TSTP Solution File: SEU280+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU280+1 : TPTP v8.1.0. Released v3.3.0.
% 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 12:39:57 EDT 2022
% Result : Theorem 0.43s 0.59s
% Output : CNFRefutation 0.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 14
% Syntax : Number of formulae : 176 ( 18 unt; 1 def)
% Number of atoms : 497 ( 140 equ)
% Maximal formula atoms : 28 ( 2 avg)
% Number of connectives : 498 ( 177 ~; 271 |; 35 &)
% ( 13 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 246 ( 27 sgn 59 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(s1_xboole_0__e6_22__wellord2,conjecture,
! [A] :
? [B] :
! [C] :
( in(C,B)
<=> ( in(C,A)
& ordinal(C) ) ) ).
fof(s1_tarski__e6_22__wellord2__1,axiom,
! [A] :
( ! [B,C,D] :
( ( B = C
& ordinal(C)
& B = D
& ordinal(D) )
=> C = D )
=> ? [B] :
! [C] :
( in(C,B)
<=> ? [D] :
( in(D,A)
& D = C
& ordinal(C) ) ) ) ).
fof(definition_0,definition,
! [A,B,C] :
( definitionFOFtoCNF_0(A,B,C)
<=> ( ~ in(C,B)
<=> ! [D] :
( D != C
| ~ in(D,A)
| ~ ordinal(C) ) ) ) ).
fof(subgoal_0,plain,
! [A] :
? [B] :
! [C] :
( in(C,B)
<=> ( in(C,A)
& ordinal(C) ) ),
inference(strip,[],[s1_xboole_0__e6_22__wellord2]) ).
fof(negate_0_0,plain,
~ ! [A] :
? [B] :
! [C] :
( in(C,B)
<=> ( in(C,A)
& ordinal(C) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A] :
! [B] :
? [C] :
( ~ in(C,B)
<=> ( in(C,A)
& ordinal(C) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [B] :
? [C] :
( ~ in(C,B)
<=> ( in(C,skolemFOFtoCNF_A_1)
& ordinal(C) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [B] :
? [C] :
( ~ in(C,B)
<=> ( in(C,skolemFOFtoCNF_A_1)
& ordinal(C) ) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [B] :
( ~ in(skolemFOFtoCNF_C_1(B),B)
<=> ( in(skolemFOFtoCNF_C_1(B),skolemFOFtoCNF_A_1)
& ordinal(skolemFOFtoCNF_C_1(B)) ) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [B] :
( ( in(skolemFOFtoCNF_C_1(B),B)
| in(skolemFOFtoCNF_C_1(B),skolemFOFtoCNF_A_1) )
& ( in(skolemFOFtoCNF_C_1(B),B)
| ordinal(skolemFOFtoCNF_C_1(B)) )
& ( ~ in(skolemFOFtoCNF_C_1(B),B)
| ~ in(skolemFOFtoCNF_C_1(B),skolemFOFtoCNF_A_1)
| ~ ordinal(skolemFOFtoCNF_C_1(B)) ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [B] :
( ~ in(skolemFOFtoCNF_C_1(B),B)
| ~ in(skolemFOFtoCNF_C_1(B),skolemFOFtoCNF_A_1)
| ~ ordinal(skolemFOFtoCNF_C_1(B)) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B,C] :
( ~ definitionFOFtoCNF_0(A,B,C)
<=> ( ~ in(C,B)
<=> ? [D] :
( D = C
& in(D,A)
& ordinal(C) ) ) ),
inference(canonicalize,[],[definition_0]) ).
fof(normalize_0_7,plain,
! [A,B,C,D] :
( ( ~ definitionFOFtoCNF_0(A,B,C)
| ~ in(C,B)
| skolemFOFtoCNF_D(A,C) = C )
& ( ~ definitionFOFtoCNF_0(A,B,C)
| ~ in(C,B)
| in(skolemFOFtoCNF_D(A,C),A) )
& ( ~ definitionFOFtoCNF_0(A,B,C)
| ~ in(C,B)
| ordinal(C) )
& ( skolemFOFtoCNF_D(A,C) = C
| definitionFOFtoCNF_0(A,B,C)
| in(C,B) )
& ( definitionFOFtoCNF_0(A,B,C)
| in(C,B)
| in(skolemFOFtoCNF_D(A,C),A) )
& ( definitionFOFtoCNF_0(A,B,C)
| in(C,B)
| ordinal(C) )
& ( D != C
| ~ definitionFOFtoCNF_0(A,B,C)
| ~ in(D,A)
| ~ ordinal(C)
| in(C,B) )
& ( D != C
| ~ in(C,B)
| ~ in(D,A)
| ~ ordinal(C)
| definitionFOFtoCNF_0(A,B,C) ) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B,C,D] :
( D != C
| ~ definitionFOFtoCNF_0(A,B,C)
| ~ in(D,A)
| ~ ordinal(C)
| in(C,B) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
( ? [B,C,D] :
( C != D
& B = C
& B = D
& ordinal(C)
& ordinal(D) )
| ! [A] :
? [B] :
! [C] :
( ~ in(C,B)
<=> ! [D] :
( D != C
| ~ in(D,A)
| ~ ordinal(C) ) ) ),
inference(canonicalize,[],[s1_tarski__e6_22__wellord2__1]) ).
fof(normalize_0_10,plain,
( ? [B,C,D] :
( C != D
& B = C
& B = D
& ordinal(C)
& ordinal(D) )
| ! [A] :
? [B] :
! [C] : definitionFOFtoCNF_0(A,B,C) ),
inference(simplify,[],[normalize_0_9,normalize_0_6]) ).
fof(normalize_0_11,plain,
! [A,C] :
( ( skolemFOFtoCNF_C != skolemFOFtoCNF_D_1
| definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_1(A),C) )
& ( skolemFOFtoCNF_B = skolemFOFtoCNF_C
| definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_1(A),C) )
& ( skolemFOFtoCNF_B = skolemFOFtoCNF_D_1
| definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_1(A),C) )
& ( definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_1(A),C)
| ordinal(skolemFOFtoCNF_C) )
& ( definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_1(A),C)
| ordinal(skolemFOFtoCNF_D_1) ) ),
inference(clausify,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,C] :
( skolemFOFtoCNF_C != skolemFOFtoCNF_D_1
| definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_1(A),C) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [B] :
( in(skolemFOFtoCNF_C_1(B),B)
| ordinal(skolemFOFtoCNF_C_1(B)) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_14,plain,
! [A,C] :
( skolemFOFtoCNF_B = skolemFOFtoCNF_D_1
| definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_1(A),C) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_15,plain,
! [A,B,C] :
( ~ definitionFOFtoCNF_0(A,B,C)
| ~ in(C,B)
| ordinal(C) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_16,plain,
! [B] :
( in(skolemFOFtoCNF_C_1(B),B)
| in(skolemFOFtoCNF_C_1(B),skolemFOFtoCNF_A_1) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_17,plain,
! [A,B,C] :
( ~ definitionFOFtoCNF_0(A,B,C)
| ~ in(C,B)
| in(skolemFOFtoCNF_D(A,C),A) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_18,plain,
! [A,B,C] :
( ~ definitionFOFtoCNF_0(A,B,C)
| ~ in(C,B)
| skolemFOFtoCNF_D(A,C) = C ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_19,plain,
! [A,C] :
( skolemFOFtoCNF_B = skolemFOFtoCNF_C
| definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_1(A),C) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_20,plain,
! [A,B,C] :
( skolemFOFtoCNF_D(A,C) = C
| definitionFOFtoCNF_0(A,B,C)
| in(C,B) ),
inference(conjunct,[],[normalize_0_7]) ).
cnf(refute_0_0,plain,
( ~ in(skolemFOFtoCNF_C_1(B),B)
| ~ in(skolemFOFtoCNF_C_1(B),skolemFOFtoCNF_A_1)
| ~ ordinal(skolemFOFtoCNF_C_1(B)) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_1,plain,
( ~ in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))),skolemFOFtoCNF_A_1)
| ~ in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))),skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)))
| ~ ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)))) ),
inference(subst,[],[refute_0_0:[bind(B,$fot(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))))]]) ).
cnf(refute_0_2,plain,
( D != C
| ~ definitionFOFtoCNF_0(A,B,C)
| ~ in(D,A)
| ~ ordinal(C)
| in(C,B) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_3,plain,
( C != C
| ~ definitionFOFtoCNF_0(A,B,C)
| ~ in(C,A)
| ~ ordinal(C)
| in(C,B) ),
inference(subst,[],[refute_0_2:[bind(D,$fot(C))]]) ).
cnf(refute_0_4,plain,
C = C,
introduced(tautology,[refl,[$fot(C)]]) ).
cnf(refute_0_5,plain,
( ~ definitionFOFtoCNF_0(A,B,C)
| ~ in(C,A)
| ~ ordinal(C)
| in(C,B) ),
inference(resolve,[$cnf( $equal(C,C) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ definitionFOFtoCNF_0(X_138,skolemFOFtoCNF_B_1(X_138),X_139)
| ~ in(X_139,X_138)
| ~ ordinal(X_139)
| in(X_139,skolemFOFtoCNF_B_1(X_138)) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(X_138)),bind(B,$fot(skolemFOFtoCNF_B_1(X_138))),bind(C,$fot(X_139))]]) ).
cnf(refute_0_7,plain,
( skolemFOFtoCNF_C != skolemFOFtoCNF_D_1
| definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_1(A),C) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_8,plain,
( in(skolemFOFtoCNF_C_1(B),B)
| ordinal(skolemFOFtoCNF_C_1(B)) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_9,plain,
( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_34)),skolemFOFtoCNF_B_1(X_34))
| ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_34))) ),
inference(subst,[],[refute_0_8:[bind(B,$fot(skolemFOFtoCNF_B_1(X_34)))]]) ).
cnf(refute_0_10,plain,
( skolemFOFtoCNF_B = skolemFOFtoCNF_D_1
| definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_1(A),C) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_11,plain,
( skolemFOFtoCNF_B = skolemFOFtoCNF_D_1
| definitionFOFtoCNF_0(X_26,skolemFOFtoCNF_B_1(X_26),X_28) ),
inference(subst,[],[refute_0_10:[bind(A,$fot(X_26)),bind(C,$fot(X_28))]]) ).
cnf(refute_0_12,plain,
( ~ definitionFOFtoCNF_0(A,B,C)
| ~ in(C,B)
| ordinal(C) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_13,plain,
( ~ definitionFOFtoCNF_0(X_26,skolemFOFtoCNF_B_1(X_26),X_28)
| ~ in(X_28,skolemFOFtoCNF_B_1(X_26))
| ordinal(X_28) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(X_26)),bind(B,$fot(skolemFOFtoCNF_B_1(X_26))),bind(C,$fot(X_28))]]) ).
cnf(refute_0_14,plain,
( ~ in(X_28,skolemFOFtoCNF_B_1(X_26))
| skolemFOFtoCNF_B = skolemFOFtoCNF_D_1
| ordinal(X_28) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(X_26,skolemFOFtoCNF_B_1(X_26),X_28) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_34)),skolemFOFtoCNF_B_1(X_34))
| skolemFOFtoCNF_B = skolemFOFtoCNF_D_1
| ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_34))) ),
inference(subst,[],[refute_0_14:[bind(X_26,$fot(X_34)),bind(X_28,$fot(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_34))))]]) ).
cnf(refute_0_16,plain,
( skolemFOFtoCNF_B = skolemFOFtoCNF_D_1
| ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_34))) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_34)),skolemFOFtoCNF_B_1(X_34)) )],[refute_0_9,refute_0_15]) ).
cnf(refute_0_17,plain,
( skolemFOFtoCNF_B = skolemFOFtoCNF_D_1
| ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))) ),
inference(subst,[],[refute_0_16:[bind(X_34,$fot(skolemFOFtoCNF_A_1))]]) ).
cnf(refute_0_18,plain,
( in(skolemFOFtoCNF_C_1(B),B)
| in(skolemFOFtoCNF_C_1(B),skolemFOFtoCNF_A_1) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_19,plain,
( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_89)),skolemFOFtoCNF_A_1)
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_89)),skolemFOFtoCNF_B_1(X_89)) ),
inference(subst,[],[refute_0_18:[bind(B,$fot(skolemFOFtoCNF_B_1(X_89)))]]) ).
cnf(refute_0_20,plain,
( skolemFOFtoCNF_B = skolemFOFtoCNF_D_1
| definitionFOFtoCNF_0(X_63,skolemFOFtoCNF_B_1(X_63),X_65) ),
inference(subst,[],[refute_0_10:[bind(A,$fot(X_63)),bind(C,$fot(X_65))]]) ).
cnf(refute_0_21,plain,
( ~ definitionFOFtoCNF_0(A,B,C)
| ~ in(C,B)
| in(skolemFOFtoCNF_D(A,C),A) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_22,plain,
( ~ definitionFOFtoCNF_0(X_63,skolemFOFtoCNF_B_1(X_63),X_65)
| ~ in(X_65,skolemFOFtoCNF_B_1(X_63))
| in(skolemFOFtoCNF_D(X_63,X_65),X_63) ),
inference(subst,[],[refute_0_21:[bind(A,$fot(X_63)),bind(B,$fot(skolemFOFtoCNF_B_1(X_63))),bind(C,$fot(X_65))]]) ).
cnf(refute_0_23,plain,
( ~ in(X_65,skolemFOFtoCNF_B_1(X_63))
| skolemFOFtoCNF_B = skolemFOFtoCNF_D_1
| in(skolemFOFtoCNF_D(X_63,X_65),X_63) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(X_63,skolemFOFtoCNF_B_1(X_63),X_65) )],[refute_0_20,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_89)),skolemFOFtoCNF_B_1(X_89))
| skolemFOFtoCNF_B = skolemFOFtoCNF_D_1
| in(skolemFOFtoCNF_D(X_89,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_89))),X_89) ),
inference(subst,[],[refute_0_23:[bind(X_63,$fot(X_89)),bind(X_65,$fot(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_89))))]]) ).
cnf(refute_0_25,plain,
( skolemFOFtoCNF_B = skolemFOFtoCNF_D_1
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_89)),skolemFOFtoCNF_A_1)
| in(skolemFOFtoCNF_D(X_89,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_89))),X_89) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_89)),skolemFOFtoCNF_B_1(X_89)) )],[refute_0_19,refute_0_24]) ).
cnf(refute_0_26,plain,
( skolemFOFtoCNF_B = skolemFOFtoCNF_D_1
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_91)),skolemFOFtoCNF_A_1)
| in(skolemFOFtoCNF_D(X_91,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_91))),X_91) ),
inference(subst,[],[refute_0_25:[bind(X_89,$fot(X_91))]]) ).
cnf(refute_0_27,plain,
( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_82)),skolemFOFtoCNF_A_1)
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_82)),skolemFOFtoCNF_B_1(X_82)) ),
inference(subst,[],[refute_0_18:[bind(B,$fot(skolemFOFtoCNF_B_1(X_82)))]]) ).
cnf(refute_0_28,plain,
( skolemFOFtoCNF_B = skolemFOFtoCNF_D_1
| definitionFOFtoCNF_0(X_57,skolemFOFtoCNF_B_1(X_57),X_59) ),
inference(subst,[],[refute_0_10:[bind(A,$fot(X_57)),bind(C,$fot(X_59))]]) ).
cnf(refute_0_29,plain,
( ~ definitionFOFtoCNF_0(A,B,C)
| ~ in(C,B)
| skolemFOFtoCNF_D(A,C) = C ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_30,plain,
( ~ definitionFOFtoCNF_0(X_57,skolemFOFtoCNF_B_1(X_57),X_59)
| ~ in(X_59,skolemFOFtoCNF_B_1(X_57))
| skolemFOFtoCNF_D(X_57,X_59) = X_59 ),
inference(subst,[],[refute_0_29:[bind(A,$fot(X_57)),bind(B,$fot(skolemFOFtoCNF_B_1(X_57))),bind(C,$fot(X_59))]]) ).
cnf(refute_0_31,plain,
( ~ in(X_59,skolemFOFtoCNF_B_1(X_57))
| skolemFOFtoCNF_B = skolemFOFtoCNF_D_1
| skolemFOFtoCNF_D(X_57,X_59) = X_59 ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(X_57,skolemFOFtoCNF_B_1(X_57),X_59) )],[refute_0_28,refute_0_30]) ).
cnf(refute_0_32,plain,
( ~ in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_82)),skolemFOFtoCNF_B_1(X_82))
| skolemFOFtoCNF_B = skolemFOFtoCNF_D_1
| skolemFOFtoCNF_D(X_82,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_82))) = skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_82)) ),
inference(subst,[],[refute_0_31:[bind(X_57,$fot(X_82)),bind(X_59,$fot(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_82))))]]) ).
cnf(refute_0_33,plain,
( skolemFOFtoCNF_B = skolemFOFtoCNF_D_1
| skolemFOFtoCNF_D(X_82,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_82))) = skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_82))
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_82)),skolemFOFtoCNF_A_1) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_82)),skolemFOFtoCNF_B_1(X_82)) )],[refute_0_27,refute_0_32]) ).
cnf(refute_0_34,plain,
( skolemFOFtoCNF_B = skolemFOFtoCNF_D_1
| skolemFOFtoCNF_D(X_91,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_91))) = skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_91))
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_91)),skolemFOFtoCNF_A_1) ),
inference(subst,[],[refute_0_33:[bind(X_82,$fot(X_91))]]) ).
cnf(refute_0_35,plain,
( skolemFOFtoCNF_D(X_91,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_91))) != skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_91))
| ~ in(skolemFOFtoCNF_D(X_91,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_91))),X_91)
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_91)),X_91) ),
introduced(tautology,[equality,[$cnf( in(skolemFOFtoCNF_D(X_91,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_91))),X_91) ),[0],$fot(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_91)))]]) ).
cnf(refute_0_36,plain,
( ~ in(skolemFOFtoCNF_D(X_91,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_91))),X_91)
| skolemFOFtoCNF_B = skolemFOFtoCNF_D_1
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_91)),X_91)
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_91)),skolemFOFtoCNF_A_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_D(X_91,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_91))),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_91))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( skolemFOFtoCNF_B = skolemFOFtoCNF_D_1
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_91)),X_91)
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_91)),skolemFOFtoCNF_A_1) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D(X_91,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_91))),X_91) )],[refute_0_26,refute_0_36]) ).
cnf(refute_0_38,plain,
( skolemFOFtoCNF_B = skolemFOFtoCNF_D_1
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)),skolemFOFtoCNF_A_1) ),
inference(subst,[],[refute_0_37:[bind(X_91,$fot(skolemFOFtoCNF_A_1))]]) ).
cnf(refute_0_39,plain,
( ~ in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)),skolemFOFtoCNF_A_1)
| ~ in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)),skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))
| ~ ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))) ),
inference(subst,[],[refute_0_0:[bind(B,$fot(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)))]]) ).
cnf(refute_0_40,plain,
( skolemFOFtoCNF_B = skolemFOFtoCNF_D_1
| definitionFOFtoCNF_0(X_95,skolemFOFtoCNF_B_1(X_95),X_97) ),
inference(subst,[],[refute_0_10:[bind(A,$fot(X_95)),bind(C,$fot(X_97))]]) ).
cnf(refute_0_41,plain,
( ~ definitionFOFtoCNF_0(X_95,skolemFOFtoCNF_B_1(X_95),X_97)
| ~ in(X_97,X_95)
| ~ ordinal(X_97)
| in(X_97,skolemFOFtoCNF_B_1(X_95)) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(X_95)),bind(B,$fot(skolemFOFtoCNF_B_1(X_95))),bind(C,$fot(X_97))]]) ).
cnf(refute_0_42,plain,
( ~ in(X_97,X_95)
| ~ ordinal(X_97)
| skolemFOFtoCNF_B = skolemFOFtoCNF_D_1
| in(X_97,skolemFOFtoCNF_B_1(X_95)) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(X_95,skolemFOFtoCNF_B_1(X_95),X_97) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
( ~ in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)),skolemFOFtoCNF_A_1)
| ~ ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)))
| skolemFOFtoCNF_B = skolemFOFtoCNF_D_1
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)),skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)) ),
inference(subst,[],[refute_0_42:[bind(X_95,$fot(skolemFOFtoCNF_A_1)),bind(X_97,$fot(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))))]]) ).
cnf(refute_0_44,plain,
( ~ ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)))
| skolemFOFtoCNF_B = skolemFOFtoCNF_D_1
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)),skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)),skolemFOFtoCNF_A_1) )],[refute_0_38,refute_0_43]) ).
cnf(refute_0_45,plain,
( skolemFOFtoCNF_B = skolemFOFtoCNF_D_1
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)),skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)) ),
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))) )],[refute_0_17,refute_0_44]) ).
cnf(refute_0_46,plain,
( ~ in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)),skolemFOFtoCNF_A_1)
| ~ ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)))
| skolemFOFtoCNF_B = skolemFOFtoCNF_D_1 ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)),skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)) )],[refute_0_45,refute_0_39]) ).
cnf(refute_0_47,plain,
( ~ ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)))
| skolemFOFtoCNF_B = skolemFOFtoCNF_D_1 ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)),skolemFOFtoCNF_A_1) )],[refute_0_38,refute_0_46]) ).
cnf(refute_0_48,plain,
skolemFOFtoCNF_B = skolemFOFtoCNF_D_1,
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))) )],[refute_0_17,refute_0_47]) ).
cnf(refute_0_49,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_50,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_51,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
( skolemFOFtoCNF_B != skolemFOFtoCNF_D_1
| skolemFOFtoCNF_D_1 = skolemFOFtoCNF_B ),
inference(subst,[],[refute_0_51:[bind(X,$fot(skolemFOFtoCNF_B)),bind(Y,$fot(skolemFOFtoCNF_D_1))]]) ).
cnf(refute_0_53,plain,
skolemFOFtoCNF_D_1 = skolemFOFtoCNF_B,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,skolemFOFtoCNF_D_1) )],[refute_0_48,refute_0_52]) ).
cnf(refute_0_54,plain,
( skolemFOFtoCNF_C != skolemFOFtoCNF_B
| skolemFOFtoCNF_D_1 != skolemFOFtoCNF_B
| skolemFOFtoCNF_C = skolemFOFtoCNF_D_1 ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1) ),[1],$fot(skolemFOFtoCNF_B)]]) ).
cnf(refute_0_55,plain,
( skolemFOFtoCNF_C != skolemFOFtoCNF_B
| skolemFOFtoCNF_C = skolemFOFtoCNF_D_1 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_D_1,skolemFOFtoCNF_B) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
( skolemFOFtoCNF_C != skolemFOFtoCNF_B
| definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_1(A),C) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1) )],[refute_0_55,refute_0_7]) ).
cnf(refute_0_57,plain,
( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_47)),skolemFOFtoCNF_B_1(X_47))
| ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_47))) ),
inference(subst,[],[refute_0_8:[bind(B,$fot(skolemFOFtoCNF_B_1(X_47)))]]) ).
cnf(refute_0_58,plain,
( skolemFOFtoCNF_B = skolemFOFtoCNF_C
| definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_1(A),C) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_59,plain,
( skolemFOFtoCNF_B = skolemFOFtoCNF_C
| definitionFOFtoCNF_0(X_26,skolemFOFtoCNF_B_1(X_26),X_28) ),
inference(subst,[],[refute_0_58:[bind(A,$fot(X_26)),bind(C,$fot(X_28))]]) ).
cnf(refute_0_60,plain,
( ~ in(X_28,skolemFOFtoCNF_B_1(X_26))
| skolemFOFtoCNF_B = skolemFOFtoCNF_C
| ordinal(X_28) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(X_26,skolemFOFtoCNF_B_1(X_26),X_28) )],[refute_0_59,refute_0_13]) ).
cnf(refute_0_61,plain,
( ~ in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_47)),skolemFOFtoCNF_B_1(X_47))
| skolemFOFtoCNF_B = skolemFOFtoCNF_C
| ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_47))) ),
inference(subst,[],[refute_0_60:[bind(X_26,$fot(X_47)),bind(X_28,$fot(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_47))))]]) ).
cnf(refute_0_62,plain,
( skolemFOFtoCNF_B = skolemFOFtoCNF_C
| ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_47))) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_47)),skolemFOFtoCNF_B_1(X_47)) )],[refute_0_57,refute_0_61]) ).
cnf(refute_0_63,plain,
( skolemFOFtoCNF_B = skolemFOFtoCNF_C
| ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))) ),
inference(subst,[],[refute_0_62:[bind(X_47,$fot(skolemFOFtoCNF_A_1))]]) ).
cnf(refute_0_64,plain,
( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_93)),skolemFOFtoCNF_A_1)
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_93)),skolemFOFtoCNF_B_1(X_93)) ),
inference(subst,[],[refute_0_18:[bind(B,$fot(skolemFOFtoCNF_B_1(X_93)))]]) ).
cnf(refute_0_65,plain,
( skolemFOFtoCNF_B = skolemFOFtoCNF_C
| definitionFOFtoCNF_0(X_63,skolemFOFtoCNF_B_1(X_63),X_65) ),
inference(subst,[],[refute_0_58:[bind(A,$fot(X_63)),bind(C,$fot(X_65))]]) ).
cnf(refute_0_66,plain,
( ~ in(X_65,skolemFOFtoCNF_B_1(X_63))
| skolemFOFtoCNF_B = skolemFOFtoCNF_C
| in(skolemFOFtoCNF_D(X_63,X_65),X_63) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(X_63,skolemFOFtoCNF_B_1(X_63),X_65) )],[refute_0_65,refute_0_22]) ).
cnf(refute_0_67,plain,
( ~ in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_93)),skolemFOFtoCNF_B_1(X_93))
| skolemFOFtoCNF_B = skolemFOFtoCNF_C
| in(skolemFOFtoCNF_D(X_93,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_93))),X_93) ),
inference(subst,[],[refute_0_66:[bind(X_63,$fot(X_93)),bind(X_65,$fot(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_93))))]]) ).
cnf(refute_0_68,plain,
( skolemFOFtoCNF_B = skolemFOFtoCNF_C
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_93)),skolemFOFtoCNF_A_1)
| in(skolemFOFtoCNF_D(X_93,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_93))),X_93) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_93)),skolemFOFtoCNF_B_1(X_93)) )],[refute_0_64,refute_0_67]) ).
cnf(refute_0_69,plain,
( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_87)),skolemFOFtoCNF_A_1)
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_87)),skolemFOFtoCNF_B_1(X_87)) ),
inference(subst,[],[refute_0_18:[bind(B,$fot(skolemFOFtoCNF_B_1(X_87)))]]) ).
cnf(refute_0_70,plain,
( skolemFOFtoCNF_B = skolemFOFtoCNF_C
| definitionFOFtoCNF_0(X_57,skolemFOFtoCNF_B_1(X_57),X_59) ),
inference(subst,[],[refute_0_58:[bind(A,$fot(X_57)),bind(C,$fot(X_59))]]) ).
cnf(refute_0_71,plain,
( ~ in(X_59,skolemFOFtoCNF_B_1(X_57))
| skolemFOFtoCNF_B = skolemFOFtoCNF_C
| skolemFOFtoCNF_D(X_57,X_59) = X_59 ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(X_57,skolemFOFtoCNF_B_1(X_57),X_59) )],[refute_0_70,refute_0_30]) ).
cnf(refute_0_72,plain,
( ~ in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_87)),skolemFOFtoCNF_B_1(X_87))
| skolemFOFtoCNF_B = skolemFOFtoCNF_C
| skolemFOFtoCNF_D(X_87,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_87))) = skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_87)) ),
inference(subst,[],[refute_0_71:[bind(X_57,$fot(X_87)),bind(X_59,$fot(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_87))))]]) ).
cnf(refute_0_73,plain,
( skolemFOFtoCNF_B = skolemFOFtoCNF_C
| skolemFOFtoCNF_D(X_87,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_87))) = skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_87))
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_87)),skolemFOFtoCNF_A_1) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_87)),skolemFOFtoCNF_B_1(X_87)) )],[refute_0_69,refute_0_72]) ).
cnf(refute_0_74,plain,
( skolemFOFtoCNF_B = skolemFOFtoCNF_C
| skolemFOFtoCNF_D(X_93,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_93))) = skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_93))
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_93)),skolemFOFtoCNF_A_1) ),
inference(subst,[],[refute_0_73:[bind(X_87,$fot(X_93))]]) ).
cnf(refute_0_75,plain,
( skolemFOFtoCNF_D(X_93,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_93))) != skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_93))
| ~ in(skolemFOFtoCNF_D(X_93,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_93))),X_93)
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_93)),X_93) ),
introduced(tautology,[equality,[$cnf( in(skolemFOFtoCNF_D(X_93,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_93))),X_93) ),[0],$fot(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_93)))]]) ).
cnf(refute_0_76,plain,
( ~ in(skolemFOFtoCNF_D(X_93,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_93))),X_93)
| skolemFOFtoCNF_B = skolemFOFtoCNF_C
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_93)),X_93)
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_93)),skolemFOFtoCNF_A_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_D(X_93,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_93))),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_93))) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
( skolemFOFtoCNF_B = skolemFOFtoCNF_C
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_93)),X_93)
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_93)),skolemFOFtoCNF_A_1) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D(X_93,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_93))),X_93) )],[refute_0_68,refute_0_76]) ).
cnf(refute_0_78,plain,
( skolemFOFtoCNF_B = skolemFOFtoCNF_C
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)),skolemFOFtoCNF_A_1) ),
inference(subst,[],[refute_0_77:[bind(X_93,$fot(skolemFOFtoCNF_A_1))]]) ).
cnf(refute_0_79,plain,
( skolemFOFtoCNF_B = skolemFOFtoCNF_C
| definitionFOFtoCNF_0(X_95,skolemFOFtoCNF_B_1(X_95),X_97) ),
inference(subst,[],[refute_0_58:[bind(A,$fot(X_95)),bind(C,$fot(X_97))]]) ).
cnf(refute_0_80,plain,
( ~ in(X_97,X_95)
| ~ ordinal(X_97)
| skolemFOFtoCNF_B = skolemFOFtoCNF_C
| in(X_97,skolemFOFtoCNF_B_1(X_95)) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(X_95,skolemFOFtoCNF_B_1(X_95),X_97) )],[refute_0_79,refute_0_41]) ).
cnf(refute_0_81,plain,
( ~ in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)),skolemFOFtoCNF_A_1)
| ~ ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)))
| skolemFOFtoCNF_B = skolemFOFtoCNF_C
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)),skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)) ),
inference(subst,[],[refute_0_80:[bind(X_95,$fot(skolemFOFtoCNF_A_1)),bind(X_97,$fot(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))))]]) ).
cnf(refute_0_82,plain,
( ~ ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)))
| skolemFOFtoCNF_B = skolemFOFtoCNF_C
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)),skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)),skolemFOFtoCNF_A_1) )],[refute_0_78,refute_0_81]) ).
cnf(refute_0_83,plain,
( skolemFOFtoCNF_B = skolemFOFtoCNF_C
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)),skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)) ),
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))) )],[refute_0_63,refute_0_82]) ).
cnf(refute_0_84,plain,
( ~ in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)),skolemFOFtoCNF_A_1)
| ~ ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)))
| skolemFOFtoCNF_B = skolemFOFtoCNF_C ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)),skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)) )],[refute_0_83,refute_0_39]) ).
cnf(refute_0_85,plain,
( ~ ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)))
| skolemFOFtoCNF_B = skolemFOFtoCNF_C ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)),skolemFOFtoCNF_A_1) )],[refute_0_78,refute_0_84]) ).
cnf(refute_0_86,plain,
skolemFOFtoCNF_B = skolemFOFtoCNF_C,
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))) )],[refute_0_63,refute_0_85]) ).
cnf(refute_0_87,plain,
( skolemFOFtoCNF_B != skolemFOFtoCNF_C
| skolemFOFtoCNF_C = skolemFOFtoCNF_B ),
inference(subst,[],[refute_0_51:[bind(X,$fot(skolemFOFtoCNF_B)),bind(Y,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_88,plain,
skolemFOFtoCNF_C = skolemFOFtoCNF_B,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
( skolemFOFtoCNF_B != skolemFOFtoCNF_B
| skolemFOFtoCNF_C != skolemFOFtoCNF_B
| skolemFOFtoCNF_C = skolemFOFtoCNF_B ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_C,skolemFOFtoCNF_B) ),[1],$fot(skolemFOFtoCNF_B)]]) ).
cnf(refute_0_90,plain,
( skolemFOFtoCNF_B != skolemFOFtoCNF_B
| skolemFOFtoCNF_C = skolemFOFtoCNF_B ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C,skolemFOFtoCNF_B) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
( skolemFOFtoCNF_B != skolemFOFtoCNF_B
| definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_1(A),C) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C,skolemFOFtoCNF_B) )],[refute_0_90,refute_0_56]) ).
cnf(refute_0_92,plain,
skolemFOFtoCNF_B = skolemFOFtoCNF_B,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_B)]]) ).
cnf(refute_0_93,plain,
definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_1(A),C),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,skolemFOFtoCNF_B) )],[refute_0_92,refute_0_91]) ).
cnf(refute_0_94,plain,
definitionFOFtoCNF_0(X_138,skolemFOFtoCNF_B_1(X_138),X_139),
inference(subst,[],[refute_0_93:[bind(A,$fot(X_138)),bind(C,$fot(X_139))]]) ).
cnf(refute_0_95,plain,
( ~ in(X_139,X_138)
| ~ ordinal(X_139)
| in(X_139,skolemFOFtoCNF_B_1(X_138)) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(X_138,skolemFOFtoCNF_B_1(X_138),X_139) )],[refute_0_94,refute_0_6]) ).
cnf(refute_0_96,plain,
( ~ in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))),skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))
| ~ ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))))
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))),skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))) ),
inference(subst,[],[refute_0_95:[bind(X_138,$fot(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))),bind(X_139,$fot(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)))))]]) ).
cnf(refute_0_97,plain,
( ~ definitionFOFtoCNF_0(X_138,skolemFOFtoCNF_B_1(X_138),X_139)
| ~ in(X_139,skolemFOFtoCNF_B_1(X_138))
| in(skolemFOFtoCNF_D(X_138,X_139),X_138) ),
inference(subst,[],[refute_0_21:[bind(A,$fot(X_138)),bind(B,$fot(skolemFOFtoCNF_B_1(X_138))),bind(C,$fot(X_139))]]) ).
cnf(refute_0_98,plain,
( ~ in(X_139,skolemFOFtoCNF_B_1(X_138))
| in(skolemFOFtoCNF_D(X_138,X_139),X_138) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(X_138,skolemFOFtoCNF_B_1(X_138),X_139) )],[refute_0_94,refute_0_97]) ).
cnf(refute_0_99,plain,
( ~ in(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1(X_138),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_138)))),skolemFOFtoCNF_B_1(X_138))
| in(skolemFOFtoCNF_D(X_138,skolemFOFtoCNF_D(skolemFOFtoCNF_B_1(X_138),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_138))))),X_138) ),
inference(subst,[],[refute_0_98:[bind(X_139,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1(X_138),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_138))))))]]) ).
cnf(refute_0_100,plain,
( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_150)),skolemFOFtoCNF_A_1)
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_150)),skolemFOFtoCNF_B_1(X_150)) ),
inference(subst,[],[refute_0_18:[bind(B,$fot(skolemFOFtoCNF_B_1(X_150)))]]) ).
cnf(refute_0_101,plain,
( ~ in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_150)),skolemFOFtoCNF_B_1(X_150))
| in(skolemFOFtoCNF_D(X_150,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_150))),X_150) ),
inference(subst,[],[refute_0_98:[bind(X_138,$fot(X_150)),bind(X_139,$fot(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_150))))]]) ).
cnf(refute_0_102,plain,
( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_150)),skolemFOFtoCNF_A_1)
| in(skolemFOFtoCNF_D(X_150,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_150))),X_150) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_150)),skolemFOFtoCNF_B_1(X_150)) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_138))),skolemFOFtoCNF_A_1)
| in(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1(X_138),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_138)))),skolemFOFtoCNF_B_1(X_138)) ),
inference(subst,[],[refute_0_102:[bind(X_150,$fot(skolemFOFtoCNF_B_1(X_138)))]]) ).
cnf(refute_0_104,plain,
( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_138))),skolemFOFtoCNF_A_1)
| in(skolemFOFtoCNF_D(X_138,skolemFOFtoCNF_D(skolemFOFtoCNF_B_1(X_138),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_138))))),X_138) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1(X_138),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_138)))),skolemFOFtoCNF_B_1(X_138)) )],[refute_0_103,refute_0_99]) ).
cnf(refute_0_105,plain,
( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_204))),skolemFOFtoCNF_A_1)
| in(skolemFOFtoCNF_D(X_204,skolemFOFtoCNF_D(skolemFOFtoCNF_B_1(X_204),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_204))))),X_204) ),
inference(subst,[],[refute_0_104:[bind(X_138,$fot(X_204))]]) ).
cnf(refute_0_106,plain,
( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_145)),skolemFOFtoCNF_A_1)
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_145)),skolemFOFtoCNF_B_1(X_145)) ),
inference(subst,[],[refute_0_18:[bind(B,$fot(skolemFOFtoCNF_B_1(X_145)))]]) ).
cnf(refute_0_107,plain,
( ~ definitionFOFtoCNF_0(X_138,skolemFOFtoCNF_B_1(X_138),X_139)
| ~ in(X_139,skolemFOFtoCNF_B_1(X_138))
| skolemFOFtoCNF_D(X_138,X_139) = X_139 ),
inference(subst,[],[refute_0_29:[bind(A,$fot(X_138)),bind(B,$fot(skolemFOFtoCNF_B_1(X_138))),bind(C,$fot(X_139))]]) ).
cnf(refute_0_108,plain,
( ~ in(X_139,skolemFOFtoCNF_B_1(X_138))
| skolemFOFtoCNF_D(X_138,X_139) = X_139 ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(X_138,skolemFOFtoCNF_B_1(X_138),X_139) )],[refute_0_94,refute_0_107]) ).
cnf(refute_0_109,plain,
( ~ in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_145)),skolemFOFtoCNF_B_1(X_145))
| skolemFOFtoCNF_D(X_145,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_145))) = skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_145)) ),
inference(subst,[],[refute_0_108:[bind(X_138,$fot(X_145)),bind(X_139,$fot(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_145))))]]) ).
cnf(refute_0_110,plain,
( skolemFOFtoCNF_D(X_145,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_145))) = skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_145))
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_145)),skolemFOFtoCNF_A_1) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_145)),skolemFOFtoCNF_B_1(X_145)) )],[refute_0_106,refute_0_109]) ).
cnf(refute_0_111,plain,
( skolemFOFtoCNF_D(skolemFOFtoCNF_B_1(X_204),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_204)))) = skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_204)))
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_204))),skolemFOFtoCNF_A_1) ),
inference(subst,[],[refute_0_110:[bind(X_145,$fot(skolemFOFtoCNF_B_1(X_204)))]]) ).
cnf(refute_0_112,plain,
( skolemFOFtoCNF_D(skolemFOFtoCNF_B_1(X_204),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_204)))) != skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_204)))
| ~ in(skolemFOFtoCNF_D(X_204,skolemFOFtoCNF_D(skolemFOFtoCNF_B_1(X_204),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_204))))),X_204)
| in(skolemFOFtoCNF_D(X_204,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_204)))),X_204) ),
introduced(tautology,[equality,[$cnf( in(skolemFOFtoCNF_D(X_204,skolemFOFtoCNF_D(skolemFOFtoCNF_B_1(X_204),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_204))))),X_204) ),[0,1],$fot(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_204))))]]) ).
cnf(refute_0_113,plain,
( ~ in(skolemFOFtoCNF_D(X_204,skolemFOFtoCNF_D(skolemFOFtoCNF_B_1(X_204),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_204))))),X_204)
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_204))),skolemFOFtoCNF_A_1)
| in(skolemFOFtoCNF_D(X_204,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_204)))),X_204) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1(X_204),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_204)))),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_204)))) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_204))),skolemFOFtoCNF_A_1)
| in(skolemFOFtoCNF_D(X_204,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_204)))),X_204) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D(X_204,skolemFOFtoCNF_D(skolemFOFtoCNF_B_1(X_204),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_204))))),X_204) )],[refute_0_105,refute_0_113]) ).
cnf(refute_0_115,plain,
( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))),skolemFOFtoCNF_A_1)
| in(skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)))),skolemFOFtoCNF_A_1) ),
inference(subst,[],[refute_0_114:[bind(X_204,$fot(skolemFOFtoCNF_A_1))]]) ).
cnf(refute_0_116,plain,
( ~ in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_138))),skolemFOFtoCNF_B_1(X_138))
| skolemFOFtoCNF_D(X_138,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_138)))) = skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_138))) ),
inference(subst,[],[refute_0_108:[bind(X_139,$fot(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_138)))))]]) ).
cnf(refute_0_117,plain,
( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152)),skolemFOFtoCNF_A_1)
| in(skolemFOFtoCNF_D(X_152,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152))),X_152) ),
inference(subst,[],[refute_0_102:[bind(X_150,$fot(X_152))]]) ).
cnf(refute_0_118,plain,
( skolemFOFtoCNF_D(X_152,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152))) = skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152))
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152)),skolemFOFtoCNF_A_1) ),
inference(subst,[],[refute_0_110:[bind(X_145,$fot(X_152))]]) ).
cnf(refute_0_119,plain,
( skolemFOFtoCNF_D(X_152,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152))) != skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152))
| ~ in(skolemFOFtoCNF_D(X_152,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152))),X_152)
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152)),X_152) ),
introduced(tautology,[equality,[$cnf( in(skolemFOFtoCNF_D(X_152,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152))),X_152) ),[0],$fot(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152)))]]) ).
cnf(refute_0_120,plain,
( ~ in(skolemFOFtoCNF_D(X_152,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152))),X_152)
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152)),X_152)
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152)),skolemFOFtoCNF_A_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_D(X_152,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152))),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152))) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152)),X_152)
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152)),skolemFOFtoCNF_A_1) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D(X_152,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152))),X_152) )],[refute_0_117,refute_0_120]) ).
cnf(refute_0_122,plain,
( skolemFOFtoCNF_D(A,C) = C
| definitionFOFtoCNF_0(A,B,C)
| in(C,B) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_123,plain,
( skolemFOFtoCNF_D(X_95,X_97) = X_97
| definitionFOFtoCNF_0(X_95,X_96,X_97)
| in(X_97,X_96) ),
inference(subst,[],[refute_0_122:[bind(A,$fot(X_95)),bind(B,$fot(X_96)),bind(C,$fot(X_97))]]) ).
cnf(refute_0_124,plain,
( ~ definitionFOFtoCNF_0(X_95,X_96,X_97)
| ~ in(X_97,X_95)
| ~ ordinal(X_97)
| in(X_97,X_96) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(X_95)),bind(B,$fot(X_96)),bind(C,$fot(X_97))]]) ).
cnf(refute_0_125,plain,
( ~ in(X_97,X_95)
| ~ ordinal(X_97)
| skolemFOFtoCNF_D(X_95,X_97) = X_97
| in(X_97,X_96) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(X_95,X_96,X_97) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
( ~ in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152)),skolemFOFtoCNF_A_1)
| ~ ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152)))
| skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152))) = skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152))
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152)),X_174) ),
inference(subst,[],[refute_0_125:[bind(X_95,$fot(skolemFOFtoCNF_A_1)),bind(X_96,$fot(X_174)),bind(X_97,$fot(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152))))]]) ).
cnf(refute_0_127,plain,
( ~ ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152)))
| skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152))) = skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152))
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152)),X_152)
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152)),X_174) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152)),skolemFOFtoCNF_A_1) )],[refute_0_121,refute_0_126]) ).
cnf(refute_0_128,plain,
( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_140)),skolemFOFtoCNF_B_1(X_140))
| ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_140))) ),
inference(subst,[],[refute_0_8:[bind(B,$fot(skolemFOFtoCNF_B_1(X_140)))]]) ).
cnf(refute_0_129,plain,
( ~ definitionFOFtoCNF_0(X_138,skolemFOFtoCNF_B_1(X_138),X_139)
| ~ in(X_139,skolemFOFtoCNF_B_1(X_138))
| ordinal(X_139) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(X_138)),bind(B,$fot(skolemFOFtoCNF_B_1(X_138))),bind(C,$fot(X_139))]]) ).
cnf(refute_0_130,plain,
( ~ in(X_139,skolemFOFtoCNF_B_1(X_138))
| ordinal(X_139) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(X_138,skolemFOFtoCNF_B_1(X_138),X_139) )],[refute_0_94,refute_0_129]) ).
cnf(refute_0_131,plain,
( ~ in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_140)),skolemFOFtoCNF_B_1(X_140))
| ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_140))) ),
inference(subst,[],[refute_0_130:[bind(X_138,$fot(X_140)),bind(X_139,$fot(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_140))))]]) ).
cnf(refute_0_132,plain,
ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_140))),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_140)),skolemFOFtoCNF_B_1(X_140)) )],[refute_0_128,refute_0_131]) ).
cnf(refute_0_133,plain,
ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152))),
inference(subst,[],[refute_0_132:[bind(X_140,$fot(X_152))]]) ).
cnf(refute_0_134,plain,
( skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152))) = skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152))
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152)),X_152)
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152)),X_174) ),
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_152))) )],[refute_0_133,refute_0_127]) ).
cnf(refute_0_135,plain,
( skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_138)))) = skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_138)))
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_138))),skolemFOFtoCNF_B_1(X_138)) ),
inference(subst,[],[refute_0_134:[bind(X_152,$fot(skolemFOFtoCNF_B_1(X_138))),bind(X_174,$fot(skolemFOFtoCNF_B_1(X_138)))]]) ).
cnf(refute_0_136,plain,
( skolemFOFtoCNF_D(X_138,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_138)))) = skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_138)))
| skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_138)))) = skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_138))) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_138))),skolemFOFtoCNF_B_1(X_138)) )],[refute_0_135,refute_0_116]) ).
cnf(refute_0_137,plain,
skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)))) = skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))),
inference(subst,[],[refute_0_136:[bind(X_138,$fot(skolemFOFtoCNF_A_1))]]) ).
cnf(refute_0_138,plain,
( skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)))) != skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)))
| ~ in(skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)))),skolemFOFtoCNF_A_1)
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))),skolemFOFtoCNF_A_1) ),
introduced(tautology,[equality,[$cnf( in(skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)))),skolemFOFtoCNF_A_1) ),[0],$fot(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))))]]) ).
cnf(refute_0_139,plain,
( ~ in(skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)))),skolemFOFtoCNF_A_1)
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))),skolemFOFtoCNF_A_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)))),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)))) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))),skolemFOFtoCNF_A_1),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)))),skolemFOFtoCNF_A_1) )],[refute_0_115,refute_0_139]) ).
cnf(refute_0_141,plain,
( ~ in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))),skolemFOFtoCNF_A_1)
| ~ ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))))
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))),skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)) ),
inference(subst,[],[refute_0_95:[bind(X_138,$fot(skolemFOFtoCNF_A_1)),bind(X_139,$fot(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)))))]]) ).
cnf(refute_0_142,plain,
( ~ ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))))
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))),skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))),skolemFOFtoCNF_A_1) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)))),
inference(subst,[],[refute_0_132:[bind(X_140,$fot(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)))]]) ).
cnf(refute_0_144,plain,
in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))),skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)),
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)))) )],[refute_0_143,refute_0_142]) ).
cnf(refute_0_145,plain,
( ~ ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))))
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))),skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))),skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)) )],[refute_0_144,refute_0_96]) ).
cnf(refute_0_146,plain,
in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))),skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))),
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)))) )],[refute_0_143,refute_0_145]) ).
cnf(refute_0_147,plain,
( ~ in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))),skolemFOFtoCNF_A_1)
| ~ ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)))) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))),skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))) )],[refute_0_146,refute_0_1]) ).
cnf(refute_0_148,plain,
~ ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)))),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1))),skolemFOFtoCNF_A_1) )],[refute_0_140,refute_0_147]) ).
cnf(refute_0_149,plain,
$false,
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_1)))) )],[refute_0_143,refute_0_148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU280+1 : TPTP v8.1.0. Released v3.3.0.
% 0.13/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n025.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 20 01:33:59 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.43/0.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.43/0.59
% 0.43/0.59 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.43/0.60
%------------------------------------------------------------------------------