TSTP Solution File: SEU171+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU171+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.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 12:39:01 EDT 2022
% Result : Theorem 0.47s 0.70s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 40
% Syntax : Number of formulae : 195 ( 71 unt; 0 def)
% Number of atoms : 419 ( 218 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 405 ( 181 ~; 160 |; 36 &)
% ( 12 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 197 ( 12 sgn 80 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d2_subset_1,axiom,
! [A,B] :
( ( ~ empty(A)
=> ( element(B,A)
<=> in(B,A) ) )
& ( empty(A)
=> ( element(B,A)
<=> empty(B) ) ) ) ).
fof(d4_xboole_0,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& ~ in(D,B) ) ) ) ).
fof(d5_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,B) = set_difference(A,B) ) ).
fof(dt_k3_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> element(subset_complement(A,B),powerset(A)) ) ).
fof(involutiveness_k3_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,subset_complement(A,B)) = B ) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( element(B,powerset(A))
& empty(B) ) ).
fof(t3_boole,axiom,
! [A] : set_difference(A,empty_set) = A ).
fof(t50_subset_1,conjecture,
! [A] :
( A != empty_set
=> ! [B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,A)
=> ( ~ in(C,B)
=> in(C,subset_complement(A,B)) ) ) ) ) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( in(A,B)
& empty(B) ) ).
fof(subgoal_0,plain,
! [A] :
( A != empty_set
=> ! [B] :
( element(B,powerset(A))
=> ! [C] :
( ( element(C,A)
& ~ in(C,B) )
=> in(C,subset_complement(A,B)) ) ) ),
inference(strip,[],[t50_subset_1]) ).
fof(negate_0_0,plain,
~ ! [A] :
( A != empty_set
=> ! [B] :
( element(B,powerset(A))
=> ! [C] :
( ( element(C,A)
& ~ in(C,B) )
=> in(C,subset_complement(A,B)) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A] :
( A != empty_set
& ? [B] :
( element(B,powerset(A))
& ? [C] :
( ~ in(C,B)
& ~ in(C,subset_complement(A,B))
& element(C,A) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( skolemFOFtoCNF_A_2 != empty_set
& ? [B] :
( element(B,powerset(skolemFOFtoCNF_A_2))
& ? [C] :
( ~ in(C,B)
& ~ in(C,subset_complement(skolemFOFtoCNF_A_2,B))
& element(C,skolemFOFtoCNF_A_2) ) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [B] :
( element(B,powerset(skolemFOFtoCNF_A_2))
& ? [C] :
( ~ in(C,B)
& ~ in(C,subset_complement(skolemFOFtoCNF_A_2,B))
& element(C,skolemFOFtoCNF_A_2) ) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( element(skolemFOFtoCNF_B_3,powerset(skolemFOFtoCNF_A_2))
& ? [C] :
( ~ in(C,skolemFOFtoCNF_B_3)
& ~ in(C,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))
& element(C,skolemFOFtoCNF_A_2) ) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
element(skolemFOFtoCNF_B_3,powerset(skolemFOFtoCNF_A_2)),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B] :
( ~ element(B,powerset(A))
| subset_complement(A,subset_complement(A,B)) = B ),
inference(canonicalize,[],[involutiveness_k3_subset_1]) ).
fof(normalize_0_6,plain,
! [A,B] :
( ~ element(B,powerset(A))
| subset_complement(A,subset_complement(A,B)) = B ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B] :
( ~ element(B,powerset(A))
| element(subset_complement(A,B),powerset(A)) ),
inference(canonicalize,[],[dt_k3_subset_1]) ).
fof(normalize_0_8,plain,
! [A,B] :
( ~ element(B,powerset(A))
| element(subset_complement(A,B),powerset(A)) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B] :
( ~ element(B,powerset(A))
| subset_complement(A,B) = set_difference(A,B) ),
inference(canonicalize,[],[d5_subset_1]) ).
fof(normalize_0_10,plain,
! [A,B] :
( ~ element(B,powerset(A))
| subset_complement(A,B) = set_difference(A,B) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(canonicalize,[],[t7_boole]) ).
fof(normalize_0_12,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A,B,C] :
( C != set_difference(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
inference(canonicalize,[],[d4_xboole_0]) ).
fof(normalize_0_14,plain,
! [A,B,C] :
( C != set_difference(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [A,B,C,D] :
( ( C != set_difference(A,B)
| ~ in(D,B)
| ~ in(D,C) )
& ( C != set_difference(A,B)
| ~ in(D,C)
| in(D,A) )
& ( ~ in(skolemFOFtoCNF_D(A,B,C),B)
| C = set_difference(A,B)
| in(skolemFOFtoCNF_D(A,B,C),C) )
& ( C = set_difference(A,B)
| in(skolemFOFtoCNF_D(A,B,C),A)
| in(skolemFOFtoCNF_D(A,B,C),C) )
& ( C != set_difference(A,B)
| ~ in(D,A)
| in(D,B)
| in(D,C) )
& ( ~ in(skolemFOFtoCNF_D(A,B,C),A)
| ~ in(skolemFOFtoCNF_D(A,B,C),C)
| C = set_difference(A,B)
| in(skolemFOFtoCNF_D(A,B,C),B) ) ),
inference(clausify,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [A,B,C] :
( C = set_difference(A,B)
| in(skolemFOFtoCNF_D(A,B,C),A)
| in(skolemFOFtoCNF_D(A,B,C),C) ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
? [C] :
( ~ in(C,skolemFOFtoCNF_B_3)
& ~ in(C,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))
& element(C,skolemFOFtoCNF_A_2) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_18,plain,
( ~ in(skolemFOFtoCNF_C,skolemFOFtoCNF_B_3)
& ~ in(skolemFOFtoCNF_C,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))
& element(skolemFOFtoCNF_C,skolemFOFtoCNF_A_2) ),
inference(skolemize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
~ in(skolemFOFtoCNF_C,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),
inference(conjunct,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
element(skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),
inference(conjunct,[],[normalize_0_18]) ).
fof(normalize_0_21,plain,
( ! [A] :
( ~ empty(A)
| ! [B] :
( ~ element(B,A)
<=> ~ empty(B) ) )
& ! [A] :
( empty(A)
| ! [B] :
( ~ element(B,A)
<=> ~ in(B,A) ) ) ),
inference(canonicalize,[],[d2_subset_1]) ).
fof(normalize_0_22,plain,
! [A] :
( empty(A)
| ! [B] :
( ~ element(B,A)
<=> ~ in(B,A) ) ),
inference(conjunct,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [A] :
( empty(A)
| ! [B] :
( ~ element(B,A)
<=> ~ in(B,A) ) ),
inference(specialize,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [A,B] :
( ( ~ element(B,A)
| empty(A)
| in(B,A) )
& ( ~ in(B,A)
| element(B,A)
| empty(A) ) ),
inference(clausify,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [A,B] :
( ~ element(B,A)
| empty(A)
| in(B,A) ),
inference(conjunct,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [A,B,C,D] :
( C != set_difference(A,B)
| ~ in(D,A)
| in(D,B)
| in(D,C) ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_27,plain,
~ in(skolemFOFtoCNF_C,skolemFOFtoCNF_B_3),
inference(conjunct,[],[normalize_0_18]) ).
fof(normalize_0_28,plain,
! [A] :
? [B] :
( element(B,powerset(A))
& empty(B) ),
inference(canonicalize,[],[rc2_subset_1]) ).
fof(normalize_0_29,plain,
! [A] :
? [B] :
( element(B,powerset(A))
& empty(B) ),
inference(specialize,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
! [A] :
( element(skolemFOFtoCNF_B_2(A),powerset(A))
& empty(skolemFOFtoCNF_B_2(A)) ),
inference(skolemize,[],[normalize_0_29]) ).
fof(normalize_0_31,plain,
! [A] : element(skolemFOFtoCNF_B_2(A),powerset(A)),
inference(conjunct,[],[normalize_0_30]) ).
fof(normalize_0_32,plain,
! [A] : empty(skolemFOFtoCNF_B_2(A)),
inference(conjunct,[],[normalize_0_30]) ).
fof(normalize_0_33,plain,
! [A] :
( ~ empty(A)
| A = empty_set ),
inference(canonicalize,[],[t6_boole]) ).
fof(normalize_0_34,plain,
! [A] :
( ~ empty(A)
| A = empty_set ),
inference(specialize,[],[normalize_0_33]) ).
fof(normalize_0_35,plain,
! [A] : set_difference(A,empty_set) = A,
inference(canonicalize,[],[t3_boole]) ).
fof(normalize_0_36,plain,
! [A] : set_difference(A,empty_set) = A,
inference(specialize,[],[normalize_0_35]) ).
fof(normalize_0_37,plain,
skolemFOFtoCNF_A_2 != empty_set,
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
element(skolemFOFtoCNF_B_3,powerset(skolemFOFtoCNF_A_2)),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_1,plain,
( ~ element(B,powerset(A))
| subset_complement(A,subset_complement(A,B)) = B ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( ~ element(skolemFOFtoCNF_B_3,powerset(skolemFOFtoCNF_A_2))
| subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = skolemFOFtoCNF_B_3 ),
inference(subst,[],[refute_0_1:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B_3))]]) ).
cnf(refute_0_3,plain,
subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = skolemFOFtoCNF_B_3,
inference(resolve,[$cnf( element(skolemFOFtoCNF_B_3,powerset(skolemFOFtoCNF_A_2)) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ element(B,powerset(A))
| element(subset_complement(A,B),powerset(A)) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( ~ element(skolemFOFtoCNF_B_3,powerset(skolemFOFtoCNF_A_2))
| element(subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3),powerset(skolemFOFtoCNF_A_2)) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B_3))]]) ).
cnf(refute_0_6,plain,
element(subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3),powerset(skolemFOFtoCNF_A_2)),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B_3,powerset(skolemFOFtoCNF_A_2)) )],[refute_0_0,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ element(B,powerset(A))
| subset_complement(A,B) = set_difference(A,B) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
( ~ element(subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3),powerset(skolemFOFtoCNF_A_2))
| subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = set_difference(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)))]]) ).
cnf(refute_0_9,plain,
subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = set_difference(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),
inference(resolve,[$cnf( element(subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3),powerset(skolemFOFtoCNF_A_2)) )],[refute_0_6,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ element(skolemFOFtoCNF_B_3,powerset(skolemFOFtoCNF_A_2))
| subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3) = set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B_3))]]) ).
cnf(refute_0_11,plain,
subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3) = set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B_3,powerset(skolemFOFtoCNF_A_2)) )],[refute_0_0,refute_0_10]) ).
cnf(refute_0_12,plain,
subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),
introduced(tautology,[refl,[$fot(subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)))]]) ).
cnf(refute_0_13,plain,
( subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3) != set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)
| subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) != subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))
| subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) ),
introduced(tautology,[equality,[$cnf( $equal(subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))) ),[1,1],$fot(set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))]]) ).
cnf(refute_0_14,plain,
( subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3) != set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)
| subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( $equal(subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),
inference(resolve,[$cnf( $equal(subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3),set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
( subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) != set_difference(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))
| subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) != subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))
| subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = set_difference(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) ),
introduced(tautology,[equality,[$cnf( $equal(subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),set_difference(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))) ),[0],$fot(subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)))]]) ).
cnf(refute_0_17,plain,
( subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) != set_difference(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))
| subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = set_difference(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( $equal(subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
set_difference(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = set_difference(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),
introduced(tautology,[refl,[$fot(set_difference(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)))]]) ).
cnf(refute_0_19,plain,
( set_difference(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) != set_difference(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))
| subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3) != set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)
| set_difference(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),set_difference(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))) ),[1,1],$fot(set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))]]) ).
cnf(refute_0_20,plain,
( subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3) != set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)
| set_difference(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),set_difference(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
set_difference(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),
inference(resolve,[$cnf( $equal(subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3),set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) )],[refute_0_11,refute_0_20]) ).
cnf(refute_0_22,plain,
( set_difference(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) != set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))
| subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) != set_difference(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))
| subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) ),
introduced(tautology,[equality,[$cnf( $equal(subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),set_difference(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))) ),[1],$fot(set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)))]]) ).
cnf(refute_0_23,plain,
( subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) != set_difference(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))
| subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) != set_difference(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))
| subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( $equal(subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),set_difference(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))) )],[refute_0_17,refute_0_23]) ).
cnf(refute_0_25,plain,
subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),
inference(resolve,[$cnf( $equal(subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),set_difference(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))) )],[refute_0_9,refute_0_24]) ).
cnf(refute_0_26,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_27,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_28,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_30,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) != set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))
| subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) != subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))
| subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) ),
inference(subst,[],[refute_0_30:[bind(X,$fot(subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)))),bind(Y,$fot(subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)))),bind(Z,$fot(set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))))]]) ).
cnf(refute_0_32,plain,
( subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) != set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))
| subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( $equal(subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))) )],[refute_0_15,refute_0_31]) ).
cnf(refute_0_33,plain,
subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),
inference(resolve,[$cnf( $equal(subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))) )],[refute_0_25,refute_0_32]) ).
cnf(refute_0_34,plain,
( subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) != set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))
| subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) != skolemFOFtoCNF_B_3
| set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = skolemFOFtoCNF_B_3 ),
introduced(tautology,[equality,[$cnf( $equal(subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_B_3) ),[0],$fot(set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)))]]) ).
cnf(refute_0_35,plain,
( subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) != skolemFOFtoCNF_B_3
| set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = skolemFOFtoCNF_B_3 ),
inference(resolve,[$cnf( $equal(subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = skolemFOFtoCNF_B_3,
inference(resolve,[$cnf( $equal(subset_complement(skolemFOFtoCNF_A_2,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_B_3) )],[refute_0_3,refute_0_35]) ).
cnf(refute_0_37,plain,
( ~ empty(B)
| ~ in(A,B) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_38,plain,
( ~ empty(X_92)
| ~ in(skolemFOFtoCNF_D(X_92,X_91,X_92),X_92) ),
inference(subst,[],[refute_0_37:[bind(A,$fot(skolemFOFtoCNF_D(X_92,X_91,X_92))),bind(B,$fot(X_92))]]) ).
cnf(refute_0_39,plain,
( C = set_difference(A,B)
| in(skolemFOFtoCNF_D(A,B,C),A)
| in(skolemFOFtoCNF_D(A,B,C),C) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_40,plain,
( X_92 = set_difference(X_92,X_91)
| in(skolemFOFtoCNF_D(X_92,X_91,X_92),X_92) ),
inference(subst,[],[refute_0_39:[bind(A,$fot(X_92)),bind(B,$fot(X_91)),bind(C,$fot(X_92))]]) ).
cnf(refute_0_41,plain,
( ~ empty(X_92)
| X_92 = set_difference(X_92,X_91) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D(X_92,X_91,X_92),X_92) )],[refute_0_40,refute_0_38]) ).
cnf(refute_0_42,plain,
( ~ empty(skolemFOFtoCNF_A_2)
| skolemFOFtoCNF_A_2 = set_difference(skolemFOFtoCNF_A_2,X_91) ),
inference(subst,[],[refute_0_41:[bind(X_92,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_43,plain,
~ in(skolemFOFtoCNF_C,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_44,plain,
( subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3) != set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)
| ~ in(skolemFOFtoCNF_C,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))
| in(skolemFOFtoCNF_C,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) ),
introduced(tautology,[equality,[$cnf( ~ in(skolemFOFtoCNF_C,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) ),[1],$fot(set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))]]) ).
cnf(refute_0_45,plain,
( ~ in(skolemFOFtoCNF_C,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))
| in(skolemFOFtoCNF_C,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( $equal(subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3),set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) )],[refute_0_11,refute_0_44]) ).
cnf(refute_0_46,plain,
~ in(skolemFOFtoCNF_C,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) )],[refute_0_45,refute_0_43]) ).
cnf(refute_0_47,plain,
element(skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_48,plain,
( ~ element(B,A)
| empty(A)
| in(B,A) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_49,plain,
( ~ element(skolemFOFtoCNF_C,skolemFOFtoCNF_A_2)
| empty(skolemFOFtoCNF_A_2)
| in(skolemFOFtoCNF_C,skolemFOFtoCNF_A_2) ),
inference(subst,[],[refute_0_48:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_50,plain,
( empty(skolemFOFtoCNF_A_2)
| in(skolemFOFtoCNF_C,skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_C,skolemFOFtoCNF_A_2) )],[refute_0_47,refute_0_49]) ).
cnf(refute_0_51,plain,
( C != set_difference(A,B)
| ~ in(D,A)
| in(D,B)
| in(D,C) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_52,plain,
( set_difference(A,B) != set_difference(A,B)
| ~ in(D,A)
| in(D,B)
| in(D,set_difference(A,B)) ),
inference(subst,[],[refute_0_51:[bind(C,$fot(set_difference(A,B)))]]) ).
cnf(refute_0_53,plain,
set_difference(A,B) = set_difference(A,B),
introduced(tautology,[refl,[$fot(set_difference(A,B))]]) ).
cnf(refute_0_54,plain,
( ~ in(D,A)
| in(D,B)
| in(D,set_difference(A,B)) ),
inference(resolve,[$cnf( $equal(set_difference(A,B),set_difference(A,B)) )],[refute_0_53,refute_0_52]) ).
cnf(refute_0_55,plain,
( ~ in(skolemFOFtoCNF_C,skolemFOFtoCNF_A_2)
| in(skolemFOFtoCNF_C,X_235)
| in(skolemFOFtoCNF_C,set_difference(skolemFOFtoCNF_A_2,X_235)) ),
inference(subst,[],[refute_0_54:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(X_235)),bind(D,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_56,plain,
( empty(skolemFOFtoCNF_A_2)
| in(skolemFOFtoCNF_C,X_235)
| in(skolemFOFtoCNF_C,set_difference(skolemFOFtoCNF_A_2,X_235)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C,skolemFOFtoCNF_A_2) )],[refute_0_50,refute_0_55]) ).
cnf(refute_0_57,plain,
( empty(skolemFOFtoCNF_A_2)
| in(skolemFOFtoCNF_C,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))
| in(skolemFOFtoCNF_C,skolemFOFtoCNF_B_3) ),
inference(subst,[],[refute_0_56:[bind(X_235,$fot(skolemFOFtoCNF_B_3))]]) ).
cnf(refute_0_58,plain,
( empty(skolemFOFtoCNF_A_2)
| in(skolemFOFtoCNF_C,skolemFOFtoCNF_B_3) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) )],[refute_0_57,refute_0_46]) ).
cnf(refute_0_59,plain,
~ in(skolemFOFtoCNF_C,skolemFOFtoCNF_B_3),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_60,plain,
empty(skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C,skolemFOFtoCNF_B_3) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
skolemFOFtoCNF_A_2 = set_difference(skolemFOFtoCNF_A_2,X_91),
inference(resolve,[$cnf( empty(skolemFOFtoCNF_A_2) )],[refute_0_60,refute_0_42]) ).
cnf(refute_0_62,plain,
( skolemFOFtoCNF_A_2 != set_difference(skolemFOFtoCNF_A_2,X_91)
| set_difference(skolemFOFtoCNF_A_2,X_91) = skolemFOFtoCNF_A_2 ),
inference(subst,[],[refute_0_28:[bind(X,$fot(skolemFOFtoCNF_A_2)),bind(Y,$fot(set_difference(skolemFOFtoCNF_A_2,X_91)))]]) ).
cnf(refute_0_63,plain,
set_difference(skolemFOFtoCNF_A_2,X_91) = skolemFOFtoCNF_A_2,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,X_91)) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = skolemFOFtoCNF_A_2,
inference(subst,[],[refute_0_63:[bind(X_91,$fot(set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)))]]) ).
cnf(refute_0_65,plain,
( set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) != skolemFOFtoCNF_A_2
| set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) != skolemFOFtoCNF_B_3
| skolemFOFtoCNF_A_2 = skolemFOFtoCNF_B_3 ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_B_3) ),[0],$fot(skolemFOFtoCNF_A_2)]]) ).
cnf(refute_0_66,plain,
( set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) != skolemFOFtoCNF_B_3
| skolemFOFtoCNF_A_2 = skolemFOFtoCNF_B_3 ),
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_A_2) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
( set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) != skolemFOFtoCNF_B_3
| subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) != set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))
| subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = skolemFOFtoCNF_B_3 ),
introduced(tautology,[equality,[$cnf( $equal(subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))) ),[1],$fot(skolemFOFtoCNF_B_3)]]) ).
cnf(refute_0_68,plain,
( subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) != set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))
| subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = skolemFOFtoCNF_B_3 ),
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_B_3) )],[refute_0_36,refute_0_67]) ).
cnf(refute_0_69,plain,
subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = skolemFOFtoCNF_B_3,
inference(resolve,[$cnf( $equal(subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))) )],[refute_0_25,refute_0_68]) ).
cnf(refute_0_70,plain,
element(skolemFOFtoCNF_B_2(A),powerset(A)),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_71,plain,
empty(skolemFOFtoCNF_B_2(A)),
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_72,plain,
( ~ empty(A)
| A = empty_set ),
inference(canonicalize,[],[normalize_0_34]) ).
cnf(refute_0_73,plain,
( ~ empty(skolemFOFtoCNF_B_2(A))
| skolemFOFtoCNF_B_2(A) = empty_set ),
inference(subst,[],[refute_0_72:[bind(A,$fot(skolemFOFtoCNF_B_2(A)))]]) ).
cnf(refute_0_74,plain,
skolemFOFtoCNF_B_2(A) = empty_set,
inference(resolve,[$cnf( empty(skolemFOFtoCNF_B_2(A)) )],[refute_0_71,refute_0_73]) ).
cnf(refute_0_75,plain,
( skolemFOFtoCNF_B_2(A) != empty_set
| ~ element(skolemFOFtoCNF_B_2(A),powerset(A))
| element(empty_set,powerset(A)) ),
introduced(tautology,[equality,[$cnf( element(skolemFOFtoCNF_B_2(A),powerset(A)) ),[0],$fot(empty_set)]]) ).
cnf(refute_0_76,plain,
( ~ element(skolemFOFtoCNF_B_2(A),powerset(A))
| element(empty_set,powerset(A)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_2(A),empty_set) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
element(empty_set,powerset(A)),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B_2(A),powerset(A)) )],[refute_0_70,refute_0_76]) ).
cnf(refute_0_78,plain,
element(empty_set,powerset(X_20)),
inference(subst,[],[refute_0_77:[bind(A,$fot(X_20))]]) ).
cnf(refute_0_79,plain,
( ~ element(empty_set,powerset(X_20))
| element(subset_complement(X_20,empty_set),powerset(X_20)) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_20)),bind(B,$fot(empty_set))]]) ).
cnf(refute_0_80,plain,
element(subset_complement(X_20,empty_set),powerset(X_20)),
inference(resolve,[$cnf( element(empty_set,powerset(X_20)) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
element(subset_complement(X_58,empty_set),powerset(X_58)),
inference(subst,[],[refute_0_80:[bind(X_20,$fot(X_58))]]) ).
cnf(refute_0_82,plain,
( ~ element(subset_complement(X_58,empty_set),powerset(X_58))
| subset_complement(X_58,subset_complement(X_58,empty_set)) = set_difference(X_58,subset_complement(X_58,empty_set)) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(X_58)),bind(B,$fot(subset_complement(X_58,empty_set)))]]) ).
cnf(refute_0_83,plain,
subset_complement(X_58,subset_complement(X_58,empty_set)) = set_difference(X_58,subset_complement(X_58,empty_set)),
inference(resolve,[$cnf( element(subset_complement(X_58,empty_set),powerset(X_58)) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
element(empty_set,powerset(X_58)),
inference(subst,[],[refute_0_77:[bind(A,$fot(X_58))]]) ).
cnf(refute_0_85,plain,
( ~ element(empty_set,powerset(X_58))
| subset_complement(X_58,empty_set) = set_difference(X_58,empty_set) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(X_58)),bind(B,$fot(empty_set))]]) ).
cnf(refute_0_86,plain,
subset_complement(X_58,empty_set) = set_difference(X_58,empty_set),
inference(resolve,[$cnf( element(empty_set,powerset(X_58)) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
set_difference(A,empty_set) = A,
inference(canonicalize,[],[normalize_0_36]) ).
cnf(refute_0_88,plain,
set_difference(X_58,empty_set) = X_58,
inference(subst,[],[refute_0_87:[bind(A,$fot(X_58))]]) ).
cnf(refute_0_89,plain,
( set_difference(X_58,empty_set) != X_58
| subset_complement(X_58,empty_set) != set_difference(X_58,empty_set)
| subset_complement(X_58,empty_set) = X_58 ),
introduced(tautology,[equality,[$cnf( $equal(subset_complement(X_58,empty_set),set_difference(X_58,empty_set)) ),[1],$fot(X_58)]]) ).
cnf(refute_0_90,plain,
( subset_complement(X_58,empty_set) != set_difference(X_58,empty_set)
| subset_complement(X_58,empty_set) = X_58 ),
inference(resolve,[$cnf( $equal(set_difference(X_58,empty_set),X_58) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
subset_complement(X_58,empty_set) = X_58,
inference(resolve,[$cnf( $equal(subset_complement(X_58,empty_set),set_difference(X_58,empty_set)) )],[refute_0_86,refute_0_90]) ).
cnf(refute_0_92,plain,
subset_complement(X_58,subset_complement(X_58,empty_set)) = subset_complement(X_58,subset_complement(X_58,empty_set)),
introduced(tautology,[refl,[$fot(subset_complement(X_58,subset_complement(X_58,empty_set)))]]) ).
cnf(refute_0_93,plain,
( subset_complement(X_58,empty_set) != X_58
| subset_complement(X_58,subset_complement(X_58,empty_set)) != subset_complement(X_58,subset_complement(X_58,empty_set))
| subset_complement(X_58,subset_complement(X_58,empty_set)) = subset_complement(X_58,X_58) ),
introduced(tautology,[equality,[$cnf( $equal(subset_complement(X_58,subset_complement(X_58,empty_set)),subset_complement(X_58,subset_complement(X_58,empty_set))) ),[1,1],$fot(X_58)]]) ).
cnf(refute_0_94,plain,
( subset_complement(X_58,empty_set) != X_58
| subset_complement(X_58,subset_complement(X_58,empty_set)) = subset_complement(X_58,X_58) ),
inference(resolve,[$cnf( $equal(subset_complement(X_58,subset_complement(X_58,empty_set)),subset_complement(X_58,subset_complement(X_58,empty_set))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
subset_complement(X_58,subset_complement(X_58,empty_set)) = subset_complement(X_58,X_58),
inference(resolve,[$cnf( $equal(subset_complement(X_58,empty_set),X_58) )],[refute_0_91,refute_0_94]) ).
cnf(refute_0_96,plain,
( subset_complement(X_58,subset_complement(X_58,empty_set)) != set_difference(X_58,subset_complement(X_58,empty_set))
| subset_complement(X_58,subset_complement(X_58,empty_set)) != subset_complement(X_58,X_58)
| subset_complement(X_58,X_58) = set_difference(X_58,subset_complement(X_58,empty_set)) ),
introduced(tautology,[equality,[$cnf( $equal(subset_complement(X_58,subset_complement(X_58,empty_set)),set_difference(X_58,subset_complement(X_58,empty_set))) ),[0],$fot(subset_complement(X_58,X_58))]]) ).
cnf(refute_0_97,plain,
( subset_complement(X_58,subset_complement(X_58,empty_set)) != set_difference(X_58,subset_complement(X_58,empty_set))
| subset_complement(X_58,X_58) = set_difference(X_58,subset_complement(X_58,empty_set)) ),
inference(resolve,[$cnf( $equal(subset_complement(X_58,subset_complement(X_58,empty_set)),subset_complement(X_58,X_58)) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
set_difference(X_58,subset_complement(X_58,empty_set)) = set_difference(X_58,subset_complement(X_58,empty_set)),
introduced(tautology,[refl,[$fot(set_difference(X_58,subset_complement(X_58,empty_set)))]]) ).
cnf(refute_0_99,plain,
( set_difference(X_58,subset_complement(X_58,empty_set)) != set_difference(X_58,subset_complement(X_58,empty_set))
| subset_complement(X_58,empty_set) != X_58
| set_difference(X_58,subset_complement(X_58,empty_set)) = set_difference(X_58,X_58) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(X_58,subset_complement(X_58,empty_set)),set_difference(X_58,subset_complement(X_58,empty_set))) ),[1,1],$fot(X_58)]]) ).
cnf(refute_0_100,plain,
( subset_complement(X_58,empty_set) != X_58
| set_difference(X_58,subset_complement(X_58,empty_set)) = set_difference(X_58,X_58) ),
inference(resolve,[$cnf( $equal(set_difference(X_58,subset_complement(X_58,empty_set)),set_difference(X_58,subset_complement(X_58,empty_set))) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
set_difference(X_58,subset_complement(X_58,empty_set)) = set_difference(X_58,X_58),
inference(resolve,[$cnf( $equal(subset_complement(X_58,empty_set),X_58) )],[refute_0_91,refute_0_100]) ).
cnf(refute_0_102,plain,
( set_difference(X_58,subset_complement(X_58,empty_set)) != set_difference(X_58,X_58)
| subset_complement(X_58,X_58) != set_difference(X_58,subset_complement(X_58,empty_set))
| subset_complement(X_58,X_58) = set_difference(X_58,X_58) ),
introduced(tautology,[equality,[$cnf( $equal(subset_complement(X_58,X_58),set_difference(X_58,subset_complement(X_58,empty_set))) ),[1],$fot(set_difference(X_58,X_58))]]) ).
cnf(refute_0_103,plain,
( subset_complement(X_58,X_58) != set_difference(X_58,subset_complement(X_58,empty_set))
| subset_complement(X_58,X_58) = set_difference(X_58,X_58) ),
inference(resolve,[$cnf( $equal(set_difference(X_58,subset_complement(X_58,empty_set)),set_difference(X_58,X_58)) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
( subset_complement(X_58,subset_complement(X_58,empty_set)) != set_difference(X_58,subset_complement(X_58,empty_set))
| subset_complement(X_58,X_58) = set_difference(X_58,X_58) ),
inference(resolve,[$cnf( $equal(subset_complement(X_58,X_58),set_difference(X_58,subset_complement(X_58,empty_set))) )],[refute_0_97,refute_0_103]) ).
cnf(refute_0_105,plain,
subset_complement(X_58,X_58) = set_difference(X_58,X_58),
inference(resolve,[$cnf( $equal(subset_complement(X_58,subset_complement(X_58,empty_set)),set_difference(X_58,subset_complement(X_58,empty_set))) )],[refute_0_83,refute_0_104]) ).
cnf(refute_0_106,plain,
element(empty_set,powerset(X_84)),
inference(subst,[],[refute_0_77:[bind(A,$fot(X_84))]]) ).
cnf(refute_0_107,plain,
( ~ element(empty_set,powerset(X_84))
| subset_complement(X_84,subset_complement(X_84,empty_set)) = empty_set ),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_84)),bind(B,$fot(empty_set))]]) ).
cnf(refute_0_108,plain,
subset_complement(X_84,subset_complement(X_84,empty_set)) = empty_set,
inference(resolve,[$cnf( element(empty_set,powerset(X_84)) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
subset_complement(X_84,X_84) = set_difference(X_84,X_84),
inference(subst,[],[refute_0_105:[bind(X_58,$fot(X_84))]]) ).
cnf(refute_0_110,plain,
subset_complement(X_84,empty_set) = X_84,
inference(subst,[],[refute_0_91:[bind(X_58,$fot(X_84))]]) ).
cnf(refute_0_111,plain,
subset_complement(X_84,subset_complement(X_84,empty_set)) = subset_complement(X_84,subset_complement(X_84,empty_set)),
introduced(tautology,[refl,[$fot(subset_complement(X_84,subset_complement(X_84,empty_set)))]]) ).
cnf(refute_0_112,plain,
( subset_complement(X_84,empty_set) != X_84
| subset_complement(X_84,subset_complement(X_84,empty_set)) != subset_complement(X_84,subset_complement(X_84,empty_set))
| subset_complement(X_84,subset_complement(X_84,empty_set)) = subset_complement(X_84,X_84) ),
introduced(tautology,[equality,[$cnf( $equal(subset_complement(X_84,subset_complement(X_84,empty_set)),subset_complement(X_84,subset_complement(X_84,empty_set))) ),[1,1],$fot(X_84)]]) ).
cnf(refute_0_113,plain,
( subset_complement(X_84,empty_set) != X_84
| subset_complement(X_84,subset_complement(X_84,empty_set)) = subset_complement(X_84,X_84) ),
inference(resolve,[$cnf( $equal(subset_complement(X_84,subset_complement(X_84,empty_set)),subset_complement(X_84,subset_complement(X_84,empty_set))) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
subset_complement(X_84,subset_complement(X_84,empty_set)) = subset_complement(X_84,X_84),
inference(resolve,[$cnf( $equal(subset_complement(X_84,empty_set),X_84) )],[refute_0_110,refute_0_113]) ).
cnf(refute_0_115,plain,
( subset_complement(X_84,X_84) != set_difference(X_84,X_84)
| subset_complement(X_84,subset_complement(X_84,empty_set)) != subset_complement(X_84,X_84)
| subset_complement(X_84,subset_complement(X_84,empty_set)) = set_difference(X_84,X_84) ),
inference(subst,[],[refute_0_30:[bind(X,$fot(subset_complement(X_84,subset_complement(X_84,empty_set)))),bind(Y,$fot(subset_complement(X_84,X_84))),bind(Z,$fot(set_difference(X_84,X_84)))]]) ).
cnf(refute_0_116,plain,
( subset_complement(X_84,X_84) != set_difference(X_84,X_84)
| subset_complement(X_84,subset_complement(X_84,empty_set)) = set_difference(X_84,X_84) ),
inference(resolve,[$cnf( $equal(subset_complement(X_84,subset_complement(X_84,empty_set)),subset_complement(X_84,X_84)) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
subset_complement(X_84,subset_complement(X_84,empty_set)) = set_difference(X_84,X_84),
inference(resolve,[$cnf( $equal(subset_complement(X_84,X_84),set_difference(X_84,X_84)) )],[refute_0_109,refute_0_116]) ).
cnf(refute_0_118,plain,
( subset_complement(X_84,subset_complement(X_84,empty_set)) != empty_set
| subset_complement(X_84,subset_complement(X_84,empty_set)) != set_difference(X_84,X_84)
| set_difference(X_84,X_84) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(subset_complement(X_84,subset_complement(X_84,empty_set)),empty_set) ),[0],$fot(set_difference(X_84,X_84))]]) ).
cnf(refute_0_119,plain,
( subset_complement(X_84,subset_complement(X_84,empty_set)) != empty_set
| set_difference(X_84,X_84) = empty_set ),
inference(resolve,[$cnf( $equal(subset_complement(X_84,subset_complement(X_84,empty_set)),set_difference(X_84,X_84)) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
set_difference(X_84,X_84) = empty_set,
inference(resolve,[$cnf( $equal(subset_complement(X_84,subset_complement(X_84,empty_set)),empty_set) )],[refute_0_108,refute_0_119]) ).
cnf(refute_0_121,plain,
set_difference(X_58,X_58) = empty_set,
inference(subst,[],[refute_0_120:[bind(X_84,$fot(X_58))]]) ).
cnf(refute_0_122,plain,
( set_difference(X_58,X_58) != empty_set
| subset_complement(X_58,X_58) != set_difference(X_58,X_58)
| subset_complement(X_58,X_58) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(subset_complement(X_58,X_58),set_difference(X_58,X_58)) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_123,plain,
( subset_complement(X_58,X_58) != set_difference(X_58,X_58)
| subset_complement(X_58,X_58) = empty_set ),
inference(resolve,[$cnf( $equal(set_difference(X_58,X_58),empty_set) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
subset_complement(X_58,X_58) = empty_set,
inference(resolve,[$cnf( $equal(subset_complement(X_58,X_58),set_difference(X_58,X_58)) )],[refute_0_105,refute_0_123]) ).
cnf(refute_0_125,plain,
subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2) = empty_set,
inference(subst,[],[refute_0_124:[bind(X_58,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_126,plain,
set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_A_2,
inference(subst,[],[refute_0_63:[bind(X_91,$fot(skolemFOFtoCNF_B_3))]]) ).
cnf(refute_0_127,plain,
subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),
introduced(tautology,[refl,[$fot(subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)))]]) ).
cnf(refute_0_128,plain,
( set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3) != skolemFOFtoCNF_A_2
| subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) != subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))
| subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2) ),
introduced(tautology,[equality,[$cnf( $equal(subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))) ),[1,1],$fot(skolemFOFtoCNF_A_2)]]) ).
cnf(refute_0_129,plain,
( set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3) != skolemFOFtoCNF_A_2
| subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( $equal(subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3))) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3),skolemFOFtoCNF_A_2) )],[refute_0_126,refute_0_129]) ).
cnf(refute_0_131,plain,
( subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) != subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2)
| subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2) != empty_set
| subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = empty_set ),
inference(subst,[],[refute_0_30:[bind(X,$fot(subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)))),bind(Y,$fot(subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2))),bind(Z,$fot(empty_set))]]) ).
cnf(refute_0_132,plain,
( subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2) != empty_set
| subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = empty_set ),
inference(resolve,[$cnf( $equal(subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2)) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) = empty_set,
inference(resolve,[$cnf( $equal(subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),empty_set) )],[refute_0_125,refute_0_132]) ).
cnf(refute_0_134,plain,
( subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) != empty_set
| subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) != skolemFOFtoCNF_B_3
| empty_set = skolemFOFtoCNF_B_3 ),
introduced(tautology,[equality,[$cnf( $equal(subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_B_3) ),[0],$fot(empty_set)]]) ).
cnf(refute_0_135,plain,
( subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) != skolemFOFtoCNF_B_3
| empty_set = skolemFOFtoCNF_B_3 ),
inference(resolve,[$cnf( $equal(subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),empty_set) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
empty_set = skolemFOFtoCNF_B_3,
inference(resolve,[$cnf( $equal(subset_complement(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_B_3) )],[refute_0_69,refute_0_135]) ).
cnf(refute_0_137,plain,
( empty_set != skolemFOFtoCNF_B_3
| skolemFOFtoCNF_B_3 = empty_set ),
inference(subst,[],[refute_0_28:[bind(X,$fot(empty_set)),bind(Y,$fot(skolemFOFtoCNF_B_3))]]) ).
cnf(refute_0_138,plain,
skolemFOFtoCNF_B_3 = empty_set,
inference(resolve,[$cnf( $equal(empty_set,skolemFOFtoCNF_B_3) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
( skolemFOFtoCNF_A_2 != skolemFOFtoCNF_B_3
| skolemFOFtoCNF_B_3 != empty_set
| skolemFOFtoCNF_A_2 = empty_set ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_A_2,empty_set) ),[0],$fot(skolemFOFtoCNF_B_3)]]) ).
cnf(refute_0_140,plain,
( skolemFOFtoCNF_A_2 != skolemFOFtoCNF_B_3
| skolemFOFtoCNF_A_2 = empty_set ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_3,empty_set) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
( set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)) != skolemFOFtoCNF_B_3
| skolemFOFtoCNF_A_2 = empty_set ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3) )],[refute_0_66,refute_0_140]) ).
cnf(refute_0_142,plain,
skolemFOFtoCNF_A_2 = empty_set,
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_B_3) )],[refute_0_36,refute_0_141]) ).
cnf(refute_0_143,plain,
skolemFOFtoCNF_A_2 != empty_set,
inference(canonicalize,[],[normalize_0_37]) ).
cnf(refute_0_144,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,empty_set) )],[refute_0_142,refute_0_143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU171+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n023.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 09:25:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.47/0.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.47/0.70
% 0.47/0.70 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.47/0.72
%------------------------------------------------------------------------------