TSTP Solution File: SET196+3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET196+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 03:33:29 EDT 2022
% Result : Theorem 0.12s 0.34s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 18 unt; 0 def)
% Number of atoms : 84 ( 15 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 76 ( 34 ~; 28 |; 7 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 88 ( 4 sgn 41 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection_defn,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,B)
& member(D,C) ) ) ).
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ) ).
fof(commutativity_of_intersection,axiom,
! [B,C] : intersection(B,C) = intersection(C,B) ).
fof(prove_intersection_is_subset,conjecture,
! [B,C] : subset(intersection(B,C),B) ).
fof(subgoal_0,plain,
! [B,C] : subset(intersection(B,C),B),
inference(strip,[],[prove_intersection_is_subset]) ).
fof(negate_0_0,plain,
~ ! [B,C] : subset(intersection(B,C),B),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B,C] : ~ subset(intersection(B,C),B),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
~ subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_B),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] :
( ~ member(D,C)
& member(D,B) ) ),
inference(canonicalize,[],[subset_defn]) ).
fof(normalize_0_3,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] :
( ~ member(D,C)
& member(D,B) ) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [B,C,D] :
( ( ~ member(skolemFOFtoCNF_D(B,C),C)
| subset(B,C) )
& ( member(skolemFOFtoCNF_D(B,C),B)
| subset(B,C) )
& ( ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [B,C] :
( ~ member(skolemFOFtoCNF_D(B,C),C)
| subset(B,C) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [B,C] :
( member(skolemFOFtoCNF_D(B,C),B)
| subset(B,C) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_7,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
<=> ( ~ member(D,B)
| ~ member(D,C) ) ),
inference(canonicalize,[],[intersection_defn]) ).
fof(normalize_0_8,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
<=> ( ~ member(D,B)
| ~ member(D,C) ) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [B,C,D] :
( ( ~ member(D,intersection(B,C))
| member(D,B) )
& ( ~ member(D,intersection(B,C))
| member(D,C) )
& ( ~ member(D,B)
| ~ member(D,C)
| member(D,intersection(B,C)) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
| member(D,C) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(canonicalize,[],[commutativity_of_intersection]) ).
fof(normalize_0_12,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(specialize,[],[normalize_0_11]) ).
cnf(refute_0_0,plain,
~ subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ member(skolemFOFtoCNF_D(B,C),C)
| subset(B,C) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( ~ member(skolemFOFtoCNF_D(intersection(X_19,X_20),X_20),X_20)
| subset(intersection(X_19,X_20),X_20) ),
inference(subst,[],[refute_0_1:[bind(B,$fot(intersection(X_19,X_20))),bind(C,$fot(X_20))]]) ).
cnf(refute_0_3,plain,
( member(skolemFOFtoCNF_D(B,C),B)
| subset(B,C) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
( member(skolemFOFtoCNF_D(intersection(X_15,X_16),C),intersection(X_15,X_16))
| subset(intersection(X_15,X_16),C) ),
inference(subst,[],[refute_0_3:[bind(B,$fot(intersection(X_15,X_16)))]]) ).
cnf(refute_0_5,plain,
( ~ member(D,intersection(B,C))
| member(D,C) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_6,plain,
( ~ member(skolemFOFtoCNF_D(intersection(X_15,X_16),C),intersection(X_15,X_16))
| member(skolemFOFtoCNF_D(intersection(X_15,X_16),C),X_16) ),
inference(subst,[],[refute_0_5:[bind(B,$fot(X_15)),bind(C,$fot(X_16)),bind(D,$fot(skolemFOFtoCNF_D(intersection(X_15,X_16),C)))]]) ).
cnf(refute_0_7,plain,
( member(skolemFOFtoCNF_D(intersection(X_15,X_16),C),X_16)
| subset(intersection(X_15,X_16),C) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(intersection(X_15,X_16),C),intersection(X_15,X_16)) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( member(skolemFOFtoCNF_D(intersection(X_19,X_20),X_20),X_20)
| subset(intersection(X_19,X_20),X_20) ),
inference(subst,[],[refute_0_7:[bind(C,$fot(X_20)),bind(X_15,$fot(X_19)),bind(X_16,$fot(X_20))]]) ).
cnf(refute_0_9,plain,
subset(intersection(X_19,X_20),X_20),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(intersection(X_19,X_20),X_20),X_20) )],[refute_0_8,refute_0_2]) ).
cnf(refute_0_10,plain,
subset(intersection(X_21,X_22),X_22),
inference(subst,[],[refute_0_9:[bind(X_19,$fot(X_21)),bind(X_20,$fot(X_22))]]) ).
cnf(refute_0_11,plain,
intersection(B,C) = intersection(C,B),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_12,plain,
intersection(X_22,X_21) = intersection(X_21,X_22),
inference(subst,[],[refute_0_11:[bind(B,$fot(X_22)),bind(C,$fot(X_21))]]) ).
cnf(refute_0_13,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_14,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_15,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( intersection(X_22,X_21) != intersection(X_21,X_22)
| intersection(X_21,X_22) = intersection(X_22,X_21) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(intersection(X_22,X_21))),bind(Y,$fot(intersection(X_21,X_22)))]]) ).
cnf(refute_0_17,plain,
intersection(X_21,X_22) = intersection(X_22,X_21),
inference(resolve,[$cnf( $equal(intersection(X_22,X_21),intersection(X_21,X_22)) )],[refute_0_12,refute_0_16]) ).
cnf(refute_0_18,plain,
( intersection(X_21,X_22) != intersection(X_22,X_21)
| ~ subset(intersection(X_21,X_22),X_22)
| subset(intersection(X_22,X_21),X_22) ),
introduced(tautology,[equality,[$cnf( subset(intersection(X_21,X_22),X_22) ),[0],$fot(intersection(X_22,X_21))]]) ).
cnf(refute_0_19,plain,
( ~ subset(intersection(X_21,X_22),X_22)
| subset(intersection(X_22,X_21),X_22) ),
inference(resolve,[$cnf( $equal(intersection(X_21,X_22),intersection(X_22,X_21)) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
subset(intersection(X_22,X_21),X_22),
inference(resolve,[$cnf( subset(intersection(X_21,X_22),X_22) )],[refute_0_10,refute_0_19]) ).
cnf(refute_0_21,plain,
subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_B),
inference(subst,[],[refute_0_20:[bind(X_21,$fot(skolemFOFtoCNF_C)),bind(X_22,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_22,plain,
$false,
inference(resolve,[$cnf( subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_B) )],[refute_0_21,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET196+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 11 05:14:47 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34
% 0.12/0.34 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35
%------------------------------------------------------------------------------