TSTP Solution File: GRP525-1 by Leo-III-SAT---1.7.10
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : GRP525-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n020.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 : Tue May 7 10:33:46 EDT 2024
% Result : Unsatisfiable 10.59s 2.96s
% Output : Refutation 10.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 9
% Syntax : Number of formulae : 49 ( 30 unt; 5 typ; 0 def)
% Number of atoms : 59 ( 58 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 344 ( 34 ~; 15 |; 0 &; 295 @)
% ( 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 : 80 ( 0 ^ 80 !; 0 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(a1_type,type,
a1: $i ).
thf(b1_type,type,
b1: $i ).
thf(divide_type,type,
divide: $i > $i > $i ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( divide @ A @ ( divide @ ( divide @ A @ B ) @ ( divide @ C @ B ) ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
thf(8,plain,
! [C: $i,B: $i,A: $i] :
( ( divide @ A @ ( divide @ ( divide @ A @ B ) @ ( divide @ C @ B ) ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
! [C: $i,B: $i,A: $i] :
( ( divide @ A @ ( divide @ ( divide @ A @ B ) @ ( divide @ C @ B ) ) )
= C ),
inference(lifteq,[status(thm)],[8]) ).
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(132,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( divide @ C @ ( inverse @ A ) )
= E )
| ( ( divide @ ( divide @ B @ B ) @ A )
!= ( divide @ ( divide @ C @ D ) @ ( divide @ E @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,9]) ).
thf(133,plain,
! [B: $i,A: $i] :
( ( divide @ B @ ( inverse @ ( divide @ A @ B ) ) )
= A ),
inference(pattern_uni,[status(thm)],[132:[bind(A,$thf( divide @ F @ G )),bind(B,$thf( G )),bind(C,$thf( G )),bind(D,$thf( G )),bind(E,$thf( F ))]]) ).
thf(157,plain,
! [B: $i,A: $i] :
( ( divide @ B @ ( inverse @ ( divide @ A @ B ) ) )
= A ),
inference(simp,[status(thm)],[133]) ).
thf(207,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( inverse @ C ) )
| ( ( divide @ B @ ( inverse @ ( divide @ A @ B ) ) )
!= ( divide @ ( divide @ D @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[157,13]) ).
thf(208,plain,
! [B: $i,A: $i] :
( ( inverse @ ( inverse @ ( divide @ A @ ( divide @ B @ B ) ) ) )
= A ),
inference(pattern_uni,[status(thm)],[207:[bind(A,$thf( H )),bind(B,$thf( divide @ K @ K )),bind(C,$thf( inverse @ ( divide @ H @ ( divide @ K @ K ) ) )),bind(D,$thf( K ))]]) ).
thf(238,plain,
! [B: $i,A: $i] :
( ( inverse @ ( inverse @ ( divide @ A @ ( divide @ B @ B ) ) ) )
= A ),
inference(simp,[status(thm)],[208]) ).
thf(270,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( inverse @ ( inverse @ C ) )
= D )
| ( ( divide @ A @ ( divide @ ( divide @ A @ B ) @ ( divide @ C @ B ) ) )
!= ( divide @ D @ ( divide @ E @ E ) ) ) ),
inference(paramod_ordered,[status(thm)],[9,238]) ).
thf(271,plain,
! [A: $i] :
( ( inverse @ ( inverse @ A ) )
= A ),
inference(pattern_uni,[status(thm)],[270:[bind(A,$thf( C )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( C )),bind(E,$thf( divide @ C @ G ))]]) ).
thf(303,plain,
! [A: $i] :
( ( inverse @ ( inverse @ A ) )
= A ),
inference(simp,[status(thm)],[271]) ).
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(467,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ A @ B )
= F )
| ( ( divide @ A @ ( divide @ ( divide @ C @ C ) @ B ) )
!= ( divide @ D @ ( divide @ ( divide @ D @ E ) @ ( divide @ F @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[11,9]) ).
thf(468,plain,
! [B: $i,A: $i] :
( ( multiply @ B @ ( divide @ A @ B ) )
= A ),
inference(pattern_uni,[status(thm)],[467:[bind(A,$thf( H )),bind(B,$thf( divide @ G @ H )),bind(C,$thf( H )),bind(D,$thf( H )),bind(E,$thf( H )),bind(F,$thf( G ))]]) ).
thf(541,plain,
! [B: $i,A: $i] :
( ( multiply @ B @ ( divide @ A @ B ) )
= A ),
inference(simp,[status(thm)],[468]) ).
thf(1,negated_conjecture,
( ( multiply @ ( inverse @ a1 ) @ a1 )
!= ( multiply @ ( inverse @ b1 ) @ b1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_1) ).
thf(5,plain,
( ( multiply @ ( inverse @ a1 ) @ a1 )
!= ( multiply @ ( inverse @ b1 ) @ b1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,plain,
( ( multiply @ ( inverse @ a1 ) @ a1 )
!= ( multiply @ ( inverse @ b1 ) @ b1 ) ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( multiply @ ( inverse @ b1 ) @ b1 )
!= ( multiply @ ( inverse @ a1 ) @ a1 ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(760,plain,
! [B: $i,A: $i] :
( ( A
!= ( multiply @ ( inverse @ a1 ) @ a1 ) )
| ( ( multiply @ B @ ( divide @ A @ B ) )
!= ( multiply @ ( inverse @ b1 ) @ b1 ) ) ),
inference(paramod_ordered,[status(thm)],[541,7]) ).
thf(768,plain,
! [A: $i] :
( ( A
!= ( inverse @ b1 ) )
| ( ( divide @ ( multiply @ ( inverse @ a1 ) @ a1 ) @ A )
!= b1 ) ),
inference(simp,[status(thm)],[760]) ).
thf(773,plain,
( ( divide @ ( multiply @ ( inverse @ a1 ) @ a1 ) @ ( inverse @ b1 ) )
!= b1 ),
inference(simp,[status(thm)],[768]) ).
thf(788,plain,
! [B: $i,A: $i] :
( ( A != b1 )
| ( ( divide @ B @ ( inverse @ ( divide @ A @ B ) ) )
!= ( divide @ ( multiply @ ( inverse @ a1 ) @ a1 ) @ ( inverse @ b1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[157,773]) ).
thf(805,plain,
! [A: $i] :
( ( A
!= ( multiply @ ( inverse @ a1 ) @ a1 ) )
| ( ( inverse @ ( divide @ b1 @ A ) )
!= ( inverse @ b1 ) ) ),
inference(simp,[status(thm)],[788]) ).
thf(820,plain,
( ( inverse @ ( divide @ b1 @ ( multiply @ ( inverse @ a1 ) @ a1 ) ) )
!= ( inverse @ b1 ) ),
inference(simp,[status(thm)],[805]) ).
thf(885,plain,
! [B: $i,A: $i] :
( ( ( inverse @ A )
!= ( inverse @ b1 ) )
| ( ( divide @ B @ ( inverse @ ( divide @ A @ B ) ) )
!= ( divide @ b1 @ ( multiply @ ( inverse @ a1 ) @ a1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[157,820]) ).
thf(900,plain,
! [B: $i,A: $i] :
( ( A != b1 )
| ( B != b1 )
| ( ( inverse @ ( divide @ A @ B ) )
!= ( multiply @ ( inverse @ a1 ) @ a1 ) ) ),
inference(simp,[status(thm)],[885]) ).
thf(938,plain,
( ( inverse @ ( divide @ b1 @ b1 ) )
!= ( multiply @ ( inverse @ a1 ) @ a1 ) ),
inference(simp,[status(thm)],[900]) ).
thf(1197,plain,
! [B: $i,A: $i] :
( ( A
!= ( inverse @ ( divide @ b1 @ b1 ) ) )
| ( ( multiply @ B @ ( divide @ A @ B ) )
!= ( multiply @ ( inverse @ a1 ) @ a1 ) ) ),
inference(paramod_ordered,[status(thm)],[541,938]) ).
thf(1218,plain,
! [A: $i] :
( ( A
!= ( inverse @ a1 ) )
| ( ( divide @ ( inverse @ ( divide @ b1 @ b1 ) ) @ A )
!= a1 ) ),
inference(simp,[status(thm)],[1197]) ).
thf(1222,plain,
( ( divide @ ( inverse @ ( divide @ b1 @ b1 ) ) @ ( inverse @ a1 ) )
!= a1 ),
inference(simp,[status(thm)],[1218]) ).
thf(15,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(16,plain,
! [B: $i,A: $i] :
( ( divide @ ( inverse @ ( divide @ B @ B ) ) @ A )
= ( inverse @ A ) ),
inference(pattern_uni,[status(thm)],[15:[bind(A,$thf( divide @ H @ H )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( divide @ H @ H ))]]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( divide @ ( inverse @ ( divide @ B @ B ) ) @ A )
= ( inverse @ A ) ),
inference(simp,[status(thm)],[16]) ).
thf(1400,plain,
( ( inverse @ ( inverse @ a1 ) )
!= a1 ),
inference(rewrite,[status(thm)],[1222,17]) ).
thf(1401,plain,
! [A: $i] :
( ( A != a1 )
| ( ( inverse @ ( inverse @ A ) )
!= ( inverse @ ( inverse @ a1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[303,1400]) ).
thf(1402,plain,
a1 != a1,
inference(pattern_uni,[status(thm)],[1401:[bind(A,$thf( a1 ))]]) ).
thf(1405,plain,
$false,
inference(simp,[status(thm)],[1402]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : GRP525-1 : TPTP v8.1.2. Released v2.6.0.
% 0.09/0.14 % Command : run_Leo-III %s %d
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 6 23:52:54 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.83/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.11/0.88 % [INFO] Parsing done (110ms).
% 1.11/0.89 % [INFO] Running in sequential loop mode.
% 1.51/1.13 % [INFO] nitpick registered as external prover.
% 1.51/1.13 % [INFO] Scanning for conjecture ...
% 1.72/1.18 % [INFO] Found a conjecture and 3 axioms. Running axiom selection ...
% 1.76/1.20 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.76/1.21 % [INFO] Problem is propositional (TPTP CNF).
% 1.76/1.21 % [INFO] Type checking passed.
% 1.76/1.21 % [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 ...
% 10.59/2.95 % [INFO] Killing All external provers ...
% 10.59/2.96 % Time passed: 2488ms (effective reasoning time: 2058ms)
% 10.59/2.96 % 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)>
% 10.59/2.96 % Axioms used in derivation (3): single_axiom, inverse, multiply
% 10.59/2.96 % No. of inferences in proof: 44
% 10.59/2.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2488 ms resp. 2058 ms w/o parsing
% 10.94/3.09 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.94/3.09 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------