TSTP Solution File: LCL414+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL414+1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 : 600s
% DateTime : Sun Jul 17 12:52:04 EDT 2022
% Result : Theorem 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 1
% Syntax : Number of formulae : 41 ( 24 unt; 0 def)
% Number of atoms : 84 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 77 ( 34 ~; 27 |; 14 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 113 ( 10 sgn 56 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thm147,conjecture,
~ ( ! [P,Q] :
( ~ a_truth(implies(P,Q))
| ~ a_truth(P)
| a_truth(Q) )
& ! [P,Q] : a_truth(implies(P,implies(Q,P)))
& ! [P,Q,R] : a_truth(implies(implies(P,implies(Q,R)),implies(implies(P,Q),implies(P,R))))
& ! [P,Q] : a_truth(implies(implies(not(P),not(Q)),implies(Q,P)))
& ? [A] : ~ a_truth(implies(A,A)) ) ).
fof(subgoal_0,plain,
( ( ! [P,Q] :
( ~ a_truth(implies(P,Q))
| ~ a_truth(P)
| a_truth(Q) )
& ! [P,Q] : a_truth(implies(P,implies(Q,P)))
& ! [P,Q,R] : a_truth(implies(implies(P,implies(Q,R)),implies(implies(P,Q),implies(P,R))))
& ! [P,Q] : a_truth(implies(implies(not(P),not(Q)),implies(Q,P))) )
=> ! [A] : a_truth(implies(A,A)) ),
inference(strip,[],[thm147]) ).
fof(negate_0_0,plain,
~ ( ( ! [P,Q] :
( ~ a_truth(implies(P,Q))
| ~ a_truth(P)
| a_truth(Q) )
& ! [P,Q] : a_truth(implies(P,implies(Q,P)))
& ! [P,Q,R] : a_truth(implies(implies(P,implies(Q,R)),implies(implies(P,Q),implies(P,R))))
& ! [P,Q] : a_truth(implies(implies(not(P),not(Q)),implies(Q,P))) )
=> ! [A] : a_truth(implies(A,A)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ? [A] : ~ a_truth(implies(A,A))
& ! [P,Q] : a_truth(implies(P,implies(Q,P)))
& ! [P,Q] : a_truth(implies(implies(not(P),not(Q)),implies(Q,P)))
& ! [P,Q] :
( ~ a_truth(P)
| ~ a_truth(implies(P,Q))
| a_truth(Q) )
& ! [P,Q,R] : a_truth(implies(implies(P,implies(Q,R)),implies(implies(P,Q),implies(P,R)))) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
? [A] : ~ a_truth(implies(A,A)),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ a_truth(implies(skolemFOFtoCNF_A,skolemFOFtoCNF_A)),
inference(skolemize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [P,Q] : a_truth(implies(P,implies(Q,P))),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_4,plain,
! [P,Q] : a_truth(implies(P,implies(Q,P))),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [P,Q] :
( ~ a_truth(P)
| ~ a_truth(implies(P,Q))
| a_truth(Q) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_6,plain,
! [P,Q] :
( ~ a_truth(P)
| ~ a_truth(implies(P,Q))
| a_truth(Q) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [P,Q] : a_truth(implies(implies(not(P),not(Q)),implies(Q,P))),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_8,plain,
! [P,Q] : a_truth(implies(implies(not(P),not(Q)),implies(Q,P))),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [P,Q,R] : a_truth(implies(implies(P,implies(Q,R)),implies(implies(P,Q),implies(P,R)))),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_10,plain,
! [P,Q,R] : a_truth(implies(implies(P,implies(Q,R)),implies(implies(P,Q),implies(P,R)))),
inference(specialize,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
~ a_truth(implies(skolemFOFtoCNF_A,skolemFOFtoCNF_A)),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
a_truth(implies(P,implies(Q,P))),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
a_truth(implies(X_7,implies(Q,X_7))),
inference(subst,[],[refute_0_1:[bind(P,$fot(X_7))]]) ).
cnf(refute_0_3,plain,
( ~ a_truth(P)
| ~ a_truth(implies(P,Q))
| a_truth(Q) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
( ~ a_truth(X_7)
| ~ a_truth(implies(X_7,implies(Q,X_7)))
| a_truth(implies(Q,X_7)) ),
inference(subst,[],[refute_0_3:[bind(P,$fot(X_7)),bind(Q,$fot(implies(Q,X_7)))]]) ).
cnf(refute_0_5,plain,
( ~ a_truth(X_7)
| a_truth(implies(Q,X_7)) ),
inference(resolve,[$cnf( a_truth(implies(X_7,implies(Q,X_7))) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ a_truth(implies(implies(implies(not(X_56),not(X_55)),X_55),implies(implies(not(X_56),not(X_55)),X_56)))
| a_truth(implies(Q,implies(implies(implies(not(X_56),not(X_55)),X_55),implies(implies(not(X_56),not(X_55)),X_56)))) ),
inference(subst,[],[refute_0_5:[bind(X_7,$fot(implies(implies(implies(not(X_56),not(X_55)),X_55),implies(implies(not(X_56),not(X_55)),X_56))))]]) ).
cnf(refute_0_7,plain,
a_truth(implies(implies(not(P),not(Q)),implies(Q,P))),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_8,plain,
a_truth(implies(implies(not(X_54),not(X_53)),implies(X_53,X_54))),
inference(subst,[],[refute_0_7:[bind(P,$fot(X_54)),bind(Q,$fot(X_53))]]) ).
cnf(refute_0_9,plain,
a_truth(implies(implies(P,implies(Q,R)),implies(implies(P,Q),implies(P,R)))),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_10,plain,
( ~ a_truth(implies(P,implies(Q,R)))
| ~ a_truth(implies(implies(P,implies(Q,R)),implies(implies(P,Q),implies(P,R))))
| a_truth(implies(implies(P,Q),implies(P,R))) ),
inference(subst,[],[refute_0_3:[bind(P,$fot(implies(P,implies(Q,R)))),bind(Q,$fot(implies(implies(P,Q),implies(P,R))))]]) ).
cnf(refute_0_11,plain,
( ~ a_truth(implies(P,implies(Q,R)))
| a_truth(implies(implies(P,Q),implies(P,R))) ),
inference(resolve,[$cnf( a_truth(implies(implies(P,implies(Q,R)),implies(implies(P,Q),implies(P,R)))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ a_truth(implies(implies(not(X_54),not(X_53)),implies(X_53,X_54)))
| a_truth(implies(implies(implies(not(X_54),not(X_53)),X_53),implies(implies(not(X_54),not(X_53)),X_54))) ),
inference(subst,[],[refute_0_11:[bind(P,$fot(implies(not(X_54),not(X_53)))),bind(Q,$fot(X_53)),bind(R,$fot(X_54))]]) ).
cnf(refute_0_13,plain,
a_truth(implies(implies(implies(not(X_54),not(X_53)),X_53),implies(implies(not(X_54),not(X_53)),X_54))),
inference(resolve,[$cnf( a_truth(implies(implies(not(X_54),not(X_53)),implies(X_53,X_54))) )],[refute_0_8,refute_0_12]) ).
cnf(refute_0_14,plain,
a_truth(implies(implies(implies(not(X_56),not(X_55)),X_55),implies(implies(not(X_56),not(X_55)),X_56))),
inference(subst,[],[refute_0_13:[bind(X_53,$fot(X_55)),bind(X_54,$fot(X_56))]]) ).
cnf(refute_0_15,plain,
a_truth(implies(Q,implies(implies(implies(not(X_56),not(X_55)),X_55),implies(implies(not(X_56),not(X_55)),X_56)))),
inference(resolve,[$cnf( a_truth(implies(implies(implies(not(X_56),not(X_55)),X_55),implies(implies(not(X_56),not(X_55)),X_56))) )],[refute_0_14,refute_0_6]) ).
cnf(refute_0_16,plain,
a_truth(implies(X_74,implies(implies(implies(not(X_56),not(X_55)),X_55),implies(implies(not(X_56),not(X_55)),X_56)))),
inference(subst,[],[refute_0_15:[bind(Q,$fot(X_74))]]) ).
cnf(refute_0_17,plain,
( ~ a_truth(implies(X_58,X_57))
| ~ a_truth(implies(implies(X_58,X_57),implies(X_58,X_58)))
| a_truth(implies(X_58,X_58)) ),
inference(subst,[],[refute_0_3:[bind(P,$fot(implies(X_58,X_57))),bind(Q,$fot(implies(X_58,X_58)))]]) ).
cnf(refute_0_18,plain,
a_truth(implies(X_54,implies(X_53,X_54))),
inference(subst,[],[refute_0_1:[bind(P,$fot(X_54)),bind(Q,$fot(X_53))]]) ).
cnf(refute_0_19,plain,
( ~ a_truth(implies(X_54,implies(X_53,X_54)))
| a_truth(implies(implies(X_54,X_53),implies(X_54,X_54))) ),
inference(subst,[],[refute_0_11:[bind(P,$fot(X_54)),bind(Q,$fot(X_53)),bind(R,$fot(X_54))]]) ).
cnf(refute_0_20,plain,
a_truth(implies(implies(X_54,X_53),implies(X_54,X_54))),
inference(resolve,[$cnf( a_truth(implies(X_54,implies(X_53,X_54))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
a_truth(implies(implies(X_58,X_57),implies(X_58,X_58))),
inference(subst,[],[refute_0_20:[bind(X_53,$fot(X_57)),bind(X_54,$fot(X_58))]]) ).
cnf(refute_0_22,plain,
( ~ a_truth(implies(X_58,X_57))
| a_truth(implies(X_58,X_58)) ),
inference(resolve,[$cnf( a_truth(implies(implies(X_58,X_57),implies(X_58,X_58))) )],[refute_0_21,refute_0_17]) ).
cnf(refute_0_23,plain,
( ~ a_truth(implies(X_74,implies(implies(implies(not(X_56),not(X_55)),X_55),implies(implies(not(X_56),not(X_55)),X_56))))
| a_truth(implies(X_74,X_74)) ),
inference(subst,[],[refute_0_22:[bind(X_57,$fot(implies(implies(implies(not(X_56),not(X_55)),X_55),implies(implies(not(X_56),not(X_55)),X_56)))),bind(X_58,$fot(X_74))]]) ).
cnf(refute_0_24,plain,
a_truth(implies(X_74,X_74)),
inference(resolve,[$cnf( a_truth(implies(X_74,implies(implies(implies(not(X_56),not(X_55)),X_55),implies(implies(not(X_56),not(X_55)),X_56)))) )],[refute_0_16,refute_0_23]) ).
cnf(refute_0_25,plain,
a_truth(implies(skolemFOFtoCNF_A,skolemFOFtoCNF_A)),
inference(subst,[],[refute_0_24:[bind(X_74,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_26,plain,
$false,
inference(resolve,[$cnf( a_truth(implies(skolemFOFtoCNF_A,skolemFOFtoCNF_A)) )],[refute_0_25,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL414+1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jul 4 03:57:19 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35
% 0.13/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.36
%------------------------------------------------------------------------------