TSTP Solution File: GRP198-1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP198-1 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:13:28 EDT 2023
% Result : Unsatisfiable 96.04s 17.75s
% Output : Refutation 96.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 12
% Syntax : Number of formulae : 102 ( 49 unt; 5 typ; 0 def)
% Number of atoms : 170 ( 169 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 1406 ( 105 ~; 73 |; 0 &;1228 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 296 ( 0 ^; 296 !; 0 ?; 296 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(b_type,type,
b: $i ).
thf(a_type,type,
a: $i ).
thf(sk1_type,type,
sk1: $i > $i > $i ).
thf(sk2_type,type,
sk2: $i > $i > $i ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( multiply @ A @ ( multiply @ B @ ( multiply @ B @ ( multiply @ B @ ( multiply @ A @ B ) ) ) ) )
= ( multiply @ B @ ( multiply @ B @ ( multiply @ B @ ( multiply @ B @ ( multiply @ A @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condition) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( multiply @ A @ ( multiply @ B @ ( multiply @ B @ ( multiply @ B @ ( multiply @ A @ B ) ) ) ) )
= ( multiply @ B @ ( multiply @ B @ ( multiply @ B @ ( multiply @ B @ ( multiply @ A @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( multiply @ A @ ( multiply @ B @ ( multiply @ B @ ( multiply @ B @ ( multiply @ A @ B ) ) ) ) )
= ( multiply @ B @ ( multiply @ B @ ( multiply @ B @ ( multiply @ B @ ( multiply @ A @ A ) ) ) ) ) ),
inference(lifteq,[status(thm)],[19]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ C )
= ( multiply @ A @ ( multiply @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_multiply) ).
thf(9,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ C )
= ( multiply @ A @ ( multiply @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ C )
= ( multiply @ A @ ( multiply @ B @ C ) ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(29,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ ( multiply @ A @ ( multiply @ B @ C ) ) @ F )
= ( multiply @ D @ ( multiply @ E @ F ) ) )
| ( ( multiply @ ( multiply @ A @ B ) @ C )
!= ( multiply @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[10,10]) ).
thf(30,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ C @ ( multiply @ D @ A ) ) @ B )
= ( multiply @ ( multiply @ C @ D ) @ ( multiply @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[29:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( multiply @ G @ H )),bind(E,$thf( C ))]]) ).
thf(61,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ C @ ( multiply @ D @ A ) ) @ B )
= ( multiply @ ( multiply @ C @ D ) @ ( multiply @ A @ B ) ) ),
inference(simp,[status(thm)],[30]) ).
thf(175,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( multiply @ C @ ( multiply @ ( multiply @ D @ A ) @ B ) )
= ( multiply @ C @ ( multiply @ D @ ( multiply @ A @ B ) ) ) ),
inference(rewrite,[status(thm)],[61,10]) ).
thf(182,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ F @ ( multiply @ ( multiply @ A @ ( multiply @ B @ C ) ) @ E ) )
= ( multiply @ F @ ( multiply @ G @ ( multiply @ D @ E ) ) ) )
| ( ( multiply @ ( multiply @ A @ B ) @ C )
!= ( multiply @ G @ D ) ) ),
inference(paramod_ordered,[status(thm)],[10,175]) ).
thf(183,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( multiply @ C @ ( multiply @ ( multiply @ D @ ( multiply @ E @ A ) ) @ B ) )
= ( multiply @ C @ ( multiply @ ( multiply @ D @ E ) @ ( multiply @ A @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[182:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( C )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( multiply @ H @ I ))]]) ).
thf(250,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( multiply @ C @ ( multiply @ ( multiply @ D @ ( multiply @ E @ A ) ) @ B ) )
= ( multiply @ C @ ( multiply @ ( multiply @ D @ E ) @ ( multiply @ A @ B ) ) ) ),
inference(simp,[status(thm)],[183]) ).
thf(1634,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( multiply @ C @ ( multiply @ D @ ( multiply @ ( multiply @ E @ A ) @ B ) ) )
= ( multiply @ C @ ( multiply @ D @ ( multiply @ E @ ( multiply @ A @ B ) ) ) ) ),
inference(rewrite,[status(thm)],[250,175]) ).
thf(1,negated_conjecture,
( ( multiply @ b @ ( multiply @ a @ ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ a ) ) ) ) )
!= ( multiply @ a @ ( multiply @ a @ ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ b ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
thf(6,plain,
( ( multiply @ b @ ( multiply @ a @ ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ a ) ) ) ) )
!= ( multiply @ a @ ( multiply @ a @ ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ b ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,plain,
( ( multiply @ b @ ( multiply @ a @ ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ a ) ) ) ) )
!= ( multiply @ a @ ( multiply @ a @ ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ b ) ) ) ) ) ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( multiply @ a @ ( multiply @ a @ ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ b ) ) ) ) )
!= ( multiply @ b @ ( multiply @ a @ ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ a ) ) ) ) ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiply @ A @ ( multiply @ B @ C ) )
!= ( multiply @ b @ ( multiply @ a @ ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ a ) ) ) ) ) )
| ( ( multiply @ ( multiply @ A @ B ) @ C )
!= ( multiply @ a @ ( multiply @ a @ ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ b ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[10,8]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( A != b )
| ( ( multiply @ B @ C )
!= ( multiply @ a @ ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ a ) ) ) ) )
| ( ( multiply @ A @ B )
!= a )
| ( C
!= ( multiply @ a @ ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ b ) ) ) ) ) ),
inference(simp,[status(thm)],[24]) ).
thf(55,plain,
! [A: $i] :
( ( ( multiply @ A @ ( multiply @ a @ ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ b ) ) ) ) )
!= ( multiply @ a @ ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ a ) ) ) ) )
| ( ( multiply @ b @ A )
!= a ) ),
inference(simp,[status(thm)],[41]) ).
thf(919,plain,
! [A: $i] :
( ( A != a )
| ( ( multiply @ a @ ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ b ) ) ) )
!= ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ a ) ) ) )
| ( ( multiply @ b @ A )
!= a ) ),
inference(simp,[status(thm)],[55]) ).
thf(1120,plain,
( ( ( multiply @ a @ ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ b ) ) ) )
!= ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ a ) ) ) )
| ( ( multiply @ b @ a )
!= a ) ),
inference(simp,[status(thm)],[919]) ).
thf(1201,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiply @ A @ ( multiply @ B @ C ) )
!= ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ a ) ) ) )
| ( ( multiply @ b @ a )
!= a )
| ( ( multiply @ ( multiply @ A @ B ) @ C )
!= ( multiply @ a @ ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ b ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[10,1120]) ).
thf(1217,plain,
! [C: $i,B: $i,A: $i] :
( ( A != b )
| ( ( multiply @ B @ C )
!= ( multiply @ b @ ( multiply @ b @ a ) ) )
| ( ( multiply @ b @ a )
!= a )
| ( ( multiply @ A @ B )
!= a )
| ( C
!= ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ b ) ) ) ) ),
inference(simp,[status(thm)],[1201]) ).
thf(1276,plain,
! [A: $i] :
( ( ( multiply @ A @ ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ b ) ) ) )
!= ( multiply @ b @ ( multiply @ b @ a ) ) )
| ( ( multiply @ b @ a )
!= a )
| ( ( multiply @ b @ A )
!= a ) ),
inference(simp,[status(thm)],[1217]) ).
thf(2120,plain,
! [A: $i] :
( ( A != b )
| ( ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ b ) ) )
!= ( multiply @ b @ a ) )
| ( ( multiply @ b @ a )
!= a )
| ( ( multiply @ b @ A )
!= a ) ),
inference(simp,[status(thm)],[1276]) ).
thf(2303,plain,
( ( ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ b ) ) )
!= ( multiply @ b @ a ) )
| ( ( multiply @ b @ a )
!= a )
| ( ( multiply @ b @ b )
!= a ) ),
inference(simp,[status(thm)],[2120]) ).
thf(2726,plain,
( ( b != b )
| ( ( multiply @ b @ ( multiply @ b @ b ) )
!= a )
| ( ( multiply @ b @ a )
!= a )
| ( ( multiply @ b @ b )
!= a ) ),
inference(simp,[status(thm)],[2303]) ).
thf(2878,plain,
( ( ( multiply @ b @ ( multiply @ b @ b ) )
!= a )
| ( ( multiply @ b @ a )
!= a )
| ( ( multiply @ b @ b )
!= a ) ),
inference(simp,[status(thm)],[2726]) ).
thf(2971,plain,
( ( ( multiply @ b @ a )
!= a )
| ( ( multiply @ b @ b )
!= a )
| ( ( multiply @ b @ ( multiply @ b @ b ) )
!= ( multiply @ b @ a ) )
| ( a != a ) ),
inference(eqfactor_ordered,[status(thm)],[2878]) ).
thf(2983,plain,
( ( ( multiply @ b @ a )
!= a )
| ( ( multiply @ b @ b )
!= a )
| ( b != b )
| ( ( multiply @ b @ b )
!= a ) ),
inference(simp,[status(thm)],[2971]) ).
thf(3010,plain,
( ( ( multiply @ b @ a )
!= a )
| ( ( multiply @ b @ b )
!= a ) ),
inference(simp,[status(thm)],[2983]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( multiply @ A @ B )
!= ( multiply @ A @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_cancellation) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiply @ A @ B )
!= ( multiply @ A @ C ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiply @ A @ B )
!= ( multiply @ A @ C ) )
| ( B = C ) ),
inference(cnf,[status(esa)],[15]) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiply @ A @ B )
!= ( multiply @ A @ C ) )
| ( B = C ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( sk2 @ A @ ( multiply @ A @ B ) )
= B ),
introduced(tautology,[new_symbols(inverse(multiply),[sk2])]) ).
thf(22,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( sk2 @ D @ ( multiply @ A @ ( multiply @ B @ C ) ) )
= E )
| ( ( multiply @ ( multiply @ A @ B ) @ C )
!= ( multiply @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[10,18]) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( sk2 @ ( multiply @ B @ C ) @ ( multiply @ B @ ( multiply @ C @ A ) ) )
= A ),
inference(pattern_uni,[status(thm)],[22:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( multiply @ F @ G )),bind(E,$thf( C ))]]) ).
thf(60,plain,
! [C: $i,B: $i,A: $i] :
( ( sk2 @ ( multiply @ B @ C ) @ ( multiply @ B @ ( multiply @ C @ A ) ) )
= A ),
inference(simp,[status(thm)],[23]) ).
thf(160,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( multiply @ E @ F ) @ ( multiply @ E @ ( multiply @ A @ ( multiply @ B @ C ) ) ) )
= D )
| ( ( multiply @ ( multiply @ A @ B ) @ C )
!= ( multiply @ F @ D ) ) ),
inference(paramod_ordered,[status(thm)],[10,60]) ).
thf(161,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( sk2 @ ( multiply @ B @ ( multiply @ C @ D ) ) @ ( multiply @ B @ ( multiply @ C @ ( multiply @ D @ A ) ) ) )
= A ),
inference(pattern_uni,[status(thm)],[160:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( C )),bind(E,$thf( E )),bind(F,$thf( multiply @ G @ H ))]]) ).
thf(170,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( sk2 @ ( multiply @ B @ ( multiply @ C @ D ) ) @ ( multiply @ B @ ( multiply @ C @ ( multiply @ D @ A ) ) ) )
= A ),
inference(simp,[status(thm)],[161]) ).
thf(301,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( multiply @ E @ ( multiply @ F @ G ) ) @ ( multiply @ A @ ( multiply @ B @ C ) ) )
= D )
| ( ( multiply @ ( multiply @ A @ B ) @ C )
!= ( multiply @ E @ ( multiply @ F @ ( multiply @ G @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[10,170]) ).
thf(302,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( sk2 @ ( multiply @ ( multiply @ A @ B ) @ ( multiply @ C @ D ) ) @ ( multiply @ A @ ( multiply @ B @ ( multiply @ C @ ( multiply @ D @ E ) ) ) ) )
= E ),
inference(pattern_uni,[status(thm)],[301:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( multiply @ J @ ( multiply @ L @ M ) )),bind(D,$thf( M )),bind(E,$thf( multiply @ H @ I )),bind(F,$thf( J )),bind(G,$thf( L ))]]) ).
thf(333,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( sk2 @ ( multiply @ ( multiply @ A @ B ) @ ( multiply @ C @ D ) ) @ ( multiply @ A @ ( multiply @ B @ ( multiply @ C @ ( multiply @ D @ E ) ) ) ) )
= E ),
inference(simp,[status(thm)],[302]) ).
thf(3298,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( sk2 @ ( multiply @ A @ ( multiply @ B @ ( multiply @ C @ D ) ) ) @ ( multiply @ A @ ( multiply @ B @ ( multiply @ C @ ( multiply @ D @ E ) ) ) ) )
= E ),
inference(rewrite,[status(thm)],[333,10]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( multiply @ A @ B )
!= ( multiply @ C @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_cancellation) ).
thf(11,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiply @ A @ B )
!= ( multiply @ C @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiply @ A @ B )
!= ( multiply @ C @ B ) )
| ( A = C ) ),
inference(cnf,[status(esa)],[11]) ).
thf(13,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiply @ A @ B )
!= ( multiply @ C @ B ) )
| ( A = C ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(14,plain,
! [B: $i,A: $i] :
( ( sk1 @ A @ ( multiply @ B @ A ) )
= B ),
introduced(tautology,[new_symbols(inverse(multiply),[sk1])]) ).
thf(31,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( sk1 @ D @ ( multiply @ A @ ( multiply @ B @ C ) ) )
= E )
| ( ( multiply @ ( multiply @ A @ B ) @ C )
!= ( multiply @ E @ D ) ) ),
inference(paramod_ordered,[status(thm)],[10,14]) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( sk1 @ A @ ( multiply @ B @ ( multiply @ C @ A ) ) )
= ( multiply @ B @ C ) ),
inference(pattern_uni,[status(thm)],[31:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( C )),bind(E,$thf( multiply @ F @ G ))]]) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ( sk1 @ A @ ( multiply @ B @ ( multiply @ C @ A ) ) )
= ( multiply @ B @ C ) ),
inference(simp,[status(thm)],[32]) ).
thf(115,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( sk1 @ D @ ( multiply @ E @ ( multiply @ A @ ( multiply @ B @ C ) ) ) )
= ( multiply @ E @ F ) )
| ( ( multiply @ ( multiply @ A @ B ) @ C )
!= ( multiply @ F @ D ) ) ),
inference(paramod_ordered,[status(thm)],[10,48]) ).
thf(116,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( sk1 @ A @ ( multiply @ B @ ( multiply @ C @ ( multiply @ D @ A ) ) ) )
= ( multiply @ B @ ( multiply @ C @ D ) ) ),
inference(pattern_uni,[status(thm)],[115:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( C )),bind(E,$thf( E )),bind(F,$thf( multiply @ G @ H ))]]) ).
thf(123,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( sk1 @ A @ ( multiply @ B @ ( multiply @ C @ ( multiply @ D @ A ) ) ) )
= ( multiply @ B @ ( multiply @ C @ D ) ) ),
inference(simp,[status(thm)],[116]) ).
thf(164,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( multiply @ E @ F ) @ ( multiply @ A @ ( multiply @ B @ C ) ) )
= D )
| ( ( multiply @ ( multiply @ A @ B ) @ C )
!= ( multiply @ E @ ( multiply @ F @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[10,60]) ).
thf(165,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( sk2 @ ( multiply @ ( multiply @ A @ B ) @ C ) @ ( multiply @ A @ ( multiply @ B @ ( multiply @ C @ D ) ) ) )
= D ),
inference(pattern_uni,[status(thm)],[164:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( multiply @ I @ J )),bind(D,$thf( J )),bind(E,$thf( multiply @ G @ H )),bind(F,$thf( I ))]]) ).
thf(172,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( sk2 @ ( multiply @ ( multiply @ A @ B ) @ C ) @ ( multiply @ A @ ( multiply @ B @ ( multiply @ C @ D ) ) ) )
= D ),
inference(simp,[status(thm)],[165]) ).
thf(384,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( sk2 @ ( multiply @ A @ ( multiply @ B @ C ) ) @ ( multiply @ A @ ( multiply @ B @ ( multiply @ C @ D ) ) ) )
= D ),
inference(rewrite,[status(thm)],[172,10]) ).
thf(178,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ ( multiply @ C @ ( multiply @ D @ ( multiply @ A @ B ) ) ) @ G )
= ( multiply @ E @ ( multiply @ F @ G ) ) )
| ( ( multiply @ C @ ( multiply @ ( multiply @ D @ A ) @ B ) )
!= ( multiply @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[175,10]) ).
thf(179,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ ( multiply @ D @ ( multiply @ E @ C ) ) ) @ B )
= ( multiply @ A @ ( multiply @ ( multiply @ ( multiply @ D @ E ) @ C ) @ B ) ) ),
inference(pattern_uni,[status(thm)],[178:[bind(A,$thf( K )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( J )),bind(E,$thf( C )),bind(F,$thf( multiply @ ( multiply @ J @ K ) @ I )),bind(G,$thf( G ))]]) ).
thf(248,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ ( multiply @ D @ ( multiply @ E @ C ) ) ) @ B )
= ( multiply @ A @ ( multiply @ ( multiply @ ( multiply @ D @ E ) @ C ) @ B ) ) ),
inference(simp,[status(thm)],[179]) ).
thf(1310,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( multiply @ ( multiply @ D @ ( multiply @ E @ C ) ) @ B ) )
= ( multiply @ A @ ( multiply @ ( multiply @ D @ E ) @ ( multiply @ C @ B ) ) ) ),
inference(rewrite,[status(thm)],[248,10,175]) ).
thf(186,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( sk1 @ E @ ( multiply @ C @ ( multiply @ D @ ( multiply @ A @ B ) ) ) )
= F )
| ( ( multiply @ C @ ( multiply @ ( multiply @ D @ A ) @ B ) )
!= ( multiply @ F @ E ) ) ),
inference(paramod_ordered,[status(thm)],[175,14]) ).
thf(187,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( sk1 @ ( multiply @ ( multiply @ C @ D ) @ B ) @ ( multiply @ A @ ( multiply @ C @ ( multiply @ D @ B ) ) ) )
= A ),
inference(pattern_uni,[status(thm)],[186:[bind(A,$thf( J )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( I )),bind(E,$thf( multiply @ ( multiply @ I @ J ) @ H )),bind(F,$thf( C ))]]) ).
thf(251,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( sk1 @ ( multiply @ ( multiply @ C @ D ) @ B ) @ ( multiply @ A @ ( multiply @ C @ ( multiply @ D @ B ) ) ) )
= A ),
inference(simp,[status(thm)],[187]) ).
thf(747,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( sk1 @ ( multiply @ C @ ( multiply @ D @ B ) ) @ ( multiply @ A @ ( multiply @ C @ ( multiply @ D @ B ) ) ) )
= A ),
inference(rewrite,[status(thm)],[251,10]) ).
thf(3039,plain,
( ( ( multiply @ b @ b )
!= a )
| ( ( multiply @ b @ a )
!= ( multiply @ b @ b ) )
| ( a != a ) ),
inference(eqfactor_ordered,[status(thm)],[3010]) ).
thf(3046,plain,
( ( ( multiply @ b @ b )
!= a )
| ( ( multiply @ b @ a )
!= ( multiply @ b @ b ) ) ),
inference(simp,[status(thm)],[3039]) ).
thf(190,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( multiply @ C @ ( multiply @ D @ ( multiply @ A @ B ) ) ) @ ( multiply @ F @ ( multiply @ G @ E ) ) )
= E )
| ( ( multiply @ C @ ( multiply @ ( multiply @ D @ A ) @ B ) )
!= ( multiply @ F @ G ) ) ),
inference(paramod_ordered,[status(thm)],[175,60]) ).
thf(191,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( sk2 @ ( multiply @ A @ ( multiply @ D @ ( multiply @ E @ C ) ) ) @ ( multiply @ A @ ( multiply @ ( multiply @ ( multiply @ D @ E ) @ C ) @ B ) ) )
= B ),
inference(pattern_uni,[status(thm)],[190:[bind(A,$thf( K )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( J )),bind(E,$thf( E )),bind(F,$thf( C )),bind(G,$thf( multiply @ ( multiply @ J @ K ) @ I ))]]) ).
thf(253,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( sk2 @ ( multiply @ A @ ( multiply @ D @ ( multiply @ E @ C ) ) ) @ ( multiply @ A @ ( multiply @ ( multiply @ ( multiply @ D @ E ) @ C ) @ B ) ) )
= B ),
inference(simp,[status(thm)],[191]) ).
thf(1979,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( sk2 @ ( multiply @ A @ ( multiply @ D @ ( multiply @ E @ C ) ) ) @ ( multiply @ A @ ( multiply @ ( multiply @ D @ E ) @ ( multiply @ C @ B ) ) ) )
= B ),
inference(rewrite,[status(thm)],[253,175]) ).
thf(2175,plain,
! [A: $i] :
( ( ( multiply @ A @ ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ b ) ) ) )
!= ( multiply @ b @ ( multiply @ b @ a ) ) )
| ( ( multiply @ b @ a )
!= a )
| ( ( multiply @ b @ A )
!= ( multiply @ b @ a ) )
| ( a != a ) ),
inference(eqfactor_ordered,[status(thm)],[1276]) ).
thf(2275,plain,
( ( ( multiply @ a @ ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ b ) ) ) )
!= ( multiply @ b @ ( multiply @ b @ a ) ) )
| ( ( multiply @ b @ a )
!= a ) ),
inference(pattern_uni,[status(thm)],[2175:[bind(A,$thf( a ))]]) ).
thf(207,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( sk1 @ E @ ( multiply @ F @ ( multiply @ C @ ( multiply @ D @ ( multiply @ A @ B ) ) ) ) )
= ( multiply @ F @ G ) )
| ( ( multiply @ C @ ( multiply @ ( multiply @ D @ A ) @ B ) )
!= ( multiply @ G @ E ) ) ),
inference(paramod_ordered,[status(thm)],[175,48]) ).
thf(208,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( sk1 @ ( multiply @ ( multiply @ D @ E ) @ C ) @ ( multiply @ B @ ( multiply @ A @ ( multiply @ D @ ( multiply @ E @ C ) ) ) ) )
= ( multiply @ B @ A ) ),
inference(pattern_uni,[status(thm)],[207:[bind(A,$thf( K )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( J )),bind(E,$thf( multiply @ ( multiply @ J @ K ) @ I )),bind(F,$thf( F )),bind(G,$thf( C ))]]) ).
thf(233,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( sk1 @ ( multiply @ ( multiply @ D @ E ) @ C ) @ ( multiply @ B @ ( multiply @ A @ ( multiply @ D @ ( multiply @ E @ C ) ) ) ) )
= ( multiply @ B @ A ) ),
inference(simp,[status(thm)],[208]) ).
thf(824,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( sk1 @ ( multiply @ D @ ( multiply @ E @ C ) ) @ ( multiply @ B @ ( multiply @ A @ ( multiply @ D @ ( multiply @ E @ C ) ) ) ) )
= ( multiply @ B @ A ) ),
inference(rewrite,[status(thm)],[233,10]) ).
thf(256,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( sk1 @ D @ ( multiply @ E @ ( multiply @ A @ ( multiply @ B @ C ) ) ) )
= ( multiply @ E @ ( multiply @ F @ G ) ) )
| ( ( multiply @ ( multiply @ A @ B ) @ C )
!= ( multiply @ F @ ( multiply @ G @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[10,123]) ).
thf(257,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( sk1 @ E @ ( multiply @ A @ ( multiply @ B @ ( multiply @ C @ ( multiply @ D @ E ) ) ) ) )
= ( multiply @ A @ ( multiply @ ( multiply @ B @ C ) @ D ) ) ),
inference(pattern_uni,[status(thm)],[256:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( multiply @ J @ K )),bind(D,$thf( K )),bind(E,$thf( E )),bind(F,$thf( multiply @ H @ I )),bind(G,$thf( J ))]]) ).
thf(275,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( sk1 @ E @ ( multiply @ A @ ( multiply @ B @ ( multiply @ C @ ( multiply @ D @ E ) ) ) ) )
= ( multiply @ A @ ( multiply @ ( multiply @ B @ C ) @ D ) ) ),
inference(simp,[status(thm)],[257]) ).
thf(2623,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( sk1 @ E @ ( multiply @ A @ ( multiply @ B @ ( multiply @ C @ ( multiply @ D @ E ) ) ) ) )
= ( multiply @ A @ ( multiply @ B @ ( multiply @ C @ D ) ) ) ),
inference(rewrite,[status(thm)],[275,175]) ).
thf(21,plain,
( ( a != b )
| ( ( multiply @ a @ ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ a ) ) ) )
!= ( multiply @ a @ ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ b ) ) ) ) ) ),
inference(simp,[status(thm)],[8]) ).
thf(62,plain,
( ( a != b )
| ( a != a )
| ( ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ a ) ) )
!= ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ b ) ) ) ) ),
inference(simp,[status(thm)],[21]) ).
thf(91,plain,
( ( a != b )
| ( ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ a ) ) )
!= ( multiply @ b @ ( multiply @ b @ ( multiply @ b @ b ) ) ) ) ),
inference(simp,[status(thm)],[62]) ).
thf(92,plain,
( ( a != b )
| ( b != b )
| ( ( multiply @ b @ ( multiply @ b @ a ) )
!= ( multiply @ b @ ( multiply @ b @ b ) ) ) ),
inference(simp,[status(thm)],[91]) ).
thf(114,plain,
( ( a != b )
| ( ( multiply @ b @ ( multiply @ b @ a ) )
!= ( multiply @ b @ ( multiply @ b @ b ) ) ) ),
inference(simp,[status(thm)],[92]) ).
thf(127,plain,
( ( a != b )
| ( b != b )
| ( ( multiply @ b @ a )
!= ( multiply @ b @ b ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(142,plain,
( ( a != b )
| ( ( multiply @ b @ a )
!= ( multiply @ b @ b ) ) ),
inference(simp,[status(thm)],[127]) ).
thf(143,plain,
( ( a != b )
| ( b != b )
| ( a != b ) ),
inference(simp,[status(thm)],[142]) ).
thf(151,plain,
a != b,
inference(simp,[status(thm)],[143]) ).
thf(47514,plain,
$false,
inference(e,[status(thm)],[20,1634,9,3010,3298,123,10,384,1310,747,14,3046,6,60,13,1979,2275,824,17,48,18,11,175,1276,55,8,2623,151,19,15,1120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP198-1 : TPTP v8.1.2. Released v2.2.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n003.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 19 02:07:47 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.87/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.17/0.90 % [INFO] Parsing done (107ms).
% 1.17/0.91 % [INFO] Running in sequential loop mode.
% 1.56/1.10 % [INFO] eprover registered as external prover.
% 1.56/1.10 % [INFO] cvc4 registered as external prover.
% 1.56/1.10 % [INFO] Scanning for conjecture ...
% 1.56/1.15 % [INFO] Found a conjecture and 4 axioms. Running axiom selection ...
% 1.56/1.17 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.56/1.17 % [INFO] Problem is propositional (TPTP CNF).
% 1.85/1.18 % [INFO] Type checking passed.
% 1.85/1.18 % [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 ...
% 96.04/17.75 % External prover 'e' found a proof!
% 96.04/17.75 % [INFO] Killing All external provers ...
% 96.04/17.75 % Time passed: 17272ms (effective reasoning time: 16835ms)
% 96.04/17.75 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 96.04/17.75 % Axioms used in derivation (4): condition, associativity_of_multiply, left_cancellation, right_cancellation
% 96.04/17.75 % No. of inferences in proof: 97
% 96.04/17.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 17272 ms resp. 16835 ms w/o parsing
% 96.04/17.79 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 96.04/17.80 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------