( a0 @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[1125:[bind(A,$thf( E )),bind(B,$thf( a )),bind(C,$thf( E @ ( a0 @ multiply ) ))]]) ).
thf(1130,plain,
! [A: $i] :
( ( A @ ( b0 @ multiply ) @ ( b @ multiply ) @ ( a @ sk2 ) )
= ( A @ ( a0 @ multiply ) ) ),
inference(simp,[status(thm)],[1126]) ).
thf(1117,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( c0 @ multiply ) @ ( a @ multiply ) )
!= ( C @ ( B @ multiply ) ) )
| ( ( A @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( B @ sk2 ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[173,1110]) ).
thf(1118,plain,
! [A: $i] :
( ( A @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( a @ sk2 ) )
= ( A @ ( c0 @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[1117:[bind(A,$thf( E )),bind(B,$thf( a )),bind(C,$thf( E @ ( c0 @ multiply ) ))]]) ).
thf(1133,plain,
! [A: $i] :
( ( A @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( a @ sk2 ) )
= ( A @ ( c0 @ multiply ) ) ),
inference(simp,[status(thm)],[1118]) ).
thf(3492,plain,
! [A: $i] :
( ( ( a @ ( c0 @ multiply ) @ ( c0 @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) )
!= ( A @ ( d0 @ multiply ) @ ( b @ multiply ) ) )
| ( ( d0 @ ( b @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( c0 @ multiply ) @ ( a @ sk2 ) )
= ( A @ ( c0 @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[2728,1133]) ).
thf(3493,plain,
( ( d0 @ ( b @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( c0 @ multiply ) @ ( a @ sk2 ) )
= ( a @ ( c0 @ multiply ) @ ( c0 @ multiply ) @ ( c0 @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[3492:[bind(A,$thf( a @ ( c0 @ multiply ) @ ( c0 @ multiply ) ))]]) ).
thf(3308,plain,
! [B: $i,A: $i] :
( ( ( d0 @ ( b @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( c0 @ multiply ) )
!= ( B @ ( A @ multiply ) ) )
| ( ( a @ ( c0 @ multiply ) @ ( c0 @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( A @ sk2 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[2728,1110]) ).
thf(3309,plain,
( ( a @ ( c0 @ multiply ) @ ( c0 @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( c0 @ sk2 ) )
= ( d0 @ ( b @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[3308:[bind(A,$thf( c0 )),bind(B,$thf( d0 @ ( b @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) ))]]) ).
thf(78,plain,
( ( ( b0 @ ( d @ multiply ) )
!= ( c0 @ ( a @ multiply ) ) )
| ( ( d0 @ ( b @ multiply ) @ ( a0 @ sk1 ) )
= c ) ),
inference(paramod_ordered,[status(thm)],[15,69]) ).
thf(79,plain,
( ( c0 != b0 )
| ( d != a )
| ( ( d0 @ ( b @ multiply ) @ ( a0 @ sk1 ) )
= c ) ),
inference(simp,[status(thm)],[78]) ).
thf(4023,plain,
! [B: $i,A: $i] :
( ( ( d0 @ ( b @ multiply ) @ ( a @ multiply ) @ ( a @ multiply ) @ ( c0 @ multiply ) )
!= ( B @ ( A @ multiply ) ) )
| ( ( a @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( B @ sk1 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[2732,67]) ).
thf(4024,plain,
( ( a @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( d0 @ ( b @ multiply ) @ ( a @ multiply ) @ ( a @ multiply ) @ sk1 ) )
= c0 ),
inference(pattern_uni,[status(thm)],[4023:[bind(A,$thf( c0 )),bind(B,$thf( d0 @ ( b @ multiply ) @ ( a @ multiply ) @ ( a @ multiply ) ))]]) ).
thf(56,plain,
( ( c0 != a0 )
| ( c != c )
| ( ( d0 @ ( d @ multiply ) )
!= ( b0 @ ( d @ multiply ) ) ) ),
inference(simp,[status(thm)],[50]) ).
thf(62,plain,
( ( c0 != a0 )
| ( ( d0 @ ( d @ multiply ) )
!= ( b0 @ ( d @ multiply ) ) ) ),
inference(simp,[status(thm)],[56]) ).
thf(898,plain,
( ( ( a0 @ ( c @ multiply ) )
!= ( d0 @ ( d @ multiply ) ) )
| ( c0 != a0 )
| ( ( b0 @ ( d @ multiply ) )
!= ( b0 @ ( d @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,62]) ).
thf(899,plain,
( ( ( a0 @ ( c @ multiply ) )
!= ( d0 @ ( d @ multiply ) ) )
| ( c0 != a0 ) ),
inference(simp,[status(thm)],[898]) ).
thf(928,plain,
( ( d0 != a0 )
| ( c != d )
| ( c0 != a0 ) ),
inference(simp,[status(thm)],[899]) ).
thf(1119,plain,
! [B: $i,A: $i] :
( ( ( a0 @ ( a @ multiply ) )
!= ( B @ ( A @ multiply ) ) )
| ( ( b0 @ ( b @ multiply ) @ ( A @ sk2 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[13,1110]) ).
thf(1120,plain,
( ( b0 @ ( b @ multiply ) @ ( a @ sk2 ) )
= a0 ),
inference(pattern_uni,[status(thm)],[1119:[bind(A,$thf( a )),bind(B,$thf( a0 ))]]) ).
thf(3436,plain,
! [A: $i] :
( ( ( a @ ( c0 @ multiply ) @ ( c0 @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) )
!= ( A @ ( d0 @ multiply ) @ ( b @ multiply ) ) )
| ( ( d0 @ ( b @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( c0 @ multiply ) @ ( A @ ( c0 @ multiply ) @ sk1 ) )
= a ) ),
inference(paramod_ordered,[status(thm)],[2728,282]) ).
thf(3437,plain,
( ( d0 @ ( b @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( c0 @ multiply ) @ ( a @ ( c0 @ multiply ) @ ( c0 @ multiply ) @ ( c0 @ multiply ) @ sk1 ) )
= a ),
inference(pattern_uni,[status(thm)],[3436:[bind(A,$thf( a @ ( c0 @ multiply ) @ ( c0 @ multiply ) ))]]) ).
thf(293,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( a0 @ multiply ) @ ( c @ multiply ) )
!= ( C @ ( B @ multiply ) ) )
| ( ( A @ ( b0 @ multiply ) @ ( d @ multiply ) @ ( C @ sk1 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[284,67]) ).
thf(294,plain,
! [A: $i] :
( ( A @ ( b0 @ multiply ) @ ( d @ multiply ) @ ( A @ ( a0 @ multiply ) @ sk1 ) )
= c ),
inference(pattern_uni,[status(thm)],[293:[bind(A,$thf( E )),bind(B,$thf( c )),bind(C,$thf( E @ ( a0 @ multiply ) ))]]) ).
thf(354,plain,
! [A: $i] :
( ( A @ ( b0 @ multiply ) @ ( d @ multiply ) @ ( A @ ( a0 @ multiply ) @ sk1 ) )
= c ),
inference(simp,[status(thm)],[294]) ).
thf(3442,plain,
! [B: $i,A: $i] :
( ( ( a @ ( c0 @ multiply ) @ ( c0 @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) )
!= ( B @ ( A @ multiply ) ) )
| ( ( d0 @ ( b @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( c0 @ multiply ) @ ( B @ sk1 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[2728,67]) ).
thf(3443,plain,
( ( d0 @ ( b @ multiply ) @ ( d0 @ multiply ) @ ( b @ multiply ) @ ( c0 @ multiply ) @ ( a @ ( c0 @ multiply ) @ ( c0 @ multiply ) @ ( d0 @ multiply ) @ sk1 ) )
= b ),
inference(pattern_uni,[status(thm)],[3442:[bind(A,$thf( b )),bind(B,$thf( a @ ( c0 @ multiply ) @ ( c0 @ multiply ) @ ( d0 @ multiply ) ))]]) ).
thf(51709,plain,
$false,
inference(e,[status(thm)],[10,3286,1112,2390,9306,2406,2623,69,1110,481,3370,25,14,1132,20,46,284,6964,9309,280,3955,2873,65,12603,1128,4316,9,53,3311,3441,3935,1131,173,13,73,360,4393,17,22,44,27,71,12,48,3376,63,18,282,2732,67,359,1130,31,3493,11,4695,2728,1133,36,146,30,19,3309,79,4024,400,928,15,62,1120,3437,354,3443]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP199-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % 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
% 0.13/0.39 % Computer : n003.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 : Fri Sep 25 14:38:55 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 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
% 0.89/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/1.18 % [INFO] Parsing done (193ms).
% 1.28/1.19 % [INFO] Running in sequential loop mode.
% 2.19/1.60 % [INFO] eprover registered as external prover.
% 2.19/1.61 % [INFO] Scanning for conjecture ...
% 2.39/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.39/1.74 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.39/1.75 % [INFO] Problem is propositional (TPTP CNF).
% 2.39/1.76 % [INFO] Type checking passed.
% 2.39/1.76 % [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 ...
% 85.41/29.88 % External prover 'e' found a proof!
% 85.41/29.88 % [INFO] Killing All external provers ...
% 85.41/29.89 % Time passed: 29350ms (effective reasoning time: 28688ms)
% 85.41/29.90 % Axioms used in derivation (4): associativity_of_multiply, nilpotency, left_cancellation, right_cancellation
% 85.41/29.90 % No. of inferences in proof: 177
% 85.41/29.90 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 29350 ms resp. 28688 ms w/o parsing
% 78.83/30.04 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 78.83/30.04 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------