TSTP Solution File: GRP558-1 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : GRP558-1 : TPTP v8.2.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n005.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 21:04:18 EDT 2024
% Result : Unsatisfiable 32.59s 5.92s
% Output : Refutation 32.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 8
% Syntax : Number of formulae : 57 ( 34 unt; 5 typ; 0 def)
% Number of atoms : 72 ( 71 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 494 ( 46 ~; 20 |; 0 &; 428 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 117 ( 0 ^ 117 !; 0 ?; 117 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(b2_type,type,
b2: $i ).
thf(a2_type,type,
a2: $i ).
thf(divide_type,type,
divide: $i > $i > $i ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( divide @ A @ ( inverse @ ( divide @ ( divide @ B @ C ) @ ( divide @ A @ C ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
thf(7,plain,
! [C: $i,B: $i,A: $i] :
( ( divide @ A @ ( inverse @ ( divide @ ( divide @ B @ C ) @ ( divide @ A @ C ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
! [C: $i,B: $i,A: $i] :
( ( divide @ A @ ( inverse @ ( divide @ ( divide @ B @ C ) @ ( divide @ A @ C ) ) ) )
= B ),
inference(lifteq,[status(thm)],[7]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( multiply @ A @ B )
= ( divide @ A @ ( inverse @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
thf(9,plain,
! [B: $i,A: $i] :
( ( multiply @ A @ B )
= ( divide @ A @ ( inverse @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,plain,
! [B: $i,A: $i] :
( ( divide @ A @ ( inverse @ B ) )
= ( multiply @ A @ B ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(11,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( divide @ ( divide @ B @ C ) @ ( divide @ A @ C ) ) )
= B ),
inference(rewrite,[status(thm)],[8,10]) ).
thf(16,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ C @ ( divide @ ( multiply @ A @ B ) @ ( divide @ C @ E ) ) )
= D )
| ( ( divide @ A @ ( inverse @ B ) )
!= ( divide @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[10,11]) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ B @ ( divide @ ( multiply @ A @ C ) @ ( divide @ B @ ( inverse @ C ) ) ) )
= A ),
inference(pattern_uni,[status(thm)],[16:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( inverse @ F ))]]) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ B @ ( divide @ ( multiply @ A @ C ) @ ( divide @ B @ ( inverse @ C ) ) ) )
= A ),
inference(simp,[status(thm)],[17]) ).
thf(55,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ B @ ( divide @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) )
= A ),
inference(rewrite,[status(thm)],[23,10]) ).
thf(65,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ E @ ( divide @ B @ ( multiply @ E @ F ) ) )
= D )
| ( ( multiply @ A @ ( divide @ ( divide @ B @ C ) @ ( divide @ A @ C ) ) )
!= ( multiply @ D @ F ) ) ),
inference(paramod_ordered,[status(thm)],[11,55]) ).
thf(66,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( divide @ B @ ( multiply @ A @ ( divide @ ( divide @ B @ D ) @ ( divide @ C @ D ) ) ) ) )
= C ),
inference(pattern_uni,[status(thm)],[65:[bind(A,$thf( K )),bind(B,$thf( I )),bind(C,$thf( L )),bind(D,$thf( K )),bind(E,$thf( E )),bind(F,$thf( divide @ ( divide @ I @ L ) @ ( divide @ K @ L ) ))]]) ).
thf(83,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( divide @ B @ ( multiply @ A @ ( divide @ ( divide @ B @ D ) @ ( divide @ C @ D ) ) ) ) )
= C ),
inference(simp,[status(thm)],[66]) ).
thf(601,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ D @ ( divide @ E @ B ) )
= F )
| ( ( multiply @ A @ ( divide @ ( divide @ B @ C ) @ ( divide @ A @ C ) ) )
!= ( multiply @ D @ ( divide @ ( divide @ E @ G ) @ ( divide @ F @ G ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[11,83]) ).
thf(602,plain,
! [B: $i,A: $i] :
( ( multiply @ A @ ( divide @ B @ B ) )
= A ),
inference(pattern_uni,[status(thm)],[601:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B )),bind(F,$thf( A )),bind(G,$thf( C ))]]) ).
thf(778,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ C @ ( divide @ D @ A ) )
= E )
| ( ( multiply @ A @ ( divide @ B @ B ) )
!= ( multiply @ C @ ( divide @ ( divide @ D @ F ) @ ( divide @ E @ F ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[602,83]) ).
thf(779,plain,
! [B: $i,A: $i] :
( ( multiply @ A @ ( divide @ B @ A ) )
= B ),
inference(pattern_uni,[status(thm)],[778:[bind(A,$thf( A )),bind(B,$thf( divide @ G @ H )),bind(C,$thf( A )),bind(D,$thf( G )),bind(E,$thf( G )),bind(F,$thf( H ))]]) ).
thf(826,plain,
! [B: $i,A: $i] :
( ( multiply @ A @ ( divide @ B @ A ) )
= B ),
inference(simp,[status(thm)],[779]) ).
thf(908,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ C @ ( multiply @ A @ B ) )
= D )
| ( ( divide @ A @ ( inverse @ B ) )
!= ( divide @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[10,826]) ).
thf(909,plain,
! [B: $i,A: $i] :
( ( multiply @ ( inverse @ B ) @ ( multiply @ A @ B ) )
= A ),
inference(pattern_uni,[status(thm)],[908:[bind(A,$thf( A )),bind(B,$thf( E )),bind(C,$thf( inverse @ E )),bind(D,$thf( A ))]]) ).
thf(1009,plain,
! [B: $i,A: $i] :
( ( multiply @ ( inverse @ B ) @ ( multiply @ A @ B ) )
= A ),
inference(simp,[status(thm)],[909]) ).
thf(2579,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ ( inverse @ D ) @ B )
= C )
| ( ( multiply @ A @ ( divide @ B @ A ) )
!= ( multiply @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[826,1009]) ).
thf(2580,plain,
! [B: $i,A: $i] :
( ( multiply @ ( inverse @ ( divide @ A @ B ) ) @ A )
= B ),
inference(pattern_uni,[status(thm)],[2579:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( divide @ E @ F ))]]) ).
thf(2728,plain,
! [B: $i,A: $i] :
( ( multiply @ ( inverse @ ( divide @ A @ B ) ) @ A )
= B ),
inference(simp,[status(thm)],[2580]) ).
thf(1,negated_conjecture,
( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 )
!= a2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).
thf(4,plain,
( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 )
!= a2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(5,plain,
( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 )
!= a2 ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(6,plain,
( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 )
!= a2 ),
inference(lifteq,[status(thm)],[5]) ).
thf(12,plain,
! [C: $i,B: $i,A: $i] :
( ( B != a2 )
| ( ( multiply @ A @ ( divide @ ( divide @ B @ C ) @ ( divide @ A @ C ) ) )
!= ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 ) ) ),
inference(paramod_ordered,[status(thm)],[11,6]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( A
!= ( multiply @ ( inverse @ b2 ) @ b2 ) )
| ( ( divide @ ( divide @ a2 @ B ) @ ( divide @ A @ B ) )
!= a2 ) ),
inference(simp,[status(thm)],[12]) ).
thf(26,plain,
! [A: $i] :
( ( divide @ ( divide @ a2 @ A ) @ ( divide @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ A ) )
!= a2 ),
inference(simp,[status(thm)],[21]) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( ( divide @ ( divide @ a2 @ C ) @ ( multiply @ A @ B ) )
!= a2 )
| ( ( divide @ A @ ( inverse @ B ) )
!= ( divide @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[10,26]) ).
thf(32,plain,
! [A: $i] :
( ( divide @ ( divide @ a2 @ ( inverse @ A ) ) @ ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ A ) )
!= a2 ),
inference(pattern_uni,[status(thm)],[31:[bind(A,$thf( multiply @ ( inverse @ b2 ) @ b2 )),bind(B,$thf( G )),bind(C,$thf( inverse @ G ))]]) ).
thf(37,plain,
! [A: $i] :
( ( divide @ ( divide @ a2 @ ( inverse @ A ) ) @ ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ A ) )
!= a2 ),
inference(simp,[status(thm)],[32]) ).
thf(41,plain,
! [A: $i] :
( ( divide @ ( multiply @ a2 @ A ) @ ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ A ) )
!= a2 ),
inference(rewrite,[status(thm)],[37,10]) ).
thf(43,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( divide @ ( multiply @ a2 @ D ) @ B )
!= a2 )
| ( ( multiply @ A @ ( divide @ ( divide @ B @ C ) @ ( divide @ A @ C ) ) )
!= ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[11,41]) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( divide @ ( multiply @ a2 @ ( divide @ ( divide @ A @ B ) @ ( divide @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ B ) ) ) @ A )
!= a2 ),
inference(pattern_uni,[status(thm)],[43:[bind(A,$thf( multiply @ ( inverse @ b2 ) @ b2 )),bind(B,$thf( J )),bind(C,$thf( M )),bind(D,$thf( divide @ ( divide @ J @ M ) @ ( divide @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ M ) ))]]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( divide @ ( multiply @ a2 @ ( divide @ ( divide @ A @ B ) @ ( divide @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ B ) ) ) @ A )
!= a2 ),
inference(simp,[status(thm)],[44]) ).
thf(736,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( divide @ A @ C )
!= a2 )
| ( ( multiply @ A @ ( divide @ B @ B ) )
!= ( multiply @ a2 @ ( divide @ ( divide @ C @ D ) @ ( divide @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[602,52]) ).
thf(737,plain,
( ( divide @ a2 @ ( multiply @ ( inverse @ b2 ) @ b2 ) )
!= a2 ),
inference(pattern_uni,[status(thm)],[736:[bind(A,$thf( a2 )),bind(B,$thf( divide @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ F )),bind(C,$thf( multiply @ ( inverse @ b2 ) @ b2 )),bind(D,$thf( F ))]]) ).
thf(958,plain,
! [B: $i,A: $i] :
( ( ( divide @ a2 @ B )
!= a2 )
| ( ( multiply @ A @ ( divide @ B @ A ) )
!= ( multiply @ ( inverse @ b2 ) @ b2 ) ) ),
inference(paramod_ordered,[status(thm)],[826,737]) ).
thf(978,plain,
! [B: $i,A: $i] :
( ( ( divide @ a2 @ B )
!= a2 )
| ( A
!= ( inverse @ b2 ) )
| ( ( divide @ B @ A )
!= b2 ) ),
inference(simp,[status(thm)],[958]) ).
thf(1029,plain,
! [A: $i] :
( ( ( divide @ a2 @ A )
!= a2 )
| ( ( divide @ A @ ( inverse @ b2 ) )
!= b2 ) ),
inference(simp,[status(thm)],[978]) ).
thf(3918,plain,
! [A: $i] :
( ( ( divide @ a2 @ A )
!= a2 )
| ( ( multiply @ A @ b2 )
!= b2 ) ),
inference(rewrite,[status(thm)],[1029,10]) ).
thf(4846,plain,
! [C: $i,B: $i,A: $i] :
( ( ( divide @ a2 @ C )
!= a2 )
| ( B != b2 )
| ( ( multiply @ ( inverse @ ( divide @ A @ B ) ) @ A )
!= ( multiply @ C @ b2 ) ) ),
inference(paramod_ordered,[status(thm)],[2728,3918]) ).
thf(4847,plain,
! [A: $i] :
( ( ( divide @ a2 @ ( inverse @ ( divide @ b2 @ A ) ) )
!= a2 )
| ( A != b2 ) ),
inference(pattern_uni,[status(thm)],[4846:[bind(A,$thf( b2 )),bind(B,$thf( F )),bind(C,$thf( inverse @ ( divide @ b2 @ F ) ))]]) ).
thf(5197,plain,
( ( divide @ a2 @ ( inverse @ ( divide @ b2 @ b2 ) ) )
!= a2 ),
inference(simp,[status(thm)],[4847]) ).
thf(5441,plain,
( ( multiply @ a2 @ ( divide @ b2 @ b2 ) )
!= a2 ),
inference(rewrite,[status(thm)],[5197,10]) ).
thf(5443,plain,
! [B: $i,A: $i] :
( ( A != a2 )
| ( ( multiply @ A @ ( divide @ B @ B ) )
!= ( multiply @ a2 @ ( divide @ b2 @ b2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[602,5441]) ).
thf(5444,plain,
a2 != a2,
inference(pattern_uni,[status(thm)],[5443:[bind(A,$thf( a2 )),bind(B,$thf( b2 ))]]) ).
thf(5485,plain,
$false,
inference(simp,[status(thm)],[5444]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP558-1 : TPTP v8.2.0. Released v2.6.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n005.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sun May 19 04:50:54 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.87/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/0.94 % [INFO] Parsing done (96ms).
% 1.20/0.95 % [INFO] Running in sequential loop mode.
% 1.45/1.16 % [INFO] nitpick registered as external prover.
% 1.45/1.17 % [INFO] Scanning for conjecture ...
% 1.77/1.25 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 1.77/1.27 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 1.77/1.28 % [INFO] Problem is propositional (TPTP CNF).
% 1.77/1.28 % [INFO] Type checking passed.
% 1.77/1.28 % [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 ...
% 32.59/5.91 % [INFO] Killing All external provers ...
% 32.59/5.91 % Time passed: 5397ms (effective reasoning time: 4957ms)
% 32.59/5.91 % Axioms used in derivation (2): single_axiom, multiply
% 32.59/5.91 % No. of inferences in proof: 52
% 32.59/5.92 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 5397 ms resp. 4957 ms w/o parsing
% 32.68/5.96 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 32.68/5.96 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------