TSTP Solution File: SET009+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET009+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 03:31:00 EDT 2022
% Result : Theorem 13.44s 13.60s
% Output : CNFRefutation 13.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 3
% Syntax : Number of formulae : 86 ( 12 unt; 0 def)
% Number of atoms : 187 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 165 ( 64 ~; 83 |; 7 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 189 ( 4 sgn 47 !; 8 ?)
% 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_subset_difference,conjecture,
! [B,C,D] :
( subset(B,C)
=> subset(difference(D,C),difference(D,B)) ) ).
fof(subgoal_0,plain,
! [B,C,D] :
( subset(B,C)
=> subset(difference(D,C),difference(D,B)) ),
inference(strip,[],[prove_subset_difference]) ).
fof(negate_0_0,plain,
~ ! [B,C,D] :
( subset(B,C)
=> subset(difference(D,C),difference(D,B)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B,C] :
( subset(B,C)
& ? [D] : ~ subset(difference(D,C),difference(D,B)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
& ? [D] : ~ subset(difference(D,skolemFOFtoCNF_C),difference(D,skolemFOFtoCNF_B)) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [D] : ~ subset(difference(D,skolemFOFtoCNF_C),difference(D,skolemFOFtoCNF_B)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ subset(difference(skolemFOFtoCNF_D_1,skolemFOFtoCNF_C),difference(skolemFOFtoCNF_D_1,skolemFOFtoCNF_B)),
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,D] :
( ~ member(D,difference(B,C))
<=> ( ~ member(D,B)
| member(D,C) ) ),
inference(canonicalize,[],[difference_defn]) ).
fof(normalize_0_6,plain,
! [B,C,D] :
( ~ member(D,difference(B,C))
<=> ( ~ member(D,B)
| member(D,C) ) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] : member(D,difference(B,C)) ),
inference(simplify,[],[normalize_0_4,normalize_0_6]) ).
fof(normalize_0_8,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] : member(D,difference(B,C)) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,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_8]) ).
fof(normalize_0_10,plain,
! [B,C] :
( member(skolemFOFtoCNF_D(B,C),difference(B,C))
| subset(B,C) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,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_6]) ).
fof(normalize_0_12,plain,
! [B,C,D] :
( ~ member(D,C)
| ~ member(D,difference(B,C)) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [B,C,D] :
( ~ member(D,difference(B,C))
| member(D,B) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_14,plain,
! [B,C,D] :
( ~ member(D,B)
| member(D,C)
| member(D,difference(B,C)) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_15,plain,
! [B,C,D] :
( ~ member(D,difference(B,C))
| ~ subset(B,C) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_16,plain,
subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
~ subset(difference(skolemFOFtoCNF_D_1,skolemFOFtoCNF_C),difference(skolemFOFtoCNF_D_1,skolemFOFtoCNF_B)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( member(skolemFOFtoCNF_D(B,C),difference(B,C))
| subset(B,C) ),
inference(canonicalize,[],[normalize_0_10]) ).
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_12]) ).
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_1500,X_1498),difference(X_1500,X_1501)),difference(X_1500,X_1501))
| subset(difference(X_1500,X_1498),difference(X_1500,X_1501)) ),
inference(subst,[],[refute_0_5:[bind(X_3,$fot(difference(X_1500,X_1498))),bind(X_4,$fot(difference(X_1500,X_1501)))]]) ).
cnf(refute_0_7,plain,
( ~ member(D,difference(B,C))
| member(D,B) ),
inference(canonicalize,[],[normalize_0_13]) ).
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_69,C),X_12),X_69)
| subset(difference(X_69,C),X_12) ),
inference(subst,[],[refute_0_13:[bind(B,$fot(X_69))]]) ).
cnf(refute_0_15,plain,
( ~ member(D,B)
| member(D,C)
| member(D,difference(B,C)) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_16,plain,
( ~ member(skolemFOFtoCNF_D(difference(X_69,C),X_12),X_69)
| member(skolemFOFtoCNF_D(difference(X_69,C),X_12),X_70)
| member(skolemFOFtoCNF_D(difference(X_69,C),X_12),difference(X_69,X_70)) ),
inference(subst,[],[refute_0_15:[bind(B,$fot(X_69)),bind(C,$fot(X_70)),bind(D,$fot(skolemFOFtoCNF_D(difference(X_69,C),X_12)))]]) ).
cnf(refute_0_17,plain,
( member(skolemFOFtoCNF_D(difference(X_69,C),X_12),X_70)
| member(skolemFOFtoCNF_D(difference(X_69,C),X_12),difference(X_69,X_70))
| subset(difference(X_69,C),X_12) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(difference(X_69,C),X_12),X_69) )],[refute_0_14,refute_0_16]) ).
cnf(refute_0_18,plain,
( member(skolemFOFtoCNF_D(difference(X_1500,X_1498),difference(X_1500,X_1501)),X_1501)
| member(skolemFOFtoCNF_D(difference(X_1500,X_1498),difference(X_1500,X_1501)),difference(X_1500,X_1501))
| subset(difference(X_1500,X_1498),difference(X_1500,X_1501)) ),
inference(subst,[],[refute_0_17:[bind(C,$fot(X_1498)),bind(X_12,$fot(difference(X_1500,X_1501))),bind(X_69,$fot(X_1500)),bind(X_70,$fot(X_1501))]]) ).
cnf(refute_0_19,plain,
( member(skolemFOFtoCNF_D(difference(X_1500,X_1498),difference(X_1500,X_1501)),X_1501)
| subset(difference(X_1500,X_1498),difference(X_1500,X_1501)) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(difference(X_1500,X_1498),difference(X_1500,X_1501)),difference(X_1500,X_1501)) )],[refute_0_18,refute_0_6]) ).
cnf(refute_0_20,plain,
( member(skolemFOFtoCNF_D(difference(X_12953,skolemFOFtoCNF_C),difference(X_12953,skolemFOFtoCNF_B)),skolemFOFtoCNF_B)
| subset(difference(X_12953,skolemFOFtoCNF_C),difference(X_12953,skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_19:[bind(X_1498,$fot(skolemFOFtoCNF_C)),bind(X_1500,$fot(X_12953)),bind(X_1501,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_21,plain,
( ~ member(skolemFOFtoCNF_D(difference(X_12947,skolemFOFtoCNF_C),X_12948),difference(difference(X_12947,skolemFOFtoCNF_C),skolemFOFtoCNF_B))
| ~ member(skolemFOFtoCNF_D(difference(X_12947,skolemFOFtoCNF_C),X_12948),skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_3:[bind(B,$fot(difference(X_12947,skolemFOFtoCNF_C))),bind(C,$fot(skolemFOFtoCNF_B)),bind(D,$fot(skolemFOFtoCNF_D(difference(X_12947,skolemFOFtoCNF_C),X_12948)))]]) ).
cnf(refute_0_22,plain,
( ~ member(D,difference(B,C))
| ~ subset(B,C) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_23,plain,
( ~ member(skolemFOFtoCNF_D(X_130,X_132),difference(X_130,X_131))
| ~ subset(X_130,X_131) ),
inference(subst,[],[refute_0_22:[bind(B,$fot(X_130)),bind(C,$fot(X_131)),bind(D,$fot(skolemFOFtoCNF_D(X_130,X_132)))]]) ).
cnf(refute_0_24,plain,
( member(skolemFOFtoCNF_D(X_69,X_9),X_69)
| subset(X_69,X_9) ),
inference(subst,[],[refute_0_11:[bind(X_8,$fot(X_69))]]) ).
cnf(refute_0_25,plain,
( ~ member(skolemFOFtoCNF_D(X_69,X_9),X_69)
| member(skolemFOFtoCNF_D(X_69,X_9),X_70)
| member(skolemFOFtoCNF_D(X_69,X_9),difference(X_69,X_70)) ),
inference(subst,[],[refute_0_15:[bind(B,$fot(X_69)),bind(C,$fot(X_70)),bind(D,$fot(skolemFOFtoCNF_D(X_69,X_9)))]]) ).
cnf(refute_0_26,plain,
( member(skolemFOFtoCNF_D(X_69,X_9),X_70)
| member(skolemFOFtoCNF_D(X_69,X_9),difference(X_69,X_70))
| subset(X_69,X_9) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(X_69,X_9),X_69) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
( member(skolemFOFtoCNF_D(X_130,X_132),X_131)
| member(skolemFOFtoCNF_D(X_130,X_132),difference(X_130,X_131))
| subset(X_130,X_132) ),
inference(subst,[],[refute_0_26:[bind(X_69,$fot(X_130)),bind(X_70,$fot(X_131)),bind(X_9,$fot(X_132))]]) ).
cnf(refute_0_28,plain,
( ~ subset(X_130,X_131)
| member(skolemFOFtoCNF_D(X_130,X_132),X_131)
| subset(X_130,X_132) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(X_130,X_132),difference(X_130,X_131)) )],[refute_0_27,refute_0_23]) ).
cnf(refute_0_29,plain,
( ~ subset(difference(X_12335,skolemFOFtoCNF_C),difference(difference(X_12335,skolemFOFtoCNF_C),skolemFOFtoCNF_B))
| member(skolemFOFtoCNF_D(difference(X_12335,skolemFOFtoCNF_C),X_132),difference(difference(X_12335,skolemFOFtoCNF_C),skolemFOFtoCNF_B))
| subset(difference(X_12335,skolemFOFtoCNF_C),X_132) ),
inference(subst,[],[refute_0_28:[bind(X_130,$fot(difference(X_12335,skolemFOFtoCNF_C))),bind(X_131,$fot(difference(difference(X_12335,skolemFOFtoCNF_C),skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_30,plain,
( ~ member(skolemFOFtoCNF_D(difference(B,C),X_12),C)
| ~ member(skolemFOFtoCNF_D(difference(B,C),X_12),difference(B,C)) ),
inference(subst,[],[refute_0_3:[bind(D,$fot(skolemFOFtoCNF_D(difference(B,C),X_12)))]]) ).
cnf(refute_0_31,plain,
( ~ member(skolemFOFtoCNF_D(difference(B,C),X_12),C)
| subset(difference(B,C),X_12) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(difference(B,C),X_12),difference(B,C)) )],[refute_0_12,refute_0_30]) ).
cnf(refute_0_32,plain,
( ~ member(skolemFOFtoCNF_D(difference(B,skolemFOFtoCNF_C),difference(difference(B,skolemFOFtoCNF_C),skolemFOFtoCNF_B)),skolemFOFtoCNF_C)
| subset(difference(B,skolemFOFtoCNF_C),difference(difference(B,skolemFOFtoCNF_C),skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_31:[bind(C,$fot(skolemFOFtoCNF_C)),bind(X_12,$fot(difference(difference(B,skolemFOFtoCNF_C),skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_33,plain,
( ~ member(skolemFOFtoCNF_D(X_207,X_208),difference(X_207,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C)))
| ~ member(skolemFOFtoCNF_D(X_207,X_208),difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) ),
inference(subst,[],[refute_0_3:[bind(B,$fot(X_207)),bind(C,$fot(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C))),bind(D,$fot(skolemFOFtoCNF_D(X_207,X_208)))]]) ).
cnf(refute_0_34,plain,
subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_35,plain,
( ~ member(skolemFOFtoCNF_D(X_133,difference(X_133,difference(B,C))),difference(B,C))
| ~ subset(B,C) ),
inference(subst,[],[refute_0_22:[bind(D,$fot(skolemFOFtoCNF_D(X_133,difference(X_133,difference(B,C)))))]]) ).
cnf(refute_0_36,plain,
( ~ member(skolemFOFtoCNF_D(X_130,difference(X_130,X_131)),difference(X_130,X_131))
| subset(X_130,difference(X_130,X_131)) ),
inference(subst,[],[refute_0_5:[bind(X_3,$fot(X_130)),bind(X_4,$fot(difference(X_130,X_131)))]]) ).
cnf(refute_0_37,plain,
( member(skolemFOFtoCNF_D(X_130,difference(X_130,X_131)),X_131)
| member(skolemFOFtoCNF_D(X_130,difference(X_130,X_131)),difference(X_130,X_131))
| subset(X_130,difference(X_130,X_131)) ),
inference(subst,[],[refute_0_26:[bind(X_69,$fot(X_130)),bind(X_70,$fot(X_131)),bind(X_9,$fot(difference(X_130,X_131)))]]) ).
cnf(refute_0_38,plain,
( member(skolemFOFtoCNF_D(X_130,difference(X_130,X_131)),X_131)
| subset(X_130,difference(X_130,X_131)) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(X_130,difference(X_130,X_131)),difference(X_130,X_131)) )],[refute_0_37,refute_0_36]) ).
cnf(refute_0_39,plain,
( member(skolemFOFtoCNF_D(X_133,difference(X_133,difference(B,C))),difference(B,C))
| subset(X_133,difference(X_133,difference(B,C))) ),
inference(subst,[],[refute_0_38:[bind(X_130,$fot(X_133)),bind(X_131,$fot(difference(B,C)))]]) ).
cnf(refute_0_40,plain,
( ~ subset(B,C)
| subset(X_133,difference(X_133,difference(B,C))) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(X_133,difference(X_133,difference(B,C))),difference(B,C)) )],[refute_0_39,refute_0_35]) ).
cnf(refute_0_41,plain,
( ~ subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| subset(X_146,difference(X_146,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C))) ),
inference(subst,[],[refute_0_40:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C)),bind(X_133,$fot(X_146))]]) ).
cnf(refute_0_42,plain,
subset(X_146,difference(X_146,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C))),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_34,refute_0_41]) ).
cnf(refute_0_43,plain,
subset(X_203,difference(X_203,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C))),
inference(subst,[],[refute_0_42:[bind(X_146,$fot(X_203))]]) ).
cnf(refute_0_44,plain,
( ~ subset(X_203,difference(X_203,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C)))
| member(skolemFOFtoCNF_D(X_203,X_205),difference(X_203,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C)))
| subset(X_203,X_205) ),
inference(subst,[],[refute_0_28:[bind(X_130,$fot(X_203)),bind(X_131,$fot(difference(X_203,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C)))),bind(X_132,$fot(X_205))]]) ).
cnf(refute_0_45,plain,
( member(skolemFOFtoCNF_D(X_203,X_205),difference(X_203,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C)))
| subset(X_203,X_205) ),
inference(resolve,[$cnf( subset(X_203,difference(X_203,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
( member(skolemFOFtoCNF_D(X_207,X_208),difference(X_207,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C)))
| subset(X_207,X_208) ),
inference(subst,[],[refute_0_45:[bind(X_203,$fot(X_207)),bind(X_205,$fot(X_208))]]) ).
cnf(refute_0_47,plain,
( ~ member(skolemFOFtoCNF_D(X_207,X_208),difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C))
| subset(X_207,X_208) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(X_207,X_208),difference(X_207,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C))) )],[refute_0_46,refute_0_33]) ).
cnf(refute_0_48,plain,
( ~ member(skolemFOFtoCNF_D(X_12332,difference(X_12332,skolemFOFtoCNF_B)),difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C))
| subset(X_12332,difference(X_12332,skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_47:[bind(X_207,$fot(X_12332)),bind(X_208,$fot(difference(X_12332,skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_49,plain,
( ~ member(skolemFOFtoCNF_D(X_133,difference(X_133,X_134)),X_134)
| member(skolemFOFtoCNF_D(X_133,difference(X_133,X_134)),C)
| member(skolemFOFtoCNF_D(X_133,difference(X_133,X_134)),difference(X_134,C)) ),
inference(subst,[],[refute_0_15:[bind(B,$fot(X_134)),bind(D,$fot(skolemFOFtoCNF_D(X_133,difference(X_133,X_134))))]]) ).
cnf(refute_0_50,plain,
( member(skolemFOFtoCNF_D(X_133,difference(X_133,X_134)),X_134)
| subset(X_133,difference(X_133,X_134)) ),
inference(subst,[],[refute_0_38:[bind(X_130,$fot(X_133)),bind(X_131,$fot(X_134))]]) ).
cnf(refute_0_51,plain,
( member(skolemFOFtoCNF_D(X_133,difference(X_133,X_134)),C)
| member(skolemFOFtoCNF_D(X_133,difference(X_133,X_134)),difference(X_134,C))
| subset(X_133,difference(X_133,X_134)) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(X_133,difference(X_133,X_134)),X_134) )],[refute_0_50,refute_0_49]) ).
cnf(refute_0_52,plain,
( member(skolemFOFtoCNF_D(X_12332,difference(X_12332,skolemFOFtoCNF_B)),difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C))
| member(skolemFOFtoCNF_D(X_12332,difference(X_12332,skolemFOFtoCNF_B)),skolemFOFtoCNF_C)
| subset(X_12332,difference(X_12332,skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_51:[bind(C,$fot(skolemFOFtoCNF_C)),bind(X_133,$fot(X_12332)),bind(X_134,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_53,plain,
( member(skolemFOFtoCNF_D(X_12332,difference(X_12332,skolemFOFtoCNF_B)),skolemFOFtoCNF_C)
| subset(X_12332,difference(X_12332,skolemFOFtoCNF_B)) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(X_12332,difference(X_12332,skolemFOFtoCNF_B)),difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) )],[refute_0_52,refute_0_48]) ).
cnf(refute_0_54,plain,
( member(skolemFOFtoCNF_D(difference(B,skolemFOFtoCNF_C),difference(difference(B,skolemFOFtoCNF_C),skolemFOFtoCNF_B)),skolemFOFtoCNF_C)
| subset(difference(B,skolemFOFtoCNF_C),difference(difference(B,skolemFOFtoCNF_C),skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_53:[bind(X_12332,$fot(difference(B,skolemFOFtoCNF_C)))]]) ).
cnf(refute_0_55,plain,
subset(difference(B,skolemFOFtoCNF_C),difference(difference(B,skolemFOFtoCNF_C),skolemFOFtoCNF_B)),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(difference(B,skolemFOFtoCNF_C),difference(difference(B,skolemFOFtoCNF_C),skolemFOFtoCNF_B)),skolemFOFtoCNF_C) )],[refute_0_54,refute_0_32]) ).
cnf(refute_0_56,plain,
subset(difference(X_12335,skolemFOFtoCNF_C),difference(difference(X_12335,skolemFOFtoCNF_C),skolemFOFtoCNF_B)),
inference(subst,[],[refute_0_55:[bind(B,$fot(X_12335))]]) ).
cnf(refute_0_57,plain,
( member(skolemFOFtoCNF_D(difference(X_12335,skolemFOFtoCNF_C),X_132),difference(difference(X_12335,skolemFOFtoCNF_C),skolemFOFtoCNF_B))
| subset(difference(X_12335,skolemFOFtoCNF_C),X_132) ),
inference(resolve,[$cnf( subset(difference(X_12335,skolemFOFtoCNF_C),difference(difference(X_12335,skolemFOFtoCNF_C),skolemFOFtoCNF_B)) )],[refute_0_56,refute_0_29]) ).
cnf(refute_0_58,plain,
( member(skolemFOFtoCNF_D(difference(X_12947,skolemFOFtoCNF_C),X_12948),difference(difference(X_12947,skolemFOFtoCNF_C),skolemFOFtoCNF_B))
| subset(difference(X_12947,skolemFOFtoCNF_C),X_12948) ),
inference(subst,[],[refute_0_57:[bind(X_12335,$fot(X_12947)),bind(X_132,$fot(X_12948))]]) ).
cnf(refute_0_59,plain,
( ~ member(skolemFOFtoCNF_D(difference(X_12947,skolemFOFtoCNF_C),X_12948),skolemFOFtoCNF_B)
| subset(difference(X_12947,skolemFOFtoCNF_C),X_12948) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(difference(X_12947,skolemFOFtoCNF_C),X_12948),difference(difference(X_12947,skolemFOFtoCNF_C),skolemFOFtoCNF_B)) )],[refute_0_58,refute_0_21]) ).
cnf(refute_0_60,plain,
( ~ member(skolemFOFtoCNF_D(difference(X_12953,skolemFOFtoCNF_C),difference(X_12953,skolemFOFtoCNF_B)),skolemFOFtoCNF_B)
| subset(difference(X_12953,skolemFOFtoCNF_C),difference(X_12953,skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_59:[bind(X_12947,$fot(X_12953)),bind(X_12948,$fot(difference(X_12953,skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_61,plain,
subset(difference(X_12953,skolemFOFtoCNF_C),difference(X_12953,skolemFOFtoCNF_B)),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(difference(X_12953,skolemFOFtoCNF_C),difference(X_12953,skolemFOFtoCNF_B)),skolemFOFtoCNF_B) )],[refute_0_20,refute_0_60]) ).
cnf(refute_0_62,plain,
subset(difference(skolemFOFtoCNF_D_1,skolemFOFtoCNF_C),difference(skolemFOFtoCNF_D_1,skolemFOFtoCNF_B)),
inference(subst,[],[refute_0_61:[bind(X_12953,$fot(skolemFOFtoCNF_D_1))]]) ).
cnf(refute_0_63,plain,
$false,
inference(resolve,[$cnf( subset(difference(skolemFOFtoCNF_D_1,skolemFOFtoCNF_C),difference(skolemFOFtoCNF_D_1,skolemFOFtoCNF_B)) )],[refute_0_62,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET009+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jul 11 10:08:33 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 13.44/13.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.44/13.60
% 13.44/13.60 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.44/13.61
%------------------------------------------------------------------------------