TSTP Solution File: SEU310+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU310+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 12:40:12 EDT 2022
% Result : Theorem 0.78s 0.95s
% Output : CNFRefutation 0.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 10
% Syntax : Number of formulae : 161 ( 22 unt; 1 def)
% Number of atoms : 539 ( 132 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 622 ( 244 ~; 303 |; 54 &)
% ( 15 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-3 aty)
% Number of variables : 223 ( 24 sgn 83 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(s1_xboole_0__e2_37_1_1__pre_topc__1,conjecture,
! [A,B] :
( ( topological_space(A)
& top_str(A)
& element(B,powerset(powerset(the_carrier(A)))) )
=> ? [C] :
! [D] :
( in(D,C)
<=> ( in(D,powerset(the_carrier(A)))
& in(set_difference(cast_as_carrier_subset(A),D),B) ) ) ) ).
fof(s1_tarski__e2_37_1_1__pre_topc__1,axiom,
! [A,B] :
( ( topological_space(A)
& top_str(A)
& element(B,powerset(powerset(the_carrier(A)))) )
=> ( ! [C,D,E] :
( ( C = D
& in(set_difference(cast_as_carrier_subset(A),D),B)
& C = E
& in(set_difference(cast_as_carrier_subset(A),E),B) )
=> D = E )
=> ? [C] :
! [D] :
( in(D,C)
<=> ? [E] :
( in(E,powerset(the_carrier(A)))
& E = D
& in(set_difference(cast_as_carrier_subset(A),D),B) ) ) ) ) ).
fof(definition_0,definition,
! [A,B,C,D] :
( definitionFOFtoCNF_0(A,B,C,D)
<=> ( ~ in(D,C)
<=> ! [E] :
( E != D
| ~ in(E,powerset(the_carrier(A)))
| ~ in(set_difference(cast_as_carrier_subset(A),D),B) ) ) ) ).
fof(subgoal_0,plain,
! [A,B] :
( ( topological_space(A)
& top_str(A)
& element(B,powerset(powerset(the_carrier(A)))) )
=> ? [C] :
! [D] :
( in(D,C)
<=> ( in(D,powerset(the_carrier(A)))
& in(set_difference(cast_as_carrier_subset(A),D),B) ) ) ),
inference(strip,[],[s1_xboole_0__e2_37_1_1__pre_topc__1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( ( topological_space(A)
& top_str(A)
& element(B,powerset(powerset(the_carrier(A)))) )
=> ? [C] :
! [D] :
( in(D,C)
<=> ( in(D,powerset(the_carrier(A)))
& in(set_difference(cast_as_carrier_subset(A),D),B) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B] :
( element(B,powerset(powerset(the_carrier(A))))
& top_str(A)
& topological_space(A)
& ! [C] :
? [D] :
( ~ in(D,C)
<=> ( in(D,powerset(the_carrier(A)))
& in(set_difference(cast_as_carrier_subset(A),D),B) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( element(skolemFOFtoCNF_B_3,powerset(powerset(the_carrier(skolemFOFtoCNF_A_1))))
& top_str(skolemFOFtoCNF_A_1)
& topological_space(skolemFOFtoCNF_A_1)
& ! [C] :
? [D] :
( ~ in(D,C)
<=> ( in(D,powerset(the_carrier(skolemFOFtoCNF_A_1)))
& in(set_difference(cast_as_carrier_subset(skolemFOFtoCNF_A_1),D),skolemFOFtoCNF_B_3) ) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [C] :
? [D] :
( ~ in(D,C)
<=> ( in(D,powerset(the_carrier(skolemFOFtoCNF_A_1)))
& in(set_difference(cast_as_carrier_subset(skolemFOFtoCNF_A_1),D),skolemFOFtoCNF_B_3) ) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [C] :
? [D] :
( ~ in(D,C)
<=> ( in(D,powerset(the_carrier(skolemFOFtoCNF_A_1)))
& in(set_difference(cast_as_carrier_subset(skolemFOFtoCNF_A_1),D),skolemFOFtoCNF_B_3) ) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [C] :
( ~ in(skolemFOFtoCNF_D_1(C),C)
<=> ( in(set_difference(cast_as_carrier_subset(skolemFOFtoCNF_A_1),skolemFOFtoCNF_D_1(C)),skolemFOFtoCNF_B_3)
& in(skolemFOFtoCNF_D_1(C),powerset(the_carrier(skolemFOFtoCNF_A_1))) ) ),
inference(skolemize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [C] :
( ( in(set_difference(cast_as_carrier_subset(skolemFOFtoCNF_A_1),skolemFOFtoCNF_D_1(C)),skolemFOFtoCNF_B_3)
| in(skolemFOFtoCNF_D_1(C),C) )
& ( in(skolemFOFtoCNF_D_1(C),C)
| in(skolemFOFtoCNF_D_1(C),powerset(the_carrier(skolemFOFtoCNF_A_1))) )
& ( ~ in(set_difference(cast_as_carrier_subset(skolemFOFtoCNF_A_1),skolemFOFtoCNF_D_1(C)),skolemFOFtoCNF_B_3)
| ~ in(skolemFOFtoCNF_D_1(C),C)
| ~ in(skolemFOFtoCNF_D_1(C),powerset(the_carrier(skolemFOFtoCNF_A_1))) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [C] :
( ~ in(set_difference(cast_as_carrier_subset(skolemFOFtoCNF_A_1),skolemFOFtoCNF_D_1(C)),skolemFOFtoCNF_B_3)
| ~ in(skolemFOFtoCNF_D_1(C),C)
| ~ in(skolemFOFtoCNF_D_1(C),powerset(the_carrier(skolemFOFtoCNF_A_1))) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,C,D] :
( ~ definitionFOFtoCNF_0(A,B,C,D)
<=> ( ~ in(D,C)
<=> ? [E] :
( E = D
& in(E,powerset(the_carrier(A)))
& in(set_difference(cast_as_carrier_subset(A),D),B) ) ) ),
inference(canonicalize,[],[definition_0]) ).
fof(normalize_0_8,plain,
! [A,B,C,D,E] :
( ( ~ definitionFOFtoCNF_0(A,B,C,D)
| ~ in(D,C)
| skolemFOFtoCNF_E(A,B,D) = D )
& ( ~ definitionFOFtoCNF_0(A,B,C,D)
| ~ in(D,C)
| in(set_difference(cast_as_carrier_subset(A),D),B) )
& ( ~ definitionFOFtoCNF_0(A,B,C,D)
| ~ in(D,C)
| in(skolemFOFtoCNF_E(A,B,D),powerset(the_carrier(A))) )
& ( skolemFOFtoCNF_E(A,B,D) = D
| definitionFOFtoCNF_0(A,B,C,D)
| in(D,C) )
& ( definitionFOFtoCNF_0(A,B,C,D)
| in(D,C)
| in(set_difference(cast_as_carrier_subset(A),D),B) )
& ( definitionFOFtoCNF_0(A,B,C,D)
| in(D,C)
| in(skolemFOFtoCNF_E(A,B,D),powerset(the_carrier(A))) )
& ( E != D
| ~ definitionFOFtoCNF_0(A,B,C,D)
| ~ in(E,powerset(the_carrier(A)))
| ~ in(set_difference(cast_as_carrier_subset(A),D),B)
| in(D,C) )
& ( E != D
| ~ in(D,C)
| ~ in(E,powerset(the_carrier(A)))
| ~ in(set_difference(cast_as_carrier_subset(A),D),B)
| definitionFOFtoCNF_0(A,B,C,D) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B,C,D] :
( ~ definitionFOFtoCNF_0(A,B,C,D)
| ~ in(D,C)
| in(set_difference(cast_as_carrier_subset(A),D),B) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
element(skolemFOFtoCNF_B_3,powerset(powerset(the_carrier(skolemFOFtoCNF_A_1)))),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_11,plain,
! [A,B] :
( ~ element(B,powerset(powerset(the_carrier(A))))
| ~ top_str(A)
| ~ topological_space(A)
| ? [C] :
! [D] :
( ~ in(D,C)
<=> ! [E] :
( E != D
| ~ in(E,powerset(the_carrier(A)))
| ~ in(set_difference(cast_as_carrier_subset(A),D),B) ) )
| ? [C,D,E] :
( D != E
& C = D
& C = E
& in(set_difference(cast_as_carrier_subset(A),D),B)
& in(set_difference(cast_as_carrier_subset(A),E),B) ) ),
inference(canonicalize,[],[s1_tarski__e2_37_1_1__pre_topc__1]) ).
fof(normalize_0_12,plain,
! [A,B] :
( ~ element(B,powerset(powerset(the_carrier(A))))
| ~ top_str(A)
| ~ topological_space(A)
| ? [C] :
! [D] :
( ~ in(D,C)
<=> ! [E] :
( E != D
| ~ in(E,powerset(the_carrier(A)))
| ~ in(set_difference(cast_as_carrier_subset(A),D),B) ) )
| ? [C,D,E] :
( D != E
& C = D
& C = E
& in(set_difference(cast_as_carrier_subset(A),D),B)
& in(set_difference(cast_as_carrier_subset(A),E),B) ) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A,B] :
( ~ element(B,powerset(powerset(the_carrier(A))))
| ~ top_str(A)
| ~ topological_space(A)
| ? [C] :
! [D] : definitionFOFtoCNF_0(A,B,C,D)
| ? [C,D,E] :
( D != E
& C = D
& C = E
& in(set_difference(cast_as_carrier_subset(A),D),B)
& in(set_difference(cast_as_carrier_subset(A),E),B) ) ),
inference(simplify,[],[normalize_0_12,normalize_0_7]) ).
fof(normalize_0_14,plain,
! [A,B,D] :
( ( skolemFOFtoCNF_D(A,B) != skolemFOFtoCNF_E_1(A,B)
| ~ element(B,powerset(powerset(the_carrier(A))))
| ~ top_str(A)
| ~ topological_space(A)
| definitionFOFtoCNF_0(A,B,skolemFOFtoCNF_C(A,B),D) )
& ( ~ element(B,powerset(powerset(the_carrier(A))))
| ~ top_str(A)
| ~ topological_space(A)
| skolemFOFtoCNF_C_1(A,B) = skolemFOFtoCNF_D(A,B)
| definitionFOFtoCNF_0(A,B,skolemFOFtoCNF_C(A,B),D) )
& ( ~ element(B,powerset(powerset(the_carrier(A))))
| ~ top_str(A)
| ~ topological_space(A)
| skolemFOFtoCNF_C_1(A,B) = skolemFOFtoCNF_E_1(A,B)
| definitionFOFtoCNF_0(A,B,skolemFOFtoCNF_C(A,B),D) )
& ( ~ element(B,powerset(powerset(the_carrier(A))))
| ~ top_str(A)
| ~ topological_space(A)
| definitionFOFtoCNF_0(A,B,skolemFOFtoCNF_C(A,B),D)
| in(set_difference(cast_as_carrier_subset(A),skolemFOFtoCNF_D(A,B)),B) )
& ( ~ element(B,powerset(powerset(the_carrier(A))))
| ~ top_str(A)
| ~ topological_space(A)
| definitionFOFtoCNF_0(A,B,skolemFOFtoCNF_C(A,B),D)
| in(set_difference(cast_as_carrier_subset(A),skolemFOFtoCNF_E_1(A,B)),B) ) ),
inference(clausify,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [A,B,D] :
( skolemFOFtoCNF_D(A,B) != skolemFOFtoCNF_E_1(A,B)
| ~ element(B,powerset(powerset(the_carrier(A))))
| ~ top_str(A)
| ~ topological_space(A)
| definitionFOFtoCNF_0(A,B,skolemFOFtoCNF_C(A,B),D) ),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
top_str(skolemFOFtoCNF_A_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_17,plain,
topological_space(skolemFOFtoCNF_A_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_18,plain,
! [C] :
( in(skolemFOFtoCNF_D_1(C),C)
| in(skolemFOFtoCNF_D_1(C),powerset(the_carrier(skolemFOFtoCNF_A_1))) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_19,plain,
! [A,B,C,D] :
( ~ definitionFOFtoCNF_0(A,B,C,D)
| ~ in(D,C)
| in(skolemFOFtoCNF_E(A,B,D),powerset(the_carrier(A))) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_20,plain,
! [A,B,D] :
( ~ element(B,powerset(powerset(the_carrier(A))))
| ~ top_str(A)
| ~ topological_space(A)
| skolemFOFtoCNF_C_1(A,B) = skolemFOFtoCNF_D(A,B)
| definitionFOFtoCNF_0(A,B,skolemFOFtoCNF_C(A,B),D) ),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_21,plain,
! [A,B,C,D] :
( ~ definitionFOFtoCNF_0(A,B,C,D)
| ~ in(D,C)
| skolemFOFtoCNF_E(A,B,D) = D ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_22,plain,
! [C] :
( in(set_difference(cast_as_carrier_subset(skolemFOFtoCNF_A_1),skolemFOFtoCNF_D_1(C)),skolemFOFtoCNF_B_3)
| in(skolemFOFtoCNF_D_1(C),C) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_23,plain,
! [A,B,C,D,E] :
( E != D
| ~ in(D,C)
| ~ in(E,powerset(the_carrier(A)))
| ~ in(set_difference(cast_as_carrier_subset(A),D),B)
| definitionFOFtoCNF_0(A,B,C,D) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_24,plain,
! [A,B,C,D,E] :
( E != D
| ~ definitionFOFtoCNF_0(A,B,C,D)
| ~ in(E,powerset(the_carrier(A)))
| ~ in(set_difference(cast_as_carrier_subset(A),D),B)
| in(D,C) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_25,plain,
! [A,B,D] :
( ~ element(B,powerset(powerset(the_carrier(A))))
| ~ top_str(A)
| ~ topological_space(A)
| skolemFOFtoCNF_C_1(A,B) = skolemFOFtoCNF_E_1(A,B)
| definitionFOFtoCNF_0(A,B,skolemFOFtoCNF_C(A,B),D) ),
inference(conjunct,[],[normalize_0_14]) ).
cnf(refute_0_0,plain,
( ~ in(set_difference(cast_as_carrier_subset(skolemFOFtoCNF_A_1),skolemFOFtoCNF_D_1(C)),skolemFOFtoCNF_B_3)
| ~ in(skolemFOFtoCNF_D_1(C),C)
| ~ in(skolemFOFtoCNF_D_1(C),powerset(the_carrier(skolemFOFtoCNF_A_1))) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_1,plain,
( ~ in(set_difference(cast_as_carrier_subset(skolemFOFtoCNF_A_1),skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),skolemFOFtoCNF_B_3)
| ~ in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),powerset(the_carrier(skolemFOFtoCNF_A_1)))
| ~ in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) ),
inference(subst,[],[refute_0_0:[bind(C,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)))]]) ).
cnf(refute_0_2,plain,
( ~ definitionFOFtoCNF_0(A,B,C,D)
| ~ in(D,C)
| in(set_difference(cast_as_carrier_subset(A),D),B) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_3,plain,
( ~ definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1504)
| ~ in(X_1504,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))
| in(set_difference(cast_as_carrier_subset(skolemFOFtoCNF_A_1),X_1504),skolemFOFtoCNF_B_3) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_A_1)),bind(B,$fot(skolemFOFtoCNF_B_3)),bind(C,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),bind(D,$fot(X_1504))]]) ).
cnf(refute_0_4,plain,
element(skolemFOFtoCNF_B_3,powerset(powerset(the_carrier(skolemFOFtoCNF_A_1)))),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_5,plain,
( skolemFOFtoCNF_D(A,B) != skolemFOFtoCNF_E_1(A,B)
| ~ element(B,powerset(powerset(the_carrier(A))))
| ~ top_str(A)
| ~ topological_space(A)
| definitionFOFtoCNF_0(A,B,skolemFOFtoCNF_C(A,B),D) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_6,plain,
( skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) != skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| ~ element(skolemFOFtoCNF_B_3,powerset(powerset(the_carrier(skolemFOFtoCNF_A_1))))
| ~ top_str(skolemFOFtoCNF_A_1)
| ~ topological_space(skolemFOFtoCNF_A_1)
| definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1465) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(skolemFOFtoCNF_A_1)),bind(B,$fot(skolemFOFtoCNF_B_3)),bind(D,$fot(X_1465))]]) ).
cnf(refute_0_7,plain,
( skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) != skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| ~ top_str(skolemFOFtoCNF_A_1)
| ~ topological_space(skolemFOFtoCNF_A_1)
| definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1465) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B_3,powerset(powerset(the_carrier(skolemFOFtoCNF_A_1)))) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
top_str(skolemFOFtoCNF_A_1),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_9,plain,
( skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) != skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| ~ topological_space(skolemFOFtoCNF_A_1)
| definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1465) ),
inference(resolve,[$cnf( top_str(skolemFOFtoCNF_A_1) )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
topological_space(skolemFOFtoCNF_A_1),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_11,plain,
( skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) != skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1465) ),
inference(resolve,[$cnf( topological_space(skolemFOFtoCNF_A_1) )],[refute_0_10,refute_0_9]) ).
cnf(refute_0_12,plain,
( in(skolemFOFtoCNF_D_1(C),C)
| in(skolemFOFtoCNF_D_1(C),powerset(the_carrier(skolemFOFtoCNF_A_1))) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_13,plain,
( in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),powerset(the_carrier(skolemFOFtoCNF_A_1)))
| in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) ),
inference(subst,[],[refute_0_12:[bind(C,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)))]]) ).
cnf(refute_0_14,plain,
( ~ definitionFOFtoCNF_0(A,B,C,D)
| ~ in(D,C)
| in(skolemFOFtoCNF_E(A,B,D),powerset(the_carrier(A))) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_15,plain,
( ~ definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1474)
| ~ in(X_1474,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))
| in(skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,X_1474),powerset(the_carrier(skolemFOFtoCNF_A_1))) ),
inference(subst,[],[refute_0_14:[bind(A,$fot(skolemFOFtoCNF_A_1)),bind(B,$fot(skolemFOFtoCNF_B_3)),bind(C,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),bind(D,$fot(X_1474))]]) ).
cnf(refute_0_16,plain,
( ~ element(B,powerset(powerset(the_carrier(A))))
| ~ top_str(A)
| ~ topological_space(A)
| skolemFOFtoCNF_C_1(A,B) = skolemFOFtoCNF_D(A,B)
| definitionFOFtoCNF_0(A,B,skolemFOFtoCNF_C(A,B),D) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_17,plain,
( ~ element(skolemFOFtoCNF_B_3,powerset(powerset(the_carrier(skolemFOFtoCNF_A_1))))
| ~ top_str(skolemFOFtoCNF_A_1)
| ~ topological_space(skolemFOFtoCNF_A_1)
| skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1473) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_A_1)),bind(B,$fot(skolemFOFtoCNF_B_3)),bind(D,$fot(X_1473))]]) ).
cnf(refute_0_18,plain,
( ~ top_str(skolemFOFtoCNF_A_1)
| ~ topological_space(skolemFOFtoCNF_A_1)
| skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1473) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B_3,powerset(powerset(the_carrier(skolemFOFtoCNF_A_1)))) )],[refute_0_4,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ topological_space(skolemFOFtoCNF_A_1)
| skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1473) ),
inference(resolve,[$cnf( top_str(skolemFOFtoCNF_A_1) )],[refute_0_8,refute_0_18]) ).
cnf(refute_0_20,plain,
( skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1473) ),
inference(resolve,[$cnf( topological_space(skolemFOFtoCNF_A_1) )],[refute_0_10,refute_0_19]) ).
cnf(refute_0_21,plain,
( skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1474) ),
inference(subst,[],[refute_0_20:[bind(X_1473,$fot(X_1474))]]) ).
cnf(refute_0_22,plain,
( ~ in(X_1474,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))
| skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| in(skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,X_1474),powerset(the_carrier(skolemFOFtoCNF_A_1))) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1474) )],[refute_0_21,refute_0_15]) ).
cnf(refute_0_23,plain,
( ~ in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))
| skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| in(skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),powerset(the_carrier(skolemFOFtoCNF_A_1))) ),
inference(subst,[],[refute_0_22:[bind(X_1474,$fot(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))))]]) ).
cnf(refute_0_24,plain,
( skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),powerset(the_carrier(skolemFOFtoCNF_A_1)))
| in(skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),powerset(the_carrier(skolemFOFtoCNF_A_1))) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) )],[refute_0_13,refute_0_23]) ).
cnf(refute_0_25,plain,
( in(skolemFOFtoCNF_D_1(X_1159),X_1159)
| in(skolemFOFtoCNF_D_1(X_1159),powerset(the_carrier(skolemFOFtoCNF_A_1))) ),
inference(subst,[],[refute_0_12:[bind(C,$fot(X_1159))]]) ).
cnf(refute_0_26,plain,
( ~ definitionFOFtoCNF_0(A,B,C,D)
| ~ in(D,C)
| skolemFOFtoCNF_E(A,B,D) = D ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_27,plain,
( ~ definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,powerset(the_carrier(skolemFOFtoCNF_A_1)),skolemFOFtoCNF_D_1(X_1157))
| ~ in(skolemFOFtoCNF_D_1(X_1157),powerset(the_carrier(skolemFOFtoCNF_A_1)))
| skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(X_1157)) = skolemFOFtoCNF_D_1(X_1157) ),
inference(subst,[],[refute_0_26:[bind(A,$fot(skolemFOFtoCNF_A_1)),bind(B,$fot(skolemFOFtoCNF_B_3)),bind(C,$fot(powerset(the_carrier(skolemFOFtoCNF_A_1)))),bind(D,$fot(skolemFOFtoCNF_D_1(X_1157)))]]) ).
cnf(refute_0_28,plain,
( in(skolemFOFtoCNF_D_1(X_1156),X_1156)
| in(skolemFOFtoCNF_D_1(X_1156),powerset(the_carrier(skolemFOFtoCNF_A_1))) ),
inference(subst,[],[refute_0_12:[bind(C,$fot(X_1156))]]) ).
cnf(refute_0_29,plain,
( in(set_difference(cast_as_carrier_subset(skolemFOFtoCNF_A_1),skolemFOFtoCNF_D_1(C)),skolemFOFtoCNF_B_3)
| in(skolemFOFtoCNF_D_1(C),C) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_30,plain,
( E != D
| ~ in(D,C)
| ~ in(E,powerset(the_carrier(A)))
| ~ in(set_difference(cast_as_carrier_subset(A),D),B)
| definitionFOFtoCNF_0(A,B,C,D) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_31,plain,
( D != D
| ~ in(D,C)
| ~ in(D,powerset(the_carrier(A)))
| ~ in(set_difference(cast_as_carrier_subset(A),D),B)
| definitionFOFtoCNF_0(A,B,C,D) ),
inference(subst,[],[refute_0_30:[bind(E,$fot(D))]]) ).
cnf(refute_0_32,plain,
D = D,
introduced(tautology,[refl,[$fot(D)]]) ).
cnf(refute_0_33,plain,
( ~ in(D,C)
| ~ in(D,powerset(the_carrier(A)))
| ~ in(set_difference(cast_as_carrier_subset(A),D),B)
| definitionFOFtoCNF_0(A,B,C,D) ),
inference(resolve,[$cnf( $equal(D,D) )],[refute_0_32,refute_0_31]) ).
cnf(refute_0_34,plain,
( ~ in(set_difference(cast_as_carrier_subset(skolemFOFtoCNF_A_1),skolemFOFtoCNF_D_1(C)),skolemFOFtoCNF_B_3)
| ~ in(skolemFOFtoCNF_D_1(C),X_1154)
| ~ in(skolemFOFtoCNF_D_1(C),powerset(the_carrier(skolemFOFtoCNF_A_1)))
| definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,X_1154,skolemFOFtoCNF_D_1(C)) ),
inference(subst,[],[refute_0_33:[bind(A,$fot(skolemFOFtoCNF_A_1)),bind(B,$fot(skolemFOFtoCNF_B_3)),bind(C,$fot(X_1154)),bind(D,$fot(skolemFOFtoCNF_D_1(C)))]]) ).
cnf(refute_0_35,plain,
( ~ in(skolemFOFtoCNF_D_1(C),X_1154)
| ~ in(skolemFOFtoCNF_D_1(C),powerset(the_carrier(skolemFOFtoCNF_A_1)))
| definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,X_1154,skolemFOFtoCNF_D_1(C))
| in(skolemFOFtoCNF_D_1(C),C) ),
inference(resolve,[$cnf( in(set_difference(cast_as_carrier_subset(skolemFOFtoCNF_A_1),skolemFOFtoCNF_D_1(C)),skolemFOFtoCNF_B_3) )],[refute_0_29,refute_0_34]) ).
cnf(refute_0_36,plain,
( ~ in(skolemFOFtoCNF_D_1(X_1156),powerset(the_carrier(skolemFOFtoCNF_A_1)))
| definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,powerset(the_carrier(skolemFOFtoCNF_A_1)),skolemFOFtoCNF_D_1(X_1156))
| in(skolemFOFtoCNF_D_1(X_1156),X_1156) ),
inference(subst,[],[refute_0_35:[bind(C,$fot(X_1156)),bind(X_1154,$fot(powerset(the_carrier(skolemFOFtoCNF_A_1))))]]) ).
cnf(refute_0_37,plain,
( definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,powerset(the_carrier(skolemFOFtoCNF_A_1)),skolemFOFtoCNF_D_1(X_1156))
| in(skolemFOFtoCNF_D_1(X_1156),X_1156) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D_1(X_1156),powerset(the_carrier(skolemFOFtoCNF_A_1))) )],[refute_0_28,refute_0_36]) ).
cnf(refute_0_38,plain,
( definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,powerset(the_carrier(skolemFOFtoCNF_A_1)),skolemFOFtoCNF_D_1(X_1157))
| in(skolemFOFtoCNF_D_1(X_1157),X_1157) ),
inference(subst,[],[refute_0_37:[bind(X_1156,$fot(X_1157))]]) ).
cnf(refute_0_39,plain,
( ~ in(skolemFOFtoCNF_D_1(X_1157),powerset(the_carrier(skolemFOFtoCNF_A_1)))
| skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(X_1157)) = skolemFOFtoCNF_D_1(X_1157)
| in(skolemFOFtoCNF_D_1(X_1157),X_1157) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,powerset(the_carrier(skolemFOFtoCNF_A_1)),skolemFOFtoCNF_D_1(X_1157)) )],[refute_0_38,refute_0_27]) ).
cnf(refute_0_40,plain,
( ~ in(skolemFOFtoCNF_D_1(X_1159),powerset(the_carrier(skolemFOFtoCNF_A_1)))
| skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(X_1159)) = skolemFOFtoCNF_D_1(X_1159)
| in(skolemFOFtoCNF_D_1(X_1159),X_1159) ),
inference(subst,[],[refute_0_39:[bind(X_1157,$fot(X_1159))]]) ).
cnf(refute_0_41,plain,
( skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(X_1159)) = skolemFOFtoCNF_D_1(X_1159)
| in(skolemFOFtoCNF_D_1(X_1159),X_1159) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D_1(X_1159),powerset(the_carrier(skolemFOFtoCNF_A_1))) )],[refute_0_25,refute_0_40]) ).
cnf(refute_0_42,plain,
( skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))) = skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))
| in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) ),
inference(subst,[],[refute_0_41:[bind(X_1159,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)))]]) ).
cnf(refute_0_43,plain,
( ~ definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1474)
| ~ in(X_1474,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))
| skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,X_1474) = X_1474 ),
inference(subst,[],[refute_0_26:[bind(A,$fot(skolemFOFtoCNF_A_1)),bind(B,$fot(skolemFOFtoCNF_B_3)),bind(C,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),bind(D,$fot(X_1474))]]) ).
cnf(refute_0_44,plain,
( ~ in(X_1474,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))
| skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,X_1474) = X_1474 ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1474) )],[refute_0_21,refute_0_43]) ).
cnf(refute_0_45,plain,
( ~ in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))
| skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))) = skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) ),
inference(subst,[],[refute_0_44:[bind(X_1474,$fot(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))))]]) ).
cnf(refute_0_46,plain,
( skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))) = skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) )],[refute_0_42,refute_0_45]) ).
cnf(refute_0_47,plain,
( skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))) != skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))
| ~ in(skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),powerset(the_carrier(skolemFOFtoCNF_A_1)))
| in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),powerset(the_carrier(skolemFOFtoCNF_A_1))) ),
introduced(tautology,[equality,[$cnf( in(skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),powerset(the_carrier(skolemFOFtoCNF_A_1))) ),[0],$fot(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)))]]) ).
cnf(refute_0_48,plain,
( ~ in(skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),powerset(the_carrier(skolemFOFtoCNF_A_1)))
| skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),powerset(the_carrier(skolemFOFtoCNF_A_1))) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),powerset(the_carrier(skolemFOFtoCNF_A_1))) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),powerset(the_carrier(skolemFOFtoCNF_A_1))) )],[refute_0_24,refute_0_48]) ).
cnf(refute_0_50,plain,
( E != D
| ~ definitionFOFtoCNF_0(A,B,C,D)
| ~ in(E,powerset(the_carrier(A)))
| ~ in(set_difference(cast_as_carrier_subset(A),D),B)
| in(D,C) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_51,plain,
( D != D
| ~ definitionFOFtoCNF_0(A,B,C,D)
| ~ in(D,powerset(the_carrier(A)))
| ~ in(set_difference(cast_as_carrier_subset(A),D),B)
| in(D,C) ),
inference(subst,[],[refute_0_50:[bind(E,$fot(D))]]) ).
cnf(refute_0_52,plain,
( ~ definitionFOFtoCNF_0(A,B,C,D)
| ~ in(D,powerset(the_carrier(A)))
| ~ in(set_difference(cast_as_carrier_subset(A),D),B)
| in(D,C) ),
inference(resolve,[$cnf( $equal(D,D) )],[refute_0_32,refute_0_51]) ).
cnf(refute_0_53,plain,
( ~ definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,X_1147,skolemFOFtoCNF_D_1(C))
| ~ in(set_difference(cast_as_carrier_subset(skolemFOFtoCNF_A_1),skolemFOFtoCNF_D_1(C)),skolemFOFtoCNF_B_3)
| ~ in(skolemFOFtoCNF_D_1(C),powerset(the_carrier(skolemFOFtoCNF_A_1)))
| in(skolemFOFtoCNF_D_1(C),X_1147) ),
inference(subst,[],[refute_0_52:[bind(A,$fot(skolemFOFtoCNF_A_1)),bind(B,$fot(skolemFOFtoCNF_B_3)),bind(C,$fot(X_1147)),bind(D,$fot(skolemFOFtoCNF_D_1(C)))]]) ).
cnf(refute_0_54,plain,
( ~ definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,X_1147,skolemFOFtoCNF_D_1(C))
| ~ in(skolemFOFtoCNF_D_1(C),powerset(the_carrier(skolemFOFtoCNF_A_1)))
| in(skolemFOFtoCNF_D_1(C),C)
| in(skolemFOFtoCNF_D_1(C),X_1147) ),
inference(resolve,[$cnf( in(set_difference(cast_as_carrier_subset(skolemFOFtoCNF_A_1),skolemFOFtoCNF_D_1(C)),skolemFOFtoCNF_B_3) )],[refute_0_29,refute_0_53]) ).
cnf(refute_0_55,plain,
( ~ definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),skolemFOFtoCNF_D_1(C))
| ~ in(skolemFOFtoCNF_D_1(C),powerset(the_carrier(skolemFOFtoCNF_A_1)))
| in(skolemFOFtoCNF_D_1(C),C)
| in(skolemFOFtoCNF_D_1(C),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) ),
inference(subst,[],[refute_0_54:[bind(X_1147,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)))]]) ).
cnf(refute_0_56,plain,
( skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),skolemFOFtoCNF_D_1(C)) ),
inference(subst,[],[refute_0_20:[bind(X_1473,$fot(skolemFOFtoCNF_D_1(C)))]]) ).
cnf(refute_0_57,plain,
( ~ in(skolemFOFtoCNF_D_1(C),powerset(the_carrier(skolemFOFtoCNF_A_1)))
| skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| in(skolemFOFtoCNF_D_1(C),C)
| in(skolemFOFtoCNF_D_1(C),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),skolemFOFtoCNF_D_1(C)) )],[refute_0_56,refute_0_55]) ).
cnf(refute_0_58,plain,
( ~ in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),powerset(the_carrier(skolemFOFtoCNF_A_1)))
| skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) ),
inference(subst,[],[refute_0_57:[bind(C,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)))]]) ).
cnf(refute_0_59,plain,
( skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),powerset(the_carrier(skolemFOFtoCNF_A_1))) )],[refute_0_49,refute_0_58]) ).
cnf(refute_0_60,plain,
( ~ definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1474)
| ~ in(X_1474,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))
| in(set_difference(cast_as_carrier_subset(skolemFOFtoCNF_A_1),X_1474),skolemFOFtoCNF_B_3) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_A_1)),bind(B,$fot(skolemFOFtoCNF_B_3)),bind(C,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),bind(D,$fot(X_1474))]]) ).
cnf(refute_0_61,plain,
( ~ in(X_1474,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))
| skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| in(set_difference(cast_as_carrier_subset(skolemFOFtoCNF_A_1),X_1474),skolemFOFtoCNF_B_3) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1474) )],[refute_0_21,refute_0_60]) ).
cnf(refute_0_62,plain,
( ~ in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))
| skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| in(set_difference(cast_as_carrier_subset(skolemFOFtoCNF_A_1),skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),skolemFOFtoCNF_B_3) ),
inference(subst,[],[refute_0_61:[bind(X_1474,$fot(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))))]]) ).
cnf(refute_0_63,plain,
( skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| in(set_difference(cast_as_carrier_subset(skolemFOFtoCNF_A_1),skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),skolemFOFtoCNF_B_3) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
( ~ in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),powerset(the_carrier(skolemFOFtoCNF_A_1)))
| ~ in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))
| skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) ),
inference(resolve,[$cnf( in(set_difference(cast_as_carrier_subset(skolemFOFtoCNF_A_1),skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),skolemFOFtoCNF_B_3) )],[refute_0_63,refute_0_1]) ).
cnf(refute_0_65,plain,
( ~ in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),powerset(the_carrier(skolemFOFtoCNF_A_1)))
| skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) )],[refute_0_59,refute_0_64]) ).
cnf(refute_0_66,plain,
skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),powerset(the_carrier(skolemFOFtoCNF_A_1))) )],[refute_0_49,refute_0_65]) ).
cnf(refute_0_67,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_68,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_69,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
( skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) != skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) ),
inference(subst,[],[refute_0_69:[bind(X,$fot(skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),bind(Y,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)))]]) ).
cnf(refute_0_71,plain,
skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) )],[refute_0_66,refute_0_70]) ).
cnf(refute_0_72,plain,
( skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) != skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) != skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) ),[1],$fot(skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))]]) ).
cnf(refute_0_73,plain,
( skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) != skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
( skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) != skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1465) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_D(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) )],[refute_0_73,refute_0_11]) ).
cnf(refute_0_75,plain,
( ~ definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1498)
| ~ in(X_1498,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))
| in(skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,X_1498),powerset(the_carrier(skolemFOFtoCNF_A_1))) ),
inference(subst,[],[refute_0_14:[bind(A,$fot(skolemFOFtoCNF_A_1)),bind(B,$fot(skolemFOFtoCNF_B_3)),bind(C,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),bind(D,$fot(X_1498))]]) ).
cnf(refute_0_76,plain,
( ~ element(B,powerset(powerset(the_carrier(A))))
| ~ top_str(A)
| ~ topological_space(A)
| skolemFOFtoCNF_C_1(A,B) = skolemFOFtoCNF_E_1(A,B)
| definitionFOFtoCNF_0(A,B,skolemFOFtoCNF_C(A,B),D) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_77,plain,
( ~ element(skolemFOFtoCNF_B_3,powerset(powerset(the_carrier(skolemFOFtoCNF_A_1))))
| ~ top_str(skolemFOFtoCNF_A_1)
| ~ topological_space(skolemFOFtoCNF_A_1)
| skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1497) ),
inference(subst,[],[refute_0_76:[bind(A,$fot(skolemFOFtoCNF_A_1)),bind(B,$fot(skolemFOFtoCNF_B_3)),bind(D,$fot(X_1497))]]) ).
cnf(refute_0_78,plain,
( ~ top_str(skolemFOFtoCNF_A_1)
| ~ topological_space(skolemFOFtoCNF_A_1)
| skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1497) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B_3,powerset(powerset(the_carrier(skolemFOFtoCNF_A_1)))) )],[refute_0_4,refute_0_77]) ).
cnf(refute_0_79,plain,
( ~ topological_space(skolemFOFtoCNF_A_1)
| skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1497) ),
inference(resolve,[$cnf( top_str(skolemFOFtoCNF_A_1) )],[refute_0_8,refute_0_78]) ).
cnf(refute_0_80,plain,
( skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1497) ),
inference(resolve,[$cnf( topological_space(skolemFOFtoCNF_A_1) )],[refute_0_10,refute_0_79]) ).
cnf(refute_0_81,plain,
( skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1498) ),
inference(subst,[],[refute_0_80:[bind(X_1497,$fot(X_1498))]]) ).
cnf(refute_0_82,plain,
( ~ in(X_1498,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))
| skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| in(skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,X_1498),powerset(the_carrier(skolemFOFtoCNF_A_1))) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1498) )],[refute_0_81,refute_0_75]) ).
cnf(refute_0_83,plain,
( ~ in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))
| skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| in(skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),powerset(the_carrier(skolemFOFtoCNF_A_1))) ),
inference(subst,[],[refute_0_82:[bind(X_1498,$fot(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))))]]) ).
cnf(refute_0_84,plain,
( skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),powerset(the_carrier(skolemFOFtoCNF_A_1)))
| in(skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),powerset(the_carrier(skolemFOFtoCNF_A_1))) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) )],[refute_0_13,refute_0_83]) ).
cnf(refute_0_85,plain,
( ~ definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1498)
| ~ in(X_1498,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))
| skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,X_1498) = X_1498 ),
inference(subst,[],[refute_0_26:[bind(A,$fot(skolemFOFtoCNF_A_1)),bind(B,$fot(skolemFOFtoCNF_B_3)),bind(C,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),bind(D,$fot(X_1498))]]) ).
cnf(refute_0_86,plain,
( ~ in(X_1498,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))
| skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,X_1498) = X_1498 ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1498) )],[refute_0_81,refute_0_85]) ).
cnf(refute_0_87,plain,
( ~ in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))
| skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))) = skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) ),
inference(subst,[],[refute_0_86:[bind(X_1498,$fot(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))))]]) ).
cnf(refute_0_88,plain,
( skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))) = skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) )],[refute_0_42,refute_0_87]) ).
cnf(refute_0_89,plain,
( ~ in(skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),powerset(the_carrier(skolemFOFtoCNF_A_1)))
| skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),powerset(the_carrier(skolemFOFtoCNF_A_1))) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))) )],[refute_0_88,refute_0_47]) ).
cnf(refute_0_90,plain,
( skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),powerset(the_carrier(skolemFOFtoCNF_A_1))) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),powerset(the_carrier(skolemFOFtoCNF_A_1))) )],[refute_0_84,refute_0_89]) ).
cnf(refute_0_91,plain,
( skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),skolemFOFtoCNF_D_1(C)) ),
inference(subst,[],[refute_0_80:[bind(X_1497,$fot(skolemFOFtoCNF_D_1(C)))]]) ).
cnf(refute_0_92,plain,
( ~ in(skolemFOFtoCNF_D_1(C),powerset(the_carrier(skolemFOFtoCNF_A_1)))
| skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| in(skolemFOFtoCNF_D_1(C),C)
| in(skolemFOFtoCNF_D_1(C),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),skolemFOFtoCNF_D_1(C)) )],[refute_0_91,refute_0_55]) ).
cnf(refute_0_93,plain,
( ~ in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),powerset(the_carrier(skolemFOFtoCNF_A_1)))
| skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) ),
inference(subst,[],[refute_0_92:[bind(C,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)))]]) ).
cnf(refute_0_94,plain,
( skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),powerset(the_carrier(skolemFOFtoCNF_A_1))) )],[refute_0_90,refute_0_93]) ).
cnf(refute_0_95,plain,
( ~ definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1498)
| ~ in(X_1498,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))
| in(set_difference(cast_as_carrier_subset(skolemFOFtoCNF_A_1),X_1498),skolemFOFtoCNF_B_3) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_A_1)),bind(B,$fot(skolemFOFtoCNF_B_3)),bind(C,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),bind(D,$fot(X_1498))]]) ).
cnf(refute_0_96,plain,
( ~ in(X_1498,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))
| skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| in(set_difference(cast_as_carrier_subset(skolemFOFtoCNF_A_1),X_1498),skolemFOFtoCNF_B_3) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1498) )],[refute_0_81,refute_0_95]) ).
cnf(refute_0_97,plain,
( ~ in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))
| skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| in(set_difference(cast_as_carrier_subset(skolemFOFtoCNF_A_1),skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),skolemFOFtoCNF_B_3) ),
inference(subst,[],[refute_0_96:[bind(X_1498,$fot(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))))]]) ).
cnf(refute_0_98,plain,
( skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| in(set_difference(cast_as_carrier_subset(skolemFOFtoCNF_A_1),skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),skolemFOFtoCNF_B_3) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) )],[refute_0_94,refute_0_97]) ).
cnf(refute_0_99,plain,
( ~ in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),powerset(the_carrier(skolemFOFtoCNF_A_1)))
| ~ in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))
| skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) ),
inference(resolve,[$cnf( in(set_difference(cast_as_carrier_subset(skolemFOFtoCNF_A_1),skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),skolemFOFtoCNF_B_3) )],[refute_0_98,refute_0_1]) ).
cnf(refute_0_100,plain,
( ~ in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),powerset(the_carrier(skolemFOFtoCNF_A_1)))
| skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) )],[refute_0_94,refute_0_99]) ).
cnf(refute_0_101,plain,
skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),powerset(the_carrier(skolemFOFtoCNF_A_1))) )],[refute_0_90,refute_0_100]) ).
cnf(refute_0_102,plain,
( skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) != skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) ),
inference(subst,[],[refute_0_69:[bind(X,$fot(skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),bind(Y,$fot(skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)))]]) ).
cnf(refute_0_103,plain,
skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
( skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) != skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) != skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) ),[1],$fot(skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))]]) ).
cnf(refute_0_105,plain,
( skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) != skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
( skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) != skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)
| definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1465) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),skolemFOFtoCNF_E_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) )],[refute_0_105,refute_0_74]) ).
cnf(refute_0_107,plain,
skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))]]) ).
cnf(refute_0_108,plain,
definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1465),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),skolemFOFtoCNF_C_1(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) )],[refute_0_107,refute_0_106]) ).
cnf(refute_0_109,plain,
definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1504),
inference(subst,[],[refute_0_108:[bind(X_1465,$fot(X_1504))]]) ).
cnf(refute_0_110,plain,
( ~ in(X_1504,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))
| in(set_difference(cast_as_carrier_subset(skolemFOFtoCNF_A_1),X_1504),skolemFOFtoCNF_B_3) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1504) )],[refute_0_109,refute_0_3]) ).
cnf(refute_0_111,plain,
( ~ in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))
| in(set_difference(cast_as_carrier_subset(skolemFOFtoCNF_A_1),skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),skolemFOFtoCNF_B_3) ),
inference(subst,[],[refute_0_110:[bind(X_1504,$fot(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))))]]) ).
cnf(refute_0_112,plain,
( ~ definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1504)
| ~ in(X_1504,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))
| in(skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,X_1504),powerset(the_carrier(skolemFOFtoCNF_A_1))) ),
inference(subst,[],[refute_0_14:[bind(A,$fot(skolemFOFtoCNF_A_1)),bind(B,$fot(skolemFOFtoCNF_B_3)),bind(C,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),bind(D,$fot(X_1504))]]) ).
cnf(refute_0_113,plain,
( ~ in(X_1504,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))
| in(skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,X_1504),powerset(the_carrier(skolemFOFtoCNF_A_1))) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1504) )],[refute_0_109,refute_0_112]) ).
cnf(refute_0_114,plain,
( ~ in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))
| in(skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),powerset(the_carrier(skolemFOFtoCNF_A_1))) ),
inference(subst,[],[refute_0_113:[bind(X_1504,$fot(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))))]]) ).
cnf(refute_0_115,plain,
( in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),powerset(the_carrier(skolemFOFtoCNF_A_1)))
| in(skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),powerset(the_carrier(skolemFOFtoCNF_A_1))) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) )],[refute_0_13,refute_0_114]) ).
cnf(refute_0_116,plain,
( ~ definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1504)
| ~ in(X_1504,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))
| skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,X_1504) = X_1504 ),
inference(subst,[],[refute_0_26:[bind(A,$fot(skolemFOFtoCNF_A_1)),bind(B,$fot(skolemFOFtoCNF_B_3)),bind(C,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),bind(D,$fot(X_1504))]]) ).
cnf(refute_0_117,plain,
( ~ in(X_1504,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))
| skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,X_1504) = X_1504 ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),X_1504) )],[refute_0_109,refute_0_116]) ).
cnf(refute_0_118,plain,
( ~ in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))
| skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))) = skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) ),
inference(subst,[],[refute_0_117:[bind(X_1504,$fot(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))))]]) ).
cnf(refute_0_119,plain,
skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))) = skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) )],[refute_0_42,refute_0_118]) ).
cnf(refute_0_120,plain,
( ~ in(skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),powerset(the_carrier(skolemFOFtoCNF_A_1)))
| in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),powerset(the_carrier(skolemFOFtoCNF_A_1))) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))) )],[refute_0_119,refute_0_47]) ).
cnf(refute_0_121,plain,
in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),powerset(the_carrier(skolemFOFtoCNF_A_1))),
inference(resolve,[$cnf( in(skolemFOFtoCNF_E(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),powerset(the_carrier(skolemFOFtoCNF_A_1))) )],[refute_0_115,refute_0_120]) ).
cnf(refute_0_122,plain,
definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),skolemFOFtoCNF_D_1(C)),
inference(subst,[],[refute_0_108:[bind(X_1465,$fot(skolemFOFtoCNF_D_1(C)))]]) ).
cnf(refute_0_123,plain,
( ~ in(skolemFOFtoCNF_D_1(C),powerset(the_carrier(skolemFOFtoCNF_A_1)))
| in(skolemFOFtoCNF_D_1(C),C)
| in(skolemFOFtoCNF_D_1(C),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3),skolemFOFtoCNF_D_1(C)) )],[refute_0_122,refute_0_55]) ).
cnf(refute_0_124,plain,
( ~ in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),powerset(the_carrier(skolemFOFtoCNF_A_1)))
| in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) ),
inference(subst,[],[refute_0_123:[bind(C,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)))]]) ).
cnf(refute_0_125,plain,
in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),powerset(the_carrier(skolemFOFtoCNF_A_1))) )],[refute_0_121,refute_0_124]) ).
cnf(refute_0_126,plain,
in(set_difference(cast_as_carrier_subset(skolemFOFtoCNF_A_1),skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),skolemFOFtoCNF_B_3),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) )],[refute_0_125,refute_0_111]) ).
cnf(refute_0_127,plain,
( ~ in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),powerset(the_carrier(skolemFOFtoCNF_A_1)))
| ~ in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( in(set_difference(cast_as_carrier_subset(skolemFOFtoCNF_A_1),skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3))),skolemFOFtoCNF_B_3) )],[refute_0_126,refute_0_1]) ).
cnf(refute_0_128,plain,
~ in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),powerset(the_carrier(skolemFOFtoCNF_A_1))) )],[refute_0_121,refute_0_127]) ).
cnf(refute_0_129,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_3)) )],[refute_0_125,refute_0_128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU310+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n021.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 : Sat Jun 18 22:40:02 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.78/0.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.78/0.95
% 0.78/0.95 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.78/0.96
%------------------------------------------------------------------------------