TSTP Solution File: SEU168+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU168+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.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 12:39:00 EDT 2022
% Result : Theorem 29.80s 30.00s
% Output : CNFRefutation 29.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 6
% Syntax : Number of formulae : 118 ( 10 unt; 1 def)
% Number of atoms : 442 ( 11 equ)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 517 ( 193 ~; 228 |; 76 &)
% ( 11 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-2 aty)
% Number of variables : 204 ( 0 sgn 115 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_zfmisc_1,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ) ).
fof(t136_zfmisc_1,conjecture,
! [A] :
? [B] :
( in(A,B)
& ! [C,D] :
( ( in(C,B)
& subset(D,C) )
=> in(D,B) )
& ! [C] :
( in(C,B)
=> in(powerset(C),B) )
& ! [C] :
~ ( subset(C,B)
& ~ are_equipotent(C,B)
& ~ in(C,B) ) ) ).
fof(t9_tarski,axiom,
! [A] :
? [B] :
( in(A,B)
& ! [C,D] :
( ( in(C,B)
& subset(D,C) )
=> in(D,B) )
& ! [C] :
~ ( in(C,B)
& ! [D] :
~ ( in(D,B)
& ! [E] :
( subset(E,C)
=> in(E,D) ) ) )
& ! [C] :
~ ( subset(C,B)
& ~ are_equipotent(C,B)
& ~ in(C,B) ) ) ).
fof(definition_0,definition,
! [B,C] :
( definitionFOFtoCNF_0(B,C)
<=> ( ~ are_equipotent(C,B)
& ~ in(C,B)
& subset(C,B) ) ) ).
fof(subgoal_0,plain,
! [A] :
? [B] :
( in(A,B)
& ! [C,D] :
( ( in(C,B)
& subset(D,C) )
=> in(D,B) )
& ! [C] :
( in(C,B)
=> in(powerset(C),B) )
& ! [C] :
~ ( subset(C,B)
& ~ are_equipotent(C,B)
& ~ in(C,B) ) ),
inference(strip,[],[t136_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A] :
? [B] :
( in(A,B)
& ! [C,D] :
( ( in(C,B)
& subset(D,C) )
=> in(D,B) )
& ! [C] :
( in(C,B)
=> in(powerset(C),B) )
& ! [C] :
~ ( subset(C,B)
& ~ are_equipotent(C,B)
& ~ in(C,B) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [B,C] :
( ~ definitionFOFtoCNF_0(B,C)
<=> ( ~ subset(C,B)
| are_equipotent(C,B)
| in(C,B) ) ),
inference(canonicalize,[],[definition_0]) ).
fof(normalize_0_1,plain,
! [B,C] :
( ( ~ are_equipotent(C,B)
| ~ definitionFOFtoCNF_0(B,C) )
& ( ~ definitionFOFtoCNF_0(B,C)
| ~ in(C,B) )
& ( ~ definitionFOFtoCNF_0(B,C)
| subset(C,B) )
& ( ~ subset(C,B)
| are_equipotent(C,B)
| definitionFOFtoCNF_0(B,C)
| in(C,B) ) ),
inference(clausify,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [B,C] :
( ~ definitionFOFtoCNF_0(B,C)
| ~ in(C,B) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A] :
? [B] :
( in(A,B)
& ! [C] :
( ~ in(C,B)
| ? [D] :
( in(D,B)
& ! [E] :
( ~ subset(E,C)
| in(E,D) ) ) )
& ! [C] :
( ~ subset(C,B)
| are_equipotent(C,B)
| in(C,B) )
& ! [C,D] :
( ~ in(C,B)
| ~ subset(D,C)
| in(D,B) ) ),
inference(canonicalize,[],[t9_tarski]) ).
fof(normalize_0_4,plain,
! [A] :
? [B] :
( in(A,B)
& ! [C] :
( ~ in(C,B)
| ? [D] :
( in(D,B)
& ! [E] :
( ~ subset(E,C)
| in(E,D) ) ) )
& ! [C] :
( ~ subset(C,B)
| are_equipotent(C,B)
| in(C,B) )
& ! [C,D] :
( ~ in(C,B)
| ~ subset(D,C)
| in(D,B) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A] :
( in(A,skolemFOFtoCNF_B(A))
& ! [C] :
( ~ in(C,skolemFOFtoCNF_B(A))
| ? [D] :
( in(D,skolemFOFtoCNF_B(A))
& ! [E] :
( ~ subset(E,C)
| in(E,D) ) ) )
& ! [C] :
( ~ subset(C,skolemFOFtoCNF_B(A))
| are_equipotent(C,skolemFOFtoCNF_B(A))
| in(C,skolemFOFtoCNF_B(A)) )
& ! [C,D] :
( ~ in(C,skolemFOFtoCNF_B(A))
| ~ subset(D,C)
| in(D,skolemFOFtoCNF_B(A)) ) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,C] :
( ~ subset(C,skolemFOFtoCNF_B(A))
| are_equipotent(C,skolemFOFtoCNF_B(A))
| in(C,skolemFOFtoCNF_B(A)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,C] :
( ~ subset(C,skolemFOFtoCNF_B(A))
| are_equipotent(C,skolemFOFtoCNF_B(A))
| in(C,skolemFOFtoCNF_B(A)) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [B,C] :
( ~ definitionFOFtoCNF_0(B,C)
| subset(C,B) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_9,plain,
? [A] :
! [B] :
( ~ in(A,B)
| ? [C] :
( ~ in(powerset(C),B)
& in(C,B) )
| ? [C] :
( ~ are_equipotent(C,B)
& ~ in(C,B)
& subset(C,B) )
| ? [C,D] :
( ~ in(D,B)
& in(C,B)
& subset(D,C) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_10,plain,
! [B] :
( ~ in(skolemFOFtoCNF_A,B)
| ? [C] :
( ~ in(powerset(C),B)
& in(C,B) )
| ? [C] :
( ~ are_equipotent(C,B)
& ~ in(C,B)
& subset(C,B) )
| ? [C,D] :
( ~ in(D,B)
& in(C,B)
& subset(D,C) ) ),
inference(skolemize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [B] :
( ~ in(skolemFOFtoCNF_A,B)
| ? [C] :
( ~ in(powerset(C),B)
& in(C,B) )
| ? [C] :
( ~ are_equipotent(C,B)
& ~ in(C,B)
& subset(C,B) )
| ? [C,D] :
( ~ in(D,B)
& in(C,B)
& subset(D,C) ) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [B] :
( ~ in(skolemFOFtoCNF_A,B)
| ? [C] : definitionFOFtoCNF_0(B,C)
| ? [C] :
( ~ in(powerset(C),B)
& in(C,B) )
| ? [C,D] :
( ~ in(D,B)
& in(C,B)
& subset(D,C) ) ),
inference(simplify,[],[normalize_0_11,normalize_0_0]) ).
fof(normalize_0_13,plain,
! [B] :
( ( ~ in(powerset(skolemFOFtoCNF_C_3(B)),B)
| ~ in(skolemFOFtoCNF_A,B)
| ~ in(skolemFOFtoCNF_D_1(B),B)
| definitionFOFtoCNF_0(B,skolemFOFtoCNF_C_2(B)) )
& ( ~ in(powerset(skolemFOFtoCNF_C_3(B)),B)
| ~ in(skolemFOFtoCNF_A,B)
| definitionFOFtoCNF_0(B,skolemFOFtoCNF_C_2(B))
| in(skolemFOFtoCNF_C_4(B),B) )
& ( ~ in(powerset(skolemFOFtoCNF_C_3(B)),B)
| ~ in(skolemFOFtoCNF_A,B)
| definitionFOFtoCNF_0(B,skolemFOFtoCNF_C_2(B))
| subset(skolemFOFtoCNF_D_1(B),skolemFOFtoCNF_C_4(B)) )
& ( ~ in(skolemFOFtoCNF_A,B)
| ~ in(skolemFOFtoCNF_D_1(B),B)
| definitionFOFtoCNF_0(B,skolemFOFtoCNF_C_2(B))
| in(skolemFOFtoCNF_C_3(B),B) )
& ( ~ in(skolemFOFtoCNF_A,B)
| definitionFOFtoCNF_0(B,skolemFOFtoCNF_C_2(B))
| in(skolemFOFtoCNF_C_3(B),B)
| in(skolemFOFtoCNF_C_4(B),B) )
& ( ~ in(skolemFOFtoCNF_A,B)
| definitionFOFtoCNF_0(B,skolemFOFtoCNF_C_2(B))
| in(skolemFOFtoCNF_C_3(B),B)
| subset(skolemFOFtoCNF_D_1(B),skolemFOFtoCNF_C_4(B)) ) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [B] :
( ~ in(powerset(skolemFOFtoCNF_C_3(B)),B)
| ~ in(skolemFOFtoCNF_A,B)
| ~ in(skolemFOFtoCNF_D_1(B),B)
| definitionFOFtoCNF_0(B,skolemFOFtoCNF_C_2(B)) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [A,C,D] :
( ~ in(C,skolemFOFtoCNF_B(A))
| ~ subset(D,C)
| in(D,skolemFOFtoCNF_B(A)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_16,plain,
! [A,C,D] :
( ~ in(C,skolemFOFtoCNF_B(A))
| ~ subset(D,C)
| in(D,skolemFOFtoCNF_B(A)) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [A,C] :
( ~ in(C,skolemFOFtoCNF_B(A))
| ? [D] :
( in(D,skolemFOFtoCNF_B(A))
& ! [E] :
( ~ subset(E,C)
| in(E,D) ) ) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_18,plain,
! [A,C] :
( ~ in(C,skolemFOFtoCNF_B(A))
| ? [D] :
( in(D,skolemFOFtoCNF_B(A))
& ! [E] :
( ~ subset(E,C)
| in(E,D) ) ) ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [A,C,E] :
( ( ~ in(C,skolemFOFtoCNF_B(A))
| in(skolemFOFtoCNF_D(A,C),skolemFOFtoCNF_B(A)) )
& ( ~ in(C,skolemFOFtoCNF_B(A))
| ~ subset(E,C)
| in(E,skolemFOFtoCNF_D(A,C)) ) ),
inference(clausify,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [A,C] :
( ~ in(C,skolemFOFtoCNF_B(A))
| in(skolemFOFtoCNF_D(A,C),skolemFOFtoCNF_B(A)) ),
inference(conjunct,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [B] :
( ~ in(skolemFOFtoCNF_A,B)
| ~ in(skolemFOFtoCNF_D_1(B),B)
| definitionFOFtoCNF_0(B,skolemFOFtoCNF_C_2(B))
| in(skolemFOFtoCNF_C_3(B),B) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_22,plain,
! [A] : in(A,skolemFOFtoCNF_B(A)),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_23,plain,
! [B] :
( ~ in(skolemFOFtoCNF_A,B)
| definitionFOFtoCNF_0(B,skolemFOFtoCNF_C_2(B))
| in(skolemFOFtoCNF_C_3(B),B)
| subset(skolemFOFtoCNF_D_1(B),skolemFOFtoCNF_C_4(B)) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_24,plain,
! [B] :
( ~ in(skolemFOFtoCNF_A,B)
| definitionFOFtoCNF_0(B,skolemFOFtoCNF_C_2(B))
| in(skolemFOFtoCNF_C_3(B),B)
| in(skolemFOFtoCNF_C_4(B),B) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_25,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(canonicalize,[],[d3_tarski]) ).
fof(normalize_0_26,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(specialize,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
! [A,B,C] :
( ( ~ in(skolemFOFtoCNF_C_1(A,B),B)
| subset(A,B) )
& ( in(skolemFOFtoCNF_C_1(A,B),A)
| subset(A,B) )
& ( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ) ),
inference(clausify,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [A,B] :
( ~ in(skolemFOFtoCNF_C_1(A,B),B)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
! [A,B] :
( B != powerset(A)
<=> ? [C] :
( ~ in(C,B)
<=> subset(C,A) ) ),
inference(canonicalize,[],[d1_zfmisc_1]) ).
fof(normalize_0_30,plain,
! [A,B] :
( B != powerset(A)
<=> ? [C] :
( ~ in(C,B)
<=> subset(C,A) ) ),
inference(specialize,[],[normalize_0_29]) ).
fof(normalize_0_31,plain,
! [A,B,C] :
( ( B != powerset(A)
| ~ in(C,B)
| subset(C,A) )
& ( B != powerset(A)
| ~ subset(C,A)
| in(C,B) )
& ( ~ in(skolemFOFtoCNF_C(A,B),B)
| ~ subset(skolemFOFtoCNF_C(A,B),A)
| B = powerset(A) )
& ( B = powerset(A)
| in(skolemFOFtoCNF_C(A,B),B)
| subset(skolemFOFtoCNF_C(A,B),A) ) ),
inference(clausify,[],[normalize_0_30]) ).
fof(normalize_0_32,plain,
! [A,B,C] :
( B != powerset(A)
| ~ in(C,B)
| subset(C,A) ),
inference(conjunct,[],[normalize_0_31]) ).
fof(normalize_0_33,plain,
! [A,B] :
( in(skolemFOFtoCNF_C_1(A,B),A)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_27]) ).
fof(normalize_0_34,plain,
! [A,C,E] :
( ~ in(C,skolemFOFtoCNF_B(A))
| ~ subset(E,C)
| in(E,skolemFOFtoCNF_D(A,C)) ),
inference(conjunct,[],[normalize_0_19]) ).
fof(normalize_0_35,plain,
! [B] :
( ~ in(powerset(skolemFOFtoCNF_C_3(B)),B)
| ~ in(skolemFOFtoCNF_A,B)
| definitionFOFtoCNF_0(B,skolemFOFtoCNF_C_2(B))
| subset(skolemFOFtoCNF_D_1(B),skolemFOFtoCNF_C_4(B)) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_36,plain,
! [B] :
( ~ in(powerset(skolemFOFtoCNF_C_3(B)),B)
| ~ in(skolemFOFtoCNF_A,B)
| definitionFOFtoCNF_0(B,skolemFOFtoCNF_C_2(B))
| in(skolemFOFtoCNF_C_4(B),B) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_37,plain,
! [B,C] :
( ~ are_equipotent(C,B)
| ~ definitionFOFtoCNF_0(B,C) ),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
( ~ definitionFOFtoCNF_0(B,C)
| ~ in(C,B) ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| ~ in(skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_0:[bind(B,$fot(skolemFOFtoCNF_B(skolemFOFtoCNF_A))),bind(C,$fot(skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A))))]]) ).
cnf(refute_0_2,plain,
( ~ subset(C,skolemFOFtoCNF_B(A))
| are_equipotent(C,skolemFOFtoCNF_B(A))
| in(C,skolemFOFtoCNF_B(A)) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( ~ subset(skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A))
| are_equipotent(skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A))
| in(skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A))))]]) ).
cnf(refute_0_4,plain,
( ~ definitionFOFtoCNF_0(B,C)
| subset(C,B) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( ~ definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| subset(skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_4:[bind(B,$fot(skolemFOFtoCNF_B(skolemFOFtoCNF_A))),bind(C,$fot(skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A))))]]) ).
cnf(refute_0_6,plain,
( ~ in(powerset(skolemFOFtoCNF_C_3(B)),B)
| ~ in(skolemFOFtoCNF_A,B)
| ~ in(skolemFOFtoCNF_D_1(B),B)
| definitionFOFtoCNF_0(B,skolemFOFtoCNF_C_2(B)) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_7,plain,
( ~ in(powerset(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A))),skolemFOFtoCNF_B(skolemFOFtoCNF_A))
| ~ in(skolemFOFtoCNF_A,skolemFOFtoCNF_B(skolemFOFtoCNF_A))
| ~ in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A))
| definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A))) ),
inference(subst,[],[refute_0_6:[bind(B,$fot(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_8,plain,
( ~ in(C,skolemFOFtoCNF_B(A))
| ~ subset(D,C)
| in(D,skolemFOFtoCNF_B(A)) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_9,plain,
( ~ in(skolemFOFtoCNF_D(skolemFOFtoCNF_A,skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A))),skolemFOFtoCNF_B(skolemFOFtoCNF_A))
| ~ subset(D,skolemFOFtoCNF_D(skolemFOFtoCNF_A,skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A))))
| in(D,skolemFOFtoCNF_B(skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_A,skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))))]]) ).
cnf(refute_0_10,plain,
( ~ in(C,skolemFOFtoCNF_B(A))
| in(skolemFOFtoCNF_D(A,C),skolemFOFtoCNF_B(A)) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_11,plain,
( ~ in(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A))
| in(skolemFOFtoCNF_D(skolemFOFtoCNF_A,skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A))),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_10:[bind(A,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A))))]]) ).
cnf(refute_0_12,plain,
( ~ in(skolemFOFtoCNF_A,B)
| ~ in(skolemFOFtoCNF_D_1(B),B)
| definitionFOFtoCNF_0(B,skolemFOFtoCNF_C_2(B))
| in(skolemFOFtoCNF_C_3(B),B) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_13,plain,
( ~ in(skolemFOFtoCNF_A,skolemFOFtoCNF_B(skolemFOFtoCNF_A))
| ~ in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A))
| definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| in(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_12:[bind(B,$fot(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_14,plain,
in(A,skolemFOFtoCNF_B(A)),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_15,plain,
in(skolemFOFtoCNF_A,skolemFOFtoCNF_B(skolemFOFtoCNF_A)),
inference(subst,[],[refute_0_14:[bind(A,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_16,plain,
( ~ in(skolemFOFtoCNF_A,B)
| definitionFOFtoCNF_0(B,skolemFOFtoCNF_C_2(B))
| in(skolemFOFtoCNF_C_3(B),B)
| subset(skolemFOFtoCNF_D_1(B),skolemFOFtoCNF_C_4(B)) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_17,plain,
( ~ in(skolemFOFtoCNF_A,skolemFOFtoCNF_B(skolemFOFtoCNF_A))
| definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| in(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A))
| subset(skolemFOFtoCNF_D_1(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_C_4(skolemFOFtoCNF_B(skolemFOFtoCNF_A))) ),
inference(subst,[],[refute_0_16:[bind(B,$fot(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_18,plain,
( definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| in(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A))
| subset(skolemFOFtoCNF_D_1(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_C_4(skolemFOFtoCNF_B(skolemFOFtoCNF_A))) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A,skolemFOFtoCNF_B(skolemFOFtoCNF_A)) )],[refute_0_15,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ in(skolemFOFtoCNF_A,B)
| definitionFOFtoCNF_0(B,skolemFOFtoCNF_C_2(B))
| in(skolemFOFtoCNF_C_3(B),B)
| in(skolemFOFtoCNF_C_4(B),B) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_20,plain,
( ~ in(skolemFOFtoCNF_A,skolemFOFtoCNF_B(skolemFOFtoCNF_A))
| definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| in(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A))
| in(skolemFOFtoCNF_C_4(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_19:[bind(B,$fot(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_21,plain,
( definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| in(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A))
| in(skolemFOFtoCNF_C_4(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A,skolemFOFtoCNF_B(skolemFOFtoCNF_A)) )],[refute_0_15,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ in(skolemFOFtoCNF_C_4(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A))
| ~ subset(X_90,skolemFOFtoCNF_C_4(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| in(X_90,skolemFOFtoCNF_B(skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_C_4(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))),bind(D,$fot(X_90))]]) ).
cnf(refute_0_23,plain,
( ~ subset(X_90,skolemFOFtoCNF_C_4(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| in(X_90,skolemFOFtoCNF_B(skolemFOFtoCNF_A))
| in(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_4(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ subset(skolemFOFtoCNF_D_1(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_C_4(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| in(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A))
| in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_23:[bind(X_90,$fot(skolemFOFtoCNF_D_1(skolemFOFtoCNF_B(skolemFOFtoCNF_A))))]]) ).
cnf(refute_0_25,plain,
( definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| in(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A))
| in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_D_1(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_C_4(skolemFOFtoCNF_B(skolemFOFtoCNF_A))) )],[refute_0_18,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ in(skolemFOFtoCNF_A,skolemFOFtoCNF_B(skolemFOFtoCNF_A))
| definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| in(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) )],[refute_0_25,refute_0_13]) ).
cnf(refute_0_27,plain,
( definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| in(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A,skolemFOFtoCNF_B(skolemFOFtoCNF_A)) )],[refute_0_15,refute_0_26]) ).
cnf(refute_0_28,plain,
( definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| in(skolemFOFtoCNF_D(skolemFOFtoCNF_A,skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A))),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) )],[refute_0_27,refute_0_11]) ).
cnf(refute_0_29,plain,
( ~ subset(D,skolemFOFtoCNF_D(skolemFOFtoCNF_A,skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A))))
| definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| in(D,skolemFOFtoCNF_B(skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D(skolemFOFtoCNF_A,skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A))),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) )],[refute_0_28,refute_0_9]) ).
cnf(refute_0_30,plain,
( ~ subset(powerset(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A))),skolemFOFtoCNF_D(skolemFOFtoCNF_A,skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A))))
| definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| in(powerset(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A))),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_29:[bind(D,$fot(powerset(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))))]]) ).
cnf(refute_0_31,plain,
( ~ in(skolemFOFtoCNF_C_1(A,B),B)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_32,plain,
( ~ in(skolemFOFtoCNF_C_1(powerset(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A))),skolemFOFtoCNF_D(skolemFOFtoCNF_A,skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))),skolemFOFtoCNF_D(skolemFOFtoCNF_A,skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A))))
| subset(powerset(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A))),skolemFOFtoCNF_D(skolemFOFtoCNF_A,skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))) ),
inference(subst,[],[refute_0_31:[bind(A,$fot(powerset(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A))))),bind(B,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_A,skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))))]]) ).
cnf(refute_0_33,plain,
( B != powerset(A)
| ~ in(C,B)
| subset(C,A) ),
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_34,plain,
( powerset(A) != powerset(A)
| ~ in(C,powerset(A))
| subset(C,A) ),
inference(subst,[],[refute_0_33:[bind(B,$fot(powerset(A)))]]) ).
cnf(refute_0_35,plain,
powerset(A) = powerset(A),
introduced(tautology,[refl,[$fot(powerset(A))]]) ).
cnf(refute_0_36,plain,
( ~ in(C,powerset(A))
| subset(C,A) ),
inference(resolve,[$cnf( $equal(powerset(A),powerset(A)) )],[refute_0_35,refute_0_34]) ).
cnf(refute_0_37,plain,
( ~ in(skolemFOFtoCNF_C_1(powerset(A),X_21),powerset(A))
| subset(skolemFOFtoCNF_C_1(powerset(A),X_21),A) ),
inference(subst,[],[refute_0_36:[bind(C,$fot(skolemFOFtoCNF_C_1(powerset(A),X_21)))]]) ).
cnf(refute_0_38,plain,
( in(skolemFOFtoCNF_C_1(A,B),A)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_33]) ).
cnf(refute_0_39,plain,
( in(skolemFOFtoCNF_C_1(powerset(A),X_21),powerset(A))
| subset(powerset(A),X_21) ),
inference(subst,[],[refute_0_38:[bind(A,$fot(powerset(A))),bind(B,$fot(X_21))]]) ).
cnf(refute_0_40,plain,
( subset(powerset(A),X_21)
| subset(skolemFOFtoCNF_C_1(powerset(A),X_21),A) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(powerset(A),X_21),powerset(A)) )],[refute_0_39,refute_0_37]) ).
cnf(refute_0_41,plain,
( subset(powerset(X_145),X_21)
| subset(skolemFOFtoCNF_C_1(powerset(X_145),X_21),X_145) ),
inference(subst,[],[refute_0_40:[bind(A,$fot(X_145))]]) ).
cnf(refute_0_42,plain,
( ~ in(C,skolemFOFtoCNF_B(A))
| ~ subset(E,C)
| in(E,skolemFOFtoCNF_D(A,C)) ),
inference(canonicalize,[],[normalize_0_34]) ).
cnf(refute_0_43,plain,
( ~ in(X_145,skolemFOFtoCNF_B(X_144))
| ~ subset(skolemFOFtoCNF_C_1(powerset(X_145),X_21),X_145)
| in(skolemFOFtoCNF_C_1(powerset(X_145),X_21),skolemFOFtoCNF_D(X_144,X_145)) ),
inference(subst,[],[refute_0_42:[bind(A,$fot(X_144)),bind(C,$fot(X_145)),bind(E,$fot(skolemFOFtoCNF_C_1(powerset(X_145),X_21)))]]) ).
cnf(refute_0_44,plain,
( ~ in(X_145,skolemFOFtoCNF_B(X_144))
| in(skolemFOFtoCNF_C_1(powerset(X_145),X_21),skolemFOFtoCNF_D(X_144,X_145))
| subset(powerset(X_145),X_21) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_C_1(powerset(X_145),X_21),X_145) )],[refute_0_41,refute_0_43]) ).
cnf(refute_0_45,plain,
( ~ in(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A))
| in(skolemFOFtoCNF_C_1(powerset(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A))),X_2702),skolemFOFtoCNF_D(skolemFOFtoCNF_A,skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A))))
| subset(powerset(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A))),X_2702) ),
inference(subst,[],[refute_0_44:[bind(X_144,$fot(skolemFOFtoCNF_A)),bind(X_145,$fot(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))),bind(X_21,$fot(X_2702))]]) ).
cnf(refute_0_46,plain,
( definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| in(skolemFOFtoCNF_C_1(powerset(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A))),X_2702),skolemFOFtoCNF_D(skolemFOFtoCNF_A,skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A))))
| subset(powerset(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A))),X_2702) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) )],[refute_0_27,refute_0_45]) ).
cnf(refute_0_47,plain,
( definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| in(skolemFOFtoCNF_C_1(powerset(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A))),skolemFOFtoCNF_D(skolemFOFtoCNF_A,skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))),skolemFOFtoCNF_D(skolemFOFtoCNF_A,skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A))))
| subset(powerset(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A))),skolemFOFtoCNF_D(skolemFOFtoCNF_A,skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))) ),
inference(subst,[],[refute_0_46:[bind(X_2702,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_A,skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))))]]) ).
cnf(refute_0_48,plain,
( definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| subset(powerset(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A))),skolemFOFtoCNF_D(skolemFOFtoCNF_A,skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(powerset(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A))),skolemFOFtoCNF_D(skolemFOFtoCNF_A,skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))),skolemFOFtoCNF_D(skolemFOFtoCNF_A,skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))) )],[refute_0_47,refute_0_32]) ).
cnf(refute_0_49,plain,
( definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| in(powerset(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A))),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( subset(powerset(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A))),skolemFOFtoCNF_D(skolemFOFtoCNF_A,skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))) )],[refute_0_48,refute_0_30]) ).
cnf(refute_0_50,plain,
( ~ in(skolemFOFtoCNF_A,skolemFOFtoCNF_B(skolemFOFtoCNF_A))
| ~ in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A))
| definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A))) ),
inference(resolve,[$cnf( in(powerset(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A))),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) )],[refute_0_49,refute_0_7]) ).
cnf(refute_0_51,plain,
( ~ in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A))
| definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A))) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A,skolemFOFtoCNF_B(skolemFOFtoCNF_A)) )],[refute_0_15,refute_0_50]) ).
cnf(refute_0_52,plain,
( ~ in(powerset(skolemFOFtoCNF_C_3(B)),B)
| ~ in(skolemFOFtoCNF_A,B)
| definitionFOFtoCNF_0(B,skolemFOFtoCNF_C_2(B))
| subset(skolemFOFtoCNF_D_1(B),skolemFOFtoCNF_C_4(B)) ),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_53,plain,
( ~ in(powerset(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A))),skolemFOFtoCNF_B(skolemFOFtoCNF_A))
| ~ in(skolemFOFtoCNF_A,skolemFOFtoCNF_B(skolemFOFtoCNF_A))
| definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| subset(skolemFOFtoCNF_D_1(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_C_4(skolemFOFtoCNF_B(skolemFOFtoCNF_A))) ),
inference(subst,[],[refute_0_52:[bind(B,$fot(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_54,plain,
( ~ in(skolemFOFtoCNF_A,skolemFOFtoCNF_B(skolemFOFtoCNF_A))
| definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| subset(skolemFOFtoCNF_D_1(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_C_4(skolemFOFtoCNF_B(skolemFOFtoCNF_A))) ),
inference(resolve,[$cnf( in(powerset(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A))),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) )],[refute_0_49,refute_0_53]) ).
cnf(refute_0_55,plain,
( definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| subset(skolemFOFtoCNF_D_1(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_C_4(skolemFOFtoCNF_B(skolemFOFtoCNF_A))) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A,skolemFOFtoCNF_B(skolemFOFtoCNF_A)) )],[refute_0_15,refute_0_54]) ).
cnf(refute_0_56,plain,
( ~ in(skolemFOFtoCNF_C_4(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A))
| ~ subset(D,skolemFOFtoCNF_C_4(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| in(D,skolemFOFtoCNF_B(skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_A)),bind(C,$fot(skolemFOFtoCNF_C_4(skolemFOFtoCNF_B(skolemFOFtoCNF_A))))]]) ).
cnf(refute_0_57,plain,
( ~ in(powerset(skolemFOFtoCNF_C_3(B)),B)
| ~ in(skolemFOFtoCNF_A,B)
| definitionFOFtoCNF_0(B,skolemFOFtoCNF_C_2(B))
| in(skolemFOFtoCNF_C_4(B),B) ),
inference(canonicalize,[],[normalize_0_36]) ).
cnf(refute_0_58,plain,
( ~ in(powerset(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A))),skolemFOFtoCNF_B(skolemFOFtoCNF_A))
| ~ in(skolemFOFtoCNF_A,skolemFOFtoCNF_B(skolemFOFtoCNF_A))
| definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| in(skolemFOFtoCNF_C_4(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_57:[bind(B,$fot(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_59,plain,
( ~ in(skolemFOFtoCNF_A,skolemFOFtoCNF_B(skolemFOFtoCNF_A))
| definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| in(skolemFOFtoCNF_C_4(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( in(powerset(skolemFOFtoCNF_C_3(skolemFOFtoCNF_B(skolemFOFtoCNF_A))),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) )],[refute_0_49,refute_0_58]) ).
cnf(refute_0_60,plain,
( definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| in(skolemFOFtoCNF_C_4(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A,skolemFOFtoCNF_B(skolemFOFtoCNF_A)) )],[refute_0_15,refute_0_59]) ).
cnf(refute_0_61,plain,
( ~ subset(D,skolemFOFtoCNF_C_4(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| in(D,skolemFOFtoCNF_B(skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_4(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) )],[refute_0_60,refute_0_56]) ).
cnf(refute_0_62,plain,
( ~ subset(skolemFOFtoCNF_D_1(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_C_4(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_61:[bind(D,$fot(skolemFOFtoCNF_D_1(skolemFOFtoCNF_B(skolemFOFtoCNF_A))))]]) ).
cnf(refute_0_63,plain,
( definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)))
| in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_D_1(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_C_4(skolemFOFtoCNF_B(skolemFOFtoCNF_A))) )],[refute_0_55,refute_0_62]) ).
cnf(refute_0_64,plain,
definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A))),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) )],[refute_0_63,refute_0_51]) ).
cnf(refute_0_65,plain,
subset(skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A)),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A))) )],[refute_0_64,refute_0_5]) ).
cnf(refute_0_66,plain,
( are_equipotent(skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A))
| in(skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) )],[refute_0_65,refute_0_3]) ).
cnf(refute_0_67,plain,
( ~ are_equipotent(C,B)
| ~ definitionFOFtoCNF_0(B,C) ),
inference(canonicalize,[],[normalize_0_37]) ).
cnf(refute_0_68,plain,
( ~ are_equipotent(skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A))
| ~ definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A))) ),
inference(subst,[],[refute_0_67:[bind(B,$fot(skolemFOFtoCNF_B(skolemFOFtoCNF_A))),bind(C,$fot(skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A))))]]) ).
cnf(refute_0_69,plain,
~ are_equipotent(skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A)),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A))) )],[refute_0_64,refute_0_68]) ).
cnf(refute_0_70,plain,
in(skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A)),
inference(resolve,[$cnf( are_equipotent(skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) )],[refute_0_66,refute_0_69]) ).
cnf(refute_0_71,plain,
~ definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A))),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A)),skolemFOFtoCNF_B(skolemFOFtoCNF_A)) )],[refute_0_70,refute_0_1]) ).
cnf(refute_0_72,plain,
$false,
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_B(skolemFOFtoCNF_A),skolemFOFtoCNF_C_2(skolemFOFtoCNF_B(skolemFOFtoCNF_A))) )],[refute_0_64,refute_0_71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU168+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.14 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 20 05:32:29 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 29.80/30.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.80/30.00
% 29.80/30.00 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 29.80/30.01
%------------------------------------------------------------------------------