TSTP Solution File: GRP524-1 by Leo-III-SAT---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : GRP524-1 : TPTP v8.2.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n013.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 : Mon May 20 21:04:13 EDT 2024
% Result : Unsatisfiable 186.44s 31.04s
% Output : Refutation 186.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 9
% Syntax : Number of formulae : 95 ( 64 unt; 5 typ; 0 def)
% Number of atoms : 116 ( 115 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 760 ( 40 ~; 26 |; 0 &; 694 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 238 ( 0 ^ 238 !; 0 ?; 238 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(divide_type,type,
divide: $i > $i > $i ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( inverse @ A )
= ( divide @ ( divide @ B @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
thf(12,plain,
! [B: $i,A: $i] :
( ( inverse @ A )
= ( divide @ ( divide @ B @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,plain,
! [B: $i,A: $i] :
( ( divide @ ( divide @ B @ B ) @ A )
= ( inverse @ A ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( divide @ A @ ( divide @ B @ ( divide @ C @ ( divide @ A @ B ) ) ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
thf(8,plain,
! [C: $i,B: $i,A: $i] :
( ( divide @ A @ ( divide @ B @ ( divide @ C @ ( divide @ A @ B ) ) ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
! [C: $i,B: $i,A: $i] :
( ( divide @ A @ ( divide @ B @ ( divide @ C @ ( divide @ A @ B ) ) ) )
= C ),
inference(lifteq,[status(thm)],[8]) ).
thf(121,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( divide @ C @ ( inverse @ A ) )
= E )
| ( ( divide @ ( divide @ B @ B ) @ A )
!= ( divide @ D @ ( divide @ E @ ( divide @ C @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,9]) ).
thf(122,plain,
! [C: $i,B: $i,A: $i] :
( ( divide @ B @ ( inverse @ ( divide @ A @ ( divide @ B @ ( divide @ C @ C ) ) ) ) )
= A ),
inference(pattern_uni,[status(thm)],[121:[bind(A,$thf( divide @ H @ ( divide @ J @ ( divide @ M @ M ) ) )),bind(B,$thf( M )),bind(C,$thf( J )),bind(D,$thf( divide @ M @ M )),bind(E,$thf( H ))]]) ).
thf(178,plain,
! [C: $i,B: $i,A: $i] :
( ( divide @ B @ ( inverse @ ( divide @ A @ ( divide @ B @ ( divide @ C @ C ) ) ) ) )
= A ),
inference(simp,[status(thm)],[122]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ B )
= ( divide @ A @ ( divide @ ( divide @ C @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
thf(10,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ B )
= ( divide @ A @ ( divide @ ( divide @ C @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,plain,
! [C: $i,B: $i,A: $i] :
( ( divide @ A @ ( divide @ ( divide @ C @ C ) @ B ) )
= ( multiply @ A @ B ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(721,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( divide @ C @ ( inverse @ A ) )
= ( multiply @ C @ D ) )
| ( ( divide @ ( divide @ B @ B ) @ A )
!= ( divide @ ( divide @ E @ E ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[13,11]) ).
thf(722,plain,
! [B: $i,A: $i] :
( ( divide @ B @ ( inverse @ A ) )
= ( multiply @ B @ A ) ),
inference(pattern_uni,[status(thm)],[721:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(815,plain,
! [B: $i,A: $i] :
( ( divide @ B @ ( inverse @ A ) )
= ( multiply @ B @ A ) ),
inference(simp,[status(thm)],[722]) ).
thf(42832,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ B @ ( divide @ A @ ( divide @ B @ ( divide @ C @ C ) ) ) )
= A ),
inference(rewrite,[status(thm)],[178,815]) ).
thf(863,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ B @ A )
= ( inverse @ C ) )
| ( ( divide @ B @ ( inverse @ A ) )
!= ( divide @ ( divide @ D @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[815,13]) ).
thf(864,plain,
! [B: $i,A: $i] :
( ( multiply @ ( divide @ A @ A ) @ B )
= ( inverse @ ( inverse @ B ) ) ),
inference(pattern_uni,[status(thm)],[863:[bind(A,$thf( G )),bind(B,$thf( divide @ F @ F )),bind(C,$thf( inverse @ G )),bind(D,$thf( F ))]]) ).
thf(948,plain,
! [B: $i,A: $i] :
( ( multiply @ ( divide @ A @ A ) @ B )
= ( inverse @ ( inverse @ B ) ) ),
inference(simp,[status(thm)],[864]) ).
thf(16,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( divide @ ( inverse @ A ) @ C )
= ( inverse @ C ) )
| ( ( divide @ ( divide @ B @ B ) @ A )
!= ( divide @ D @ D ) ) ),
inference(paramod_ordered,[status(thm)],[13,13]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( divide @ ( inverse @ ( divide @ B @ B ) ) @ A )
= ( inverse @ A ) ),
inference(pattern_uni,[status(thm)],[16:[bind(A,$thf( divide @ H @ H )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( divide @ H @ H ))]]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( divide @ ( inverse @ ( divide @ B @ B ) ) @ A )
= ( inverse @ A ) ),
inference(simp,[status(thm)],[17]) ).
thf(128,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( inverse @ D ) )
| ( ( divide @ A @ ( divide @ B @ ( divide @ C @ ( divide @ A @ B ) ) ) )
!= ( divide @ ( inverse @ ( divide @ E @ E ) ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[9,18]) ).
thf(129,plain,
! [C: $i,B: $i,A: $i] :
( ( inverse @ ( divide @ B @ ( divide @ A @ ( divide @ ( inverse @ ( divide @ C @ C ) ) @ B ) ) ) )
= A ),
inference(pattern_uni,[status(thm)],[128:[bind(A,$thf( inverse @ ( divide @ Q @ Q ) )),bind(B,$thf( N )),bind(C,$thf( K )),bind(D,$thf( divide @ N @ ( divide @ K @ ( divide @ ( inverse @ ( divide @ Q @ Q ) ) @ N ) ) )),bind(E,$thf( Q ))]]) ).
thf(154,plain,
! [C: $i,B: $i,A: $i] :
( ( inverse @ ( divide @ B @ ( divide @ A @ ( divide @ ( inverse @ ( divide @ C @ C ) ) @ B ) ) ) )
= A ),
inference(simp,[status(thm)],[129]) ).
thf(3077,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( inverse @ ( divide @ D @ ( divide @ C @ ( inverse @ A ) ) ) )
= C )
| ( ( divide @ ( inverse @ ( divide @ B @ B ) ) @ A )
!= ( divide @ ( inverse @ ( divide @ E @ E ) ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[18,154]) ).
thf(3078,plain,
! [B: $i,A: $i] :
( ( inverse @ ( divide @ A @ ( divide @ B @ ( inverse @ A ) ) ) )
= B ),
inference(pattern_uni,[status(thm)],[3077:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(3287,plain,
! [B: $i,A: $i] :
( ( inverse @ ( divide @ A @ ( divide @ B @ ( inverse @ A ) ) ) )
= B ),
inference(simp,[status(thm)],[3078]) ).
thf(3371,plain,
! [B: $i,A: $i] :
( ( inverse @ ( divide @ A @ ( multiply @ B @ A ) ) )
= B ),
inference(rewrite,[status(thm)],[3287,815]) ).
thf(3419,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( inverse @ ( divide @ C @ ( inverse @ ( inverse @ B ) ) ) )
= D )
| ( ( multiply @ ( divide @ A @ A ) @ B )
!= ( multiply @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[948,3371]) ).
thf(3420,plain,
! [B: $i,A: $i] :
( ( inverse @ ( divide @ A @ ( inverse @ ( inverse @ A ) ) ) )
= ( divide @ B @ B ) ),
inference(pattern_uni,[status(thm)],[3419:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( divide @ F @ F ))]]) ).
thf(3589,plain,
! [B: $i,A: $i] :
( ( inverse @ ( divide @ A @ ( inverse @ ( inverse @ A ) ) ) )
= ( divide @ B @ B ) ),
inference(simp,[status(thm)],[3420]) ).
thf(4504,plain,
! [B: $i,A: $i] :
( ( inverse @ ( multiply @ A @ ( inverse @ A ) ) )
= ( divide @ B @ B ) ),
inference(rewrite,[status(thm)],[3589,815]) ).
thf(3402,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( inverse @ ( inverse @ A ) )
= D )
| ( ( divide @ ( inverse @ ( divide @ B @ B ) ) @ A )
!= ( divide @ C @ ( multiply @ D @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,3371]) ).
thf(3403,plain,
! [B: $i,A: $i] :
( ( inverse @ ( inverse @ ( multiply @ A @ ( inverse @ ( divide @ B @ B ) ) ) ) )
= A ),
inference(pattern_uni,[status(thm)],[3402:[bind(A,$thf( multiply @ H @ ( inverse @ ( divide @ L @ L ) ) )),bind(B,$thf( L )),bind(C,$thf( inverse @ ( divide @ L @ L ) )),bind(D,$thf( H ))]]) ).
thf(3581,plain,
! [B: $i,A: $i] :
( ( inverse @ ( inverse @ ( multiply @ A @ ( inverse @ ( divide @ B @ B ) ) ) ) )
= A ),
inference(simp,[status(thm)],[3403]) ).
thf(4506,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( inverse @ ( divide @ B @ B ) )
= C )
| ( ( inverse @ ( multiply @ A @ ( inverse @ A ) ) )
!= ( inverse @ ( multiply @ C @ ( inverse @ ( divide @ D @ D ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4504,3581]) ).
thf(4507,plain,
! [B: $i,A: $i] :
( ( inverse @ ( divide @ A @ A ) )
= ( divide @ B @ B ) ),
inference(pattern_uni,[status(thm)],[4506:[bind(A,$thf( divide @ F @ F )),bind(B,$thf( B )),bind(C,$thf( divide @ F @ F )),bind(D,$thf( F ))]]) ).
thf(4891,plain,
! [B: $i,A: $i] :
( ( inverse @ ( divide @ A @ A ) )
= ( divide @ B @ B ) ),
inference(simp,[status(thm)],[4507]) ).
thf(5698,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( inverse @ ( divide @ A @ A ) )
= ( multiply @ D @ C ) )
| ( ( divide @ B @ B )
!= ( divide @ D @ ( inverse @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[4891,815]) ).
thf(5699,plain,
! [B: $i,A: $i] :
( ( inverse @ ( divide @ A @ A ) )
= ( multiply @ ( inverse @ B ) @ B ) ),
inference(pattern_uni,[status(thm)],[5698:[bind(A,$thf( A )),bind(B,$thf( inverse @ E )),bind(C,$thf( E )),bind(D,$thf( inverse @ E ))]]) ).
thf(5974,plain,
! [B: $i,A: $i] :
( ( inverse @ ( divide @ A @ A ) )
= ( multiply @ ( inverse @ B ) @ B ) ),
inference(simp,[status(thm)],[5699]) ).
thf(10000,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( divide @ B @ B )
= ( multiply @ ( inverse @ D ) @ D ) )
| ( ( inverse @ ( divide @ A @ A ) )
!= ( inverse @ ( divide @ C @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[4891,5974]) ).
thf(10001,plain,
! [B: $i,A: $i] :
( ( divide @ A @ A )
= ( multiply @ ( inverse @ B ) @ B ) ),
inference(pattern_uni,[status(thm)],[10000:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(10466,plain,
! [B: $i,A: $i] :
( ( divide @ A @ A )
= ( multiply @ ( inverse @ B ) @ B ) ),
inference(simp,[status(thm)],[10001]) ).
thf(9998,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ ( inverse @ B ) @ B )
= ( divide @ D @ D ) )
| ( ( inverse @ ( divide @ A @ A ) )
!= ( inverse @ ( divide @ C @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[5974,4891]) ).
thf(9999,plain,
! [B: $i,A: $i] :
( ( multiply @ ( inverse @ A ) @ A )
= ( divide @ B @ B ) ),
inference(pattern_uni,[status(thm)],[9998:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(10465,plain,
! [B: $i,A: $i] :
( ( multiply @ ( inverse @ A ) @ A )
= ( divide @ B @ B ) ),
inference(simp,[status(thm)],[9999]) ).
thf(11279,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( divide @ A @ A )
= ( divide @ D @ D ) )
| ( ( multiply @ ( inverse @ B ) @ B )
!= ( multiply @ ( inverse @ C ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[10466,10465]) ).
thf(11280,plain,
! [B: $i,A: $i] :
( ( divide @ A @ A )
= ( divide @ B @ B ) ),
inference(pattern_uni,[status(thm)],[11279:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(11489,plain,
! [B: $i,A: $i] :
( ( divide @ A @ A )
= ( divide @ B @ B ) ),
inference(simp,[status(thm)],[11280]) ).
thf(114,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( divide @ D @ ( divide @ E @ C ) )
= F )
| ( ( divide @ A @ ( divide @ B @ ( divide @ C @ ( divide @ A @ B ) ) ) )
!= ( divide @ F @ ( divide @ D @ E ) ) ) ),
inference(paramod_ordered,[status(thm)],[9,9]) ).
thf(115,plain,
! [C: $i,B: $i,A: $i] :
( ( divide @ C @ ( divide @ ( divide @ A @ ( divide @ B @ C ) ) @ A ) )
= B ),
inference(pattern_uni,[status(thm)],[114:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( G )),bind(D,$thf( J )),bind(E,$thf( divide @ G @ ( divide @ I @ J ) )),bind(F,$thf( I ))]]) ).
thf(175,plain,
! [C: $i,B: $i,A: $i] :
( ( divide @ C @ ( divide @ ( divide @ A @ ( divide @ B @ C ) ) @ A ) )
= B ),
inference(simp,[status(thm)],[115]) ).
thf(38664,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( multiply @ D @ E ) )
| ( ( divide @ C @ ( divide @ ( divide @ A @ ( divide @ B @ C ) ) @ A ) )
!= ( divide @ D @ ( divide @ ( divide @ F @ F ) @ E ) ) ) ),
inference(paramod_ordered,[status(thm)],[175,11]) ).
thf(38665,plain,
! [B: $i,A: $i] :
( ( multiply @ B @ ( divide @ A @ B ) )
= A ),
inference(pattern_uni,[status(thm)],[38664:[bind(A,$thf( divide @ I @ J )),bind(B,$thf( I )),bind(C,$thf( J )),bind(D,$thf( J )),bind(E,$thf( divide @ I @ J )),bind(F,$thf( divide @ I @ J ))]]) ).
thf(39109,plain,
! [B: $i,A: $i] :
( ( multiply @ B @ ( divide @ A @ B ) )
= A ),
inference(simp,[status(thm)],[38665]) ).
thf(39523,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ D @ ( divide @ B @ B ) )
= C )
| ( ( divide @ A @ A )
!= ( divide @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[11489,39109]) ).
thf(39524,plain,
! [B: $i,A: $i] :
( ( multiply @ A @ ( divide @ B @ B ) )
= A ),
inference(pattern_uni,[status(thm)],[39523:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(42885,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( multiply @ B @ ( divide @ A @ ( divide @ B @ ( divide @ C @ C ) ) ) )
!= ( multiply @ D @ ( divide @ E @ E ) ) ) ),
inference(paramod_ordered,[status(thm)],[42832,39524]) ).
thf(42886,plain,
! [B: $i,A: $i] :
( ( divide @ A @ ( divide @ B @ B ) )
= A ),
inference(pattern_uni,[status(thm)],[42885:[bind(A,$thf( divide @ F @ ( divide @ I @ I ) )),bind(B,$thf( F )),bind(C,$thf( I )),bind(D,$thf( F )),bind(E,$thf( divide @ F @ ( divide @ I @ I ) ))]]) ).
thf(43182,plain,
! [B: $i,A: $i] :
( ( divide @ A @ ( divide @ B @ B ) )
= A ),
inference(simp,[status(thm)],[42886]) ).
thf(55627,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( divide @ C @ ( divide @ D @ A ) )
= E )
| ( ( divide @ A @ ( divide @ B @ B ) )
!= ( divide @ E @ ( divide @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[43182,9]) ).
thf(55628,plain,
! [B: $i,A: $i] :
( ( divide @ B @ ( divide @ B @ A ) )
= A ),
inference(pattern_uni,[status(thm)],[55627:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( B )),bind(E,$thf( A ))]]) ).
thf(132,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( divide @ C @ ( inverse @ A ) )
= E )
| ( ( divide @ ( inverse @ ( divide @ B @ B ) ) @ A )
!= ( divide @ D @ ( divide @ E @ ( divide @ C @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,9]) ).
thf(133,plain,
! [C: $i,B: $i,A: $i] :
( ( divide @ B @ ( inverse @ ( divide @ A @ ( divide @ B @ ( inverse @ ( divide @ C @ C ) ) ) ) ) )
= A ),
inference(pattern_uni,[status(thm)],[132:[bind(A,$thf( divide @ I @ ( divide @ K @ ( inverse @ ( divide @ O @ O ) ) ) )),bind(B,$thf( O )),bind(C,$thf( K )),bind(D,$thf( inverse @ ( divide @ O @ O ) )),bind(E,$thf( I ))]]) ).
thf(156,plain,
! [C: $i,B: $i,A: $i] :
( ( divide @ B @ ( inverse @ ( divide @ A @ ( divide @ B @ ( inverse @ ( divide @ C @ C ) ) ) ) ) )
= A ),
inference(simp,[status(thm)],[133]) ).
thf(7018,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ B @ ( divide @ A @ ( divide @ B @ ( inverse @ ( divide @ C @ C ) ) ) ) )
= A ),
inference(rewrite,[status(thm)],[156,815]) ).
thf(1,negated_conjecture,
( ( multiply @ a @ b )
!= ( multiply @ b @ a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_4) ).
thf(5,plain,
( ( multiply @ a @ b )
!= ( multiply @ b @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,plain,
( ( multiply @ a @ b )
!= ( multiply @ b @ a ) ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( multiply @ b @ a )
!= ( multiply @ a @ b ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(7158,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( multiply @ a @ b ) )
| ( ( multiply @ B @ ( divide @ A @ ( divide @ B @ ( inverse @ ( divide @ C @ C ) ) ) ) )
!= ( multiply @ b @ a ) ) ),
inference(paramod_ordered,[status(thm)],[7018,7]) ).
thf(7251,plain,
! [B: $i,A: $i] :
( ( A != b )
| ( ( divide @ ( multiply @ a @ b ) @ ( divide @ A @ ( inverse @ ( divide @ B @ B ) ) ) )
!= a ) ),
inference(simp,[status(thm)],[7158]) ).
thf(7320,plain,
! [A: $i] :
( ( divide @ ( multiply @ a @ b ) @ ( divide @ b @ ( inverse @ ( divide @ A @ A ) ) ) )
!= a ),
inference(simp,[status(thm)],[7251]) ).
thf(7399,plain,
! [A: $i] :
( ( divide @ ( multiply @ a @ b ) @ ( multiply @ b @ ( divide @ A @ A ) ) )
!= a ),
inference(rewrite,[status(thm)],[7320,815]) ).
thf(39506,plain,
! [C: $i,B: $i,A: $i] :
( ( ( divide @ ( multiply @ a @ b ) @ A )
!= a )
| ( ( multiply @ B @ ( divide @ A @ B ) )
!= ( multiply @ b @ ( divide @ C @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[39109,7399]) ).
thf(39507,plain,
( ( divide @ ( multiply @ a @ b ) @ b )
!= a ),
inference(pattern_uni,[status(thm)],[39506:[bind(A,$thf( b )),bind(B,$thf( b )),bind(C,$thf( b ))]]) ).
thf(69434,plain,
! [B: $i,A: $i] :
( ( A != a )
| ( ( divide @ B @ ( divide @ B @ A ) )
!= ( divide @ ( multiply @ a @ b ) @ b ) ) ),
inference(paramod_ordered,[status(thm)],[55628,39507]) ).
thf(69793,plain,
! [A: $i] :
( ( A
!= ( multiply @ a @ b ) )
| ( ( divide @ A @ a )
!= b ) ),
inference(simp,[status(thm)],[69434]) ).
thf(70006,plain,
( ( divide @ ( multiply @ a @ b ) @ a )
!= b ),
inference(simp,[status(thm)],[69793]) ).
thf(119,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( divide @ C @ ( divide @ D @ ( divide @ E @ ( inverse @ A ) ) ) )
= E )
| ( ( divide @ ( divide @ B @ B ) @ A )
!= ( divide @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[13,9]) ).
thf(120,plain,
! [C: $i,B: $i,A: $i] :
( ( divide @ ( divide @ C @ C ) @ ( divide @ A @ ( divide @ B @ ( inverse @ A ) ) ) )
= B ),
inference(pattern_uni,[status(thm)],[119:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( divide @ G @ G )),bind(D,$thf( A )),bind(E,$thf( E ))]]) ).
thf(177,plain,
! [C: $i,B: $i,A: $i] :
( ( divide @ ( divide @ C @ C ) @ ( divide @ A @ ( divide @ B @ ( inverse @ A ) ) ) )
= B ),
inference(simp,[status(thm)],[120]) ).
thf(41530,plain,
! [C: $i,B: $i,A: $i] :
( ( divide @ ( divide @ C @ C ) @ ( divide @ A @ ( multiply @ B @ A ) ) )
= B ),
inference(rewrite,[status(thm)],[177,815]) ).
thf(41770,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( divide @ F @ B )
= E )
| ( ( divide @ ( divide @ C @ C ) @ ( divide @ A @ ( multiply @ B @ A ) ) )
!= ( divide @ ( divide @ D @ ( divide @ E @ F ) ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[41530,175]) ).
thf(41771,plain,
! [B: $i,A: $i] :
( ( divide @ ( multiply @ A @ B ) @ A )
= B ),
inference(pattern_uni,[status(thm)],[41770:[bind(A,$thf( J )),bind(B,$thf( I )),bind(C,$thf( divide @ J @ ( multiply @ I @ J ) )),bind(D,$thf( divide @ J @ ( multiply @ I @ J ) )),bind(E,$thf( J )),bind(F,$thf( multiply @ I @ J ))]]) ).
thf(42011,plain,
! [B: $i,A: $i] :
( ( divide @ ( multiply @ A @ B ) @ A )
= B ),
inference(simp,[status(thm)],[41771]) ).
thf(70204,plain,
b != b,
inference(rewrite,[status(thm)],[70006,42011]) ).
thf(70205,plain,
$false,
inference(simp,[status(thm)],[70204]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP524-1 : TPTP v8.2.0. Bugfixed v2.7.0.
% 0.12/0.17 % Command : run_Leo-III %s %d
% 0.15/0.38 % Computer : n013.cluster.edu
% 0.15/0.38 % Model : x86_64 x86_64
% 0.15/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.38 % Memory : 8042.1875MB
% 0.15/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38 % CPULimit : 300
% 0.15/0.38 % WCLimit : 300
% 0.15/0.38 % DateTime : Sun May 19 04:31:24 EDT 2024
% 0.15/0.38 % CPUTime :
% 0.90/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.08/1.01 % [INFO] Parsing done (103ms).
% 1.08/1.02 % [INFO] Running in sequential loop mode.
% 1.60/1.25 % [INFO] nitpick registered as external prover.
% 1.64/1.25 % [INFO] Scanning for conjecture ...
% 1.64/1.30 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 1.79/1.31 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.79/1.32 % [INFO] Problem is propositional (TPTP CNF).
% 1.79/1.33 % [INFO] Type checking passed.
% 1.79/1.33 % [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 ...
% 186.44/31.03 % [INFO] Killing All external provers ...
% 186.44/31.03 % Time passed: 30485ms (effective reasoning time: 30011ms)
% 186.44/31.04 % Axioms used in derivation (3): inverse, single_axiom, multiply
% 186.44/31.04 % No. of inferences in proof: 90
% 186.44/31.04 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 30485 ms resp. 30011 ms w/o parsing
% 186.51/31.11 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 186.51/31.11 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------