TSTP Solution File: SET585+3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET585+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n006.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 03:35:38 EDT 2022
% Result : Theorem 0.23s 0.48s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 43 ( 29 unt; 0 def)
% Number of atoms : 65 ( 16 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 46 ( 24 ~; 20 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 93 ( 13 sgn 36 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(transitivity_of_subset,axiom,
! [B,C,D] :
( ( subset(B,C)
& subset(C,D) )
=> subset(B,D) ) ).
fof(subset_of_union,axiom,
! [B,C] : subset(B,union(B,C)) ).
fof(intersection_is_subset,axiom,
! [B,C] : subset(intersection(B,C),B) ).
fof(commutativity_of_intersection,axiom,
! [B,C] : intersection(B,C) = intersection(C,B) ).
fof(prove_intersection_subset_of_union,conjecture,
! [B,C,D] : subset(intersection(B,C),union(B,D)) ).
fof(subgoal_0,plain,
! [B,C,D] : subset(intersection(B,C),union(B,D)),
inference(strip,[],[prove_intersection_subset_of_union]) ).
fof(negate_0_0,plain,
~ ! [B,C,D] : subset(intersection(B,C),union(B,D)),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B,C,D] : ~ subset(intersection(B,C),union(B,D)),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
~ subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C),union(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [B,C] : subset(B,union(B,C)),
inference(canonicalize,[],[subset_of_union]) ).
fof(normalize_0_3,plain,
! [B,C] : subset(B,union(B,C)),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [B,C] : subset(intersection(B,C),B),
inference(canonicalize,[],[intersection_is_subset]) ).
fof(normalize_0_5,plain,
! [B,C] : subset(intersection(B,C),B),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(canonicalize,[],[commutativity_of_intersection]) ).
fof(normalize_0_7,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [B,C,D] :
( ~ subset(B,C)
| ~ subset(C,D)
| subset(B,D) ),
inference(canonicalize,[],[transitivity_of_subset]) ).
fof(normalize_0_9,plain,
! [B,C,D] :
( ~ subset(B,C)
| ~ subset(C,D)
| subset(B,D) ),
inference(specialize,[],[normalize_0_8]) ).
cnf(refute_0_0,plain,
~ subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C),union(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
subset(B,union(B,C)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
subset(X_139,union(X_139,C)),
inference(subst,[],[refute_0_1:[bind(B,$fot(X_139))]]) ).
cnf(refute_0_3,plain,
subset(intersection(B,C),B),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
intersection(B,C) = intersection(C,B),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( intersection(B,C) != intersection(C,B)
| ~ subset(intersection(B,C),B)
| subset(intersection(C,B),B) ),
introduced(tautology,[equality,[$cnf( subset(intersection(B,C),B) ),[0],$fot(intersection(C,B))]]) ).
cnf(refute_0_6,plain,
( ~ subset(intersection(B,C),B)
| subset(intersection(C,B),B) ),
inference(resolve,[$cnf( $equal(intersection(B,C),intersection(C,B)) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
subset(intersection(C,B),B),
inference(resolve,[$cnf( subset(intersection(B,C),B) )],[refute_0_3,refute_0_6]) ).
cnf(refute_0_8,plain,
subset(intersection(C,X_66),X_66),
inference(subst,[],[refute_0_7:[bind(B,$fot(X_66))]]) ).
cnf(refute_0_9,plain,
( ~ subset(B,C)
| ~ subset(C,D)
| subset(B,D) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_10,plain,
( ~ subset(X_66,X_67)
| ~ subset(intersection(C,X_66),X_66)
| subset(intersection(C,X_66),X_67) ),
inference(subst,[],[refute_0_9:[bind(B,$fot(intersection(C,X_66))),bind(C,$fot(X_66)),bind(D,$fot(X_67))]]) ).
cnf(refute_0_11,plain,
( ~ subset(X_66,X_67)
| subset(intersection(C,X_66),X_67) ),
inference(resolve,[$cnf( subset(intersection(C,X_66),X_66) )],[refute_0_8,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ subset(X_139,union(X_139,C))
| subset(intersection(X_138,X_139),union(X_139,C)) ),
inference(subst,[],[refute_0_11:[bind(C,$fot(X_138)),bind(X_66,$fot(X_139)),bind(X_67,$fot(union(X_139,C)))]]) ).
cnf(refute_0_13,plain,
subset(intersection(X_138,X_139),union(X_139,C)),
inference(resolve,[$cnf( subset(X_139,union(X_139,C)) )],[refute_0_2,refute_0_12]) ).
cnf(refute_0_14,plain,
subset(intersection(X_151,X_152),union(X_152,X_150)),
inference(subst,[],[refute_0_13:[bind(C,$fot(X_150)),bind(X_138,$fot(X_151)),bind(X_139,$fot(X_152))]]) ).
cnf(refute_0_15,plain,
intersection(X_152,X_151) = intersection(X_151,X_152),
inference(subst,[],[refute_0_4:[bind(B,$fot(X_152)),bind(C,$fot(X_151))]]) ).
cnf(refute_0_16,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_17,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_18,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( intersection(X_152,X_151) != intersection(X_151,X_152)
| intersection(X_151,X_152) = intersection(X_152,X_151) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(intersection(X_152,X_151))),bind(Y,$fot(intersection(X_151,X_152)))]]) ).
cnf(refute_0_20,plain,
intersection(X_151,X_152) = intersection(X_152,X_151),
inference(resolve,[$cnf( $equal(intersection(X_152,X_151),intersection(X_151,X_152)) )],[refute_0_15,refute_0_19]) ).
cnf(refute_0_21,plain,
( intersection(X_151,X_152) != intersection(X_152,X_151)
| ~ subset(intersection(X_151,X_152),union(X_152,X_150))
| subset(intersection(X_152,X_151),union(X_152,X_150)) ),
introduced(tautology,[equality,[$cnf( subset(intersection(X_151,X_152),union(X_152,X_150)) ),[0],$fot(intersection(X_152,X_151))]]) ).
cnf(refute_0_22,plain,
( ~ subset(intersection(X_151,X_152),union(X_152,X_150))
| subset(intersection(X_152,X_151),union(X_152,X_150)) ),
inference(resolve,[$cnf( $equal(intersection(X_151,X_152),intersection(X_152,X_151)) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
subset(intersection(X_152,X_151),union(X_152,X_150)),
inference(resolve,[$cnf( subset(intersection(X_151,X_152),union(X_152,X_150)) )],[refute_0_14,refute_0_22]) ).
cnf(refute_0_24,plain,
subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C),union(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)),
inference(subst,[],[refute_0_23:[bind(X_150,$fot(skolemFOFtoCNF_D_2)),bind(X_151,$fot(skolemFOFtoCNF_C)),bind(X_152,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_25,plain,
$false,
inference(resolve,[$cnf( subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C),union(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)) )],[refute_0_24,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : SET585+3 : TPTP v8.1.0. Released v2.2.0.
% 0.15/0.15 % Command : metis --show proof --show saturation %s
% 0.15/0.36 % Computer : n006.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Sun Jul 10 13:54:36 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.15/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.23/0.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.48
% 0.23/0.48 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.23/0.49
%------------------------------------------------------------------------------