TSTP Solution File: SET611+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET611+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 03:35:56 EDT 2022
% Result : Theorem 25.29s 25.47s
% Output : CNFRefutation 25.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 16
% Syntax : Number of formulae : 178 ( 41 unt; 0 def)
% Number of atoms : 391 ( 83 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 398 ( 185 ~; 158 |; 24 &)
% ( 26 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 299 ( 17 sgn 136 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection_defn,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,B)
& member(D,C) ) ) ).
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(commutativity_of_intersection,axiom,
! [B,C] : intersection(B,C) = intersection(C,B) ).
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ) ).
fof(empty_defn,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ) ).
fof(prove_th84,conjecture,
! [B,C] :
( intersection(B,C) = empty_set
<=> difference(B,C) = B ) ).
fof(subgoal_0,plain,
! [B,C] :
( intersection(B,C) = empty_set
=> difference(B,C) = B ),
inference(strip,[],[prove_th84]) ).
fof(subgoal_1,plain,
! [B,C] :
( difference(B,C) = B
=> intersection(B,C) = empty_set ),
inference(strip,[],[prove_th84]) ).
fof(negate_0_0,plain,
~ ! [B,C] :
( intersection(B,C) = empty_set
=> difference(B,C) = B ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [B,C] :
( B != C
<=> ( ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(canonicalize,[],[equal_defn]) ).
fof(normalize_0_1,plain,
! [B,C] :
( B != C
<=> ( ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,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_1]) ).
fof(normalize_0_3,plain,
! [B,C] :
( ~ subset(B,C)
| ~ subset(C,B)
| B = C ),
inference(conjunct,[],[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_2(B,C),difference(B,C))
| subset(B,C) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [B,C] :
( member(skolemFOFtoCNF_D_2(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,intersection(B,C))
<=> ( ~ member(D,B)
| ~ member(D,C) ) ),
inference(canonicalize,[],[intersection_defn]) ).
fof(normalize_0_16,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
<=> ( ~ member(D,B)
| ~ member(D,C) ) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,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_16]) ).
fof(normalize_0_18,plain,
! [B,C,D] :
( ~ member(D,B)
| ~ member(D,C)
| member(D,intersection(B,C)) ),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
? [B,C] :
( difference(B,C) != B
& intersection(B,C) = empty_set ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_20,plain,
( difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) != skolemFOFtoCNF_B
& intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) = empty_set ),
inference(skolemize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) = empty_set,
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [B] : ~ member(B,empty_set),
inference(canonicalize,[],[empty_set_defn]) ).
fof(normalize_0_23,plain,
! [B] : ~ member(B,empty_set),
inference(specialize,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) != skolemFOFtoCNF_B,
inference(conjunct,[],[normalize_0_20]) ).
cnf(refute_0_0,plain,
( ~ subset(B,C)
| ~ subset(C,B)
| B = C ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ subset(X_313,difference(X_313,X_314))
| ~ subset(difference(X_313,X_314),X_313)
| X_313 = difference(X_313,X_314) ),
inference(subst,[],[refute_0_0:[bind(B,$fot(X_313)),bind(C,$fot(difference(X_313,X_314)))]]) ).
cnf(refute_0_2,plain,
( member(skolemFOFtoCNF_D_2(B,C),difference(B,C))
| subset(B,C) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_3,plain,
( member(skolemFOFtoCNF_D_2(X_37,X_38),difference(X_37,X_38))
| subset(X_37,X_38) ),
inference(subst,[],[refute_0_2:[bind(B,$fot(X_37)),bind(C,$fot(X_38))]]) ).
cnf(refute_0_4,plain,
( ~ member(D,C)
| ~ member(D,difference(B,C)) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_5,plain,
( ~ member(skolemFOFtoCNF_D_2(X_37,X_38),X_38)
| ~ member(skolemFOFtoCNF_D_2(X_37,X_38),difference(X_37,X_38)) ),
inference(subst,[],[refute_0_4:[bind(B,$fot(X_37)),bind(C,$fot(X_38)),bind(D,$fot(skolemFOFtoCNF_D_2(X_37,X_38)))]]) ).
cnf(refute_0_6,plain,
( ~ member(skolemFOFtoCNF_D_2(X_37,X_38),X_38)
| subset(X_37,X_38) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_2(X_37,X_38),difference(X_37,X_38)) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ member(skolemFOFtoCNF_D_2(difference(X_310,X_311),X_310),X_310)
| subset(difference(X_310,X_311),X_310) ),
inference(subst,[],[refute_0_6:[bind(X_37,$fot(difference(X_310,X_311))),bind(X_38,$fot(X_310))]]) ).
cnf(refute_0_8,plain,
( ~ member(D,difference(B,C))
| member(D,B) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_9,plain,
( ~ member(skolemFOFtoCNF_D_2(difference(B,C),X_68),difference(B,C))
| member(skolemFOFtoCNF_D_2(difference(B,C),X_68),B) ),
inference(subst,[],[refute_0_8:[bind(D,$fot(skolemFOFtoCNF_D_2(difference(B,C),X_68)))]]) ).
cnf(refute_0_10,plain,
( member(skolemFOFtoCNF_D_2(X_40,X_41),difference(X_40,X_41))
| subset(X_40,X_41) ),
inference(subst,[],[refute_0_2:[bind(B,$fot(X_40)),bind(C,$fot(X_41))]]) ).
cnf(refute_0_11,plain,
( ~ member(skolemFOFtoCNF_D_2(X_40,X_41),difference(X_40,X_41))
| member(skolemFOFtoCNF_D_2(X_40,X_41),X_40) ),
inference(subst,[],[refute_0_8:[bind(B,$fot(X_40)),bind(C,$fot(X_41)),bind(D,$fot(skolemFOFtoCNF_D_2(X_40,X_41)))]]) ).
cnf(refute_0_12,plain,
( member(skolemFOFtoCNF_D_2(X_40,X_41),X_40)
| subset(X_40,X_41) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_2(X_40,X_41),difference(X_40,X_41)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( member(skolemFOFtoCNF_D_2(difference(B,C),X_68),difference(B,C))
| subset(difference(B,C),X_68) ),
inference(subst,[],[refute_0_12:[bind(X_40,$fot(difference(B,C))),bind(X_41,$fot(X_68))]]) ).
cnf(refute_0_14,plain,
( member(skolemFOFtoCNF_D_2(difference(B,C),X_68),B)
| subset(difference(B,C),X_68) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_2(difference(B,C),X_68),difference(B,C)) )],[refute_0_13,refute_0_9]) ).
cnf(refute_0_15,plain,
( member(skolemFOFtoCNF_D_2(difference(X_310,X_311),X_310),X_310)
| subset(difference(X_310,X_311),X_310) ),
inference(subst,[],[refute_0_14:[bind(B,$fot(X_310)),bind(C,$fot(X_311)),bind(X_68,$fot(X_310))]]) ).
cnf(refute_0_16,plain,
subset(difference(X_310,X_311),X_310),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_2(difference(X_310,X_311),X_310),X_310) )],[refute_0_15,refute_0_7]) ).
cnf(refute_0_17,plain,
subset(difference(X_313,X_314),X_313),
inference(subst,[],[refute_0_16:[bind(X_310,$fot(X_313)),bind(X_311,$fot(X_314))]]) ).
cnf(refute_0_18,plain,
( ~ subset(X_313,difference(X_313,X_314))
| X_313 = difference(X_313,X_314) ),
inference(resolve,[$cnf( subset(difference(X_313,X_314),X_313) )],[refute_0_17,refute_0_1]) ).
cnf(refute_0_19,plain,
( ~ subset(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1))
| skolemFOFtoCNF_B = difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_18:[bind(X_313,$fot(skolemFOFtoCNF_B)),bind(X_314,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_20,plain,
( ~ member(skolemFOFtoCNF_D_2(X_1359,difference(X_1359,X_1360)),difference(X_1359,X_1360))
| subset(X_1359,difference(X_1359,X_1360)) ),
inference(subst,[],[refute_0_6:[bind(X_37,$fot(X_1359)),bind(X_38,$fot(difference(X_1359,X_1360)))]]) ).
cnf(refute_0_21,plain,
( member(skolemFOFtoCNF_D_2(X_185,X_41),X_185)
| subset(X_185,X_41) ),
inference(subst,[],[refute_0_12:[bind(X_40,$fot(X_185))]]) ).
cnf(refute_0_22,plain,
( ~ member(D,B)
| member(D,C)
| member(D,difference(B,C)) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_23,plain,
( ~ member(skolemFOFtoCNF_D_2(X_185,X_41),X_185)
| member(skolemFOFtoCNF_D_2(X_185,X_41),X_186)
| member(skolemFOFtoCNF_D_2(X_185,X_41),difference(X_185,X_186)) ),
inference(subst,[],[refute_0_22:[bind(B,$fot(X_185)),bind(C,$fot(X_186)),bind(D,$fot(skolemFOFtoCNF_D_2(X_185,X_41)))]]) ).
cnf(refute_0_24,plain,
( member(skolemFOFtoCNF_D_2(X_185,X_41),X_186)
| member(skolemFOFtoCNF_D_2(X_185,X_41),difference(X_185,X_186))
| subset(X_185,X_41) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_2(X_185,X_41),X_185) )],[refute_0_21,refute_0_23]) ).
cnf(refute_0_25,plain,
( member(skolemFOFtoCNF_D_2(X_1359,difference(X_1359,X_1360)),X_1360)
| member(skolemFOFtoCNF_D_2(X_1359,difference(X_1359,X_1360)),difference(X_1359,X_1360))
| subset(X_1359,difference(X_1359,X_1360)) ),
inference(subst,[],[refute_0_24:[bind(X_185,$fot(X_1359)),bind(X_186,$fot(X_1360)),bind(X_41,$fot(difference(X_1359,X_1360)))]]) ).
cnf(refute_0_26,plain,
( member(skolemFOFtoCNF_D_2(X_1359,difference(X_1359,X_1360)),X_1360)
| subset(X_1359,difference(X_1359,X_1360)) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_2(X_1359,difference(X_1359,X_1360)),difference(X_1359,X_1360)) )],[refute_0_25,refute_0_20]) ).
cnf(refute_0_27,plain,
( member(skolemFOFtoCNF_D_2(X_2321,difference(X_2321,X_2322)),X_2322)
| subset(X_2321,difference(X_2321,X_2322)) ),
inference(subst,[],[refute_0_26:[bind(X_1359,$fot(X_2321)),bind(X_1360,$fot(X_2322))]]) ).
cnf(refute_0_28,plain,
( member(skolemFOFtoCNF_D_2(X_182,X_41),X_182)
| subset(X_182,X_41) ),
inference(subst,[],[refute_0_12:[bind(X_40,$fot(X_182))]]) ).
cnf(refute_0_29,plain,
( ~ member(D,B)
| ~ member(D,C)
| member(D,intersection(B,C)) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_30,plain,
( ~ member(skolemFOFtoCNF_D_2(X_182,X_41),X_182)
| ~ member(skolemFOFtoCNF_D_2(X_182,X_41),X_183)
| member(skolemFOFtoCNF_D_2(X_182,X_41),intersection(X_182,X_183)) ),
inference(subst,[],[refute_0_29:[bind(B,$fot(X_182)),bind(C,$fot(X_183)),bind(D,$fot(skolemFOFtoCNF_D_2(X_182,X_41)))]]) ).
cnf(refute_0_31,plain,
( ~ member(skolemFOFtoCNF_D_2(X_182,X_41),X_183)
| member(skolemFOFtoCNF_D_2(X_182,X_41),intersection(X_182,X_183))
| subset(X_182,X_41) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_2(X_182,X_41),X_182) )],[refute_0_28,refute_0_30]) ).
cnf(refute_0_32,plain,
( ~ member(skolemFOFtoCNF_D_2(X_2321,difference(X_2321,X_2322)),X_2322)
| member(skolemFOFtoCNF_D_2(X_2321,difference(X_2321,X_2322)),intersection(X_2321,X_2322))
| subset(X_2321,difference(X_2321,X_2322)) ),
inference(subst,[],[refute_0_31:[bind(X_182,$fot(X_2321)),bind(X_183,$fot(X_2322)),bind(X_41,$fot(difference(X_2321,X_2322)))]]) ).
cnf(refute_0_33,plain,
( member(skolemFOFtoCNF_D_2(X_2321,difference(X_2321,X_2322)),intersection(X_2321,X_2322))
| subset(X_2321,difference(X_2321,X_2322)) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_2(X_2321,difference(X_2321,X_2322)),X_2322) )],[refute_0_27,refute_0_32]) ).
cnf(refute_0_34,plain,
( member(skolemFOFtoCNF_D_2(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1))
| subset(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) ),
inference(subst,[],[refute_0_33:[bind(X_2321,$fot(skolemFOFtoCNF_B)),bind(X_2322,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_35,plain,
intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) = empty_set,
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_36,plain,
( intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) != empty_set
| ~ member(skolemFOFtoCNF_D_2(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1))
| member(skolemFOFtoCNF_D_2(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)),empty_set) ),
introduced(tautology,[equality,[$cnf( member(skolemFOFtoCNF_D_2(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_37,plain,
( ~ member(skolemFOFtoCNF_D_2(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1))
| member(skolemFOFtoCNF_D_2(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)),empty_set) ),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),empty_set) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( member(skolemFOFtoCNF_D_2(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)),empty_set)
| subset(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_2(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
~ member(B,empty_set),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_40,plain,
~ member(skolemFOFtoCNF_D_2(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)),empty_set),
inference(subst,[],[refute_0_39:[bind(B,$fot(skolemFOFtoCNF_D_2(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1))))]]) ).
cnf(refute_0_41,plain,
subset(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_2(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)),empty_set) )],[refute_0_38,refute_0_40]) ).
cnf(refute_0_42,plain,
skolemFOFtoCNF_B = difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) )],[refute_0_41,refute_0_19]) ).
cnf(refute_0_43,plain,
difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) != skolemFOFtoCNF_B,
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_44,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_45,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_46,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
( skolemFOFtoCNF_B != difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)
| difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) = skolemFOFtoCNF_B ),
inference(subst,[],[refute_0_46:[bind(X,$fot(skolemFOFtoCNF_B)),bind(Y,$fot(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)))]]) ).
cnf(refute_0_48,plain,
skolemFOFtoCNF_B != difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( $equal(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_B) )],[refute_0_47,refute_0_43]) ).
cnf(refute_0_49,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) )],[refute_0_42,refute_0_48]) ).
fof(negate_1_0,plain,
~ ! [B,C] :
( difference(B,C) = B
=> intersection(B,C) = empty_set ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [B] :
( ~ empty(B)
<=> ? [C] : member(C,B) ),
inference(canonicalize,[],[empty_defn]) ).
fof(normalize_1_1,plain,
! [B] :
( ~ empty(B)
<=> ? [C] : member(C,B) ),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
! [B,C] :
( ( ~ empty(B)
| ~ member(C,B) )
& ( empty(B)
| member(skolemFOFtoCNF_C(B),B) ) ),
inference(clausify,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [B] :
( empty(B)
| member(skolemFOFtoCNF_C(B),B) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
<=> ( ~ member(D,B)
| ~ member(D,C) ) ),
inference(canonicalize,[],[intersection_defn]) ).
fof(normalize_1_5,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
<=> ( ~ member(D,B)
| ~ member(D,C) ) ),
inference(specialize,[],[normalize_1_4]) ).
fof(normalize_1_6,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_1_5]) ).
fof(normalize_1_7,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
| member(D,C) ),
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
! [B,C,D] :
( ~ member(D,difference(B,C))
<=> ( ~ member(D,B)
| member(D,C) ) ),
inference(canonicalize,[],[difference_defn]) ).
fof(normalize_1_9,plain,
! [B,C,D] :
( ~ member(D,difference(B,C))
<=> ( ~ member(D,B)
| member(D,C) ) ),
inference(specialize,[],[normalize_1_8]) ).
fof(normalize_1_10,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_1_9]) ).
fof(normalize_1_11,plain,
! [B,C,D] :
( ~ member(D,C)
| ~ member(D,difference(B,C)) ),
inference(conjunct,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
? [B,C] :
( intersection(B,C) != empty_set
& difference(B,C) = B ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_13,plain,
( intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) != empty_set
& difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) = skolemFOFtoCNF_B_1 ),
inference(skolemize,[],[normalize_1_12]) ).
fof(normalize_1_14,plain,
difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) = skolemFOFtoCNF_B_1,
inference(conjunct,[],[normalize_1_13]) ).
fof(normalize_1_15,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(canonicalize,[],[commutativity_of_intersection]) ).
fof(normalize_1_16,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(specialize,[],[normalize_1_15]) ).
fof(normalize_1_17,plain,
! [B,C] :
( ~ empty(B)
| ~ member(C,B) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_18,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] :
( ~ member(D,C)
& member(D,B) ) ),
inference(canonicalize,[],[subset_defn]) ).
fof(normalize_1_19,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] : member(D,difference(B,C)) ),
inference(simplify,[],[normalize_1_18,normalize_1_9]) ).
fof(normalize_1_20,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] : member(D,difference(B,C)) ),
inference(specialize,[],[normalize_1_19]) ).
fof(normalize_1_21,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_1_20]) ).
fof(normalize_1_22,plain,
! [B,C] :
( member(skolemFOFtoCNF_D_2(B,C),difference(B,C))
| subset(B,C) ),
inference(conjunct,[],[normalize_1_21]) ).
fof(normalize_1_23,plain,
! [B,C,D] :
( ~ member(D,difference(B,C))
| member(D,B) ),
inference(conjunct,[],[normalize_1_10]) ).
fof(normalize_1_24,plain,
! [B] : ~ member(B,empty_set),
inference(canonicalize,[],[empty_set_defn]) ).
fof(normalize_1_25,plain,
! [B] : ~ member(B,empty_set),
inference(specialize,[],[normalize_1_24]) ).
fof(normalize_1_26,plain,
! [B,C] :
( B != C
<=> ( ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(canonicalize,[],[equal_defn]) ).
fof(normalize_1_27,plain,
! [B,C] :
( B != C
<=> ( ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(specialize,[],[normalize_1_26]) ).
fof(normalize_1_28,plain,
! [B,C] :
( ( B != C
| subset(B,C) )
& ( B != C
| subset(C,B) )
& ( ~ subset(B,C)
| ~ subset(C,B)
| B = C ) ),
inference(clausify,[],[normalize_1_27]) ).
fof(normalize_1_29,plain,
! [B,C] :
( ~ subset(B,C)
| ~ subset(C,B)
| B = C ),
inference(conjunct,[],[normalize_1_28]) ).
fof(normalize_1_30,plain,
intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) != empty_set,
inference(conjunct,[],[normalize_1_13]) ).
cnf(refute_1_0,plain,
( empty(B)
| member(skolemFOFtoCNF_C(B),B) ),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_1,plain,
( empty(intersection(X_2346,X_2347))
| member(skolemFOFtoCNF_C(intersection(X_2346,X_2347)),intersection(X_2346,X_2347)) ),
inference(subst,[],[refute_1_0:[bind(B,$fot(intersection(X_2346,X_2347)))]]) ).
cnf(refute_1_2,plain,
( ~ member(D,intersection(B,C))
| member(D,C) ),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_3,plain,
( ~ member(skolemFOFtoCNF_C(intersection(X_2346,X_2347)),intersection(X_2346,X_2347))
| member(skolemFOFtoCNF_C(intersection(X_2346,X_2347)),X_2347) ),
inference(subst,[],[refute_1_2:[bind(B,$fot(X_2346)),bind(C,$fot(X_2347)),bind(D,$fot(skolemFOFtoCNF_C(intersection(X_2346,X_2347))))]]) ).
cnf(refute_1_4,plain,
( empty(intersection(X_2346,X_2347))
| member(skolemFOFtoCNF_C(intersection(X_2346,X_2347)),X_2347) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_C(intersection(X_2346,X_2347)),intersection(X_2346,X_2347)) )],[refute_1_1,refute_1_3]) ).
cnf(refute_1_5,plain,
( empty(intersection(skolemFOFtoCNF_C_2,skolemFOFtoCNF_B_1))
| member(skolemFOFtoCNF_C(intersection(skolemFOFtoCNF_C_2,skolemFOFtoCNF_B_1)),skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_1_4:[bind(X_2346,$fot(skolemFOFtoCNF_C_2)),bind(X_2347,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_1_6,plain,
( empty(intersection(X_2346,skolemFOFtoCNF_C_2))
| member(skolemFOFtoCNF_C(intersection(X_2346,skolemFOFtoCNF_C_2)),skolemFOFtoCNF_C_2) ),
inference(subst,[],[refute_1_4:[bind(X_2347,$fot(skolemFOFtoCNF_C_2))]]) ).
cnf(refute_1_7,plain,
( ~ member(D,C)
| ~ member(D,difference(B,C)) ),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_8,plain,
( ~ member(X_2365,difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2))
| ~ member(X_2365,skolemFOFtoCNF_C_2) ),
inference(subst,[],[refute_1_7:[bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_C_2)),bind(D,$fot(X_2365))]]) ).
cnf(refute_1_9,plain,
difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) = skolemFOFtoCNF_B_1,
inference(canonicalize,[],[normalize_1_14]) ).
cnf(refute_1_10,plain,
( difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) != skolemFOFtoCNF_B_1
| ~ member(X_2365,skolemFOFtoCNF_B_1)
| member(X_2365,difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)) ),
introduced(tautology,[equality,[$cnf( ~ member(X_2365,difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)) ),[1],$fot(skolemFOFtoCNF_B_1)]]) ).
cnf(refute_1_11,plain,
( ~ member(X_2365,skolemFOFtoCNF_B_1)
| member(X_2365,difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)) ),
inference(resolve,[$cnf( $equal(difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),skolemFOFtoCNF_B_1) )],[refute_1_9,refute_1_10]) ).
cnf(refute_1_12,plain,
( ~ member(X_2365,skolemFOFtoCNF_B_1)
| ~ member(X_2365,skolemFOFtoCNF_C_2) ),
inference(resolve,[$cnf( member(X_2365,difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)) )],[refute_1_11,refute_1_8]) ).
cnf(refute_1_13,plain,
( ~ member(skolemFOFtoCNF_C(intersection(X_2346,skolemFOFtoCNF_C_2)),skolemFOFtoCNF_B_1)
| ~ member(skolemFOFtoCNF_C(intersection(X_2346,skolemFOFtoCNF_C_2)),skolemFOFtoCNF_C_2) ),
inference(subst,[],[refute_1_12:[bind(X_2365,$fot(skolemFOFtoCNF_C(intersection(X_2346,skolemFOFtoCNF_C_2))))]]) ).
cnf(refute_1_14,plain,
( ~ member(skolemFOFtoCNF_C(intersection(X_2346,skolemFOFtoCNF_C_2)),skolemFOFtoCNF_B_1)
| empty(intersection(X_2346,skolemFOFtoCNF_C_2)) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_C(intersection(X_2346,skolemFOFtoCNF_C_2)),skolemFOFtoCNF_C_2) )],[refute_1_6,refute_1_13]) ).
cnf(refute_1_15,plain,
( ~ member(skolemFOFtoCNF_C(intersection(X_2367,skolemFOFtoCNF_C_2)),skolemFOFtoCNF_B_1)
| empty(intersection(X_2367,skolemFOFtoCNF_C_2)) ),
inference(subst,[],[refute_1_14:[bind(X_2346,$fot(X_2367))]]) ).
cnf(refute_1_16,plain,
intersection(B,C) = intersection(C,B),
inference(canonicalize,[],[normalize_1_16]) ).
cnf(refute_1_17,plain,
intersection(skolemFOFtoCNF_C_2,X_2367) = intersection(X_2367,skolemFOFtoCNF_C_2),
inference(subst,[],[refute_1_16:[bind(B,$fot(skolemFOFtoCNF_C_2)),bind(C,$fot(X_2367))]]) ).
cnf(refute_1_18,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_19,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_20,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_18,refute_1_19]) ).
cnf(refute_1_21,plain,
( intersection(skolemFOFtoCNF_C_2,X_2367) != intersection(X_2367,skolemFOFtoCNF_C_2)
| intersection(X_2367,skolemFOFtoCNF_C_2) = intersection(skolemFOFtoCNF_C_2,X_2367) ),
inference(subst,[],[refute_1_20:[bind(X,$fot(intersection(skolemFOFtoCNF_C_2,X_2367))),bind(Y,$fot(intersection(X_2367,skolemFOFtoCNF_C_2)))]]) ).
cnf(refute_1_22,plain,
intersection(X_2367,skolemFOFtoCNF_C_2) = intersection(skolemFOFtoCNF_C_2,X_2367),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_C_2,X_2367),intersection(X_2367,skolemFOFtoCNF_C_2)) )],[refute_1_17,refute_1_21]) ).
cnf(refute_1_23,plain,
( intersection(X_2367,skolemFOFtoCNF_C_2) != intersection(skolemFOFtoCNF_C_2,X_2367)
| ~ member(skolemFOFtoCNF_C(intersection(skolemFOFtoCNF_C_2,X_2367)),skolemFOFtoCNF_B_1)
| member(skolemFOFtoCNF_C(intersection(X_2367,skolemFOFtoCNF_C_2)),skolemFOFtoCNF_B_1) ),
introduced(tautology,[equality,[$cnf( ~ member(skolemFOFtoCNF_C(intersection(X_2367,skolemFOFtoCNF_C_2)),skolemFOFtoCNF_B_1) ),[0,0],$fot(intersection(skolemFOFtoCNF_C_2,X_2367))]]) ).
cnf(refute_1_24,plain,
( ~ member(skolemFOFtoCNF_C(intersection(skolemFOFtoCNF_C_2,X_2367)),skolemFOFtoCNF_B_1)
| member(skolemFOFtoCNF_C(intersection(X_2367,skolemFOFtoCNF_C_2)),skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( $equal(intersection(X_2367,skolemFOFtoCNF_C_2),intersection(skolemFOFtoCNF_C_2,X_2367)) )],[refute_1_22,refute_1_23]) ).
cnf(refute_1_25,plain,
( ~ member(skolemFOFtoCNF_C(intersection(skolemFOFtoCNF_C_2,X_2367)),skolemFOFtoCNF_B_1)
| empty(intersection(X_2367,skolemFOFtoCNF_C_2)) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_C(intersection(X_2367,skolemFOFtoCNF_C_2)),skolemFOFtoCNF_B_1) )],[refute_1_24,refute_1_15]) ).
cnf(refute_1_26,plain,
( ~ member(skolemFOFtoCNF_C(intersection(skolemFOFtoCNF_C_2,skolemFOFtoCNF_B_1)),skolemFOFtoCNF_B_1)
| empty(intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)) ),
inference(subst,[],[refute_1_25:[bind(X_2367,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_1_27,plain,
( empty(intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2))
| empty(intersection(skolemFOFtoCNF_C_2,skolemFOFtoCNF_B_1)) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_C(intersection(skolemFOFtoCNF_C_2,skolemFOFtoCNF_B_1)),skolemFOFtoCNF_B_1) )],[refute_1_5,refute_1_26]) ).
cnf(refute_1_28,plain,
( intersection(B,C) != intersection(C,B)
| intersection(C,B) = intersection(B,C) ),
inference(subst,[],[refute_1_20:[bind(X,$fot(intersection(B,C))),bind(Y,$fot(intersection(C,B)))]]) ).
cnf(refute_1_29,plain,
intersection(C,B) = intersection(B,C),
inference(resolve,[$cnf( $equal(intersection(B,C),intersection(C,B)) )],[refute_1_16,refute_1_28]) ).
cnf(refute_1_30,plain,
intersection(skolemFOFtoCNF_C_2,skolemFOFtoCNF_B_1) = intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),
inference(subst,[],[refute_1_29:[bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_C_2))]]) ).
cnf(refute_1_31,plain,
( intersection(skolemFOFtoCNF_C_2,skolemFOFtoCNF_B_1) != intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)
| ~ empty(intersection(skolemFOFtoCNF_C_2,skolemFOFtoCNF_B_1))
| empty(intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)) ),
introduced(tautology,[equality,[$cnf( empty(intersection(skolemFOFtoCNF_C_2,skolemFOFtoCNF_B_1)) ),[0],$fot(intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2))]]) ).
cnf(refute_1_32,plain,
( ~ empty(intersection(skolemFOFtoCNF_C_2,skolemFOFtoCNF_B_1))
| empty(intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)) ),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_C_2,skolemFOFtoCNF_B_1),intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)) )],[refute_1_30,refute_1_31]) ).
cnf(refute_1_33,plain,
empty(intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)),
inference(resolve,[$cnf( empty(intersection(skolemFOFtoCNF_C_2,skolemFOFtoCNF_B_1)) )],[refute_1_27,refute_1_32]) ).
cnf(refute_1_34,plain,
( ~ empty(B)
| ~ member(C,B) ),
inference(canonicalize,[],[normalize_1_17]) ).
cnf(refute_1_35,plain,
( ~ empty(X_2406)
| ~ member(skolemFOFtoCNF_D_2(X_2406,X_2407),X_2406) ),
inference(subst,[],[refute_1_34:[bind(B,$fot(X_2406)),bind(C,$fot(skolemFOFtoCNF_D_2(X_2406,X_2407)))]]) ).
cnf(refute_1_36,plain,
( member(skolemFOFtoCNF_D_2(B,C),difference(B,C))
| subset(B,C) ),
inference(canonicalize,[],[normalize_1_22]) ).
cnf(refute_1_37,plain,
( member(skolemFOFtoCNF_D_2(X_2379,X_2380),difference(X_2379,X_2380))
| subset(X_2379,X_2380) ),
inference(subst,[],[refute_1_36:[bind(B,$fot(X_2379)),bind(C,$fot(X_2380))]]) ).
cnf(refute_1_38,plain,
( ~ member(D,difference(B,C))
| member(D,B) ),
inference(canonicalize,[],[normalize_1_23]) ).
cnf(refute_1_39,plain,
( ~ member(skolemFOFtoCNF_D_2(X_2379,X_2380),difference(X_2379,X_2380))
| member(skolemFOFtoCNF_D_2(X_2379,X_2380),X_2379) ),
inference(subst,[],[refute_1_38:[bind(B,$fot(X_2379)),bind(C,$fot(X_2380)),bind(D,$fot(skolemFOFtoCNF_D_2(X_2379,X_2380)))]]) ).
cnf(refute_1_40,plain,
( member(skolemFOFtoCNF_D_2(X_2379,X_2380),X_2379)
| subset(X_2379,X_2380) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_2(X_2379,X_2380),difference(X_2379,X_2380)) )],[refute_1_37,refute_1_39]) ).
cnf(refute_1_41,plain,
( member(skolemFOFtoCNF_D_2(X_2406,X_2407),X_2406)
| subset(X_2406,X_2407) ),
inference(subst,[],[refute_1_40:[bind(X_2379,$fot(X_2406)),bind(X_2380,$fot(X_2407))]]) ).
cnf(refute_1_42,plain,
( ~ empty(X_2406)
| subset(X_2406,X_2407) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_2(X_2406,X_2407),X_2406) )],[refute_1_41,refute_1_35]) ).
cnf(refute_1_43,plain,
( ~ empty(intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2))
| subset(intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),X_2417) ),
inference(subst,[],[refute_1_42:[bind(X_2406,$fot(intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2))),bind(X_2407,$fot(X_2417))]]) ).
cnf(refute_1_44,plain,
subset(intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),X_2417),
inference(resolve,[$cnf( empty(intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)) )],[refute_1_33,refute_1_43]) ).
cnf(refute_1_45,plain,
subset(intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),empty_set),
inference(subst,[],[refute_1_44:[bind(X_2417,$fot(empty_set))]]) ).
cnf(refute_1_46,plain,
~ member(B,empty_set),
inference(canonicalize,[],[normalize_1_25]) ).
cnf(refute_1_47,plain,
~ member(skolemFOFtoCNF_D_2(empty_set,X_2407),empty_set),
inference(subst,[],[refute_1_46:[bind(B,$fot(skolemFOFtoCNF_D_2(empty_set,X_2407)))]]) ).
cnf(refute_1_48,plain,
( member(skolemFOFtoCNF_D_2(empty_set,X_2407),empty_set)
| subset(empty_set,X_2407) ),
inference(subst,[],[refute_1_40:[bind(X_2379,$fot(empty_set)),bind(X_2380,$fot(X_2407))]]) ).
cnf(refute_1_49,plain,
subset(empty_set,X_2407),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_2(empty_set,X_2407),empty_set) )],[refute_1_48,refute_1_47]) ).
cnf(refute_1_50,plain,
subset(empty_set,X_2480),
inference(subst,[],[refute_1_49:[bind(X_2407,$fot(X_2480))]]) ).
cnf(refute_1_51,plain,
( ~ subset(B,C)
| ~ subset(C,B)
| B = C ),
inference(canonicalize,[],[normalize_1_29]) ).
cnf(refute_1_52,plain,
( ~ subset(X_2480,empty_set)
| ~ subset(empty_set,X_2480)
| empty_set = X_2480 ),
inference(subst,[],[refute_1_51:[bind(B,$fot(empty_set)),bind(C,$fot(X_2480))]]) ).
cnf(refute_1_53,plain,
( ~ subset(X_2480,empty_set)
| empty_set = X_2480 ),
inference(resolve,[$cnf( subset(empty_set,X_2480) )],[refute_1_50,refute_1_52]) ).
cnf(refute_1_54,plain,
( ~ subset(intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),empty_set)
| empty_set = intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) ),
inference(subst,[],[refute_1_53:[bind(X_2480,$fot(intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)))]]) ).
cnf(refute_1_55,plain,
empty_set = intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),
inference(resolve,[$cnf( subset(intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),empty_set) )],[refute_1_45,refute_1_54]) ).
cnf(refute_1_56,plain,
intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) != empty_set,
inference(canonicalize,[],[normalize_1_30]) ).
cnf(refute_1_57,plain,
( empty_set != intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)
| intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) = empty_set ),
inference(subst,[],[refute_1_20:[bind(X,$fot(empty_set)),bind(Y,$fot(intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)))]]) ).
cnf(refute_1_58,plain,
empty_set != intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),empty_set) )],[refute_1_57,refute_1_56]) ).
cnf(refute_1_59,plain,
$false,
inference(resolve,[$cnf( $equal(empty_set,intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)) )],[refute_1_55,refute_1_58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET611+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.14 % Command : metis --show proof --show saturation %s
% 0.15/0.35 % Computer : n010.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Sun Jul 10 14:24:15 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.15/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 25.29/25.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.29/25.47
% 25.29/25.47 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 25.29/25.47
%------------------------------------------------------------------------------