TSTP Solution File: SET590+3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET590+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 03:35:41 EDT 2022
% Result : Theorem 0.13s 0.36s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 35 ( 9 unt; 0 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 69 ( 31 ~; 25 |; 5 &)
% ( 7 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 78 ( 3 sgn 38 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(difference_defn,axiom,
! [B,C,D] :
( member(D,difference(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(prove_th49,conjecture,
! [B,C] : subset(difference(B,C),B) ).
fof(subgoal_0,plain,
! [B,C] : subset(difference(B,C),B),
inference(strip,[],[prove_th49]) ).
fof(negate_0_0,plain,
~ ! [B,C] : subset(difference(B,C),B),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B,C] : ~ subset(difference(B,C),B),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
~ subset(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_B),
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,D] :
( ~ member(D,difference(B,C))
<=> ( ~ member(D,B)
| member(D,C) ) ),
inference(canonicalize,[],[difference_defn]) ).
fof(normalize_0_4,plain,
! [B,C,D] :
( ~ member(D,difference(B,C))
<=> ( ~ member(D,B)
| member(D,C) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] : member(D,difference(B,C)) ),
inference(simplify,[],[normalize_0_2,normalize_0_4]) ).
fof(normalize_0_6,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] : member(D,difference(B,C)) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [B,C,D] :
( ( ~ member(D,difference(B,C))
| ~ subset(B,C) )
& ( member(skolemFOFtoCNF_D(B,C),difference(B,C))
| subset(B,C) ) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [B,C] :
( member(skolemFOFtoCNF_D(B,C),difference(B,C))
| subset(B,C) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [B,C,D] :
( ( ~ member(D,C)
| ~ member(D,difference(B,C)) )
& ( ~ member(D,difference(B,C))
| member(D,B) )
& ( ~ member(D,B)
| member(D,C)
| member(D,difference(B,C)) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_10,plain,
! [B,C,D] :
( ~ member(D,C)
| ~ member(D,difference(B,C)) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [B,C,D] :
( ~ member(D,difference(B,C))
| member(D,B) ),
inference(conjunct,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
~ subset(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( member(skolemFOFtoCNF_D(B,C),difference(B,C))
| subset(B,C) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_2,plain,
( member(skolemFOFtoCNF_D(X_3,X_4),difference(X_3,X_4))
| subset(X_3,X_4) ),
inference(subst,[],[refute_0_1:[bind(B,$fot(X_3)),bind(C,$fot(X_4))]]) ).
cnf(refute_0_3,plain,
( ~ member(D,C)
| ~ member(D,difference(B,C)) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_4,plain,
( ~ member(skolemFOFtoCNF_D(X_3,X_4),X_4)
| ~ member(skolemFOFtoCNF_D(X_3,X_4),difference(X_3,X_4)) ),
inference(subst,[],[refute_0_3:[bind(B,$fot(X_3)),bind(C,$fot(X_4)),bind(D,$fot(skolemFOFtoCNF_D(X_3,X_4)))]]) ).
cnf(refute_0_5,plain,
( ~ member(skolemFOFtoCNF_D(X_3,X_4),X_4)
| subset(X_3,X_4) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(X_3,X_4),difference(X_3,X_4)) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ member(skolemFOFtoCNF_D(difference(X_46,X_47),X_46),X_46)
| subset(difference(X_46,X_47),X_46) ),
inference(subst,[],[refute_0_5:[bind(X_3,$fot(difference(X_46,X_47))),bind(X_4,$fot(X_46))]]) ).
cnf(refute_0_7,plain,
( ~ member(D,difference(B,C))
| member(D,B) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_8,plain,
( ~ member(skolemFOFtoCNF_D(difference(B,C),X_12),difference(B,C))
| member(skolemFOFtoCNF_D(difference(B,C),X_12),B) ),
inference(subst,[],[refute_0_7:[bind(D,$fot(skolemFOFtoCNF_D(difference(B,C),X_12)))]]) ).
cnf(refute_0_9,plain,
( member(skolemFOFtoCNF_D(X_8,X_9),difference(X_8,X_9))
| subset(X_8,X_9) ),
inference(subst,[],[refute_0_1:[bind(B,$fot(X_8)),bind(C,$fot(X_9))]]) ).
cnf(refute_0_10,plain,
( ~ member(skolemFOFtoCNF_D(X_8,X_9),difference(X_8,X_9))
| member(skolemFOFtoCNF_D(X_8,X_9),X_8) ),
inference(subst,[],[refute_0_7:[bind(B,$fot(X_8)),bind(C,$fot(X_9)),bind(D,$fot(skolemFOFtoCNF_D(X_8,X_9)))]]) ).
cnf(refute_0_11,plain,
( member(skolemFOFtoCNF_D(X_8,X_9),X_8)
| subset(X_8,X_9) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(X_8,X_9),difference(X_8,X_9)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( member(skolemFOFtoCNF_D(difference(B,C),X_12),difference(B,C))
| subset(difference(B,C),X_12) ),
inference(subst,[],[refute_0_11:[bind(X_8,$fot(difference(B,C))),bind(X_9,$fot(X_12))]]) ).
cnf(refute_0_13,plain,
( member(skolemFOFtoCNF_D(difference(B,C),X_12),B)
| subset(difference(B,C),X_12) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(difference(B,C),X_12),difference(B,C)) )],[refute_0_12,refute_0_8]) ).
cnf(refute_0_14,plain,
( member(skolemFOFtoCNF_D(difference(X_46,X_47),X_46),X_46)
| subset(difference(X_46,X_47),X_46) ),
inference(subst,[],[refute_0_13:[bind(B,$fot(X_46)),bind(C,$fot(X_47)),bind(X_12,$fot(X_46))]]) ).
cnf(refute_0_15,plain,
subset(difference(X_46,X_47),X_46),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(difference(X_46,X_47),X_46),X_46) )],[refute_0_14,refute_0_6]) ).
cnf(refute_0_16,plain,
subset(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_B),
inference(subst,[],[refute_0_15:[bind(X_46,$fot(skolemFOFtoCNF_B)),bind(X_47,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_17,plain,
$false,
inference(resolve,[$cnf( subset(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_B) )],[refute_0_16,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET590+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n027.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 : Sat Jul 9 23:23:47 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36
% 0.13/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.36
%------------------------------------------------------------------------------