TSTP Solution File: SET148+3 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET148+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.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 : Tue Jul 19 03:33:05 EDT 2022
% Result : Theorem 0.19s 0.35s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 16 unt; 0 def)
% Number of atoms : 31 ( 20 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 12 ~; 7 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 12 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset_intersection,axiom,
! [B,C] :
( subset(B,C)
=> intersection(B,C) = B ) ).
fof(reflexivity_of_subset,axiom,
! [B] : subset(B,B) ).
fof(prove_idempotency_of_intersection,conjecture,
! [B] : intersection(B,B) = B ).
fof(subgoal_0,plain,
! [B] : intersection(B,B) = B,
inference(strip,[],[prove_idempotency_of_intersection]) ).
fof(negate_0_0,plain,
~ ! [B] : intersection(B,B) = B,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B] : intersection(B,B) != B,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_B) != skolemFOFtoCNF_B,
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [B] : subset(B,B),
inference(canonicalize,[],[reflexivity_of_subset]) ).
fof(normalize_0_3,plain,
! [B] : subset(B,B),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [B,C] :
( ~ subset(B,C)
| intersection(B,C) = B ),
inference(canonicalize,[],[subset_intersection]) ).
fof(normalize_0_5,plain,
! [B,C] :
( ~ subset(B,C)
| intersection(B,C) = B ),
inference(specialize,[],[normalize_0_4]) ).
cnf(refute_0_0,plain,
intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_B) != skolemFOFtoCNF_B,
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
subset(B,B),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
subset(X_4,X_4),
inference(subst,[],[refute_0_1:[bind(B,$fot(X_4))]]) ).
cnf(refute_0_3,plain,
( ~ subset(B,C)
| intersection(B,C) = B ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
( ~ subset(X_4,X_4)
| intersection(X_4,X_4) = X_4 ),
inference(subst,[],[refute_0_3:[bind(B,$fot(X_4)),bind(C,$fot(X_4))]]) ).
cnf(refute_0_5,plain,
intersection(X_4,X_4) = X_4,
inference(resolve,[$cnf( subset(X_4,X_4) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_B) = skolemFOFtoCNF_B,
inference(subst,[],[refute_0_5:[bind(X_4,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_7,plain,
( intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_B) != skolemFOFtoCNF_B
| skolemFOFtoCNF_B != skolemFOFtoCNF_B
| intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_B) = skolemFOFtoCNF_B ),
introduced(tautology,[equality,[$cnf( ~ $equal(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_B),skolemFOFtoCNF_B) ),[0],$fot(skolemFOFtoCNF_B)]]) ).
cnf(refute_0_8,plain,
( skolemFOFtoCNF_B != skolemFOFtoCNF_B
| intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_B) = skolemFOFtoCNF_B ),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_B),skolemFOFtoCNF_B) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
skolemFOFtoCNF_B != skolemFOFtoCNF_B,
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_B),skolemFOFtoCNF_B) )],[refute_0_8,refute_0_0]) ).
cnf(refute_0_10,plain,
skolemFOFtoCNF_B = skolemFOFtoCNF_B,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_B)]]) ).
cnf(refute_0_11,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,skolemFOFtoCNF_B) )],[refute_0_10,refute_0_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET148+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n023.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 : 600
% 0.13/0.34 % DateTime : Sat Jul 9 22:34:40 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.19/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.35
% 0.19/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.36
%------------------------------------------------------------------------------