TSTP Solution File: SET624+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET624+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 03:36:06 EDT 2022
% Result : Theorem 2.22s 2.37s
% Output : CNFRefutation 2.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 4
% Syntax : Number of formulae : 96 ( 22 unt; 0 def)
% Number of atoms : 221 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 227 ( 102 ~; 88 |; 21 &)
% ( 11 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 134 ( 10 sgn 85 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(union_defn,axiom,
! [B,C,D] :
( member(D,union(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(symmetry_of_intersect,axiom,
! [B,C] :
( intersect(B,C)
=> intersect(C,B) ) ).
fof(prove_intersect_with_union,conjecture,
! [B,C,D] :
( intersect(B,union(C,D))
<=> ( intersect(B,C)
| intersect(B,D) ) ) ).
fof(subgoal_0,plain,
! [B,C,D] :
( ( intersect(B,union(C,D))
& ~ intersect(B,C) )
=> intersect(B,D) ),
inference(strip,[],[prove_intersect_with_union]) ).
fof(subgoal_1,plain,
! [B,C,D] :
( ( intersect(B,C)
| intersect(B,D) )
=> intersect(B,union(C,D)) ),
inference(strip,[],[prove_intersect_with_union]) ).
fof(negate_0_0,plain,
~ ! [B,C,D] :
( ( intersect(B,union(C,D))
& ~ intersect(B,C) )
=> intersect(B,D) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B,C,D] :
( ~ intersect(B,C)
& ~ intersect(B,D)
& intersect(B,union(C,D)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
& ~ intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)
& intersect(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
intersect(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [B,C] :
( ~ intersect(B,C)
<=> ! [D] :
( ~ member(D,B)
| ~ member(D,C) ) ),
inference(canonicalize,[],[intersect_defn]) ).
fof(normalize_0_4,plain,
! [B,C] :
( ~ intersect(B,C)
<=> ! [D] :
( ~ member(D,B)
| ~ member(D,C) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [B,C,D] :
( ( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),B) )
& ( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),C) )
& ( ~ member(D,B)
| ~ member(D,C)
| intersect(B,C) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [B,C] :
( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),B) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [B,C,D] :
( ~ member(D,B)
| ~ member(D,C)
| intersect(B,C) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_8,plain,
! [B,C] :
( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),C) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_9,plain,
! [B,C,D] :
( ~ member(D,union(B,C))
<=> ( ~ member(D,B)
& ~ member(D,C) ) ),
inference(canonicalize,[],[union_defn]) ).
fof(normalize_0_10,plain,
! [B,C,D] :
( ~ member(D,union(B,C))
<=> ( ~ member(D,B)
& ~ member(D,C) ) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [B,C,D] :
( ( ~ member(D,B)
| member(D,union(B,C)) )
& ( ~ member(D,C)
| member(D,union(B,C)) )
& ( ~ member(D,union(B,C))
| member(D,B)
| member(D,C) ) ),
inference(clausify,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [B,C,D] :
( ~ member(D,union(B,C))
| member(D,B)
| member(D,C) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
~ intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_14,plain,
~ intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
intersect(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),B) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( ~ intersect(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_1:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)))]]) ).
cnf(refute_0_3,plain,
member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_B),
inference(resolve,[$cnf( intersect(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ member(D,B)
| ~ member(D,C)
| intersect(B,C) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),X_228)
| ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_B)
| intersect(skolemFOFtoCNF_B,X_228) ),
inference(subst,[],[refute_0_4:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(X_228)),bind(D,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))))]]) ).
cnf(refute_0_6,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),X_228)
| intersect(skolemFOFtoCNF_B,X_228) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_B) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_C)
| intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_6:[bind(X_228,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_8,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_D_2)
| intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2) ),
inference(subst,[],[refute_0_6:[bind(X_228,$fot(skolemFOFtoCNF_D_2))]]) ).
cnf(refute_0_9,plain,
( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),C) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_10,plain,
( ~ intersect(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) ),
inference(subst,[],[refute_0_9:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)))]]) ).
cnf(refute_0_11,plain,
member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),
inference(resolve,[$cnf( intersect(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) )],[refute_0_0,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ member(D,union(B,C))
| member(D,B)
| member(D,C) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_13,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_C)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_D_2) ),
inference(subst,[],[refute_0_12:[bind(B,$fot(skolemFOFtoCNF_C)),bind(C,$fot(skolemFOFtoCNF_D_2)),bind(D,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))))]]) ).
cnf(refute_0_14,plain,
( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_C)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_D_2) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,plain,
( intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_D_2) )],[refute_0_14,refute_0_8]) ).
cnf(refute_0_16,plain,
~ intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_17,plain,
member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_C),
inference(resolve,[$cnf( intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_C) )],[refute_0_17,refute_0_7]) ).
cnf(refute_0_19,plain,
~ intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_20,plain,
$false,
inference(resolve,[$cnf( intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_18,refute_0_19]) ).
fof(negate_1_0,plain,
~ ! [B,C,D] :
( ( intersect(B,C)
| intersect(B,D) )
=> intersect(B,union(C,D)) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [B,C,D] :
( ~ intersect(B,union(C,D))
& ( intersect(B,C)
| intersect(B,D) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( ~ intersect(skolemFOFtoCNF_B_1,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3))
& ( intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3) ) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
~ intersect(skolemFOFtoCNF_B_1,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3)),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [B,C] :
( ~ intersect(B,C)
| intersect(C,B) ),
inference(canonicalize,[],[symmetry_of_intersect]) ).
fof(normalize_1_4,plain,
! [B,C] :
( ~ intersect(B,C)
| intersect(C,B) ),
inference(specialize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [B,C,D] :
( ~ member(D,union(B,C))
<=> ( ~ member(D,B)
& ~ member(D,C) ) ),
inference(canonicalize,[],[union_defn]) ).
fof(normalize_1_6,plain,
! [B,C,D] :
( ~ member(D,union(B,C))
<=> ( ~ member(D,B)
& ~ member(D,C) ) ),
inference(specialize,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [B,C,D] :
( ( ~ member(D,B)
| member(D,union(B,C)) )
& ( ~ member(D,C)
| member(D,union(B,C)) )
& ( ~ member(D,union(B,C))
| member(D,B)
| member(D,C) ) ),
inference(clausify,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
! [B,C,D] :
( ~ member(D,B)
| member(D,union(B,C)) ),
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [B,C] :
( ~ intersect(B,C)
<=> ! [D] :
( ~ member(D,B)
| ~ member(D,C) ) ),
inference(canonicalize,[],[intersect_defn]) ).
fof(normalize_1_10,plain,
! [B,C] :
( ~ intersect(B,C)
<=> ! [D] :
( ~ member(D,B)
| ~ member(D,C) ) ),
inference(specialize,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
! [B,C,D] :
( ( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),B) )
& ( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),C) )
& ( ~ member(D,B)
| ~ member(D,C)
| intersect(B,C) ) ),
inference(clausify,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
! [B,C] :
( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),C) ),
inference(conjunct,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
( intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3) ),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_14,plain,
! [B,C,D] :
( ~ member(D,C)
| member(D,union(B,C)) ),
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_15,plain,
! [B,C] :
( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),B) ),
inference(conjunct,[],[normalize_1_11]) ).
fof(normalize_1_16,plain,
! [B,C,D] :
( ~ member(D,B)
| ~ member(D,C)
| intersect(B,C) ),
inference(conjunct,[],[normalize_1_11]) ).
cnf(refute_1_0,plain,
~ intersect(skolemFOFtoCNF_B_1,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3)),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
( ~ intersect(B,C)
| intersect(C,B) ),
inference(canonicalize,[],[normalize_1_4]) ).
cnf(refute_1_2,plain,
( ~ intersect(union(skolemFOFtoCNF_C_1,X_3357),skolemFOFtoCNF_B_1)
| intersect(skolemFOFtoCNF_B_1,union(skolemFOFtoCNF_C_1,X_3357)) ),
inference(subst,[],[refute_1_1:[bind(B,$fot(union(skolemFOFtoCNF_C_1,X_3357))),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_1_3,plain,
( ~ member(D,B)
| member(D,union(B,C)) ),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_4,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),union(skolemFOFtoCNF_C_1,C)) ),
inference(subst,[],[refute_1_3:[bind(B,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)))]]) ).
cnf(refute_1_5,plain,
( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),C) ),
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_6,plain,
( ~ intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_1_5:[bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_1_7,plain,
( intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3) ),
inference(canonicalize,[],[normalize_1_13]) ).
cnf(refute_1_8,plain,
( ~ intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3),skolemFOFtoCNF_D_3) ),
inference(subst,[],[refute_1_5:[bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_D_3))]]) ).
cnf(refute_1_9,plain,
( intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3),skolemFOFtoCNF_D_3) ),
inference(resolve,[$cnf( intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3) )],[refute_1_7,refute_1_8]) ).
cnf(refute_1_10,plain,
( ~ member(D,C)
| member(D,union(B,C)) ),
inference(canonicalize,[],[normalize_1_14]) ).
cnf(refute_1_11,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3),skolemFOFtoCNF_D_3)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3),union(X_1158,skolemFOFtoCNF_D_3)) ),
inference(subst,[],[refute_1_10:[bind(B,$fot(X_1158)),bind(C,$fot(skolemFOFtoCNF_D_3)),bind(D,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3)))]]) ).
cnf(refute_1_12,plain,
( intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3),union(X_1158,skolemFOFtoCNF_D_3)) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3),skolemFOFtoCNF_D_3) )],[refute_1_9,refute_1_11]) ).
cnf(refute_1_13,plain,
( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),B) ),
inference(canonicalize,[],[normalize_1_15]) ).
cnf(refute_1_14,plain,
( ~ intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3),skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_1_13:[bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_D_3))]]) ).
cnf(refute_1_15,plain,
( intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3),skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3) )],[refute_1_7,refute_1_14]) ).
cnf(refute_1_16,plain,
( ~ member(D,B)
| ~ member(D,C)
| intersect(B,C) ),
inference(canonicalize,[],[normalize_1_16]) ).
cnf(refute_1_17,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3),X_1280)
| ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3),skolemFOFtoCNF_B_1)
| intersect(skolemFOFtoCNF_B_1,X_1280) ),
inference(subst,[],[refute_1_16:[bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(X_1280)),bind(D,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3)))]]) ).
cnf(refute_1_18,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3),X_1280)
| intersect(skolemFOFtoCNF_B_1,X_1280)
| intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3),skolemFOFtoCNF_B_1) )],[refute_1_15,refute_1_17]) ).
cnf(refute_1_19,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3),union(X_1158,skolemFOFtoCNF_D_3))
| intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| intersect(skolemFOFtoCNF_B_1,union(X_1158,skolemFOFtoCNF_D_3)) ),
inference(subst,[],[refute_1_18:[bind(X_1280,$fot(union(X_1158,skolemFOFtoCNF_D_3)))]]) ).
cnf(refute_1_20,plain,
( intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| intersect(skolemFOFtoCNF_B_1,union(X_1158,skolemFOFtoCNF_D_3)) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3),union(X_1158,skolemFOFtoCNF_D_3)) )],[refute_1_12,refute_1_19]) ).
cnf(refute_1_21,plain,
( intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| intersect(skolemFOFtoCNF_B_1,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3)) ),
inference(subst,[],[refute_1_20:[bind(X_1158,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_1_22,plain,
intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( intersect(skolemFOFtoCNF_B_1,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3)) )],[refute_1_21,refute_1_0]) ).
cnf(refute_1_23,plain,
member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) )],[refute_1_22,refute_1_6]) ).
cnf(refute_1_24,plain,
member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),union(skolemFOFtoCNF_C_1,C)),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1) )],[refute_1_23,refute_1_4]) ).
cnf(refute_1_25,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),B)
| ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),skolemFOFtoCNF_B_1)
| intersect(B,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_1_16:[bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)))]]) ).
cnf(refute_1_26,plain,
( ~ intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_1_13:[bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_1_27,plain,
member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) )],[refute_1_22,refute_1_26]) ).
cnf(refute_1_28,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),B)
| intersect(B,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),skolemFOFtoCNF_B_1) )],[refute_1_27,refute_1_25]) ).
cnf(refute_1_29,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),union(skolemFOFtoCNF_C_1,C))
| intersect(union(skolemFOFtoCNF_C_1,C),skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_1_28:[bind(B,$fot(union(skolemFOFtoCNF_C_1,C)))]]) ).
cnf(refute_1_30,plain,
intersect(union(skolemFOFtoCNF_C_1,C),skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),union(skolemFOFtoCNF_C_1,C)) )],[refute_1_24,refute_1_29]) ).
cnf(refute_1_31,plain,
intersect(union(skolemFOFtoCNF_C_1,X_3357),skolemFOFtoCNF_B_1),
inference(subst,[],[refute_1_30:[bind(C,$fot(X_3357))]]) ).
cnf(refute_1_32,plain,
intersect(skolemFOFtoCNF_B_1,union(skolemFOFtoCNF_C_1,X_3357)),
inference(resolve,[$cnf( intersect(union(skolemFOFtoCNF_C_1,X_3357),skolemFOFtoCNF_B_1) )],[refute_1_31,refute_1_2]) ).
cnf(refute_1_33,plain,
intersect(skolemFOFtoCNF_B_1,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3)),
inference(subst,[],[refute_1_32:[bind(X_3357,$fot(skolemFOFtoCNF_D_3))]]) ).
cnf(refute_1_34,plain,
$false,
inference(resolve,[$cnf( intersect(skolemFOFtoCNF_B_1,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3)) )],[refute_1_33,refute_1_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET624+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n018.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 : Sun Jul 10 21:18:13 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.22/2.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.22/2.37
% 2.22/2.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.22/2.38
%------------------------------------------------------------------------------