TSTP Solution File: SET586+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET586+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 03:35:39 EDT 2022
% Result : Theorem 25.00s 25.24s
% Output : CNFRefutation 25.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 66 ( 17 unt; 0 def)
% Number of atoms : 141 ( 15 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 130 ( 55 ~; 56 |; 9 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 133 ( 2 sgn 53 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection_defn,axiom,
! [B,C,D] :
( member(D,intersection(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(commutativity_of_intersection,axiom,
! [B,C] : intersection(B,C) = intersection(C,B) ).
fof(prove_intersection_of_subset,conjecture,
! [B,C,D] :
( subset(B,C)
=> subset(intersection(B,D),intersection(C,D)) ) ).
fof(subgoal_0,plain,
! [B,C,D] :
( subset(B,C)
=> subset(intersection(B,D),intersection(C,D)) ),
inference(strip,[],[prove_intersection_of_subset]) ).
fof(negate_0_0,plain,
~ ! [B,C,D] :
( subset(B,C)
=> subset(intersection(B,D),intersection(C,D)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B,C] :
( subset(B,C)
& ? [D] : ~ subset(intersection(B,D),intersection(C,D)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
& ? [D] : ~ subset(intersection(skolemFOFtoCNF_B,D),intersection(skolemFOFtoCNF_C,D)) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [D] : ~ subset(intersection(skolemFOFtoCNF_B,D),intersection(skolemFOFtoCNF_C,D)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] :
( ~ member(D,C)
& member(D,B) ) ),
inference(canonicalize,[],[subset_defn]) ).
fof(normalize_0_5,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] :
( ~ member(D,C)
& member(D,B) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [B,C,D] :
( ( ~ member(skolemFOFtoCNF_D(B,C),C)
| subset(B,C) )
& ( member(skolemFOFtoCNF_D(B,C),B)
| subset(B,C) )
& ( ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [B,C] :
( ~ member(skolemFOFtoCNF_D(B,C),C)
| subset(B,C) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [B,C] :
( member(skolemFOFtoCNF_D(B,C),B)
| subset(B,C) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_9,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
<=> ( ~ member(D,B)
| ~ member(D,C) ) ),
inference(canonicalize,[],[intersection_defn]) ).
fof(normalize_0_10,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
<=> ( ~ member(D,B)
| ~ member(D,C) ) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [B,C,D] :
( ( ~ member(D,intersection(B,C))
| member(D,B) )
& ( ~ member(D,intersection(B,C))
| member(D,C) )
& ( ~ member(D,B)
| ~ member(D,C)
| member(D,intersection(B,C)) ) ),
inference(clausify,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
| member(D,C) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [B,C,D] :
( ~ member(D,B)
| ~ member(D,C)
| member(D,intersection(B,C)) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_14,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
| member(D,B) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_15,plain,
subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_16,plain,
! [B,C,D] :
( ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_17,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(canonicalize,[],[commutativity_of_intersection]) ).
fof(normalize_0_18,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(specialize,[],[normalize_0_17]) ).
cnf(refute_0_0,plain,
~ subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ member(skolemFOFtoCNF_D(B,C),C)
| subset(B,C) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_2,plain,
( ~ member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,X_2620),intersection(X_2620,skolemFOFtoCNF_C)),intersection(X_2620,skolemFOFtoCNF_C))
| subset(intersection(skolemFOFtoCNF_B,X_2620),intersection(X_2620,skolemFOFtoCNF_C)) ),
inference(subst,[],[refute_0_1:[bind(B,$fot(intersection(skolemFOFtoCNF_B,X_2620))),bind(C,$fot(intersection(X_2620,skolemFOFtoCNF_C)))]]) ).
cnf(refute_0_3,plain,
( member(skolemFOFtoCNF_D(B,C),B)
| subset(B,C) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_4,plain,
( member(skolemFOFtoCNF_D(intersection(X_15,X_16),C),intersection(X_15,X_16))
| subset(intersection(X_15,X_16),C) ),
inference(subst,[],[refute_0_3:[bind(B,$fot(intersection(X_15,X_16)))]]) ).
cnf(refute_0_5,plain,
( ~ member(D,intersection(B,C))
| member(D,C) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_6,plain,
( ~ member(skolemFOFtoCNF_D(intersection(X_15,X_16),C),intersection(X_15,X_16))
| member(skolemFOFtoCNF_D(intersection(X_15,X_16),C),X_16) ),
inference(subst,[],[refute_0_5:[bind(B,$fot(X_15)),bind(C,$fot(X_16)),bind(D,$fot(skolemFOFtoCNF_D(intersection(X_15,X_16),C)))]]) ).
cnf(refute_0_7,plain,
( member(skolemFOFtoCNF_D(intersection(X_15,X_16),C),X_16)
| subset(intersection(X_15,X_16),C) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(intersection(X_15,X_16),C),intersection(X_15,X_16)) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,X_2601),X_2602),X_2601)
| subset(intersection(skolemFOFtoCNF_B,X_2601),X_2602) ),
inference(subst,[],[refute_0_7:[bind(C,$fot(X_2602)),bind(X_15,$fot(skolemFOFtoCNF_B)),bind(X_16,$fot(X_2601))]]) ).
cnf(refute_0_9,plain,
( ~ member(D,B)
| ~ member(D,C)
| member(D,intersection(B,C)) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_10,plain,
( ~ member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,X_87),X_86),B)
| ~ member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,X_87),X_86),skolemFOFtoCNF_C)
| member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,X_87),X_86),intersection(B,skolemFOFtoCNF_C)) ),
inference(subst,[],[refute_0_9:[bind(C,$fot(skolemFOFtoCNF_C)),bind(D,$fot(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,X_87),X_86)))]]) ).
cnf(refute_0_11,plain,
( member(skolemFOFtoCNF_D(intersection(X_12,X_13),C),intersection(X_12,X_13))
| subset(intersection(X_12,X_13),C) ),
inference(subst,[],[refute_0_3:[bind(B,$fot(intersection(X_12,X_13)))]]) ).
cnf(refute_0_12,plain,
( ~ member(D,intersection(B,C))
| member(D,B) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_13,plain,
( ~ member(skolemFOFtoCNF_D(intersection(X_12,X_13),C),intersection(X_12,X_13))
| member(skolemFOFtoCNF_D(intersection(X_12,X_13),C),X_12) ),
inference(subst,[],[refute_0_12:[bind(B,$fot(X_12)),bind(C,$fot(X_13)),bind(D,$fot(skolemFOFtoCNF_D(intersection(X_12,X_13),C)))]]) ).
cnf(refute_0_14,plain,
( member(skolemFOFtoCNF_D(intersection(X_12,X_13),C),X_12)
| subset(intersection(X_12,X_13),C) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(intersection(X_12,X_13),C),intersection(X_12,X_13)) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,plain,
( member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,X_13),C),skolemFOFtoCNF_B)
| subset(intersection(skolemFOFtoCNF_B,X_13),C) ),
inference(subst,[],[refute_0_14:[bind(X_12,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_16,plain,
subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_17,plain,
( ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_18,plain,
( ~ member(X_33,skolemFOFtoCNF_B)
| ~ subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| member(X_33,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_17:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C)),bind(D,$fot(X_33))]]) ).
cnf(refute_0_19,plain,
( ~ member(X_33,skolemFOFtoCNF_B)
| member(X_33,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_16,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,X_13),C),skolemFOFtoCNF_B)
| member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,X_13),C),skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_19:[bind(X_33,$fot(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,X_13),C)))]]) ).
cnf(refute_0_21,plain,
( member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,X_13),C),skolemFOFtoCNF_C)
| subset(intersection(skolemFOFtoCNF_B,X_13),C) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,X_13),C),skolemFOFtoCNF_B) )],[refute_0_15,refute_0_20]) ).
cnf(refute_0_22,plain,
( member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,X_87),X_86),skolemFOFtoCNF_C)
| subset(intersection(skolemFOFtoCNF_B,X_87),X_86) ),
inference(subst,[],[refute_0_21:[bind(C,$fot(X_86)),bind(X_13,$fot(X_87))]]) ).
cnf(refute_0_23,plain,
( ~ member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,X_87),X_86),B)
| member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,X_87),X_86),intersection(B,skolemFOFtoCNF_C))
| subset(intersection(skolemFOFtoCNF_B,X_87),X_86) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,X_87),X_86),skolemFOFtoCNF_C) )],[refute_0_22,refute_0_10]) ).
cnf(refute_0_24,plain,
( ~ member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,X_2601),X_2602),X_2601)
| member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,X_2601),X_2602),intersection(X_2601,skolemFOFtoCNF_C))
| subset(intersection(skolemFOFtoCNF_B,X_2601),X_2602) ),
inference(subst,[],[refute_0_23:[bind(B,$fot(X_2601)),bind(X_86,$fot(X_2602)),bind(X_87,$fot(X_2601))]]) ).
cnf(refute_0_25,plain,
( member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,X_2601),X_2602),intersection(X_2601,skolemFOFtoCNF_C))
| subset(intersection(skolemFOFtoCNF_B,X_2601),X_2602) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,X_2601),X_2602),X_2601) )],[refute_0_8,refute_0_24]) ).
cnf(refute_0_26,plain,
( member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,X_2620),intersection(X_2620,skolemFOFtoCNF_C)),intersection(X_2620,skolemFOFtoCNF_C))
| subset(intersection(skolemFOFtoCNF_B,X_2620),intersection(X_2620,skolemFOFtoCNF_C)) ),
inference(subst,[],[refute_0_25:[bind(X_2601,$fot(X_2620)),bind(X_2602,$fot(intersection(X_2620,skolemFOFtoCNF_C)))]]) ).
cnf(refute_0_27,plain,
subset(intersection(skolemFOFtoCNF_B,X_2620),intersection(X_2620,skolemFOFtoCNF_C)),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(intersection(skolemFOFtoCNF_B,X_2620),intersection(X_2620,skolemFOFtoCNF_C)),intersection(X_2620,skolemFOFtoCNF_C)) )],[refute_0_26,refute_0_2]) ).
cnf(refute_0_28,plain,
subset(intersection(skolemFOFtoCNF_B,X_2622),intersection(X_2622,skolemFOFtoCNF_C)),
inference(subst,[],[refute_0_27:[bind(X_2620,$fot(X_2622))]]) ).
cnf(refute_0_29,plain,
intersection(B,C) = intersection(C,B),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_30,plain,
intersection(skolemFOFtoCNF_C,X_2622) = intersection(X_2622,skolemFOFtoCNF_C),
inference(subst,[],[refute_0_29:[bind(B,$fot(skolemFOFtoCNF_C)),bind(C,$fot(X_2622))]]) ).
cnf(refute_0_31,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_32,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_33,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
( intersection(skolemFOFtoCNF_C,X_2622) != intersection(X_2622,skolemFOFtoCNF_C)
| intersection(X_2622,skolemFOFtoCNF_C) = intersection(skolemFOFtoCNF_C,X_2622) ),
inference(subst,[],[refute_0_33:[bind(X,$fot(intersection(skolemFOFtoCNF_C,X_2622))),bind(Y,$fot(intersection(X_2622,skolemFOFtoCNF_C)))]]) ).
cnf(refute_0_35,plain,
intersection(X_2622,skolemFOFtoCNF_C) = intersection(skolemFOFtoCNF_C,X_2622),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_C,X_2622),intersection(X_2622,skolemFOFtoCNF_C)) )],[refute_0_30,refute_0_34]) ).
cnf(refute_0_36,plain,
( intersection(X_2622,skolemFOFtoCNF_C) != intersection(skolemFOFtoCNF_C,X_2622)
| ~ subset(intersection(skolemFOFtoCNF_B,X_2622),intersection(X_2622,skolemFOFtoCNF_C))
| subset(intersection(skolemFOFtoCNF_B,X_2622),intersection(skolemFOFtoCNF_C,X_2622)) ),
introduced(tautology,[equality,[$cnf( subset(intersection(skolemFOFtoCNF_B,X_2622),intersection(X_2622,skolemFOFtoCNF_C)) ),[1],$fot(intersection(skolemFOFtoCNF_C,X_2622))]]) ).
cnf(refute_0_37,plain,
( ~ subset(intersection(skolemFOFtoCNF_B,X_2622),intersection(X_2622,skolemFOFtoCNF_C))
| subset(intersection(skolemFOFtoCNF_B,X_2622),intersection(skolemFOFtoCNF_C,X_2622)) ),
inference(resolve,[$cnf( $equal(intersection(X_2622,skolemFOFtoCNF_C),intersection(skolemFOFtoCNF_C,X_2622)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
subset(intersection(skolemFOFtoCNF_B,X_2622),intersection(skolemFOFtoCNF_C,X_2622)),
inference(resolve,[$cnf( subset(intersection(skolemFOFtoCNF_B,X_2622),intersection(X_2622,skolemFOFtoCNF_C)) )],[refute_0_28,refute_0_37]) ).
cnf(refute_0_39,plain,
subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),
inference(subst,[],[refute_0_38:[bind(X_2622,$fot(skolemFOFtoCNF_D_2))]]) ).
cnf(refute_0_40,plain,
$false,
inference(resolve,[$cnf( subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) )],[refute_0_39,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET586+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 11 07:37:12 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 25.00/25.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.00/25.24
% 25.00/25.24 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 25.10/25.25
%------------------------------------------------------------------------------