TSTP Solution File: SET633+3 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET633+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 03:36:12 EDT 2022
% Result : Theorem 0.20s 0.47s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 16 unt; 0 def)
% Number of atoms : 62 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 51 ( 22 ~; 17 |; 8 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 24 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(symmetric_difference_defn,axiom,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)) ).
fof(union_subset,axiom,
! [B,C,D] :
( ( subset(B,C)
& subset(D,C) )
=> subset(union(B,D),C) ) ).
fof(prove_th115,conjecture,
! [B,C,D] :
( ( subset(difference(B,C),D)
& subset(difference(C,B),D) )
=> subset(symmetric_difference(B,C),D) ) ).
fof(subgoal_0,plain,
! [B,C,D] :
( ( subset(difference(B,C),D)
& subset(difference(C,B),D) )
=> subset(symmetric_difference(B,C),D) ),
inference(strip,[],[prove_th115]) ).
fof(negate_0_0,plain,
~ ! [B,C,D] :
( ( subset(difference(B,C),D)
& subset(difference(C,B),D) )
=> subset(symmetric_difference(B,C),D) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B,C,D] :
( ~ subset(symmetric_difference(B,C),D)
& subset(difference(B,C),D)
& subset(difference(C,B),D) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ subset(symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2)
& subset(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2)
& subset(difference(skolemFOFtoCNF_C,skolemFOFtoCNF_B),skolemFOFtoCNF_D_2) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
subset(difference(skolemFOFtoCNF_C,skolemFOFtoCNF_B),skolemFOFtoCNF_D_2),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
subset(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_4,plain,
! [B,C,D] :
( ~ subset(B,C)
| ~ subset(D,C)
| subset(union(B,D),C) ),
inference(canonicalize,[],[union_subset]) ).
fof(normalize_0_5,plain,
! [B,C,D] :
( ~ subset(B,C)
| ~ subset(D,C)
| subset(union(B,D),C) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
inference(canonicalize,[],[symmetric_difference_defn]) ).
fof(normalize_0_7,plain,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
~ subset(symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
subset(difference(skolemFOFtoCNF_C,skolemFOFtoCNF_B),skolemFOFtoCNF_D_2),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
subset(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
( ~ subset(B,C)
| ~ subset(D,C)
| subset(union(B,D),C) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( ~ subset(X_154,skolemFOFtoCNF_D_2)
| ~ subset(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2)
| subset(union(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),X_154),skolemFOFtoCNF_D_2) ),
inference(subst,[],[refute_0_2:[bind(B,$fot(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C))),bind(C,$fot(skolemFOFtoCNF_D_2)),bind(D,$fot(X_154))]]) ).
cnf(refute_0_4,plain,
( ~ subset(X_154,skolemFOFtoCNF_D_2)
| subset(union(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),X_154),skolemFOFtoCNF_D_2) ),
inference(resolve,[$cnf( subset(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ subset(difference(skolemFOFtoCNF_C,skolemFOFtoCNF_B),skolemFOFtoCNF_D_2)
| subset(union(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),difference(skolemFOFtoCNF_C,skolemFOFtoCNF_B)),skolemFOFtoCNF_D_2) ),
inference(subst,[],[refute_0_4:[bind(X_154,$fot(difference(skolemFOFtoCNF_C,skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_6,plain,
subset(union(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),difference(skolemFOFtoCNF_C,skolemFOFtoCNF_B)),skolemFOFtoCNF_D_2),
inference(resolve,[$cnf( subset(difference(skolemFOFtoCNF_C,skolemFOFtoCNF_B),skolemFOFtoCNF_D_2) )],[refute_0_0,refute_0_5]) ).
cnf(refute_0_7,plain,
symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_8,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_9,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_10,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( symmetric_difference(B,C) != union(difference(B,C),difference(C,B))
| union(difference(B,C),difference(C,B)) = symmetric_difference(B,C) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(symmetric_difference(B,C))),bind(Y,$fot(union(difference(B,C),difference(C,B))))]]) ).
cnf(refute_0_12,plain,
union(difference(B,C),difference(C,B)) = symmetric_difference(B,C),
inference(resolve,[$cnf( $equal(symmetric_difference(B,C),union(difference(B,C),difference(C,B))) )],[refute_0_7,refute_0_11]) ).
cnf(refute_0_13,plain,
union(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),difference(skolemFOFtoCNF_C,skolemFOFtoCNF_B)) = symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(subst,[],[refute_0_12:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_14,plain,
( union(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),difference(skolemFOFtoCNF_C,skolemFOFtoCNF_B)) != symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| ~ subset(union(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),difference(skolemFOFtoCNF_C,skolemFOFtoCNF_B)),skolemFOFtoCNF_D_2)
| subset(symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2) ),
introduced(tautology,[equality,[$cnf( subset(union(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),difference(skolemFOFtoCNF_C,skolemFOFtoCNF_B)),skolemFOFtoCNF_D_2) ),[0],$fot(symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C))]]) ).
cnf(refute_0_15,plain,
( ~ subset(union(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),difference(skolemFOFtoCNF_C,skolemFOFtoCNF_B)),skolemFOFtoCNF_D_2)
| subset(symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2) ),
inference(resolve,[$cnf( $equal(union(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),difference(skolemFOFtoCNF_C,skolemFOFtoCNF_B)),symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
subset(symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2),
inference(resolve,[$cnf( subset(union(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),difference(skolemFOFtoCNF_C,skolemFOFtoCNF_B)),skolemFOFtoCNF_D_2) )],[refute_0_6,refute_0_15]) ).
cnf(refute_0_17,plain,
~ subset(symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_18,plain,
$false,
inference(resolve,[$cnf( subset(symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2) )],[refute_0_16,refute_0_17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET633+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n029.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 : Sat Jul 9 22:10:16 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.47
% 0.20/0.47 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.47
%------------------------------------------------------------------------------