TSTP Solution File: SET636+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET636+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 03:36:14 EDT 2022
% Result : Theorem 0.18s 0.41s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of formulae : 115 ( 27 unt; 0 def)
% Number of atoms : 242 ( 43 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 246 ( 119 ~; 80 |; 17 &)
% ( 24 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 179 ( 8 sgn 109 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection_defn,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,B)
& member(D,C) ) ) ).
fof(intersect_defn,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,B)
& member(D,C) ) ) ).
fof(empty_set_defn,axiom,
! [B] : ~ member(B,empty_set) ).
fof(disjoint_defn,axiom,
! [B,C] :
( disjoint(B,C)
<=> ~ intersect(B,C) ) ).
fof(equal_defn,axiom,
! [B,C] :
( B = C
<=> ( subset(B,C)
& subset(C,B) ) ) ).
fof(symmetry_of_intersect,axiom,
! [B,C] :
( intersect(B,C)
=> intersect(C,B) ) ).
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ) ).
fof(prove_th118,conjecture,
! [B,C] :
( disjoint(B,C)
<=> intersection(B,C) = empty_set ) ).
fof(subgoal_0,plain,
! [B,C] :
( disjoint(B,C)
=> intersection(B,C) = empty_set ),
inference(strip,[],[prove_th118]) ).
fof(subgoal_1,plain,
! [B,C] :
( intersection(B,C) = empty_set
=> disjoint(B,C) ),
inference(strip,[],[prove_th118]) ).
fof(negate_0_0,plain,
~ ! [B,C] :
( disjoint(B,C)
=> intersection(B,C) = empty_set ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [B,C] :
( ~ disjoint(B,C)
<=> intersect(B,C) ),
inference(canonicalize,[],[disjoint_defn]) ).
fof(normalize_0_1,plain,
! [B,C] :
( ~ disjoint(B,C)
<=> intersect(B,C) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [B,C] :
( ( ~ disjoint(B,C)
| ~ intersect(B,C) )
& ( disjoint(B,C)
| intersect(B,C) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [B,C] :
( ~ disjoint(B,C)
| ~ intersect(B,C) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [B,C] :
( intersection(B,C) != empty_set
& disjoint(B,C) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) != empty_set
& disjoint(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) != empty_set,
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [B] : ~ member(B,empty_set),
inference(canonicalize,[],[empty_set_defn]) ).
fof(normalize_0_8,plain,
! [B] : ~ member(B,empty_set),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] :
( ~ member(D,C)
& member(D,B) ) ),
inference(canonicalize,[],[subset_defn]) ).
fof(normalize_0_10,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] :
( ~ member(D,C)
& member(D,B) ) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [B,C,D] :
( ( ~ member(skolemFOFtoCNF_D_1(B,C),C)
| subset(B,C) )
& ( member(skolemFOFtoCNF_D_1(B,C),B)
| subset(B,C) )
& ( ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ) ),
inference(clausify,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [B,C] :
( member(skolemFOFtoCNF_D_1(B,C),B)
| subset(B,C) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [B,C] :
( B != C
<=> ( ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(canonicalize,[],[equal_defn]) ).
fof(normalize_0_14,plain,
! [B,C] :
( B != C
<=> ( ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,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_14]) ).
fof(normalize_0_16,plain,
! [B,C] :
( ~ subset(B,C)
| ~ subset(C,B)
| B = C ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [B,C] :
( ~ intersect(B,C)
<=> ! [D] :
( ~ member(D,B)
| ~ member(D,C) ) ),
inference(canonicalize,[],[intersect_defn]) ).
fof(normalize_0_18,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
<=> ( ~ member(D,B)
| ~ member(D,C) ) ),
inference(canonicalize,[],[intersection_defn]) ).
fof(normalize_0_19,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
<=> ( ~ member(D,B)
| ~ member(D,C) ) ),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [B,C] :
( ~ intersect(B,C)
<=> ! [D] : ~ member(D,intersection(B,C)) ),
inference(simplify,[],[normalize_0_17,normalize_0_19]) ).
fof(normalize_0_21,plain,
! [B,C] :
( ~ intersect(B,C)
<=> ! [D] : ~ member(D,intersection(B,C)) ),
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [B,C,D] :
( ( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),intersection(B,C)) )
& ( ~ member(D,intersection(B,C))
| intersect(B,C) ) ),
inference(clausify,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
| intersect(B,C) ),
inference(conjunct,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
disjoint(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
( ~ disjoint(B,C)
| ~ intersect(B,C) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ disjoint(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)
| ~ intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_0:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_2,plain,
intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) != empty_set,
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
~ member(B,empty_set),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_4,plain,
~ member(skolemFOFtoCNF_D_1(empty_set,X_20),empty_set),
inference(subst,[],[refute_0_3:[bind(B,$fot(skolemFOFtoCNF_D_1(empty_set,X_20)))]]) ).
cnf(refute_0_5,plain,
( member(skolemFOFtoCNF_D_1(B,C),B)
| subset(B,C) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_6,plain,
( member(skolemFOFtoCNF_D_1(empty_set,X_20),empty_set)
| subset(empty_set,X_20) ),
inference(subst,[],[refute_0_5:[bind(B,$fot(empty_set)),bind(C,$fot(X_20))]]) ).
cnf(refute_0_7,plain,
subset(empty_set,X_20),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(empty_set,X_20),empty_set) )],[refute_0_6,refute_0_4]) ).
cnf(refute_0_8,plain,
subset(empty_set,X_145),
inference(subst,[],[refute_0_7:[bind(X_20,$fot(X_145))]]) ).
cnf(refute_0_9,plain,
( ~ subset(B,C)
| ~ subset(C,B)
| B = C ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_10,plain,
( ~ subset(X_145,empty_set)
| ~ subset(empty_set,X_145)
| empty_set = X_145 ),
inference(subst,[],[refute_0_9:[bind(B,$fot(empty_set)),bind(C,$fot(X_145))]]) ).
cnf(refute_0_11,plain,
( ~ subset(X_145,empty_set)
| empty_set = X_145 ),
inference(resolve,[$cnf( subset(empty_set,X_145) )],[refute_0_8,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ subset(intersection(X_165,X_166),empty_set)
| empty_set = intersection(X_165,X_166) ),
inference(subst,[],[refute_0_11:[bind(X_145,$fot(intersection(X_165,X_166)))]]) ).
cnf(refute_0_13,plain,
( member(skolemFOFtoCNF_D_1(intersection(X_41,X_42),C),intersection(X_41,X_42))
| subset(intersection(X_41,X_42),C) ),
inference(subst,[],[refute_0_5:[bind(B,$fot(intersection(X_41,X_42)))]]) ).
cnf(refute_0_14,plain,
( ~ member(D,intersection(B,C))
| intersect(B,C) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_15,plain,
( ~ member(skolemFOFtoCNF_D_1(intersection(X_41,X_42),C),intersection(X_41,X_42))
| intersect(X_41,X_42) ),
inference(subst,[],[refute_0_14:[bind(B,$fot(X_41)),bind(C,$fot(X_42)),bind(D,$fot(skolemFOFtoCNF_D_1(intersection(X_41,X_42),C)))]]) ).
cnf(refute_0_16,plain,
( intersect(X_41,X_42)
| subset(intersection(X_41,X_42),C) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(intersection(X_41,X_42),C),intersection(X_41,X_42)) )],[refute_0_13,refute_0_15]) ).
cnf(refute_0_17,plain,
( intersect(X_165,X_166)
| subset(intersection(X_165,X_166),empty_set) ),
inference(subst,[],[refute_0_16:[bind(C,$fot(empty_set)),bind(X_41,$fot(X_165)),bind(X_42,$fot(X_166))]]) ).
cnf(refute_0_18,plain,
( empty_set = intersection(X_165,X_166)
| intersect(X_165,X_166) ),
inference(resolve,[$cnf( subset(intersection(X_165,X_166),empty_set) )],[refute_0_17,refute_0_12]) ).
cnf(refute_0_19,plain,
( empty_set = intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)
| intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_18:[bind(X_165,$fot(skolemFOFtoCNF_B)),bind(X_166,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_20,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_21,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_22,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( empty_set != intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)
| intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) = empty_set ),
inference(subst,[],[refute_0_22:[bind(X,$fot(empty_set)),bind(Y,$fot(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)))]]) ).
cnf(refute_0_24,plain,
( intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) = empty_set
| intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( $equal(empty_set,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) )],[refute_0_19,refute_0_23]) ).
cnf(refute_0_25,plain,
( empty_set != empty_set
| intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) != empty_set
| intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),empty_set) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_26,plain,
( empty_set != empty_set
| intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) = empty_set
| intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),empty_set) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
( empty_set != empty_set
| intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),empty_set) )],[refute_0_26,refute_0_2]) ).
cnf(refute_0_28,plain,
empty_set = empty_set,
introduced(tautology,[refl,[$fot(empty_set)]]) ).
cnf(refute_0_29,plain,
intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_0_28,refute_0_27]) ).
cnf(refute_0_30,plain,
~ disjoint(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) )],[refute_0_29,refute_0_1]) ).
cnf(refute_0_31,plain,
disjoint(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_32,plain,
$false,
inference(resolve,[$cnf( disjoint(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) )],[refute_0_31,refute_0_30]) ).
fof(negate_1_0,plain,
~ ! [B,C] :
( intersection(B,C) = empty_set
=> disjoint(B,C) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [B,C] :
( ~ disjoint(B,C)
<=> intersect(B,C) ),
inference(canonicalize,[],[disjoint_defn]) ).
fof(normalize_1_1,plain,
! [B,C] :
( ~ disjoint(B,C)
<=> intersect(B,C) ),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
! [B,C] :
( ( ~ disjoint(B,C)
| ~ intersect(B,C) )
& ( disjoint(B,C)
| intersect(B,C) ) ),
inference(clausify,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [B,C] :
( ~ disjoint(B,C)
| ~ intersect(B,C) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
! [B,C] :
( disjoint(B,C)
| intersect(B,C) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_5,plain,
! [B,C] :
( ~ intersect(B,C)
| intersect(C,B) ),
inference(canonicalize,[],[symmetry_of_intersect]) ).
fof(normalize_1_6,plain,
! [B,C] :
( ~ intersect(B,C)
| intersect(C,B) ),
inference(specialize,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [B,C] :
( ~ intersect(B,C)
<=> ! [D] :
( ~ member(D,B)
| ~ member(D,C) ) ),
inference(canonicalize,[],[intersect_defn]) ).
fof(normalize_1_8,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
<=> ( ~ member(D,B)
| ~ member(D,C) ) ),
inference(canonicalize,[],[intersection_defn]) ).
fof(normalize_1_9,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
<=> ( ~ member(D,B)
| ~ member(D,C) ) ),
inference(specialize,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
! [B,C] :
( ~ intersect(B,C)
<=> ! [D] : ~ member(D,intersection(B,C)) ),
inference(simplify,[],[normalize_1_7,normalize_1_9]) ).
fof(normalize_1_11,plain,
! [B,C] :
( ~ intersect(B,C)
<=> ! [D] : ~ member(D,intersection(B,C)) ),
inference(specialize,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
! [B,C,D] :
( ( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),intersection(B,C)) )
& ( ~ member(D,intersection(B,C))
| intersect(B,C) ) ),
inference(clausify,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
! [B,C] :
( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),intersection(B,C)) ),
inference(conjunct,[],[normalize_1_12]) ).
fof(normalize_1_14,plain,
? [B,C] :
( ~ disjoint(B,C)
& intersection(B,C) = empty_set ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_15,plain,
( ~ disjoint(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)
& intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) = empty_set ),
inference(skolemize,[],[normalize_1_14]) ).
fof(normalize_1_16,plain,
intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) = empty_set,
inference(conjunct,[],[normalize_1_15]) ).
fof(normalize_1_17,plain,
! [B] : ~ member(B,empty_set),
inference(canonicalize,[],[empty_set_defn]) ).
fof(normalize_1_18,plain,
! [B] : ~ member(B,empty_set),
inference(specialize,[],[normalize_1_17]) ).
fof(normalize_1_19,plain,
~ disjoint(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),
inference(conjunct,[],[normalize_1_15]) ).
cnf(refute_1_0,plain,
( ~ disjoint(B,C)
| ~ intersect(B,C) ),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_1,plain,
( ~ disjoint(X_183,X_182)
| ~ intersect(X_183,X_182) ),
inference(subst,[],[refute_1_0:[bind(B,$fot(X_183)),bind(C,$fot(X_182))]]) ).
cnf(refute_1_2,plain,
( disjoint(B,C)
| intersect(B,C) ),
inference(canonicalize,[],[normalize_1_4]) ).
cnf(refute_1_3,plain,
( disjoint(X_180,X_181)
| intersect(X_180,X_181) ),
inference(subst,[],[refute_1_2:[bind(B,$fot(X_180)),bind(C,$fot(X_181))]]) ).
cnf(refute_1_4,plain,
( ~ intersect(B,C)
| intersect(C,B) ),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_5,plain,
( ~ intersect(X_180,X_181)
| intersect(X_181,X_180) ),
inference(subst,[],[refute_1_4:[bind(B,$fot(X_180)),bind(C,$fot(X_181))]]) ).
cnf(refute_1_6,plain,
( disjoint(X_180,X_181)
| intersect(X_181,X_180) ),
inference(resolve,[$cnf( intersect(X_180,X_181) )],[refute_1_3,refute_1_5]) ).
cnf(refute_1_7,plain,
( disjoint(X_182,X_183)
| intersect(X_183,X_182) ),
inference(subst,[],[refute_1_6:[bind(X_180,$fot(X_182)),bind(X_181,$fot(X_183))]]) ).
cnf(refute_1_8,plain,
( ~ disjoint(X_183,X_182)
| disjoint(X_182,X_183) ),
inference(resolve,[$cnf( intersect(X_183,X_182) )],[refute_1_7,refute_1_1]) ).
cnf(refute_1_9,plain,
( ~ disjoint(skolemFOFtoCNF_C_2,skolemFOFtoCNF_B_1)
| disjoint(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) ),
inference(subst,[],[refute_1_8:[bind(X_182,$fot(skolemFOFtoCNF_B_1)),bind(X_183,$fot(skolemFOFtoCNF_C_2))]]) ).
cnf(refute_1_10,plain,
( disjoint(X_198,X_197)
| intersect(X_197,X_198) ),
inference(subst,[],[refute_1_6:[bind(X_180,$fot(X_198)),bind(X_181,$fot(X_197))]]) ).
cnf(refute_1_11,plain,
( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),intersection(B,C)) ),
inference(canonicalize,[],[normalize_1_13]) ).
cnf(refute_1_12,plain,
( ~ intersect(X_197,X_198)
| member(skolemFOFtoCNF_D(X_197,X_198),intersection(X_197,X_198)) ),
inference(subst,[],[refute_1_11:[bind(B,$fot(X_197)),bind(C,$fot(X_198))]]) ).
cnf(refute_1_13,plain,
( disjoint(X_198,X_197)
| member(skolemFOFtoCNF_D(X_197,X_198),intersection(X_197,X_198)) ),
inference(resolve,[$cnf( intersect(X_197,X_198) )],[refute_1_10,refute_1_12]) ).
cnf(refute_1_14,plain,
( disjoint(skolemFOFtoCNF_C_2,skolemFOFtoCNF_B_1)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)) ),
inference(subst,[],[refute_1_13:[bind(X_197,$fot(skolemFOFtoCNF_B_1)),bind(X_198,$fot(skolemFOFtoCNF_C_2))]]) ).
cnf(refute_1_15,plain,
intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) = empty_set,
inference(canonicalize,[],[normalize_1_16]) ).
cnf(refute_1_16,plain,
( intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) != empty_set
| ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2))
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),empty_set) ),
introduced(tautology,[equality,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)) ),[1],$fot(empty_set)]]) ).
cnf(refute_1_17,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2))
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),empty_set) ),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),empty_set) )],[refute_1_15,refute_1_16]) ).
cnf(refute_1_18,plain,
( disjoint(skolemFOFtoCNF_C_2,skolemFOFtoCNF_B_1)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),empty_set) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)) )],[refute_1_14,refute_1_17]) ).
cnf(refute_1_19,plain,
~ member(B,empty_set),
inference(canonicalize,[],[normalize_1_18]) ).
cnf(refute_1_20,plain,
~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),empty_set),
inference(subst,[],[refute_1_19:[bind(B,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)))]]) ).
cnf(refute_1_21,plain,
disjoint(skolemFOFtoCNF_C_2,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),empty_set) )],[refute_1_18,refute_1_20]) ).
cnf(refute_1_22,plain,
disjoint(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),
inference(resolve,[$cnf( disjoint(skolemFOFtoCNF_C_2,skolemFOFtoCNF_B_1) )],[refute_1_21,refute_1_9]) ).
cnf(refute_1_23,plain,
~ disjoint(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),
inference(canonicalize,[],[normalize_1_19]) ).
cnf(refute_1_24,plain,
$false,
inference(resolve,[$cnf( disjoint(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) )],[refute_1_22,refute_1_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET636+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n025.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 04:21:17 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.41
% 0.18/0.41 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.42
%------------------------------------------------------------------------------