TSTP Solution File: SET605+3 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET605+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 03:35:52 EDT 2022
% Result : Theorem 0.12s 0.35s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 16 unt; 0 def)
% Number of atoms : 37 ( 23 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 29 ( 17 ~; 8 |; 1 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 3 sgn 22 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset_of_union,axiom,
! [B,C] : subset(B,union(B,C)) ).
fof(difference_empty_set,axiom,
! [B,C] :
( difference(B,C) = empty_set
<=> subset(B,C) ) ).
fof(prove_th76,conjecture,
! [B,C] : difference(B,union(B,C)) = empty_set ).
fof(subgoal_0,plain,
! [B,C] : difference(B,union(B,C)) = empty_set,
inference(strip,[],[prove_th76]) ).
fof(negate_0_0,plain,
~ ! [B,C] : difference(B,union(B,C)) = empty_set,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B,C] : difference(B,union(B,C)) != empty_set,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) != empty_set,
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] :
( difference(B,C) != empty_set
<=> ~ subset(B,C) ),
inference(canonicalize,[],[difference_empty_set]) ).
fof(normalize_0_5,plain,
! [B,C] :
( difference(B,C) != empty_set
<=> ~ subset(B,C) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [B,C] :
( ( difference(B,C) != empty_set
| subset(B,C) )
& ( ~ subset(B,C)
| difference(B,C) = empty_set ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [B,C] :
( ~ subset(B,C)
| difference(B,C) = empty_set ),
inference(conjunct,[],[normalize_0_6]) ).
cnf(refute_0_0,plain,
difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) != empty_set,
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(X_13,union(X_13,C)),
inference(subst,[],[refute_0_1:[bind(B,$fot(X_13))]]) ).
cnf(refute_0_3,plain,
( ~ subset(B,C)
| difference(B,C) = empty_set ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_4,plain,
( ~ subset(X_13,union(X_13,C))
| difference(X_13,union(X_13,C)) = empty_set ),
inference(subst,[],[refute_0_3:[bind(B,$fot(X_13)),bind(C,$fot(union(X_13,C)))]]) ).
cnf(refute_0_5,plain,
difference(X_13,union(X_13,C)) = empty_set,
inference(resolve,[$cnf( subset(X_13,union(X_13,C)) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) = empty_set,
inference(subst,[],[refute_0_5:[bind(C,$fot(skolemFOFtoCNF_C_1)),bind(X_13,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_7,plain,
( difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) != empty_set
| empty_set != empty_set
| difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) = empty_set ),
introduced(tautology,[equality,[$cnf( ~ $equal(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)),empty_set) ),[0],$fot(empty_set)]]) ).
cnf(refute_0_8,plain,
( empty_set != empty_set
| difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) = empty_set ),
inference(resolve,[$cnf( $equal(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)),empty_set) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
empty_set != empty_set,
inference(resolve,[$cnf( $equal(difference(skolemFOFtoCNF_B,union(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)),empty_set) )],[refute_0_8,refute_0_0]) ).
cnf(refute_0_10,plain,
empty_set = empty_set,
introduced(tautology,[refl,[$fot(empty_set)]]) ).
cnf(refute_0_11,plain,
$false,
inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_0_10,refute_0_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET605+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 11 02:05:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.35
% 0.12/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.36
%------------------------------------------------------------------------------