TSTP Solution File: SEU284+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU284+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 12:39:59 EDT 2022
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 15
% Syntax : Number of formulae : 148 ( 16 unt; 1 def)
% Number of atoms : 470 ( 245 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 511 ( 189 ~; 262 |; 52 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-2 aty)
% Number of variables : 165 ( 14 sgn 64 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(s3_funct_1__e16_22__wellord2,conjecture,
! [A] :
? [B] :
( relation(B)
& function(B)
& relation_dom(B) = A
& ! [C] :
( in(C,A)
=> apply(B,C) = singleton(C) ) ) ).
fof(s2_funct_1__e16_22__wellord2__1,axiom,
! [A] :
( ( ! [B,C,D] :
( ( in(B,A)
& C = singleton(B)
& D = singleton(B) )
=> C = D )
& ! [B] :
~ ( in(B,A)
& ! [C] : C != singleton(B) ) )
=> ? [B] :
( relation(B)
& function(B)
& relation_dom(B) = A
& ! [C] :
( in(C,A)
=> apply(B,C) = singleton(C) ) ) ) ).
fof(definition_0,definition,
! [A,B,C,D] :
( definitionFOFtoCNF_0(A,B,C,D)
<=> ( C != D
& C = singleton(B)
& D = singleton(B)
& in(B,A) ) ) ).
fof(subgoal_0,plain,
! [A] :
? [B] :
( relation(B)
& function(B)
& relation_dom(B) = A
& ! [C] :
( in(C,A)
=> apply(B,C) = singleton(C) ) ),
inference(strip,[],[s3_funct_1__e16_22__wellord2]) ).
fof(negate_0_0,plain,
~ ! [A] :
? [B] :
( relation(B)
& function(B)
& relation_dom(B) = A
& ! [C] :
( in(C,A)
=> apply(B,C) = singleton(C) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A] :
! [B] :
( relation_dom(B) != A
| ~ function(B)
| ~ relation(B)
| ? [C] :
( apply(B,C) != singleton(C)
& in(C,A) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [B] :
( relation_dom(B) != skolemFOFtoCNF_A_6
| ~ function(B)
| ~ relation(B)
| ? [C] :
( apply(B,C) != singleton(C)
& in(C,skolemFOFtoCNF_A_6) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [B] :
( relation_dom(B) != skolemFOFtoCNF_A_6
| ~ function(B)
| ~ relation(B)
| ? [C] :
( apply(B,C) != singleton(C)
& in(C,skolemFOFtoCNF_A_6) ) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [B] :
( ( apply(B,skolemFOFtoCNF_C_1(B)) != singleton(skolemFOFtoCNF_C_1(B))
| relation_dom(B) != skolemFOFtoCNF_A_6
| ~ function(B)
| ~ relation(B) )
& ( relation_dom(B) != skolemFOFtoCNF_A_6
| ~ function(B)
| ~ relation(B)
| in(skolemFOFtoCNF_C_1(B),skolemFOFtoCNF_A_6) ) ),
inference(clausify,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [B] :
( apply(B,skolemFOFtoCNF_C_1(B)) != singleton(skolemFOFtoCNF_C_1(B))
| relation_dom(B) != skolemFOFtoCNF_A_6
| ~ function(B)
| ~ relation(B) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A] :
( ? [B] :
( in(B,A)
& ! [C] : C != singleton(B) )
| ? [B] :
( relation_dom(B) = A
& function(B)
& relation(B)
& ! [C] :
( ~ in(C,A)
| apply(B,C) = singleton(C) ) )
| ? [B,C,D] :
( C != D
& C = singleton(B)
& D = singleton(B)
& in(B,A) ) ),
inference(canonicalize,[],[s2_funct_1__e16_22__wellord2__1]) ).
fof(normalize_0_6,plain,
! [A] :
( ? [B] :
( in(B,A)
& ! [C] : C != singleton(B) )
| ? [B] :
( relation_dom(B) = A
& function(B)
& relation(B)
& ! [C] :
( ~ in(C,A)
| apply(B,C) = singleton(C) ) )
| ? [B,C,D] :
( C != D
& C = singleton(B)
& D = singleton(B)
& in(B,A) ) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,C,D] :
( ~ definitionFOFtoCNF_0(A,B,C,D)
<=> ( C != singleton(B)
| D != singleton(B)
| ~ in(B,A)
| C = D ) ),
inference(canonicalize,[],[definition_0]) ).
fof(normalize_0_8,plain,
! [A] :
( ? [B] :
( in(B,A)
& ! [C] : C != singleton(B) )
| ? [B] :
( relation_dom(B) = A
& function(B)
& relation(B)
& ! [C] :
( ~ in(C,A)
| apply(B,C) = singleton(C) ) )
| ? [B,C,D] : definitionFOFtoCNF_0(A,B,C,D) ),
inference(simplify,[],[normalize_0_6,normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,C,C0] :
( ( C != singleton(skolemFOFtoCNF_B(A))
| relation_dom(skolemFOFtoCNF_B_1(A)) = A
| definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_2(A),skolemFOFtoCNF_C(A),skolemFOFtoCNF_D(A)) )
& ( C != singleton(skolemFOFtoCNF_B(A))
| definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_2(A),skolemFOFtoCNF_C(A),skolemFOFtoCNF_D(A))
| function(skolemFOFtoCNF_B_1(A)) )
& ( C != singleton(skolemFOFtoCNF_B(A))
| definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_2(A),skolemFOFtoCNF_C(A),skolemFOFtoCNF_D(A))
| relation(skolemFOFtoCNF_B_1(A)) )
& ( relation_dom(skolemFOFtoCNF_B_1(A)) = A
| definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_2(A),skolemFOFtoCNF_C(A),skolemFOFtoCNF_D(A))
| in(skolemFOFtoCNF_B(A),A) )
& ( definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_2(A),skolemFOFtoCNF_C(A),skolemFOFtoCNF_D(A))
| function(skolemFOFtoCNF_B_1(A))
| in(skolemFOFtoCNF_B(A),A) )
& ( definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_2(A),skolemFOFtoCNF_C(A),skolemFOFtoCNF_D(A))
| in(skolemFOFtoCNF_B(A),A)
| relation(skolemFOFtoCNF_B_1(A)) )
& ( C != singleton(skolemFOFtoCNF_B(A))
| ~ in(C0,A)
| apply(skolemFOFtoCNF_B_1(A),C0) = singleton(C0)
| definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_2(A),skolemFOFtoCNF_C(A),skolemFOFtoCNF_D(A)) )
& ( ~ in(C0,A)
| apply(skolemFOFtoCNF_B_1(A),C0) = singleton(C0)
| definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_2(A),skolemFOFtoCNF_C(A),skolemFOFtoCNF_D(A))
| in(skolemFOFtoCNF_B(A),A) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,C,C0] :
( C != singleton(skolemFOFtoCNF_B(A))
| ~ in(C0,A)
| apply(skolemFOFtoCNF_B_1(A),C0) = singleton(C0)
| definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_2(A),skolemFOFtoCNF_C(A),skolemFOFtoCNF_D(A)) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [B] :
( relation_dom(B) != skolemFOFtoCNF_A_6
| ~ function(B)
| ~ relation(B)
| in(skolemFOFtoCNF_C_1(B),skolemFOFtoCNF_A_6) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_12,plain,
! [A,C] :
( C != singleton(skolemFOFtoCNF_B(A))
| relation_dom(skolemFOFtoCNF_B_1(A)) = A
| definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_2(A),skolemFOFtoCNF_C(A),skolemFOFtoCNF_D(A)) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_13,plain,
! [A,C] :
( C != singleton(skolemFOFtoCNF_B(A))
| definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_2(A),skolemFOFtoCNF_C(A),skolemFOFtoCNF_D(A))
| function(skolemFOFtoCNF_B_1(A)) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_14,plain,
! [A,B,C,D] :
( ( C != D
| ~ definitionFOFtoCNF_0(A,B,C,D) )
& ( ~ definitionFOFtoCNF_0(A,B,C,D)
| C = singleton(B) )
& ( ~ definitionFOFtoCNF_0(A,B,C,D)
| D = singleton(B) )
& ( ~ definitionFOFtoCNF_0(A,B,C,D)
| in(B,A) )
& ( C != singleton(B)
| D != singleton(B)
| ~ in(B,A)
| C = D
| definitionFOFtoCNF_0(A,B,C,D) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_15,plain,
! [A,B,C,D] :
( ~ definitionFOFtoCNF_0(A,B,C,D)
| C = singleton(B) ),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [A,B,C,D] :
( ~ definitionFOFtoCNF_0(A,B,C,D)
| D = singleton(B) ),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_17,plain,
! [A,C] :
( C != singleton(skolemFOFtoCNF_B(A))
| definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_2(A),skolemFOFtoCNF_C(A),skolemFOFtoCNF_D(A))
| relation(skolemFOFtoCNF_B_1(A)) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_18,plain,
! [A,B,C,D] :
( C != D
| ~ definitionFOFtoCNF_0(A,B,C,D) ),
inference(conjunct,[],[normalize_0_14]) ).
cnf(refute_0_0,plain,
( apply(B,skolemFOFtoCNF_C_1(B)) != singleton(skolemFOFtoCNF_C_1(B))
| relation_dom(B) != skolemFOFtoCNF_A_6
| ~ function(B)
| ~ relation(B) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_1,plain,
( apply(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))) != singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)))
| relation_dom(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) != skolemFOFtoCNF_A_6
| ~ function(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| ~ relation(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) ),
inference(subst,[],[refute_0_0:[bind(B,$fot(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)))]]) ).
cnf(refute_0_2,plain,
( C != singleton(skolemFOFtoCNF_B(A))
| ~ in(C0,A)
| apply(skolemFOFtoCNF_B_1(A),C0) = singleton(C0)
| definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_2(A),skolemFOFtoCNF_C(A),skolemFOFtoCNF_D(A)) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_3,plain,
( singleton(skolemFOFtoCNF_B(A)) != singleton(skolemFOFtoCNF_B(A))
| ~ in(C0,A)
| apply(skolemFOFtoCNF_B_1(A),C0) = singleton(C0)
| definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_2(A),skolemFOFtoCNF_C(A),skolemFOFtoCNF_D(A)) ),
inference(subst,[],[refute_0_2:[bind(C,$fot(singleton(skolemFOFtoCNF_B(A))))]]) ).
cnf(refute_0_4,plain,
singleton(skolemFOFtoCNF_B(A)) = singleton(skolemFOFtoCNF_B(A)),
introduced(tautology,[refl,[$fot(singleton(skolemFOFtoCNF_B(A)))]]) ).
cnf(refute_0_5,plain,
( ~ in(C0,A)
| apply(skolemFOFtoCNF_B_1(A),C0) = singleton(C0)
| definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_2(A),skolemFOFtoCNF_C(A),skolemFOFtoCNF_D(A)) ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_B(A)),singleton(skolemFOFtoCNF_B(A))) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_A_6)
| apply(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))) = singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)))
| definitionFOFtoCNF_0(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6),skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(skolemFOFtoCNF_A_6)),bind(C0,$fot(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))))]]) ).
cnf(refute_0_7,plain,
( relation_dom(B) != skolemFOFtoCNF_A_6
| ~ function(B)
| ~ relation(B)
| in(skolemFOFtoCNF_C_1(B),skolemFOFtoCNF_A_6) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_8,plain,
( relation_dom(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) != skolemFOFtoCNF_A_6
| ~ function(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| ~ relation(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_A_6) ),
inference(subst,[],[refute_0_7:[bind(B,$fot(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)))]]) ).
cnf(refute_0_9,plain,
( C != singleton(skolemFOFtoCNF_B(A))
| relation_dom(skolemFOFtoCNF_B_1(A)) = A
| definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_2(A),skolemFOFtoCNF_C(A),skolemFOFtoCNF_D(A)) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_10,plain,
( singleton(skolemFOFtoCNF_B(A)) != singleton(skolemFOFtoCNF_B(A))
| relation_dom(skolemFOFtoCNF_B_1(A)) = A
| definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_2(A),skolemFOFtoCNF_C(A),skolemFOFtoCNF_D(A)) ),
inference(subst,[],[refute_0_9:[bind(C,$fot(singleton(skolemFOFtoCNF_B(A))))]]) ).
cnf(refute_0_11,plain,
( relation_dom(skolemFOFtoCNF_B_1(A)) = A
| definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_2(A),skolemFOFtoCNF_C(A),skolemFOFtoCNF_D(A)) ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_B(A)),singleton(skolemFOFtoCNF_B(A))) )],[refute_0_4,refute_0_10]) ).
cnf(refute_0_12,plain,
( relation_dom(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) = skolemFOFtoCNF_A_6
| definitionFOFtoCNF_0(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6),skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)) ),
inference(subst,[],[refute_0_11:[bind(A,$fot(skolemFOFtoCNF_A_6))]]) ).
cnf(refute_0_13,plain,
( C != singleton(skolemFOFtoCNF_B(A))
| definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_2(A),skolemFOFtoCNF_C(A),skolemFOFtoCNF_D(A))
| function(skolemFOFtoCNF_B_1(A)) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_14,plain,
( singleton(skolemFOFtoCNF_B(A)) != singleton(skolemFOFtoCNF_B(A))
| definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_2(A),skolemFOFtoCNF_C(A),skolemFOFtoCNF_D(A))
| function(skolemFOFtoCNF_B_1(A)) ),
inference(subst,[],[refute_0_13:[bind(C,$fot(singleton(skolemFOFtoCNF_B(A))))]]) ).
cnf(refute_0_15,plain,
( definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_2(A),skolemFOFtoCNF_C(A),skolemFOFtoCNF_D(A))
| function(skolemFOFtoCNF_B_1(A)) ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_B(A)),singleton(skolemFOFtoCNF_B(A))) )],[refute_0_4,refute_0_14]) ).
cnf(refute_0_16,plain,
( definitionFOFtoCNF_0(X_22,skolemFOFtoCNF_B_2(X_22),skolemFOFtoCNF_C(X_22),skolemFOFtoCNF_D(X_22))
| function(skolemFOFtoCNF_B_1(X_22)) ),
inference(subst,[],[refute_0_15:[bind(A,$fot(X_22))]]) ).
cnf(refute_0_17,plain,
( ~ definitionFOFtoCNF_0(A,B,C,D)
| C = singleton(B) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_18,plain,
( ~ definitionFOFtoCNF_0(X_22,skolemFOFtoCNF_B_2(X_22),skolemFOFtoCNF_C(X_22),skolemFOFtoCNF_D(X_22))
| skolemFOFtoCNF_C(X_22) = singleton(skolemFOFtoCNF_B_2(X_22)) ),
inference(subst,[],[refute_0_17:[bind(A,$fot(X_22)),bind(B,$fot(skolemFOFtoCNF_B_2(X_22))),bind(C,$fot(skolemFOFtoCNF_C(X_22))),bind(D,$fot(skolemFOFtoCNF_D(X_22)))]]) ).
cnf(refute_0_19,plain,
( skolemFOFtoCNF_C(X_22) = singleton(skolemFOFtoCNF_B_2(X_22))
| function(skolemFOFtoCNF_B_1(X_22)) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(X_22,skolemFOFtoCNF_B_2(X_22),skolemFOFtoCNF_C(X_22),skolemFOFtoCNF_D(X_22)) )],[refute_0_16,refute_0_18]) ).
cnf(refute_0_20,plain,
( definitionFOFtoCNF_0(X_29,skolemFOFtoCNF_B_2(X_29),skolemFOFtoCNF_C(X_29),skolemFOFtoCNF_D(X_29))
| function(skolemFOFtoCNF_B_1(X_29)) ),
inference(subst,[],[refute_0_15:[bind(A,$fot(X_29))]]) ).
cnf(refute_0_21,plain,
( ~ definitionFOFtoCNF_0(A,B,C,D)
| D = singleton(B) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_22,plain,
( ~ definitionFOFtoCNF_0(X_29,skolemFOFtoCNF_B_2(X_29),skolemFOFtoCNF_C(X_29),skolemFOFtoCNF_D(X_29))
| skolemFOFtoCNF_D(X_29) = singleton(skolemFOFtoCNF_B_2(X_29)) ),
inference(subst,[],[refute_0_21:[bind(A,$fot(X_29)),bind(B,$fot(skolemFOFtoCNF_B_2(X_29))),bind(C,$fot(skolemFOFtoCNF_C(X_29))),bind(D,$fot(skolemFOFtoCNF_D(X_29)))]]) ).
cnf(refute_0_23,plain,
( skolemFOFtoCNF_D(X_29) = singleton(skolemFOFtoCNF_B_2(X_29))
| function(skolemFOFtoCNF_B_1(X_29)) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(X_29,skolemFOFtoCNF_B_2(X_29),skolemFOFtoCNF_C(X_29),skolemFOFtoCNF_D(X_29)) )],[refute_0_20,refute_0_22]) ).
cnf(refute_0_24,plain,
( skolemFOFtoCNF_D(X_22) = singleton(skolemFOFtoCNF_B_2(X_22))
| function(skolemFOFtoCNF_B_1(X_22)) ),
inference(subst,[],[refute_0_23:[bind(X_29,$fot(X_22))]]) ).
cnf(refute_0_25,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_26,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_27,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( skolemFOFtoCNF_D(X_22) != singleton(skolemFOFtoCNF_B_2(X_22))
| singleton(skolemFOFtoCNF_B_2(X_22)) = skolemFOFtoCNF_D(X_22) ),
inference(subst,[],[refute_0_27:[bind(X,$fot(skolemFOFtoCNF_D(X_22))),bind(Y,$fot(singleton(skolemFOFtoCNF_B_2(X_22))))]]) ).
cnf(refute_0_29,plain,
( singleton(skolemFOFtoCNF_B_2(X_22)) = skolemFOFtoCNF_D(X_22)
| function(skolemFOFtoCNF_B_1(X_22)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_D(X_22),singleton(skolemFOFtoCNF_B_2(X_22))) )],[refute_0_24,refute_0_28]) ).
cnf(refute_0_30,plain,
( singleton(skolemFOFtoCNF_B_2(X_22)) != skolemFOFtoCNF_D(X_22)
| skolemFOFtoCNF_C(X_22) != singleton(skolemFOFtoCNF_B_2(X_22))
| skolemFOFtoCNF_C(X_22) = skolemFOFtoCNF_D(X_22) ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_C(X_22),singleton(skolemFOFtoCNF_B_2(X_22))) ),[1],$fot(skolemFOFtoCNF_D(X_22))]]) ).
cnf(refute_0_31,plain,
( skolemFOFtoCNF_C(X_22) != singleton(skolemFOFtoCNF_B_2(X_22))
| skolemFOFtoCNF_C(X_22) = skolemFOFtoCNF_D(X_22)
| function(skolemFOFtoCNF_B_1(X_22)) ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_B_2(X_22)),skolemFOFtoCNF_D(X_22)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( skolemFOFtoCNF_C(X_22) = skolemFOFtoCNF_D(X_22)
| function(skolemFOFtoCNF_B_1(X_22)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C(X_22),singleton(skolemFOFtoCNF_B_2(X_22))) )],[refute_0_19,refute_0_31]) ).
cnf(refute_0_33,plain,
( skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)
| function(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) ),
inference(subst,[],[refute_0_32:[bind(X_22,$fot(skolemFOFtoCNF_A_6))]]) ).
cnf(refute_0_34,plain,
( C != singleton(skolemFOFtoCNF_B(A))
| definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_2(A),skolemFOFtoCNF_C(A),skolemFOFtoCNF_D(A))
| relation(skolemFOFtoCNF_B_1(A)) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_35,plain,
( singleton(skolemFOFtoCNF_B(A)) != singleton(skolemFOFtoCNF_B(A))
| definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_2(A),skolemFOFtoCNF_C(A),skolemFOFtoCNF_D(A))
| relation(skolemFOFtoCNF_B_1(A)) ),
inference(subst,[],[refute_0_34:[bind(C,$fot(singleton(skolemFOFtoCNF_B(A))))]]) ).
cnf(refute_0_36,plain,
( definitionFOFtoCNF_0(A,skolemFOFtoCNF_B_2(A),skolemFOFtoCNF_C(A),skolemFOFtoCNF_D(A))
| relation(skolemFOFtoCNF_B_1(A)) ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_B(A)),singleton(skolemFOFtoCNF_B(A))) )],[refute_0_4,refute_0_35]) ).
cnf(refute_0_37,plain,
( definitionFOFtoCNF_0(X_22,skolemFOFtoCNF_B_2(X_22),skolemFOFtoCNF_C(X_22),skolemFOFtoCNF_D(X_22))
| relation(skolemFOFtoCNF_B_1(X_22)) ),
inference(subst,[],[refute_0_36:[bind(A,$fot(X_22))]]) ).
cnf(refute_0_38,plain,
( skolemFOFtoCNF_C(X_22) = singleton(skolemFOFtoCNF_B_2(X_22))
| relation(skolemFOFtoCNF_B_1(X_22)) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(X_22,skolemFOFtoCNF_B_2(X_22),skolemFOFtoCNF_C(X_22),skolemFOFtoCNF_D(X_22)) )],[refute_0_37,refute_0_18]) ).
cnf(refute_0_39,plain,
( definitionFOFtoCNF_0(X_29,skolemFOFtoCNF_B_2(X_29),skolemFOFtoCNF_C(X_29),skolemFOFtoCNF_D(X_29))
| relation(skolemFOFtoCNF_B_1(X_29)) ),
inference(subst,[],[refute_0_36:[bind(A,$fot(X_29))]]) ).
cnf(refute_0_40,plain,
( skolemFOFtoCNF_D(X_29) = singleton(skolemFOFtoCNF_B_2(X_29))
| relation(skolemFOFtoCNF_B_1(X_29)) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(X_29,skolemFOFtoCNF_B_2(X_29),skolemFOFtoCNF_C(X_29),skolemFOFtoCNF_D(X_29)) )],[refute_0_39,refute_0_22]) ).
cnf(refute_0_41,plain,
( skolemFOFtoCNF_D(X_22) = singleton(skolemFOFtoCNF_B_2(X_22))
| relation(skolemFOFtoCNF_B_1(X_22)) ),
inference(subst,[],[refute_0_40:[bind(X_29,$fot(X_22))]]) ).
cnf(refute_0_42,plain,
( singleton(skolemFOFtoCNF_B_2(X_22)) = skolemFOFtoCNF_D(X_22)
| relation(skolemFOFtoCNF_B_1(X_22)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_D(X_22),singleton(skolemFOFtoCNF_B_2(X_22))) )],[refute_0_41,refute_0_28]) ).
cnf(refute_0_43,plain,
( skolemFOFtoCNF_C(X_22) != singleton(skolemFOFtoCNF_B_2(X_22))
| skolemFOFtoCNF_C(X_22) = skolemFOFtoCNF_D(X_22)
| relation(skolemFOFtoCNF_B_1(X_22)) ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_B_2(X_22)),skolemFOFtoCNF_D(X_22)) )],[refute_0_42,refute_0_30]) ).
cnf(refute_0_44,plain,
( skolemFOFtoCNF_C(X_22) = skolemFOFtoCNF_D(X_22)
| relation(skolemFOFtoCNF_B_1(X_22)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C(X_22),singleton(skolemFOFtoCNF_B_2(X_22))) )],[refute_0_38,refute_0_43]) ).
cnf(refute_0_45,plain,
( skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)
| relation(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) ),
inference(subst,[],[refute_0_44:[bind(X_22,$fot(skolemFOFtoCNF_A_6))]]) ).
cnf(refute_0_46,plain,
( ~ definitionFOFtoCNF_0(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6),skolemFOFtoCNF_D(skolemFOFtoCNF_A_6))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = singleton(skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6)) ),
inference(subst,[],[refute_0_17:[bind(A,$fot(skolemFOFtoCNF_A_6)),bind(B,$fot(skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6))),bind(C,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_A_6))),bind(D,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)))]]) ).
cnf(refute_0_47,plain,
( relation_dom(skolemFOFtoCNF_B_1(X_22)) != skolemFOFtoCNF_A_6
| ~ function(skolemFOFtoCNF_B_1(X_22))
| ~ relation(skolemFOFtoCNF_B_1(X_22))
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_22)),skolemFOFtoCNF_A_6) ),
inference(subst,[],[refute_0_7:[bind(B,$fot(skolemFOFtoCNF_B_1(X_22)))]]) ).
cnf(refute_0_48,plain,
( relation_dom(skolemFOFtoCNF_B_1(X_22)) = X_22
| definitionFOFtoCNF_0(X_22,skolemFOFtoCNF_B_2(X_22),skolemFOFtoCNF_C(X_22),skolemFOFtoCNF_D(X_22)) ),
inference(subst,[],[refute_0_11:[bind(A,$fot(X_22))]]) ).
cnf(refute_0_49,plain,
( relation_dom(skolemFOFtoCNF_B_1(X_22)) = X_22
| skolemFOFtoCNF_C(X_22) = singleton(skolemFOFtoCNF_B_2(X_22)) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(X_22,skolemFOFtoCNF_B_2(X_22),skolemFOFtoCNF_C(X_22),skolemFOFtoCNF_D(X_22)) )],[refute_0_48,refute_0_18]) ).
cnf(refute_0_50,plain,
( relation_dom(skolemFOFtoCNF_B_1(X_29)) = X_29
| definitionFOFtoCNF_0(X_29,skolemFOFtoCNF_B_2(X_29),skolemFOFtoCNF_C(X_29),skolemFOFtoCNF_D(X_29)) ),
inference(subst,[],[refute_0_11:[bind(A,$fot(X_29))]]) ).
cnf(refute_0_51,plain,
( relation_dom(skolemFOFtoCNF_B_1(X_29)) = X_29
| skolemFOFtoCNF_D(X_29) = singleton(skolemFOFtoCNF_B_2(X_29)) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(X_29,skolemFOFtoCNF_B_2(X_29),skolemFOFtoCNF_C(X_29),skolemFOFtoCNF_D(X_29)) )],[refute_0_50,refute_0_22]) ).
cnf(refute_0_52,plain,
( relation_dom(skolemFOFtoCNF_B_1(X_22)) = X_22
| skolemFOFtoCNF_D(X_22) = singleton(skolemFOFtoCNF_B_2(X_22)) ),
inference(subst,[],[refute_0_51:[bind(X_29,$fot(X_22))]]) ).
cnf(refute_0_53,plain,
( relation_dom(skolemFOFtoCNF_B_1(X_22)) = X_22
| singleton(skolemFOFtoCNF_B_2(X_22)) = skolemFOFtoCNF_D(X_22) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_D(X_22),singleton(skolemFOFtoCNF_B_2(X_22))) )],[refute_0_52,refute_0_28]) ).
cnf(refute_0_54,plain,
( skolemFOFtoCNF_C(X_22) != singleton(skolemFOFtoCNF_B_2(X_22))
| relation_dom(skolemFOFtoCNF_B_1(X_22)) = X_22
| skolemFOFtoCNF_C(X_22) = skolemFOFtoCNF_D(X_22) ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_B_2(X_22)),skolemFOFtoCNF_D(X_22)) )],[refute_0_53,refute_0_30]) ).
cnf(refute_0_55,plain,
( relation_dom(skolemFOFtoCNF_B_1(X_22)) = X_22
| skolemFOFtoCNF_C(X_22) = skolemFOFtoCNF_D(X_22) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C(X_22),singleton(skolemFOFtoCNF_B_2(X_22))) )],[refute_0_49,refute_0_54]) ).
cnf(refute_0_56,plain,
( X_22 != skolemFOFtoCNF_A_6
| relation_dom(skolemFOFtoCNF_B_1(X_22)) != X_22
| relation_dom(skolemFOFtoCNF_B_1(X_22)) = skolemFOFtoCNF_A_6 ),
introduced(tautology,[equality,[$cnf( $equal(relation_dom(skolemFOFtoCNF_B_1(X_22)),X_22) ),[1],$fot(skolemFOFtoCNF_A_6)]]) ).
cnf(refute_0_57,plain,
( X_22 != skolemFOFtoCNF_A_6
| relation_dom(skolemFOFtoCNF_B_1(X_22)) = skolemFOFtoCNF_A_6
| skolemFOFtoCNF_C(X_22) = skolemFOFtoCNF_D(X_22) ),
inference(resolve,[$cnf( $equal(relation_dom(skolemFOFtoCNF_B_1(X_22)),X_22) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
( X_22 != skolemFOFtoCNF_A_6
| ~ function(skolemFOFtoCNF_B_1(X_22))
| ~ relation(skolemFOFtoCNF_B_1(X_22))
| skolemFOFtoCNF_C(X_22) = skolemFOFtoCNF_D(X_22)
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(X_22)),skolemFOFtoCNF_A_6) ),
inference(resolve,[$cnf( $equal(relation_dom(skolemFOFtoCNF_B_1(X_22)),skolemFOFtoCNF_A_6) )],[refute_0_57,refute_0_47]) ).
cnf(refute_0_59,plain,
( skolemFOFtoCNF_A_6 != skolemFOFtoCNF_A_6
| ~ function(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| ~ relation(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_A_6) ),
inference(subst,[],[refute_0_58:[bind(X_22,$fot(skolemFOFtoCNF_A_6))]]) ).
cnf(refute_0_60,plain,
skolemFOFtoCNF_A_6 = skolemFOFtoCNF_A_6,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_A_6)]]) ).
cnf(refute_0_61,plain,
( ~ function(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| ~ relation(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_A_6) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_6,skolemFOFtoCNF_A_6) )],[refute_0_60,refute_0_59]) ).
cnf(refute_0_62,plain,
( ~ function(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_A_6) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) )],[refute_0_45,refute_0_61]) ).
cnf(refute_0_63,plain,
( skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_A_6) ),
inference(resolve,[$cnf( function(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) )],[refute_0_33,refute_0_62]) ).
cnf(refute_0_64,plain,
( apply(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))) = singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)
| definitionFOFtoCNF_0(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6),skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_A_6) )],[refute_0_63,refute_0_6]) ).
cnf(refute_0_65,plain,
( apply(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))) = singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = singleton(skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_6) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6),skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)) )],[refute_0_64,refute_0_46]) ).
cnf(refute_0_66,plain,
( apply(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))) != singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)))
| singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))) != singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)))
| apply(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))) = singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))),singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)))) ),[0],$fot(singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))))]]) ).
cnf(refute_0_67,plain,
( singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))) != singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)))
| apply(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))) = singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = singleton(skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_6) ),
inference(resolve,[$cnf( $equal(apply(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))),singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)))) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
( relation_dom(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) != skolemFOFtoCNF_A_6
| singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))) != singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)))
| ~ function(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| ~ relation(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = singleton(skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_6) ),
inference(resolve,[$cnf( $equal(apply(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))),singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)))) )],[refute_0_67,refute_0_1]) ).
cnf(refute_0_69,plain,
singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))) = singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))),
introduced(tautology,[refl,[$fot(singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))))]]) ).
cnf(refute_0_70,plain,
( relation_dom(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) != skolemFOFtoCNF_A_6
| ~ function(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| ~ relation(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = singleton(skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_6) ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))),singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)))) )],[refute_0_69,refute_0_68]) ).
cnf(refute_0_71,plain,
( relation_dom(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) = skolemFOFtoCNF_A_6
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_6) ),
inference(subst,[],[refute_0_55:[bind(X_22,$fot(skolemFOFtoCNF_A_6))]]) ).
cnf(refute_0_72,plain,
( relation_dom(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) != skolemFOFtoCNF_A_6
| skolemFOFtoCNF_A_6 != skolemFOFtoCNF_A_6
| relation_dom(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) = skolemFOFtoCNF_A_6 ),
introduced(tautology,[equality,[$cnf( ~ $equal(relation_dom(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_A_6) ),[0],$fot(skolemFOFtoCNF_A_6)]]) ).
cnf(refute_0_73,plain,
( skolemFOFtoCNF_A_6 != skolemFOFtoCNF_A_6
| relation_dom(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) = skolemFOFtoCNF_A_6
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_6) ),
inference(resolve,[$cnf( $equal(relation_dom(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_A_6) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
( skolemFOFtoCNF_A_6 != skolemFOFtoCNF_A_6
| ~ function(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| ~ relation(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = singleton(skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_6) ),
inference(resolve,[$cnf( $equal(relation_dom(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_A_6) )],[refute_0_73,refute_0_70]) ).
cnf(refute_0_75,plain,
( ~ function(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| ~ relation(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = singleton(skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_6) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_6,skolemFOFtoCNF_A_6) )],[refute_0_60,refute_0_74]) ).
cnf(refute_0_76,plain,
( ~ function(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = singleton(skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_6) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) )],[refute_0_45,refute_0_75]) ).
cnf(refute_0_77,plain,
( skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = singleton(skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_6) ),
inference(resolve,[$cnf( function(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) )],[refute_0_33,refute_0_76]) ).
cnf(refute_0_78,plain,
( ~ definitionFOFtoCNF_0(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6),skolemFOFtoCNF_D(skolemFOFtoCNF_A_6))
| skolemFOFtoCNF_D(skolemFOFtoCNF_A_6) = singleton(skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6)) ),
inference(subst,[],[refute_0_21:[bind(A,$fot(skolemFOFtoCNF_A_6)),bind(B,$fot(skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6))),bind(C,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_A_6))),bind(D,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)))]]) ).
cnf(refute_0_79,plain,
( apply(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))) = singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)
| skolemFOFtoCNF_D(skolemFOFtoCNF_A_6) = singleton(skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6)) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6),skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)) )],[refute_0_64,refute_0_78]) ).
cnf(refute_0_80,plain,
( singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))) != singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)))
| apply(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))) = singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)
| skolemFOFtoCNF_D(skolemFOFtoCNF_A_6) = singleton(skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6)) ),
inference(resolve,[$cnf( $equal(apply(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))),singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)))) )],[refute_0_79,refute_0_66]) ).
cnf(refute_0_81,plain,
( relation_dom(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) != skolemFOFtoCNF_A_6
| singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))) != singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)))
| ~ function(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| ~ relation(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)
| skolemFOFtoCNF_D(skolemFOFtoCNF_A_6) = singleton(skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6)) ),
inference(resolve,[$cnf( $equal(apply(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))),singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)))) )],[refute_0_80,refute_0_1]) ).
cnf(refute_0_82,plain,
( relation_dom(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) != skolemFOFtoCNF_A_6
| ~ function(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| ~ relation(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)
| skolemFOFtoCNF_D(skolemFOFtoCNF_A_6) = singleton(skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6)) ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))),singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)))) )],[refute_0_69,refute_0_81]) ).
cnf(refute_0_83,plain,
( skolemFOFtoCNF_A_6 != skolemFOFtoCNF_A_6
| ~ function(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| ~ relation(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)
| skolemFOFtoCNF_D(skolemFOFtoCNF_A_6) = singleton(skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6)) ),
inference(resolve,[$cnf( $equal(relation_dom(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_A_6) )],[refute_0_73,refute_0_82]) ).
cnf(refute_0_84,plain,
( ~ function(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| ~ relation(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)
| skolemFOFtoCNF_D(skolemFOFtoCNF_A_6) = singleton(skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_6,skolemFOFtoCNF_A_6) )],[refute_0_60,refute_0_83]) ).
cnf(refute_0_85,plain,
( ~ function(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)
| skolemFOFtoCNF_D(skolemFOFtoCNF_A_6) = singleton(skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6)) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) )],[refute_0_45,refute_0_84]) ).
cnf(refute_0_86,plain,
( skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)
| skolemFOFtoCNF_D(skolemFOFtoCNF_A_6) = singleton(skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6)) ),
inference(resolve,[$cnf( function(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) )],[refute_0_33,refute_0_85]) ).
cnf(refute_0_87,plain,
( skolemFOFtoCNF_D(skolemFOFtoCNF_A_6) != singleton(skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6))
| singleton(skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6)) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_6) ),
inference(subst,[],[refute_0_27:[bind(X,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_A_6))),bind(Y,$fot(singleton(skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6))))]]) ).
cnf(refute_0_88,plain,
( singleton(skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6)) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_6) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_D(skolemFOFtoCNF_A_6),singleton(skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6))) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
( singleton(skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6)) != skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) != singleton(skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_6) ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_C(skolemFOFtoCNF_A_6),singleton(skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6))) ),[1],$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_A_6))]]) ).
cnf(refute_0_90,plain,
( skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) != singleton(skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_6) ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_6),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C(skolemFOFtoCNF_A_6),singleton(skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6))) )],[refute_0_77,refute_0_90]) ).
cnf(refute_0_92,plain,
( skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) != skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)
| skolemFOFtoCNF_D(skolemFOFtoCNF_A_6) = skolemFOFtoCNF_C(skolemFOFtoCNF_A_6) ),
inference(subst,[],[refute_0_27:[bind(X,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_A_6))),bind(Y,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)))]]) ).
cnf(refute_0_93,plain,
skolemFOFtoCNF_D(skolemFOFtoCNF_A_6) = skolemFOFtoCNF_C(skolemFOFtoCNF_A_6),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C(skolemFOFtoCNF_A_6),skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
( skolemFOFtoCNF_D(skolemFOFtoCNF_A_6) != skolemFOFtoCNF_C(skolemFOFtoCNF_A_6)
| ~ definitionFOFtoCNF_0(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6),skolemFOFtoCNF_D(skolemFOFtoCNF_A_6))
| definitionFOFtoCNF_0(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6)) ),
introduced(tautology,[equality,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6),skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)) ),[3],$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_A_6))]]) ).
cnf(refute_0_95,plain,
( ~ definitionFOFtoCNF_0(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6),skolemFOFtoCNF_D(skolemFOFtoCNF_A_6))
| definitionFOFtoCNF_0(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_D(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6)) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
( relation_dom(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) = skolemFOFtoCNF_A_6
| definitionFOFtoCNF_0(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6)) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6),skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)) )],[refute_0_12,refute_0_95]) ).
cnf(refute_0_97,plain,
( C != D
| ~ definitionFOFtoCNF_0(A,B,C,D) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_98,plain,
( D != D
| ~ definitionFOFtoCNF_0(A,B,D,D) ),
inference(subst,[],[refute_0_97:[bind(C,$fot(D))]]) ).
cnf(refute_0_99,plain,
D = D,
introduced(tautology,[refl,[$fot(D)]]) ).
cnf(refute_0_100,plain,
~ definitionFOFtoCNF_0(A,B,D,D),
inference(resolve,[$cnf( $equal(D,D) )],[refute_0_99,refute_0_98]) ).
cnf(refute_0_101,plain,
~ definitionFOFtoCNF_0(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6)),
inference(subst,[],[refute_0_100:[bind(A,$fot(skolemFOFtoCNF_A_6)),bind(B,$fot(skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6))),bind(D,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_A_6)))]]) ).
cnf(refute_0_102,plain,
relation_dom(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) = skolemFOFtoCNF_A_6,
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6)) )],[refute_0_96,refute_0_101]) ).
cnf(refute_0_103,plain,
( skolemFOFtoCNF_A_6 != skolemFOFtoCNF_A_6
| relation_dom(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) = skolemFOFtoCNF_A_6 ),
inference(resolve,[$cnf( $equal(relation_dom(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_A_6) )],[refute_0_102,refute_0_72]) ).
cnf(refute_0_104,plain,
( skolemFOFtoCNF_A_6 != skolemFOFtoCNF_A_6
| ~ function(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| ~ relation(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_A_6) ),
inference(resolve,[$cnf( $equal(relation_dom(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_A_6) )],[refute_0_103,refute_0_8]) ).
cnf(refute_0_105,plain,
( ~ function(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| ~ relation(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_A_6) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_6,skolemFOFtoCNF_A_6) )],[refute_0_60,refute_0_104]) ).
cnf(refute_0_106,plain,
( definitionFOFtoCNF_0(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6),skolemFOFtoCNF_D(skolemFOFtoCNF_A_6))
| function(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) ),
inference(subst,[],[refute_0_15:[bind(A,$fot(skolemFOFtoCNF_A_6))]]) ).
cnf(refute_0_107,plain,
( definitionFOFtoCNF_0(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6))
| function(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6),skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)) )],[refute_0_106,refute_0_95]) ).
cnf(refute_0_108,plain,
function(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6)) )],[refute_0_107,refute_0_101]) ).
cnf(refute_0_109,plain,
( ~ relation(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_A_6) ),
inference(resolve,[$cnf( function(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) )],[refute_0_108,refute_0_105]) ).
cnf(refute_0_110,plain,
( definitionFOFtoCNF_0(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6),skolemFOFtoCNF_D(skolemFOFtoCNF_A_6))
| relation(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) ),
inference(subst,[],[refute_0_36:[bind(A,$fot(skolemFOFtoCNF_A_6))]]) ).
cnf(refute_0_111,plain,
( definitionFOFtoCNF_0(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6))
| relation(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6),skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)) )],[refute_0_110,refute_0_95]) ).
cnf(refute_0_112,plain,
relation(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6)) )],[refute_0_111,refute_0_101]) ).
cnf(refute_0_113,plain,
in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_A_6),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) )],[refute_0_112,refute_0_109]) ).
cnf(refute_0_114,plain,
( apply(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))) = singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)))
| definitionFOFtoCNF_0(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6),skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_A_6) )],[refute_0_113,refute_0_6]) ).
cnf(refute_0_115,plain,
( apply(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))) = singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)))
| definitionFOFtoCNF_0(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6)) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6),skolemFOFtoCNF_D(skolemFOFtoCNF_A_6)) )],[refute_0_114,refute_0_95]) ).
cnf(refute_0_116,plain,
apply(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))) = singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B_2(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6)) )],[refute_0_115,refute_0_101]) ).
cnf(refute_0_117,plain,
( singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))) != singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)))
| apply(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))) = singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))) ),
inference(resolve,[$cnf( $equal(apply(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))),singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)))) )],[refute_0_116,refute_0_66]) ).
cnf(refute_0_118,plain,
( relation_dom(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) != skolemFOFtoCNF_A_6
| singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))) != singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)))
| ~ function(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| ~ relation(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) ),
inference(resolve,[$cnf( $equal(apply(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6),skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))),singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)))) )],[refute_0_117,refute_0_1]) ).
cnf(refute_0_119,plain,
( relation_dom(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) != skolemFOFtoCNF_A_6
| ~ function(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| ~ relation(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))),singleton(skolemFOFtoCNF_C_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)))) )],[refute_0_69,refute_0_118]) ).
cnf(refute_0_120,plain,
( skolemFOFtoCNF_A_6 != skolemFOFtoCNF_A_6
| ~ function(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| ~ relation(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) ),
inference(resolve,[$cnf( $equal(relation_dom(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_A_6) )],[refute_0_103,refute_0_119]) ).
cnf(refute_0_121,plain,
( ~ function(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6))
| ~ relation(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_6,skolemFOFtoCNF_A_6) )],[refute_0_60,refute_0_120]) ).
cnf(refute_0_122,plain,
~ relation(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)),
inference(resolve,[$cnf( function(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) )],[refute_0_108,refute_0_121]) ).
cnf(refute_0_123,plain,
$false,
inference(resolve,[$cnf( relation(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_6)) )],[refute_0_112,refute_0_122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU284+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 20 02:42:00 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.38
% 0.12/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.18/0.40
%------------------------------------------------------------------------------