TSTP Solution File: SET603+3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET603+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n004.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 03:35:50 EDT 2022
% Result : Theorem 0.20s 0.45s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 71 ( 22 unt; 0 def)
% Number of atoms : 150 ( 35 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 145 ( 66 ~; 60 |; 8 &)
% ( 10 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 129 ( 5 sgn 51 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(difference_defn,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( member(D,B)
& ~ member(D,C) ) ) ).
fof(empty_set_defn,axiom,
! [B] : ~ member(B,empty_set) ).
fof(equal_defn,axiom,
! [B,C] :
( B = C
<=> ( subset(B,C)
& subset(C,B) ) ) ).
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ) ).
fof(prove_th74,conjecture,
! [B] : difference(B,empty_set) = B ).
fof(subgoal_0,plain,
! [B] : difference(B,empty_set) = B,
inference(strip,[],[prove_th74]) ).
fof(negate_0_0,plain,
~ ! [B] : difference(B,empty_set) = B,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B] : difference(B,empty_set) != B,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
difference(skolemFOFtoCNF_B,empty_set) != skolemFOFtoCNF_B,
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [B,C] :
( B != C
<=> ( ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(canonicalize,[],[equal_defn]) ).
fof(normalize_0_3,plain,
! [B,C] :
( B != C
<=> ( ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [B,C] :
( ( B != C
| subset(B,C) )
& ( B != C
| subset(C,B) )
& ( ~ subset(B,C)
| ~ subset(C,B)
| B = C ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [B,C] :
( ~ subset(B,C)
| ~ subset(C,B)
| B = C ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] :
( ~ member(D,C)
& member(D,B) ) ),
inference(canonicalize,[],[subset_defn]) ).
fof(normalize_0_7,plain,
! [B,C,D] :
( ~ member(D,difference(B,C))
<=> ( ~ member(D,B)
| member(D,C) ) ),
inference(canonicalize,[],[difference_defn]) ).
fof(normalize_0_8,plain,
! [B,C,D] :
( ~ member(D,difference(B,C))
<=> ( ~ member(D,B)
| member(D,C) ) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] : member(D,difference(B,C)) ),
inference(simplify,[],[normalize_0_6,normalize_0_8]) ).
fof(normalize_0_10,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] : member(D,difference(B,C)) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [B,C,D] :
( ( ~ member(D,difference(B,C))
| ~ subset(B,C) )
& ( member(skolemFOFtoCNF_D_2(B,C),difference(B,C))
| subset(B,C) ) ),
inference(clausify,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [B,C] :
( member(skolemFOFtoCNF_D_2(B,C),difference(B,C))
| subset(B,C) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,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_8]) ).
fof(normalize_0_14,plain,
! [B,C,D] :
( ~ member(D,C)
| ~ member(D,difference(B,C)) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [B,C,D] :
( ~ member(D,difference(B,C))
| member(D,B) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_16,plain,
! [B] : ~ member(B,empty_set),
inference(canonicalize,[],[empty_set_defn]) ).
fof(normalize_0_17,plain,
! [B] : ~ member(B,empty_set),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [B,C,D] :
( ~ member(D,B)
| member(D,C)
| member(D,difference(B,C)) ),
inference(conjunct,[],[normalize_0_13]) ).
cnf(refute_0_0,plain,
difference(skolemFOFtoCNF_B,empty_set) != skolemFOFtoCNF_B,
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ subset(B,C)
| ~ subset(C,B)
| B = C ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( ~ subset(X_129,difference(X_129,X_130))
| ~ subset(difference(X_129,X_130),X_129)
| X_129 = difference(X_129,X_130) ),
inference(subst,[],[refute_0_1:[bind(B,$fot(X_129)),bind(C,$fot(difference(X_129,X_130)))]]) ).
cnf(refute_0_3,plain,
( member(skolemFOFtoCNF_D_2(B,C),difference(B,C))
| subset(B,C) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_4,plain,
( member(skolemFOFtoCNF_D_2(X_9,X_10),difference(X_9,X_10))
| subset(X_9,X_10) ),
inference(subst,[],[refute_0_3:[bind(B,$fot(X_9)),bind(C,$fot(X_10))]]) ).
cnf(refute_0_5,plain,
( ~ member(D,C)
| ~ member(D,difference(B,C)) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_6,plain,
( ~ member(skolemFOFtoCNF_D_2(X_9,X_10),X_10)
| ~ member(skolemFOFtoCNF_D_2(X_9,X_10),difference(X_9,X_10)) ),
inference(subst,[],[refute_0_5:[bind(B,$fot(X_9)),bind(C,$fot(X_10)),bind(D,$fot(skolemFOFtoCNF_D_2(X_9,X_10)))]]) ).
cnf(refute_0_7,plain,
( ~ member(skolemFOFtoCNF_D_2(X_9,X_10),X_10)
| subset(X_9,X_10) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_2(X_9,X_10),difference(X_9,X_10)) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ member(skolemFOFtoCNF_D_2(difference(X_126,X_127),X_126),X_126)
| subset(difference(X_126,X_127),X_126) ),
inference(subst,[],[refute_0_7:[bind(X_10,$fot(X_126)),bind(X_9,$fot(difference(X_126,X_127)))]]) ).
cnf(refute_0_9,plain,
( ~ member(D,difference(B,C))
| member(D,B) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_10,plain,
( ~ member(skolemFOFtoCNF_D_2(difference(B,C),X_18),difference(B,C))
| member(skolemFOFtoCNF_D_2(difference(B,C),X_18),B) ),
inference(subst,[],[refute_0_9:[bind(D,$fot(skolemFOFtoCNF_D_2(difference(B,C),X_18)))]]) ).
cnf(refute_0_11,plain,
( member(skolemFOFtoCNF_D_2(X_14,X_15),difference(X_14,X_15))
| subset(X_14,X_15) ),
inference(subst,[],[refute_0_3:[bind(B,$fot(X_14)),bind(C,$fot(X_15))]]) ).
cnf(refute_0_12,plain,
( ~ member(skolemFOFtoCNF_D_2(X_14,X_15),difference(X_14,X_15))
| member(skolemFOFtoCNF_D_2(X_14,X_15),X_14) ),
inference(subst,[],[refute_0_9:[bind(B,$fot(X_14)),bind(C,$fot(X_15)),bind(D,$fot(skolemFOFtoCNF_D_2(X_14,X_15)))]]) ).
cnf(refute_0_13,plain,
( member(skolemFOFtoCNF_D_2(X_14,X_15),X_14)
| subset(X_14,X_15) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_2(X_14,X_15),difference(X_14,X_15)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( member(skolemFOFtoCNF_D_2(difference(B,C),X_18),difference(B,C))
| subset(difference(B,C),X_18) ),
inference(subst,[],[refute_0_13:[bind(X_14,$fot(difference(B,C))),bind(X_15,$fot(X_18))]]) ).
cnf(refute_0_15,plain,
( member(skolemFOFtoCNF_D_2(difference(B,C),X_18),B)
| subset(difference(B,C),X_18) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_2(difference(B,C),X_18),difference(B,C)) )],[refute_0_14,refute_0_10]) ).
cnf(refute_0_16,plain,
( member(skolemFOFtoCNF_D_2(difference(X_126,X_127),X_126),X_126)
| subset(difference(X_126,X_127),X_126) ),
inference(subst,[],[refute_0_15:[bind(B,$fot(X_126)),bind(C,$fot(X_127)),bind(X_18,$fot(X_126))]]) ).
cnf(refute_0_17,plain,
subset(difference(X_126,X_127),X_126),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_2(difference(X_126,X_127),X_126),X_126) )],[refute_0_16,refute_0_8]) ).
cnf(refute_0_18,plain,
subset(difference(X_129,X_130),X_129),
inference(subst,[],[refute_0_17:[bind(X_126,$fot(X_129)),bind(X_127,$fot(X_130))]]) ).
cnf(refute_0_19,plain,
( ~ subset(X_129,difference(X_129,X_130))
| X_129 = difference(X_129,X_130) ),
inference(resolve,[$cnf( subset(difference(X_129,X_130),X_129) )],[refute_0_18,refute_0_2]) ).
cnf(refute_0_20,plain,
( ~ subset(X_278,difference(X_278,empty_set))
| X_278 = difference(X_278,empty_set) ),
inference(subst,[],[refute_0_19:[bind(X_129,$fot(X_278)),bind(X_130,$fot(empty_set))]]) ).
cnf(refute_0_21,plain,
~ member(B,empty_set),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_22,plain,
~ member(skolemFOFtoCNF_D_2(X_276,difference(X_276,empty_set)),empty_set),
inference(subst,[],[refute_0_21:[bind(B,$fot(skolemFOFtoCNF_D_2(X_276,difference(X_276,empty_set))))]]) ).
cnf(refute_0_23,plain,
( ~ member(skolemFOFtoCNF_D_2(X_273,difference(X_273,X_274)),difference(X_273,X_274))
| subset(X_273,difference(X_273,X_274)) ),
inference(subst,[],[refute_0_7:[bind(X_10,$fot(difference(X_273,X_274))),bind(X_9,$fot(X_273))]]) ).
cnf(refute_0_24,plain,
( member(skolemFOFtoCNF_D_2(X_101,X_15),X_101)
| subset(X_101,X_15) ),
inference(subst,[],[refute_0_13:[bind(X_14,$fot(X_101))]]) ).
cnf(refute_0_25,plain,
( ~ member(D,B)
| member(D,C)
| member(D,difference(B,C)) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_26,plain,
( ~ member(skolemFOFtoCNF_D_2(X_101,X_15),X_101)
| member(skolemFOFtoCNF_D_2(X_101,X_15),X_102)
| member(skolemFOFtoCNF_D_2(X_101,X_15),difference(X_101,X_102)) ),
inference(subst,[],[refute_0_25:[bind(B,$fot(X_101)),bind(C,$fot(X_102)),bind(D,$fot(skolemFOFtoCNF_D_2(X_101,X_15)))]]) ).
cnf(refute_0_27,plain,
( member(skolemFOFtoCNF_D_2(X_101,X_15),X_102)
| member(skolemFOFtoCNF_D_2(X_101,X_15),difference(X_101,X_102))
| subset(X_101,X_15) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_2(X_101,X_15),X_101) )],[refute_0_24,refute_0_26]) ).
cnf(refute_0_28,plain,
( member(skolemFOFtoCNF_D_2(X_273,difference(X_273,X_274)),X_274)
| member(skolemFOFtoCNF_D_2(X_273,difference(X_273,X_274)),difference(X_273,X_274))
| subset(X_273,difference(X_273,X_274)) ),
inference(subst,[],[refute_0_27:[bind(X_101,$fot(X_273)),bind(X_102,$fot(X_274)),bind(X_15,$fot(difference(X_273,X_274)))]]) ).
cnf(refute_0_29,plain,
( member(skolemFOFtoCNF_D_2(X_273,difference(X_273,X_274)),X_274)
| subset(X_273,difference(X_273,X_274)) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_2(X_273,difference(X_273,X_274)),difference(X_273,X_274)) )],[refute_0_28,refute_0_23]) ).
cnf(refute_0_30,plain,
( member(skolemFOFtoCNF_D_2(X_276,difference(X_276,empty_set)),empty_set)
| subset(X_276,difference(X_276,empty_set)) ),
inference(subst,[],[refute_0_29:[bind(X_273,$fot(X_276)),bind(X_274,$fot(empty_set))]]) ).
cnf(refute_0_31,plain,
subset(X_276,difference(X_276,empty_set)),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_2(X_276,difference(X_276,empty_set)),empty_set) )],[refute_0_30,refute_0_22]) ).
cnf(refute_0_32,plain,
subset(X_278,difference(X_278,empty_set)),
inference(subst,[],[refute_0_31:[bind(X_276,$fot(X_278))]]) ).
cnf(refute_0_33,plain,
X_278 = difference(X_278,empty_set),
inference(resolve,[$cnf( subset(X_278,difference(X_278,empty_set)) )],[refute_0_32,refute_0_20]) ).
cnf(refute_0_34,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_35,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_36,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( X_278 != difference(X_278,empty_set)
| difference(X_278,empty_set) = X_278 ),
inference(subst,[],[refute_0_36:[bind(X,$fot(X_278)),bind(Y,$fot(difference(X_278,empty_set)))]]) ).
cnf(refute_0_38,plain,
difference(X_278,empty_set) = X_278,
inference(resolve,[$cnf( $equal(X_278,difference(X_278,empty_set)) )],[refute_0_33,refute_0_37]) ).
cnf(refute_0_39,plain,
difference(skolemFOFtoCNF_B,empty_set) = skolemFOFtoCNF_B,
inference(subst,[],[refute_0_38:[bind(X_278,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_40,plain,
( difference(skolemFOFtoCNF_B,empty_set) != skolemFOFtoCNF_B
| skolemFOFtoCNF_B != skolemFOFtoCNF_B
| difference(skolemFOFtoCNF_B,empty_set) = skolemFOFtoCNF_B ),
introduced(tautology,[equality,[$cnf( ~ $equal(difference(skolemFOFtoCNF_B,empty_set),skolemFOFtoCNF_B) ),[0],$fot(skolemFOFtoCNF_B)]]) ).
cnf(refute_0_41,plain,
( skolemFOFtoCNF_B != skolemFOFtoCNF_B
| difference(skolemFOFtoCNF_B,empty_set) = skolemFOFtoCNF_B ),
inference(resolve,[$cnf( $equal(difference(skolemFOFtoCNF_B,empty_set),skolemFOFtoCNF_B) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
skolemFOFtoCNF_B != skolemFOFtoCNF_B,
inference(resolve,[$cnf( $equal(difference(skolemFOFtoCNF_B,empty_set),skolemFOFtoCNF_B) )],[refute_0_41,refute_0_0]) ).
cnf(refute_0_43,plain,
skolemFOFtoCNF_B = skolemFOFtoCNF_B,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_B)]]) ).
cnf(refute_0_44,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,skolemFOFtoCNF_B) )],[refute_0_43,refute_0_42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET603+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 : n004.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 14:35:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.45
% 0.20/0.45 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.46
%------------------------------------------------------------------------------