TSTP Solution File: GRP560-1 by Leo-III-SAT---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : GRP560-1 : TPTP v8.2.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n010.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 21:04:19 EDT 2024
% Result : Unsatisfiable 148.14s 22.10s
% Output : Refutation 148.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 8
% Syntax : Number of formulae : 69 ( 38 unt; 5 typ; 0 def)
% Number of atoms : 95 ( 94 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 585 ( 66 ~; 31 |; 0 &; 488 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 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 : 152 ( 0 ^ 152 !; 0 ?; 152 :)
% 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(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( divide @ A @ ( inverse @ ( divide @ ( divide @ B @ C ) @ ( divide @ A @ C ) ) ) )
= B ),
file('/export/starexec/sandbox2/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/sandbox2/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(13,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( divide @ ( divide @ B @ C ) @ ( divide @ A @ C ) ) )
= B ),
inference(rewrite,[status(thm)],[8,10]) ).
thf(15,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)],[10,13]) ).
thf(16,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ B @ ( divide @ ( multiply @ A @ C ) @ ( divide @ B @ ( inverse @ C ) ) ) )
= A ),
inference(pattern_uni,[status(thm)],[15:[bind(A,$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)],[16]) ).
thf(53,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ B @ ( divide @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) )
= A ),
inference(rewrite,[status(thm)],[23,10]) ).
thf(64,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ E @ ( divide @ ( multiply @ D @ F ) @ B ) )
= D )
| ( ( multiply @ A @ ( divide @ ( divide @ B @ C ) @ ( divide @ A @ C ) ) )
!= ( multiply @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[13,53]) ).
thf(65,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( multiply @ C @ ( divide @ ( multiply @ A @ ( divide @ ( divide @ B @ D ) @ ( divide @ C @ D ) ) ) @ B ) )
= A ),
inference(pattern_uni,[status(thm)],[64:[bind(A,$thf( K )),bind(B,$thf( I )),bind(C,$thf( L )),bind(D,$thf( D )),bind(E,$thf( K )),bind(F,$thf( divide @ ( divide @ I @ L ) @ ( divide @ K @ L ) ))]]) ).
thf(79,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( multiply @ C @ ( divide @ ( multiply @ A @ ( divide @ ( divide @ B @ D ) @ ( divide @ C @ D ) ) ) @ B ) )
= A ),
inference(simp,[status(thm)],[65]) ).
thf(311,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ F @ ( divide @ B @ E ) )
= D )
| ( ( multiply @ A @ ( divide @ ( divide @ B @ C ) @ ( divide @ A @ C ) ) )
!= ( multiply @ D @ ( divide @ ( divide @ E @ G ) @ ( divide @ F @ G ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,79]) ).
thf(312,plain,
! [B: $i,A: $i] :
( ( multiply @ A @ ( divide @ B @ B ) )
= A ),
inference(pattern_uni,[status(thm)],[311:[bind(A,$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(560,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ E @ ( divide @ A @ D ) )
= C )
| ( ( multiply @ A @ ( divide @ B @ B ) )
!= ( multiply @ C @ ( divide @ ( divide @ D @ F ) @ ( divide @ E @ F ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[312,79]) ).
thf(561,plain,
! [B: $i,A: $i] :
( ( multiply @ B @ ( divide @ A @ B ) )
= A ),
inference(pattern_uni,[status(thm)],[560:[bind(A,$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(615,plain,
! [B: $i,A: $i] :
( ( multiply @ B @ ( divide @ A @ B ) )
= A ),
inference(simp,[status(thm)],[561]) ).
thf(666,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ D @ ( multiply @ A @ B ) )
= C )
| ( ( divide @ A @ ( inverse @ B ) )
!= ( divide @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[10,615]) ).
thf(667,plain,
! [B: $i,A: $i] :
( ( multiply @ ( inverse @ B ) @ ( multiply @ A @ B ) )
= A ),
inference(pattern_uni,[status(thm)],[666:[bind(A,$thf( A )),bind(B,$thf( E )),bind(C,$thf( A )),bind(D,$thf( inverse @ E ))]]) ).
thf(760,plain,
! [B: $i,A: $i] :
( ( multiply @ ( inverse @ B ) @ ( multiply @ A @ B ) )
= A ),
inference(simp,[status(thm)],[667]) ).
thf(1586,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ ( inverse @ D ) @ A )
= C )
| ( ( multiply @ B @ ( divide @ A @ B ) )
!= ( multiply @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[615,760]) ).
thf(1587,plain,
! [B: $i,A: $i] :
( ( multiply @ ( inverse @ ( divide @ A @ B ) ) @ A )
= B ),
inference(pattern_uni,[status(thm)],[1586:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( divide @ E @ F ))]]) ).
thf(1767,plain,
! [B: $i,A: $i] :
( ( multiply @ ( inverse @ ( divide @ A @ B ) ) @ A )
= B ),
inference(simp,[status(thm)],[1587]) ).
thf(3384,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( multiply @ ( inverse @ ( divide @ A @ B ) ) @ A )
!= ( multiply @ C @ ( divide @ D @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[1767,312]) ).
thf(3385,plain,
! [B: $i,A: $i] :
( ( inverse @ ( divide @ ( divide @ B @ B ) @ A ) )
= A ),
inference(pattern_uni,[status(thm)],[3384:[bind(A,$thf( divide @ I @ I )),bind(B,$thf( G )),bind(C,$thf( inverse @ ( divide @ ( divide @ I @ I ) @ G ) )),bind(D,$thf( I ))]]) ).
thf(3557,plain,
! [B: $i,A: $i] :
( ( inverse @ ( divide @ ( divide @ B @ B ) @ A ) )
= A ),
inference(simp,[status(thm)],[3385]) ).
thf(1,negated_conjecture,
( ( multiply @ a @ b )
!= ( multiply @ b @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_4) ).
thf(4,plain,
( ( multiply @ a @ b )
!= ( multiply @ b @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(5,plain,
( ( multiply @ a @ b )
!= ( multiply @ b @ a ) ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(6,plain,
( ( multiply @ b @ a )
!= ( multiply @ a @ b ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(14,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( multiply @ a @ b ) )
| ( ( multiply @ A @ ( divide @ ( divide @ B @ C ) @ ( divide @ A @ C ) ) )
!= ( multiply @ b @ a ) ) ),
inference(paramod_ordered,[status(thm)],[13,6]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( A != b )
| ( ( divide @ ( divide @ ( multiply @ a @ b ) @ B ) @ ( divide @ A @ B ) )
!= a ) ),
inference(simp,[status(thm)],[14]) ).
thf(26,plain,
! [A: $i] :
( ( divide @ ( divide @ ( multiply @ a @ b ) @ A ) @ ( divide @ b @ A ) )
!= a ),
inference(simp,[status(thm)],[21]) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( ( divide @ ( multiply @ A @ B ) @ ( divide @ b @ C ) )
!= a )
| ( ( divide @ A @ ( inverse @ B ) )
!= ( divide @ ( multiply @ a @ b ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[10,26]) ).
thf(32,plain,
! [A: $i] :
( ( divide @ ( multiply @ ( multiply @ a @ b ) @ A ) @ ( divide @ b @ ( inverse @ A ) ) )
!= a ),
inference(pattern_uni,[status(thm)],[31:[bind(A,$thf( multiply @ a @ b )),bind(B,$thf( F )),bind(C,$thf( inverse @ F ))]]) ).
thf(36,plain,
! [A: $i] :
( ( divide @ ( multiply @ ( multiply @ a @ b ) @ A ) @ ( divide @ b @ ( inverse @ A ) ) )
!= a ),
inference(simp,[status(thm)],[32]) ).
thf(40,plain,
! [A: $i] :
( ( divide @ ( multiply @ ( multiply @ a @ b ) @ A ) @ ( multiply @ b @ A ) )
!= a ),
inference(rewrite,[status(thm)],[36,10]) ).
thf(69,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( divide @ A @ ( multiply @ b @ D ) )
!= a )
| ( ( multiply @ B @ ( divide @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) )
!= ( multiply @ ( multiply @ a @ b ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[53,40]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ( divide @ A @ ( multiply @ b @ ( divide @ ( multiply @ A @ B ) @ ( multiply @ ( multiply @ a @ b ) @ B ) ) ) )
!= a ),
inference(pattern_uni,[status(thm)],[69:[bind(A,$thf( I )),bind(B,$thf( multiply @ a @ b )),bind(C,$thf( L )),bind(D,$thf( divide @ ( multiply @ I @ L ) @ ( multiply @ ( multiply @ a @ b ) @ L ) ))]]) ).
thf(81,plain,
! [B: $i,A: $i] :
( ( divide @ A @ ( multiply @ b @ ( divide @ ( multiply @ A @ B ) @ ( multiply @ ( multiply @ a @ b ) @ B ) ) ) )
!= a ),
inference(simp,[status(thm)],[70]) ).
thf(544,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( divide @ C @ A )
!= a )
| ( ( multiply @ A @ ( divide @ B @ B ) )
!= ( multiply @ b @ ( divide @ ( multiply @ C @ D ) @ ( multiply @ ( multiply @ a @ b ) @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[312,81]) ).
thf(545,plain,
( ( divide @ ( multiply @ a @ b ) @ b )
!= a ),
inference(pattern_uni,[status(thm)],[544:[bind(A,$thf( b )),bind(B,$thf( multiply @ ( multiply @ a @ b ) @ F )),bind(C,$thf( multiply @ a @ b )),bind(D,$thf( F ))]]) ).
thf(620,plain,
! [B: $i,A: $i] :
( ( ( multiply @ A @ B )
!= a )
| ( ( divide @ A @ ( inverse @ B ) )
!= ( divide @ ( multiply @ a @ b ) @ b ) ) ),
inference(paramod_ordered,[status(thm)],[10,545]) ).
thf(630,plain,
! [B: $i,A: $i] :
( ( ( multiply @ A @ B )
!= a )
| ( A
!= ( multiply @ a @ b ) )
| ( ( inverse @ B )
!= b ) ),
inference(simp,[status(thm)],[620]) ).
thf(636,plain,
! [A: $i] :
( ( ( multiply @ ( multiply @ a @ b ) @ A )
!= a )
| ( ( inverse @ A )
!= b ) ),
inference(simp,[status(thm)],[630]) ).
thf(1015,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != a )
| ( ( inverse @ D )
!= b )
| ( ( multiply @ A @ ( divide @ ( divide @ B @ C ) @ ( divide @ A @ C ) ) )
!= ( multiply @ ( multiply @ a @ b ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[13,636]) ).
thf(1016,plain,
! [B: $i,A: $i] :
( ( A != a )
| ( ( inverse @ ( divide @ ( divide @ A @ B ) @ ( divide @ ( multiply @ a @ b ) @ B ) ) )
!= b ) ),
inference(pattern_uni,[status(thm)],[1015:[bind(A,$thf( multiply @ a @ b )),bind(B,$thf( I )),bind(C,$thf( L )),bind(D,$thf( divide @ ( divide @ I @ L ) @ ( divide @ ( multiply @ a @ b ) @ L ) ))]]) ).
thf(1037,plain,
! [A: $i] :
( ( inverse @ ( divide @ ( divide @ a @ A ) @ ( divide @ ( multiply @ a @ b ) @ A ) ) )
!= b ),
inference(simp,[status(thm)],[1016]) ).
thf(16849,plain,
! [C: $i,B: $i,A: $i] :
( ( A != b )
| ( ( inverse @ ( divide @ ( divide @ B @ B ) @ A ) )
!= ( inverse @ ( divide @ ( divide @ a @ C ) @ ( divide @ ( multiply @ a @ b ) @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3557,1037]) ).
thf(16850,plain,
( ( divide @ ( multiply @ a @ b ) @ a )
!= b ),
inference(pattern_uni,[status(thm)],[16849:[bind(A,$thf( divide @ ( multiply @ a @ b ) @ a )),bind(B,$thf( a )),bind(C,$thf( a ))]]) ).
thf(17269,plain,
! [B: $i,A: $i] :
( ( ( divide @ A @ a )
!= b )
| ( ( multiply @ B @ ( divide @ A @ B ) )
!= ( multiply @ a @ b ) ) ),
inference(paramod_ordered,[status(thm)],[615,16850]) ).
thf(17295,plain,
! [B: $i,A: $i] :
( ( ( divide @ A @ a )
!= b )
| ( B != a )
| ( ( divide @ A @ B )
!= b ) ),
inference(simp,[status(thm)],[17269]) ).
thf(17321,plain,
! [A: $i] :
( ( divide @ A @ a )
!= b ),
inference(simp,[status(thm)],[17295]) ).
thf(17333,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiply @ A @ B )
!= b )
| ( ( divide @ A @ ( inverse @ B ) )
!= ( divide @ C @ a ) ) ),
inference(paramod_ordered,[status(thm)],[10,17321]) ).
thf(17346,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiply @ A @ B )
!= b )
| ( A != C )
| ( ( inverse @ B )
!= a ) ),
inference(simp,[status(thm)],[17333]) ).
thf(17349,plain,
! [B: $i,A: $i] :
( ( ( multiply @ B @ A )
!= b )
| ( ( inverse @ A )
!= a ) ),
inference(simp,[status(thm)],[17346]) ).
thf(31850,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != b )
| ( ( inverse @ C )
!= a )
| ( ( multiply @ ( inverse @ ( divide @ A @ B ) ) @ A )
!= ( multiply @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1767,17349]) ).
thf(31851,plain,
! [B: $i,A: $i] :
( ( B != b )
| ( ( inverse @ A )
!= a ) ),
inference(pattern_uni,[status(thm)],[31850:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( inverse @ ( divide @ F @ G ) ))]]) ).
thf(31916,plain,
! [A: $i] :
( ( inverse @ A )
!= a ),
inference(simp,[status(thm)],[31851]) ).
thf(32344,plain,
! [C: $i,B: $i,A: $i] :
( ( A != a )
| ( ( inverse @ ( divide @ ( divide @ B @ B ) @ A ) )
!= ( inverse @ C ) ) ),
inference(paramod_ordered,[status(thm)],[3557,31916]) ).
thf(32345,plain,
! [A: $i] : ( A != a ),
inference(pattern_uni,[status(thm)],[32344:[bind(A,$thf( E )),bind(B,$thf( G )),bind(C,$thf( divide @ ( divide @ G @ G ) @ E ))]]) ).
thf(32350,plain,
$false,
inference(simp,[status(thm)],[32345]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP560-1 : TPTP v8.2.0. Bugfixed v2.7.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n010.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun May 19 05:18:24 EDT 2024
% 0.14/0.36 % CPUTime :
% 1.02/0.91 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.08/1.01 % [INFO] Parsing done (101ms).
% 1.08/1.02 % [INFO] Running in sequential loop mode.
% 1.67/1.27 % [INFO] nitpick registered as external prover.
% 1.67/1.27 % [INFO] Scanning for conjecture ...
% 1.89/1.32 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 1.89/1.34 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 1.89/1.35 % [INFO] Problem is propositional (TPTP CNF).
% 1.89/1.35 % [INFO] Type checking passed.
% 1.89/1.36 % [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 ...
% 148.14/22.09 % [INFO] Killing All external provers ...
% 148.14/22.09 % Time passed: 21549ms (effective reasoning time: 21068ms)
% 148.14/22.10 % Axioms used in derivation (2): single_axiom, multiply
% 148.14/22.10 % No. of inferences in proof: 64
% 148.14/22.10 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 21549 ms resp. 21068 ms w/o parsing
% 148.14/22.14 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 148.14/22.14 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------