TSTP Solution File: SET194+3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET194+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 03:33:28 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 : 75 ( 33 ~; 27 |; 8 &)
% ( 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 : 87 ( 6 sgn 41 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(union_defn,axiom,
! [B,C,D] :
( member(D,union(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_union,axiom,
! [B,C] : union(B,C) = union(C,B) ).
fof(prove_subset_of_union,conjecture,
! [B,C] : subset(B,union(B,C)) ).
fof(subgoal_0,plain,
! [B,C] : subset(B,union(B,C)),
inference(strip,[],[prove_subset_of_union]) ).
fof(negate_0_0,plain,
~ ! [B,C] : subset(B,union(B,C)),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B,C] : ~ subset(B,union(B,C)),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
~ subset(skolemFOFtoCNF_B,union(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),
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,union(B,C))
<=> ( ~ member(D,B)
& ~ member(D,C) ) ),
inference(canonicalize,[],[union_defn]) ).
fof(normalize_0_8,plain,
! [B,C,D] :
( ~ member(D,union(B,C))
<=> ( ~ member(D,B)
& ~ member(D,C) ) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [B,C,D] :
( ( ~ member(D,B)
| member(D,union(B,C)) )
& ( ~ member(D,C)
| member(D,union(B,C)) )
& ( ~ member(D,union(B,C))
| member(D,B)
| member(D,C) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [B,C,D] :
( ~ member(D,C)
| member(D,union(B,C)) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [B,C] : union(B,C) = union(C,B),
inference(canonicalize,[],[commutativity_of_union]) ).
fof(normalize_0_12,plain,
! [B,C] : union(B,C) = union(C,B),
inference(specialize,[],[normalize_0_11]) ).
cnf(refute_0_0,plain,
~ subset(skolemFOFtoCNF_B,union(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),
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(X_15,union(X_14,X_15)),union(X_14,X_15))
| subset(X_15,union(X_14,X_15)) ),
inference(subst,[],[refute_0_1:[bind(B,$fot(X_15)),bind(C,$fot(union(X_14,X_15)))]]) ).
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(X_11,C),X_11)
| subset(X_11,C) ),
inference(subst,[],[refute_0_3:[bind(B,$fot(X_11))]]) ).
cnf(refute_0_5,plain,
( ~ member(D,C)
| member(D,union(B,C)) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_6,plain,
( ~ member(skolemFOFtoCNF_D(X_11,C),X_11)
| member(skolemFOFtoCNF_D(X_11,C),union(X_10,X_11)) ),
inference(subst,[],[refute_0_5:[bind(B,$fot(X_10)),bind(C,$fot(X_11)),bind(D,$fot(skolemFOFtoCNF_D(X_11,C)))]]) ).
cnf(refute_0_7,plain,
( member(skolemFOFtoCNF_D(X_11,C),union(X_10,X_11))
| subset(X_11,C) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(X_11,C),X_11) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( member(skolemFOFtoCNF_D(X_15,union(X_14,X_15)),union(X_14,X_15))
| subset(X_15,union(X_14,X_15)) ),
inference(subst,[],[refute_0_7:[bind(C,$fot(union(X_14,X_15))),bind(X_10,$fot(X_14)),bind(X_11,$fot(X_15))]]) ).
cnf(refute_0_9,plain,
subset(X_15,union(X_14,X_15)),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(X_15,union(X_14,X_15)),union(X_14,X_15)) )],[refute_0_8,refute_0_2]) ).
cnf(refute_0_10,plain,
subset(X_17,union(X_16,X_17)),
inference(subst,[],[refute_0_9:[bind(X_14,$fot(X_16)),bind(X_15,$fot(X_17))]]) ).
cnf(refute_0_11,plain,
union(B,C) = union(C,B),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_12,plain,
union(X_17,X_16) = union(X_16,X_17),
inference(subst,[],[refute_0_11:[bind(B,$fot(X_17)),bind(C,$fot(X_16))]]) ).
cnf(refute_0_13,plain,
X = X,
introduced(tautology,[refl,[$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( $equal(X,X) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( union(X_17,X_16) != union(X_16,X_17)
| union(X_16,X_17) = union(X_17,X_16) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(union(X_17,X_16))),bind(Y,$fot(union(X_16,X_17)))]]) ).
cnf(refute_0_17,plain,
union(X_16,X_17) = union(X_17,X_16),
inference(resolve,[$cnf( $equal(union(X_17,X_16),union(X_16,X_17)) )],[refute_0_12,refute_0_16]) ).
cnf(refute_0_18,plain,
( union(X_16,X_17) != union(X_17,X_16)
| ~ subset(X_17,union(X_16,X_17))
| subset(X_17,union(X_17,X_16)) ),
introduced(tautology,[equality,[$cnf( subset(X_17,union(X_16,X_17)) ),[1],$fot(union(X_17,X_16))]]) ).
cnf(refute_0_19,plain,
( ~ subset(X_17,union(X_16,X_17))
| subset(X_17,union(X_17,X_16)) ),
inference(resolve,[$cnf( $equal(union(X_16,X_17),union(X_17,X_16)) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
subset(X_17,union(X_17,X_16)),
inference(resolve,[$cnf( subset(X_17,union(X_16,X_17)) )],[refute_0_10,refute_0_19]) ).
cnf(refute_0_21,plain,
subset(skolemFOFtoCNF_B,union(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),
inference(subst,[],[refute_0_20:[bind(X_16,$fot(skolemFOFtoCNF_C)),bind(X_17,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_22,plain,
$false,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,union(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) )],[refute_0_21,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET194+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n023.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 : Sun Jul 10 13:44:40 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
% 0.12/0.34
%------------------------------------------------------------------------------