TSTP Solution File: SET618+3 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET618+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.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 03:36:02 EDT 2022
% Result : Theorem 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 38 ( 29 unt; 0 def)
% Number of atoms : 51 ( 50 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 18 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 15 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(symmetric_difference_defn,axiom,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)) ).
fof(idempotency_of_union,axiom,
! [B] : union(B,B) = B ).
fof(self_difference_is_empty_set,axiom,
! [B] : difference(B,B) = empty_set ).
fof(prove_th93,conjecture,
! [B] : symmetric_difference(B,B) = empty_set ).
fof(subgoal_0,plain,
! [B] : symmetric_difference(B,B) = empty_set,
inference(strip,[],[prove_th93]) ).
fof(negate_0_0,plain,
~ ! [B] : symmetric_difference(B,B) = empty_set,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B] : symmetric_difference(B,B) != empty_set,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_B) != empty_set,
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [B] : union(B,B) = B,
inference(canonicalize,[],[idempotency_of_union]) ).
fof(normalize_0_3,plain,
! [B] : union(B,B) = B,
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]) ).
fof(normalize_0_6,plain,
! [B] : difference(B,B) = empty_set,
inference(canonicalize,[],[self_difference_is_empty_set]) ).
fof(normalize_0_7,plain,
! [B] : difference(B,B) = empty_set,
inference(specialize,[],[normalize_0_6]) ).
cnf(refute_0_0,plain,
symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_B) != empty_set,
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
union(B,B) = B,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
union(difference(X_11,X_11),difference(X_11,X_11)) = difference(X_11,X_11),
inference(subst,[],[refute_0_1:[bind(B,$fot(difference(X_11,X_11)))]]) ).
cnf(refute_0_3,plain,
symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
symmetric_difference(X_11,X_11) = union(difference(X_11,X_11),difference(X_11,X_11)),
inference(subst,[],[refute_0_3:[bind(B,$fot(X_11)),bind(C,$fot(X_11))]]) ).
cnf(refute_0_5,plain,
X = X,
introduced(tautology,[refl,[$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( $equal(X,X) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( symmetric_difference(X_11,X_11) != union(difference(X_11,X_11),difference(X_11,X_11))
| union(difference(X_11,X_11),difference(X_11,X_11)) = symmetric_difference(X_11,X_11) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(symmetric_difference(X_11,X_11))),bind(Y,$fot(union(difference(X_11,X_11),difference(X_11,X_11))))]]) ).
cnf(refute_0_9,plain,
union(difference(X_11,X_11),difference(X_11,X_11)) = symmetric_difference(X_11,X_11),
inference(resolve,[$cnf( $equal(symmetric_difference(X_11,X_11),union(difference(X_11,X_11),difference(X_11,X_11))) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
( union(difference(X_11,X_11),difference(X_11,X_11)) != difference(X_11,X_11)
| union(difference(X_11,X_11),difference(X_11,X_11)) != symmetric_difference(X_11,X_11)
| symmetric_difference(X_11,X_11) = difference(X_11,X_11) ),
introduced(tautology,[equality,[$cnf( $equal(union(difference(X_11,X_11),difference(X_11,X_11)),difference(X_11,X_11)) ),[0],$fot(symmetric_difference(X_11,X_11))]]) ).
cnf(refute_0_11,plain,
( union(difference(X_11,X_11),difference(X_11,X_11)) != difference(X_11,X_11)
| symmetric_difference(X_11,X_11) = difference(X_11,X_11) ),
inference(resolve,[$cnf( $equal(union(difference(X_11,X_11),difference(X_11,X_11)),symmetric_difference(X_11,X_11)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
symmetric_difference(X_11,X_11) = difference(X_11,X_11),
inference(resolve,[$cnf( $equal(union(difference(X_11,X_11),difference(X_11,X_11)),difference(X_11,X_11)) )],[refute_0_2,refute_0_11]) ).
cnf(refute_0_13,plain,
difference(B,B) = empty_set,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_14,plain,
difference(X_11,X_11) = empty_set,
inference(subst,[],[refute_0_13:[bind(B,$fot(X_11))]]) ).
cnf(refute_0_15,plain,
( difference(X_11,X_11) != empty_set
| symmetric_difference(X_11,X_11) != difference(X_11,X_11)
| symmetric_difference(X_11,X_11) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(symmetric_difference(X_11,X_11),difference(X_11,X_11)) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_16,plain,
( symmetric_difference(X_11,X_11) != difference(X_11,X_11)
| symmetric_difference(X_11,X_11) = empty_set ),
inference(resolve,[$cnf( $equal(difference(X_11,X_11),empty_set) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
symmetric_difference(X_11,X_11) = empty_set,
inference(resolve,[$cnf( $equal(symmetric_difference(X_11,X_11),difference(X_11,X_11)) )],[refute_0_12,refute_0_16]) ).
cnf(refute_0_18,plain,
symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_B) = empty_set,
inference(subst,[],[refute_0_17:[bind(X_11,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_19,plain,
( empty_set != empty_set
| symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_B) != empty_set
| symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_B) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_B),empty_set) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_20,plain,
( empty_set != empty_set
| symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_B) = empty_set ),
inference(resolve,[$cnf( $equal(symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_B),empty_set) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
empty_set != empty_set,
inference(resolve,[$cnf( $equal(symmetric_difference(skolemFOFtoCNF_B,skolemFOFtoCNF_B),empty_set) )],[refute_0_20,refute_0_0]) ).
cnf(refute_0_22,plain,
empty_set = empty_set,
introduced(tautology,[refl,[$fot(empty_set)]]) ).
cnf(refute_0_23,plain,
$false,
inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_0_22,refute_0_21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET618+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n007.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 : Sun Jul 10 06:27:46 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35
% 0.13/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.35
%------------------------------------------------------------------------------