TSTP Solution File: GRP405-1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP405-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n031.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 11:13:55 EDT 2023
% Result : Unsatisfiable 51.22s 12.35s
% Output : Refutation 51.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 17 unt; 5 typ; 0 def)
% Number of atoms : 47 ( 46 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 738 ( 31 ~; 17 |; 0 &; 690 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 84 ( 0 ^; 84 !; 0 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(a3_type,type,
a3: $i ).
thf(b3_type,type,
b3: $i ).
thf(c3_type,type,
c3: $i ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(1,negated_conjecture,
( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 )
!= ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_3) ).
thf(3,plain,
( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 )
!= ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,plain,
( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 )
!= ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 )
!= ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ A @ B ) ) @ C ) ) @ ( inverse @ ( multiply @ B @ ( multiply @ ( inverse @ B ) @ B ) ) ) ) ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
thf(6,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ A @ B ) ) @ C ) ) @ ( inverse @ ( multiply @ B @ ( multiply @ ( inverse @ B ) @ B ) ) ) ) ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ A @ B ) ) @ C ) ) @ ( inverse @ ( multiply @ B @ ( multiply @ ( inverse @ B ) @ B ) ) ) ) ) )
= C ),
inference(lifteq,[status(thm)],[6]) ).
thf(10,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiply @ C @ c3 )
!= ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) )
| ( ( multiply @ A @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ A @ B ) ) @ C ) ) @ ( inverse @ ( multiply @ B @ ( multiply @ ( inverse @ B ) @ B ) ) ) ) ) )
!= ( multiply @ a3 @ b3 ) ) ),
inference(paramod_ordered,[status(thm)],[7,5]) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] :
( ( C != a3 )
| ( ( multiply @ b3 @ c3 )
!= c3 )
| ( A != a3 )
| ( ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ A @ B ) ) @ C ) ) @ ( inverse @ ( multiply @ B @ ( multiply @ ( inverse @ B ) @ B ) ) ) ) )
!= b3 ) ),
inference(simp,[status(thm)],[10]) ).
thf(29,plain,
! [A: $i] :
( ( ( multiply @ b3 @ c3 )
!= c3 )
| ( ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ a3 @ A ) ) @ a3 ) ) @ ( inverse @ ( multiply @ A @ ( multiply @ ( inverse @ A ) @ A ) ) ) ) )
!= b3 ) ),
inference(simp,[status(thm)],[20]) ).
thf(12,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ D @ ( inverse @ ( multiply @ ( inverse @ C ) @ ( inverse @ ( multiply @ E @ ( multiply @ ( inverse @ E ) @ E ) ) ) ) ) )
= F )
| ( ( multiply @ A @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ A @ B ) ) @ C ) ) @ ( inverse @ ( multiply @ B @ ( multiply @ ( inverse @ B ) @ B ) ) ) ) ) )
!= ( multiply @ ( inverse @ ( multiply @ D @ E ) ) @ F ) ) ),
inference(paramod_ordered,[status(thm)],[7,7]) ).
thf(13,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( multiply @ B @ ( inverse @ ( multiply @ ( inverse @ A ) @ ( inverse @ ( multiply @ C @ ( multiply @ ( inverse @ C ) @ C ) ) ) ) ) )
= ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ B @ C ) ) @ D ) ) @ A ) ) @ ( inverse @ ( multiply @ D @ ( multiply @ ( inverse @ D ) @ D ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[12:[bind(A,$thf( inverse @ ( multiply @ T @ U ) )),bind(B,$thf( Z )),bind(C,$thf( O )),bind(D,$thf( T )),bind(E,$thf( U )),bind(F,$thf( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ T @ U ) ) @ Z ) ) @ O ) ) @ ( inverse @ ( multiply @ Z @ ( multiply @ ( inverse @ Z ) @ Z ) ) ) ) ))]]) ).
thf(34,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( multiply @ B @ ( inverse @ ( multiply @ ( inverse @ A ) @ ( inverse @ ( multiply @ C @ ( multiply @ ( inverse @ C ) @ C ) ) ) ) ) )
= ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ B @ C ) ) @ D ) ) @ A ) ) @ ( inverse @ ( multiply @ D @ ( multiply @ ( inverse @ D ) @ D ) ) ) ) ) ),
inference(simp,[status(thm)],[13]) ).
thf(139,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ B @ C ) ) @ D ) ) @ A ) ) @ ( inverse @ ( multiply @ D @ ( multiply @ ( inverse @ D ) @ D ) ) ) ) )
= G )
| ( ( multiply @ B @ ( inverse @ ( multiply @ ( inverse @ A ) @ ( inverse @ ( multiply @ C @ ( multiply @ ( inverse @ C ) @ C ) ) ) ) ) )
!= ( multiply @ E @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ E @ F ) ) @ G ) ) @ ( inverse @ ( multiply @ F @ ( multiply @ ( inverse @ F ) @ F ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[34,7]) ).
thf(140,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ D @ A ) ) @ B ) ) @ ( multiply @ ( inverse @ ( multiply @ D @ A ) ) @ C ) ) ) @ ( inverse @ ( multiply @ B @ ( multiply @ ( inverse @ B ) @ B ) ) ) ) )
= C ),
inference(pattern_uni,[status(thm)],[139:[bind(A,$thf( multiply @ ( inverse @ ( multiply @ K @ C ) ) @ I )),bind(B,$thf( K )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( K )),bind(F,$thf( C )),bind(G,$thf( I ))]]) ).
thf(229,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ D @ A ) ) @ B ) ) @ ( multiply @ ( inverse @ ( multiply @ D @ A ) ) @ C ) ) ) @ ( inverse @ ( multiply @ B @ ( multiply @ ( inverse @ B ) @ B ) ) ) ) )
= C ),
inference(simp,[status(thm)],[140]) ).
thf(8,plain,
( ( ( multiply @ a3 @ b3 )
!= a3 )
| ( ( multiply @ b3 @ c3 )
!= c3 ) ),
inference(simp,[status(thm)],[5]) ).
thf(61,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiply @ a3 @ b3 )
!= a3 )
| ( C != c3 )
| ( ( multiply @ A @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ A @ B ) ) @ C ) ) @ ( inverse @ ( multiply @ B @ ( multiply @ ( inverse @ B ) @ B ) ) ) ) ) )
!= ( multiply @ b3 @ c3 ) ) ),
inference(paramod_ordered,[status(thm)],[7,8]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ( ( multiply @ a3 @ b3 )
!= a3 )
| ( A != b3 )
| ( ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ A @ B ) ) @ c3 ) ) @ ( inverse @ ( multiply @ B @ ( multiply @ ( inverse @ B ) @ B ) ) ) ) )
!= c3 ) ),
inference(simp,[status(thm)],[61]) ).
thf(66,plain,
! [A: $i] :
( ( ( multiply @ a3 @ b3 )
!= a3 )
| ( ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ b3 @ A ) ) @ c3 ) ) @ ( inverse @ ( multiply @ A @ ( multiply @ ( inverse @ A ) @ A ) ) ) ) )
!= c3 ) ),
inference(simp,[status(thm)],[65]) ).
thf(9,plain,
! [C: $i,B: $i,A: $i] :
( ( C
!= ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) )
| ( ( multiply @ A @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ A @ B ) ) @ C ) ) @ ( inverse @ ( multiply @ B @ ( multiply @ ( inverse @ B ) @ B ) ) ) ) ) )
!= ( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) ) ),
inference(paramod_ordered,[status(thm)],[7,5]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( A
!= ( multiply @ a3 @ b3 ) )
| ( ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ A @ B ) ) @ ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) ) @ ( inverse @ ( multiply @ B @ ( multiply @ ( inverse @ B ) @ B ) ) ) ) )
!= c3 ) ),
inference(simp,[status(thm)],[9]) ).
thf(31,plain,
! [A: $i] :
( ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( multiply @ a3 @ b3 ) @ A ) ) @ ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) ) @ ( inverse @ ( multiply @ A @ ( multiply @ ( inverse @ A ) @ A ) ) ) ) )
!= c3 ),
inference(simp,[status(thm)],[23]) ).
thf(16,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ D @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ C ) @ F ) ) @ ( inverse @ ( multiply @ E @ ( multiply @ ( inverse @ E ) @ E ) ) ) ) ) )
= F )
| ( ( multiply @ A @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ A @ B ) ) @ C ) ) @ ( inverse @ ( multiply @ B @ ( multiply @ ( inverse @ B ) @ B ) ) ) ) ) )
!= ( multiply @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[7,7]) ).
thf(17,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( multiply @ C @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ B ) @ A ) ) @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ C @ D ) ) @ B ) ) @ ( inverse @ ( multiply @ D @ ( multiply @ ( inverse @ D ) @ D ) ) ) ) ) @ ( multiply @ ( inverse @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ C @ D ) ) @ B ) ) @ ( inverse @ ( multiply @ D @ ( multiply @ ( inverse @ D ) @ D ) ) ) ) ) ) @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ C @ D ) ) @ B ) ) @ ( inverse @ ( multiply @ D @ ( multiply @ ( inverse @ D ) @ D ) ) ) ) ) ) ) ) ) ) )
= A ),
inference(pattern_uni,[status(thm)],[16:[bind(A,$thf( N )),bind(B,$thf( T )),bind(C,$thf( L )),bind(D,$thf( N )),bind(E,$thf( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ N @ T ) ) @ L ) ) @ ( inverse @ ( multiply @ T @ ( multiply @ ( inverse @ T ) @ T ) ) ) ) )),bind(F,$thf( F ))]]) ).
thf(26,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( multiply @ C @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ B ) @ A ) ) @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ C @ D ) ) @ B ) ) @ ( inverse @ ( multiply @ D @ ( multiply @ ( inverse @ D ) @ D ) ) ) ) ) @ ( multiply @ ( inverse @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ C @ D ) ) @ B ) ) @ ( inverse @ ( multiply @ D @ ( multiply @ ( inverse @ D ) @ D ) ) ) ) ) ) @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ C @ D ) ) @ B ) ) @ ( inverse @ ( multiply @ D @ ( multiply @ ( inverse @ D ) @ D ) ) ) ) ) ) ) ) ) ) )
= A ),
inference(simp,[status(thm)],[17]) ).
thf(146,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ E @ ( multiply @ B @ ( inverse @ ( multiply @ ( inverse @ A ) @ ( inverse @ ( multiply @ C @ ( multiply @ ( inverse @ C ) @ C ) ) ) ) ) ) )
= G )
| ( ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ B @ C ) ) @ D ) ) @ A ) ) @ ( inverse @ ( multiply @ D @ ( multiply @ ( inverse @ D ) @ D ) ) ) ) )
!= ( inverse @ ( multiply @ ( inverse @ ( multiply @ ( inverse @ ( multiply @ E @ F ) ) @ G ) ) @ ( inverse @ ( multiply @ F @ ( multiply @ ( inverse @ F ) @ F ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[34,7]) ).
thf(147,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( inverse @ ( multiply @ B @ C ) ) @ ( multiply @ B @ ( inverse @ ( multiply @ ( inverse @ A ) @ ( inverse @ ( multiply @ C @ ( multiply @ ( inverse @ C ) @ C ) ) ) ) ) ) )
= A ),
inference(pattern_uni,[status(thm)],[146:[bind(A,$thf( A )),bind(B,$thf( I )),bind(C,$thf( J )),bind(D,$thf( D )),bind(E,$thf( inverse @ ( multiply @ I @ J ) )),bind(F,$thf( D )),bind(G,$thf( A ))]]) ).
thf(232,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( inverse @ ( multiply @ B @ C ) ) @ ( multiply @ B @ ( inverse @ ( multiply @ ( inverse @ A ) @ ( inverse @ ( multiply @ C @ ( multiply @ ( inverse @ C ) @ C ) ) ) ) ) ) )
= A ),
inference(simp,[status(thm)],[147]) ).
thf(2387,plain,
$false,
inference(e,[status(thm)],[5,29,6,229,34,7,66,3,31,26,8,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP405-1 : TPTP v8.1.2. Released v2.6.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n031.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 : Fri May 19 02:25:11 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.88/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.00/0.93 % [INFO] Parsing done (98ms).
% 1.00/0.94 % [INFO] Running in sequential loop mode.
% 1.58/1.13 % [INFO] eprover registered as external prover.
% 1.58/1.13 % [INFO] cvc4 registered as external prover.
% 1.58/1.14 % [INFO] Scanning for conjecture ...
% 1.58/1.18 % [INFO] Found a conjecture and 1 axioms. Running axiom selection ...
% 1.77/1.20 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 1.77/1.21 % [INFO] Problem is propositional (TPTP CNF).
% 1.77/1.21 % [INFO] Type checking passed.
% 1.77/1.21 % [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 ...
% 51.22/12.35 % External prover 'e' found a proof!
% 51.22/12.35 % [INFO] Killing All external provers ...
% 51.22/12.35 % Time passed: 11844ms (effective reasoning time: 11407ms)
% 51.22/12.35 % 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)>
% 51.22/12.35 % Axioms used in derivation (1): single_axiom
% 51.22/12.35 % No. of inferences in proof: 30
% 51.22/12.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 11844 ms resp. 11407 ms w/o parsing
% 51.22/12.39 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 51.22/12.39 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------