TSTP Solution File: SET599+3 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET599+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 03:35:47 EDT 2022
% Result : Theorem 0.13s 0.36s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 21 unt; 0 def)
% Number of atoms : 33 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 11 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 43 ( 1 sgn 18 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(symmetric_difference_defn,axiom,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)) ).
fof(subset_of_union,axiom,
! [B,C] : subset(B,union(B,C)) ).
fof(prove_th58,conjecture,
! [B,C] : subset(difference(B,C),symmetric_difference(B,C)) ).
fof(subgoal_0,plain,
! [B,C] : subset(difference(B,C),symmetric_difference(B,C)),
inference(strip,[],[prove_th58]) ).
fof(negate_0_0,plain,
~ ! [B,C] : subset(difference(B,C),symmetric_difference(B,C)),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B,C] : ~ subset(difference(B,C),symmetric_difference(B,C)),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
~ subset(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),
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] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
inference(canonicalize,[],[symmetric_difference_defn]) ).
fof(normalize_0_5,plain,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
inference(specialize,[],[normalize_0_4]) ).
cnf(refute_0_0,plain,
~ subset(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),
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(difference(X_9,X_10),union(difference(X_9,X_10),difference(X_10,X_9))),
inference(subst,[],[refute_0_1:[bind(B,$fot(difference(X_9,X_10))),bind(C,$fot(difference(X_10,X_9)))]]) ).
cnf(refute_0_3,plain,
symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
symmetric_difference(X_9,X_10) = union(difference(X_9,X_10),difference(X_10,X_9)),
inference(subst,[],[refute_0_3:[bind(B,$fot(X_9)),bind(C,$fot(X_10))]]) ).
cnf(refute_0_5,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_6,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_7,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( symmetric_difference(X_9,X_10) != union(difference(X_9,X_10),difference(X_10,X_9))
| union(difference(X_9,X_10),difference(X_10,X_9)) = symmetric_difference(X_9,X_10) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(symmetric_difference(X_9,X_10))),bind(Y,$fot(union(difference(X_9,X_10),difference(X_10,X_9))))]]) ).
cnf(refute_0_9,plain,
union(difference(X_9,X_10),difference(X_10,X_9)) = symmetric_difference(X_9,X_10),
inference(resolve,[$cnf( $equal(symmetric_difference(X_9,X_10),union(difference(X_9,X_10),difference(X_10,X_9))) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
( union(difference(X_9,X_10),difference(X_10,X_9)) != symmetric_difference(X_9,X_10)
| ~ subset(difference(X_9,X_10),union(difference(X_9,X_10),difference(X_10,X_9)))
| subset(difference(X_9,X_10),symmetric_difference(X_9,X_10)) ),
introduced(tautology,[equality,[$cnf( subset(difference(X_9,X_10),union(difference(X_9,X_10),difference(X_10,X_9))) ),[1],$fot(symmetric_difference(X_9,X_10))]]) ).
cnf(refute_0_11,plain,
( ~ subset(difference(X_9,X_10),union(difference(X_9,X_10),difference(X_10,X_9)))
| subset(difference(X_9,X_10),symmetric_difference(X_9,X_10)) ),
inference(resolve,[$cnf( $equal(union(difference(X_9,X_10),difference(X_10,X_9)),symmetric_difference(X_9,X_10)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
subset(difference(X_9,X_10),symmetric_difference(X_9,X_10)),
inference(resolve,[$cnf( subset(difference(X_9,X_10),union(difference(X_9,X_10),difference(X_10,X_9))) )],[refute_0_2,refute_0_11]) ).
cnf(refute_0_13,plain,
subset(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),
inference(subst,[],[refute_0_12:[bind(X_10,$fot(skolemFOFtoCNF_C)),bind(X_9,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_14,plain,
$false,
inference(resolve,[$cnf( subset(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) )],[refute_0_13,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET599+3 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n008.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 : Sun Jul 10 21:33:23 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.36
% 0.13/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.36
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