TSTP Solution File: SEU144+2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU144+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n011.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 12:38:43 EDT 2022
% Result : Theorem 1.45s 1.63s
% Output : CNFRefutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 39
% Syntax : Number of formulae : 206 ( 102 unt; 0 def)
% Number of atoms : 400 ( 262 equ)
% Maximal formula atoms : 20 ( 1 avg)
% Number of connectives : 352 ( 158 ~; 145 |; 20 &)
% ( 24 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 336 ( 15 sgn 116 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A) ).
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ) ).
fof(d2_xboole_0,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ) ).
fof(l2_zfmisc_1,conjecture,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ) ).
fof(l32_xboole_1,lemma,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ) ).
fof(t1_boole,axiom,
! [A] : set_union2(A,empty_set) = A ).
fof(t37_xboole_1,lemma,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ) ).
fof(t39_xboole_1,lemma,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B) ).
fof(t3_boole,axiom,
! [A] : set_difference(A,empty_set) = A ).
fof(t40_xboole_1,lemma,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B) ).
fof(t48_xboole_1,lemma,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B) ).
fof(t4_boole,axiom,
! [A] : set_difference(empty_set,A) = empty_set ).
fof(subgoal_0,plain,
! [A,B] :
( subset(singleton(A),B)
=> in(A,B) ),
inference(strip,[],[l2_zfmisc_1]) ).
fof(subgoal_1,plain,
! [A,B] :
( in(A,B)
=> subset(singleton(A),B) ),
inference(strip,[],[l2_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( subset(singleton(A),B)
=> in(A,B) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(canonicalize,[],[d1_tarski]) ).
fof(normalize_0_1,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B,C] :
( ( B != singleton(A)
| C != A
| in(C,B) )
& ( B != singleton(A)
| ~ in(C,B)
| C = A )
& ( skolemFOFtoCNF_C(A,B) != A
| ~ in(skolemFOFtoCNF_C(A,B),B)
| B = singleton(A) )
& ( B = singleton(A)
| skolemFOFtoCNF_C(A,B) = A
| in(skolemFOFtoCNF_C(A,B),B) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B,C] :
( B != singleton(A)
| C != A
| in(C,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B,C] :
( C != set_union2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
inference(canonicalize,[],[d2_xboole_0]) ).
fof(normalize_0_5,plain,
! [A,B,C] :
( C != set_union2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B,C,D] :
( ( C != set_union2(A,B)
| ~ in(D,A)
| in(D,C) )
& ( C != set_union2(A,B)
| ~ in(D,B)
| in(D,C) )
& ( ~ in(skolemFOFtoCNF_D_1(A,B,C),A)
| ~ in(skolemFOFtoCNF_D_1(A,B,C),C)
| C = set_union2(A,B) )
& ( ~ in(skolemFOFtoCNF_D_1(A,B,C),B)
| ~ in(skolemFOFtoCNF_D_1(A,B,C),C)
| C = set_union2(A,B) )
& ( C != set_union2(A,B)
| ~ in(D,C)
| in(D,A)
| in(D,B) )
& ( C = set_union2(A,B)
| in(skolemFOFtoCNF_D_1(A,B,C),A)
| in(skolemFOFtoCNF_D_1(A,B,C),B)
| in(skolemFOFtoCNF_D_1(A,B,C),C) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,C,D] :
( C != set_union2(A,B)
| ~ in(D,B)
| in(D,C) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(canonicalize,[],[t48_xboole_1]) ).
fof(normalize_0_9,plain,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
inference(canonicalize,[],[t40_xboole_1]) ).
fof(normalize_0_11,plain,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(canonicalize,[],[commutativity_k3_xboole_0]) ).
fof(normalize_0_13,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
inference(canonicalize,[],[t39_xboole_1]) ).
fof(normalize_0_15,plain,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[commutativity_k2_xboole_0]) ).
fof(normalize_0_17,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [A] : set_union2(A,empty_set) = A,
inference(canonicalize,[],[t1_boole]) ).
fof(normalize_0_19,plain,
! [A] : set_union2(A,empty_set) = A,
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(canonicalize,[],[t4_boole]) ).
fof(normalize_0_21,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [A] : set_difference(A,empty_set) = A,
inference(canonicalize,[],[t3_boole]) ).
fof(normalize_0_23,plain,
! [A] : set_difference(A,empty_set) = A,
inference(specialize,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
? [A,B] :
( ~ in(A,B)
& subset(singleton(A),B) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_25,plain,
( ~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
& subset(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) ),
inference(skolemize,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
subset(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
! [A,B] :
( set_difference(A,B) != empty_set
<=> ~ subset(A,B) ),
inference(canonicalize,[],[t37_xboole_1]) ).
fof(normalize_0_28,plain,
! [A,B] :
( set_difference(A,B) != empty_set
<=> ~ subset(A,B) ),
inference(specialize,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
! [A,B] :
( ( set_difference(A,B) != empty_set
| subset(A,B) )
& ( ~ subset(A,B)
| set_difference(A,B) = empty_set ) ),
inference(clausify,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
! [A,B] :
( ~ subset(A,B)
| set_difference(A,B) = empty_set ),
inference(conjunct,[],[normalize_0_29]) ).
fof(normalize_0_31,plain,
~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_25]) ).
cnf(refute_0_0,plain,
( B != singleton(A)
| C != A
| in(C,B) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( A != A
| singleton(A) != singleton(A)
| in(A,singleton(A)) ),
inference(subst,[],[refute_0_0:[bind(B,$fot(singleton(A))),bind(C,$fot(A))]]) ).
cnf(refute_0_2,plain,
A = A,
introduced(tautology,[refl,[$fot(A)]]) ).
cnf(refute_0_3,plain,
( singleton(A) != singleton(A)
| in(A,singleton(A)) ),
inference(resolve,[$cnf( $equal(A,A) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
singleton(A) = singleton(A),
introduced(tautology,[refl,[$fot(singleton(A))]]) ).
cnf(refute_0_5,plain,
in(A,singleton(A)),
inference(resolve,[$cnf( $equal(singleton(A),singleton(A)) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
in(X_327,singleton(X_327)),
inference(subst,[],[refute_0_5:[bind(A,$fot(X_327))]]) ).
cnf(refute_0_7,plain,
( C != set_union2(A,B)
| ~ in(D,B)
| in(D,C) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_8,plain,
( set_union2(A,B) != set_union2(A,B)
| ~ in(D,B)
| in(D,set_union2(A,B)) ),
inference(subst,[],[refute_0_7:[bind(C,$fot(set_union2(A,B)))]]) ).
cnf(refute_0_9,plain,
set_union2(A,B) = set_union2(A,B),
introduced(tautology,[refl,[$fot(set_union2(A,B))]]) ).
cnf(refute_0_10,plain,
( ~ in(D,B)
| in(D,set_union2(A,B)) ),
inference(resolve,[$cnf( $equal(set_union2(A,B),set_union2(A,B)) )],[refute_0_9,refute_0_8]) ).
cnf(refute_0_11,plain,
( ~ in(X_327,singleton(X_327))
| in(X_327,set_union2(X_325,singleton(X_327))) ),
inference(subst,[],[refute_0_10:[bind(A,$fot(X_325)),bind(B,$fot(singleton(X_327))),bind(D,$fot(X_327))]]) ).
cnf(refute_0_12,plain,
in(X_327,set_union2(X_325,singleton(X_327))),
inference(resolve,[$cnf( in(X_327,singleton(X_327)) )],[refute_0_6,refute_0_11]) ).
cnf(refute_0_13,plain,
in(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))),
inference(subst,[],[refute_0_12:[bind(X_325,$fot(skolemFOFtoCNF_B_1)),bind(X_327,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_14,plain,
set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_15,plain,
set_difference(set_union2(A,X_53),set_difference(set_union2(A,X_53),X_53)) = set_intersection2(set_union2(A,X_53),X_53),
inference(subst,[],[refute_0_14:[bind(A,$fot(set_union2(A,X_53))),bind(B,$fot(X_53))]]) ).
cnf(refute_0_16,plain,
set_difference(set_union2(A,B),B) = set_difference(A,B),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_17,plain,
set_difference(set_union2(A,X_53),X_53) = set_difference(A,X_53),
inference(subst,[],[refute_0_16:[bind(B,$fot(X_53))]]) ).
cnf(refute_0_18,plain,
( set_difference(set_union2(A,X_53),X_53) != set_difference(A,X_53)
| set_difference(set_union2(A,X_53),set_difference(set_union2(A,X_53),X_53)) != set_intersection2(set_union2(A,X_53),X_53)
| set_difference(set_union2(A,X_53),set_difference(A,X_53)) = set_intersection2(set_union2(A,X_53),X_53) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(A,X_53),set_difference(set_union2(A,X_53),X_53)),set_intersection2(set_union2(A,X_53),X_53)) ),[0,1],$fot(set_difference(A,X_53))]]) ).
cnf(refute_0_19,plain,
( set_difference(set_union2(A,X_53),set_difference(set_union2(A,X_53),X_53)) != set_intersection2(set_union2(A,X_53),X_53)
| set_difference(set_union2(A,X_53),set_difference(A,X_53)) = set_intersection2(set_union2(A,X_53),X_53) ),
inference(resolve,[$cnf( $equal(set_difference(set_union2(A,X_53),X_53),set_difference(A,X_53)) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
set_difference(set_union2(A,X_53),set_difference(A,X_53)) = set_intersection2(set_union2(A,X_53),X_53),
inference(resolve,[$cnf( $equal(set_difference(set_union2(A,X_53),set_difference(set_union2(A,X_53),X_53)),set_intersection2(set_union2(A,X_53),X_53)) )],[refute_0_15,refute_0_19]) ).
cnf(refute_0_21,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_22,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_23,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_24,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( set_intersection2(A,B) != set_intersection2(B,A)
| set_intersection2(B,A) = set_intersection2(A,B) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(set_intersection2(A,B))),bind(Y,$fot(set_intersection2(B,A)))]]) ).
cnf(refute_0_26,plain,
set_intersection2(B,A) = set_intersection2(A,B),
inference(resolve,[$cnf( $equal(set_intersection2(A,B),set_intersection2(B,A)) )],[refute_0_21,refute_0_25]) ).
cnf(refute_0_27,plain,
set_intersection2(set_union2(A,X_53),X_53) = set_intersection2(X_53,set_union2(A,X_53)),
inference(subst,[],[refute_0_26:[bind(A,$fot(X_53)),bind(B,$fot(set_union2(A,X_53)))]]) ).
cnf(refute_0_28,plain,
( set_difference(set_union2(A,X_53),set_difference(A,X_53)) != set_intersection2(set_union2(A,X_53),X_53)
| set_intersection2(set_union2(A,X_53),X_53) != set_intersection2(X_53,set_union2(A,X_53))
| set_difference(set_union2(A,X_53),set_difference(A,X_53)) = set_intersection2(X_53,set_union2(A,X_53)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(set_union2(A,X_53),set_difference(A,X_53)),set_intersection2(X_53,set_union2(A,X_53))) ),[0],$fot(set_intersection2(set_union2(A,X_53),X_53))]]) ).
cnf(refute_0_29,plain,
( set_difference(set_union2(A,X_53),set_difference(A,X_53)) != set_intersection2(set_union2(A,X_53),X_53)
| set_difference(set_union2(A,X_53),set_difference(A,X_53)) = set_intersection2(X_53,set_union2(A,X_53)) ),
inference(resolve,[$cnf( $equal(set_intersection2(set_union2(A,X_53),X_53),set_intersection2(X_53,set_union2(A,X_53))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
set_difference(set_union2(A,X_53),set_difference(A,X_53)) = set_intersection2(X_53,set_union2(A,X_53)),
inference(resolve,[$cnf( $equal(set_difference(set_union2(A,X_53),set_difference(A,X_53)),set_intersection2(set_union2(A,X_53),X_53)) )],[refute_0_20,refute_0_29]) ).
cnf(refute_0_31,plain,
set_difference(A,set_difference(A,set_union2(X_76,A))) = set_intersection2(A,set_union2(X_76,A)),
inference(subst,[],[refute_0_14:[bind(B,$fot(set_union2(X_76,A)))]]) ).
cnf(refute_0_32,plain,
set_difference(set_union2(A,set_union2(A,X_72)),set_union2(A,X_72)) = set_difference(A,set_union2(A,X_72)),
inference(subst,[],[refute_0_16:[bind(B,$fot(set_union2(A,X_72)))]]) ).
cnf(refute_0_33,plain,
set_union2(A,set_difference(B,A)) = set_union2(A,B),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_34,plain,
set_union2(A,set_difference(set_union2(X_47,A),A)) = set_union2(A,set_union2(X_47,A)),
inference(subst,[],[refute_0_33:[bind(B,$fot(set_union2(X_47,A)))]]) ).
cnf(refute_0_35,plain,
set_difference(set_union2(X_47,A),A) = set_difference(X_47,A),
inference(subst,[],[refute_0_16:[bind(A,$fot(X_47)),bind(B,$fot(A))]]) ).
cnf(refute_0_36,plain,
( set_difference(set_union2(X_47,A),A) != set_difference(X_47,A)
| set_union2(A,set_difference(set_union2(X_47,A),A)) != set_union2(A,set_union2(X_47,A))
| set_union2(A,set_difference(X_47,A)) = set_union2(A,set_union2(X_47,A)) ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(A,set_difference(set_union2(X_47,A),A)),set_union2(A,set_union2(X_47,A))) ),[0,1],$fot(set_difference(X_47,A))]]) ).
cnf(refute_0_37,plain,
( set_union2(A,set_difference(set_union2(X_47,A),A)) != set_union2(A,set_union2(X_47,A))
| set_union2(A,set_difference(X_47,A)) = set_union2(A,set_union2(X_47,A)) ),
inference(resolve,[$cnf( $equal(set_difference(set_union2(X_47,A),A),set_difference(X_47,A)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
set_union2(A,set_difference(X_47,A)) = set_union2(A,set_union2(X_47,A)),
inference(resolve,[$cnf( $equal(set_union2(A,set_difference(set_union2(X_47,A),A)),set_union2(A,set_union2(X_47,A))) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
set_union2(A,set_difference(X_47,A)) = set_union2(A,X_47),
inference(subst,[],[refute_0_33:[bind(B,$fot(X_47))]]) ).
cnf(refute_0_40,plain,
( set_union2(A,set_difference(X_47,A)) != set_union2(A,X_47)
| set_union2(A,set_difference(X_47,A)) != set_union2(A,set_union2(X_47,A))
| set_union2(A,X_47) = set_union2(A,set_union2(X_47,A)) ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(A,set_difference(X_47,A)),set_union2(A,set_union2(X_47,A))) ),[0],$fot(set_union2(A,X_47))]]) ).
cnf(refute_0_41,plain,
( set_union2(A,set_difference(X_47,A)) != set_union2(A,set_union2(X_47,A))
| set_union2(A,X_47) = set_union2(A,set_union2(X_47,A)) ),
inference(resolve,[$cnf( $equal(set_union2(A,set_difference(X_47,A)),set_union2(A,X_47)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
set_union2(A,X_47) = set_union2(A,set_union2(X_47,A)),
inference(resolve,[$cnf( $equal(set_union2(A,set_difference(X_47,A)),set_union2(A,set_union2(X_47,A))) )],[refute_0_38,refute_0_41]) ).
cnf(refute_0_43,plain,
set_union2(X_50,X_51) = set_union2(X_50,set_union2(X_51,X_50)),
inference(subst,[],[refute_0_42:[bind(A,$fot(X_50)),bind(X_47,$fot(X_51))]]) ).
cnf(refute_0_44,plain,
set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_45,plain,
set_union2(X_50,X_51) = set_union2(X_51,X_50),
inference(subst,[],[refute_0_44:[bind(A,$fot(X_50)),bind(B,$fot(X_51))]]) ).
cnf(refute_0_46,plain,
( set_union2(X_50,X_51) != set_union2(X_51,X_50)
| set_union2(X_51,X_50) = set_union2(X_50,X_51) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(set_union2(X_50,X_51))),bind(Y,$fot(set_union2(X_51,X_50)))]]) ).
cnf(refute_0_47,plain,
set_union2(X_51,X_50) = set_union2(X_50,X_51),
inference(resolve,[$cnf( $equal(set_union2(X_50,X_51),set_union2(X_51,X_50)) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
( set_union2(X_50,X_51) != set_union2(X_50,set_union2(X_51,X_50))
| set_union2(X_51,X_50) != set_union2(X_50,X_51)
| set_union2(X_50,X_51) = set_union2(X_50,set_union2(X_50,X_51)) ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(X_50,X_51),set_union2(X_50,set_union2(X_51,X_50))) ),[1,1],$fot(set_union2(X_50,X_51))]]) ).
cnf(refute_0_49,plain,
( set_union2(X_50,X_51) != set_union2(X_50,set_union2(X_51,X_50))
| set_union2(X_50,X_51) = set_union2(X_50,set_union2(X_50,X_51)) ),
inference(resolve,[$cnf( $equal(set_union2(X_51,X_50),set_union2(X_50,X_51)) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
set_union2(X_50,X_51) = set_union2(X_50,set_union2(X_50,X_51)),
inference(resolve,[$cnf( $equal(set_union2(X_50,X_51),set_union2(X_50,set_union2(X_51,X_50))) )],[refute_0_43,refute_0_49]) ).
cnf(refute_0_51,plain,
set_union2(A,X_72) = set_union2(A,set_union2(A,X_72)),
inference(subst,[],[refute_0_50:[bind(X_50,$fot(A)),bind(X_51,$fot(X_72))]]) ).
cnf(refute_0_52,plain,
( set_union2(A,X_72) != set_union2(A,set_union2(A,X_72))
| set_union2(A,set_union2(A,X_72)) = set_union2(A,X_72) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(set_union2(A,X_72))),bind(Y,$fot(set_union2(A,set_union2(A,X_72))))]]) ).
cnf(refute_0_53,plain,
set_union2(A,set_union2(A,X_72)) = set_union2(A,X_72),
inference(resolve,[$cnf( $equal(set_union2(A,X_72),set_union2(A,set_union2(A,X_72))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
( set_difference(set_union2(A,set_union2(A,X_72)),set_union2(A,X_72)) != set_difference(A,set_union2(A,X_72))
| set_union2(A,set_union2(A,X_72)) != set_union2(A,X_72)
| set_difference(set_union2(A,X_72),set_union2(A,X_72)) = set_difference(A,set_union2(A,X_72)) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(A,set_union2(A,X_72)),set_union2(A,X_72)),set_difference(A,set_union2(A,X_72))) ),[0,0],$fot(set_union2(A,X_72))]]) ).
cnf(refute_0_55,plain,
( set_difference(set_union2(A,set_union2(A,X_72)),set_union2(A,X_72)) != set_difference(A,set_union2(A,X_72))
| set_difference(set_union2(A,X_72),set_union2(A,X_72)) = set_difference(A,set_union2(A,X_72)) ),
inference(resolve,[$cnf( $equal(set_union2(A,set_union2(A,X_72)),set_union2(A,X_72)) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
set_difference(set_union2(A,X_72),set_union2(A,X_72)) = set_difference(A,set_union2(A,X_72)),
inference(resolve,[$cnf( $equal(set_difference(set_union2(A,set_union2(A,X_72)),set_union2(A,X_72)),set_difference(A,set_union2(A,X_72))) )],[refute_0_32,refute_0_55]) ).
cnf(refute_0_57,plain,
set_difference(set_union2(empty_set,X_48),X_48) = set_difference(empty_set,X_48),
inference(subst,[],[refute_0_16:[bind(A,$fot(empty_set)),bind(B,$fot(X_48))]]) ).
cnf(refute_0_58,plain,
set_union2(A,empty_set) = A,
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_59,plain,
set_union2(A,empty_set) = set_union2(empty_set,A),
inference(subst,[],[refute_0_44:[bind(B,$fot(empty_set))]]) ).
cnf(refute_0_60,plain,
( set_union2(A,empty_set) != A
| set_union2(A,empty_set) != set_union2(empty_set,A)
| set_union2(empty_set,A) = A ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(A,empty_set),A) ),[0],$fot(set_union2(empty_set,A))]]) ).
cnf(refute_0_61,plain,
( set_union2(A,empty_set) != A
| set_union2(empty_set,A) = A ),
inference(resolve,[$cnf( $equal(set_union2(A,empty_set),set_union2(empty_set,A)) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
set_union2(empty_set,A) = A,
inference(resolve,[$cnf( $equal(set_union2(A,empty_set),A) )],[refute_0_58,refute_0_61]) ).
cnf(refute_0_63,plain,
set_union2(empty_set,X_48) = X_48,
inference(subst,[],[refute_0_62:[bind(A,$fot(X_48))]]) ).
cnf(refute_0_64,plain,
( set_difference(set_union2(empty_set,X_48),X_48) != set_difference(empty_set,X_48)
| set_union2(empty_set,X_48) != X_48
| set_difference(X_48,X_48) = set_difference(empty_set,X_48) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(empty_set,X_48),X_48),set_difference(empty_set,X_48)) ),[0,0],$fot(X_48)]]) ).
cnf(refute_0_65,plain,
( set_difference(set_union2(empty_set,X_48),X_48) != set_difference(empty_set,X_48)
| set_difference(X_48,X_48) = set_difference(empty_set,X_48) ),
inference(resolve,[$cnf( $equal(set_union2(empty_set,X_48),X_48) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
set_difference(X_48,X_48) = set_difference(empty_set,X_48),
inference(resolve,[$cnf( $equal(set_difference(set_union2(empty_set,X_48),X_48),set_difference(empty_set,X_48)) )],[refute_0_57,refute_0_65]) ).
cnf(refute_0_67,plain,
set_difference(empty_set,A) = empty_set,
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_68,plain,
set_difference(empty_set,X_48) = empty_set,
inference(subst,[],[refute_0_67:[bind(A,$fot(X_48))]]) ).
cnf(refute_0_69,plain,
( set_difference(X_48,X_48) != set_difference(empty_set,X_48)
| set_difference(empty_set,X_48) != empty_set
| set_difference(X_48,X_48) = empty_set ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(X_48,X_48),empty_set) ),[0],$fot(set_difference(empty_set,X_48))]]) ).
cnf(refute_0_70,plain,
( set_difference(X_48,X_48) != set_difference(empty_set,X_48)
| set_difference(X_48,X_48) = empty_set ),
inference(resolve,[$cnf( $equal(set_difference(empty_set,X_48),empty_set) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
set_difference(X_48,X_48) = empty_set,
inference(resolve,[$cnf( $equal(set_difference(X_48,X_48),set_difference(empty_set,X_48)) )],[refute_0_66,refute_0_70]) ).
cnf(refute_0_72,plain,
set_difference(set_union2(A,X_72),set_union2(A,X_72)) = empty_set,
inference(subst,[],[refute_0_71:[bind(X_48,$fot(set_union2(A,X_72)))]]) ).
cnf(refute_0_73,plain,
( set_difference(set_union2(A,X_72),set_union2(A,X_72)) != empty_set
| set_difference(set_union2(A,X_72),set_union2(A,X_72)) != set_difference(A,set_union2(A,X_72))
| empty_set = set_difference(A,set_union2(A,X_72)) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(A,X_72),set_union2(A,X_72)),set_difference(A,set_union2(A,X_72))) ),[0],$fot(empty_set)]]) ).
cnf(refute_0_74,plain,
( set_difference(set_union2(A,X_72),set_union2(A,X_72)) != set_difference(A,set_union2(A,X_72))
| empty_set = set_difference(A,set_union2(A,X_72)) ),
inference(resolve,[$cnf( $equal(set_difference(set_union2(A,X_72),set_union2(A,X_72)),empty_set) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
empty_set = set_difference(A,set_union2(A,X_72)),
inference(resolve,[$cnf( $equal(set_difference(set_union2(A,X_72),set_union2(A,X_72)),set_difference(A,set_union2(A,X_72))) )],[refute_0_56,refute_0_74]) ).
cnf(refute_0_76,plain,
empty_set = set_difference(X_73,set_union2(X_73,X_74)),
inference(subst,[],[refute_0_75:[bind(A,$fot(X_73)),bind(X_72,$fot(X_74))]]) ).
cnf(refute_0_77,plain,
set_union2(X_74,X_73) = set_union2(X_73,X_74),
inference(subst,[],[refute_0_44:[bind(A,$fot(X_74)),bind(B,$fot(X_73))]]) ).
cnf(refute_0_78,plain,
( set_union2(X_74,X_73) != set_union2(X_73,X_74)
| set_union2(X_73,X_74) = set_union2(X_74,X_73) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(set_union2(X_74,X_73))),bind(Y,$fot(set_union2(X_73,X_74)))]]) ).
cnf(refute_0_79,plain,
set_union2(X_73,X_74) = set_union2(X_74,X_73),
inference(resolve,[$cnf( $equal(set_union2(X_74,X_73),set_union2(X_73,X_74)) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
( empty_set != set_difference(X_73,set_union2(X_73,X_74))
| set_union2(X_73,X_74) != set_union2(X_74,X_73)
| empty_set = set_difference(X_73,set_union2(X_74,X_73)) ),
introduced(tautology,[equality,[$cnf( $equal(empty_set,set_difference(X_73,set_union2(X_73,X_74))) ),[1,1],$fot(set_union2(X_74,X_73))]]) ).
cnf(refute_0_81,plain,
( empty_set != set_difference(X_73,set_union2(X_73,X_74))
| empty_set = set_difference(X_73,set_union2(X_74,X_73)) ),
inference(resolve,[$cnf( $equal(set_union2(X_73,X_74),set_union2(X_74,X_73)) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
empty_set = set_difference(X_73,set_union2(X_74,X_73)),
inference(resolve,[$cnf( $equal(empty_set,set_difference(X_73,set_union2(X_73,X_74))) )],[refute_0_76,refute_0_81]) ).
cnf(refute_0_83,plain,
empty_set = set_difference(A,set_union2(X_76,A)),
inference(subst,[],[refute_0_82:[bind(X_73,$fot(A)),bind(X_74,$fot(X_76))]]) ).
cnf(refute_0_84,plain,
( empty_set != set_difference(A,set_union2(X_76,A))
| set_difference(A,set_union2(X_76,A)) = empty_set ),
inference(subst,[],[refute_0_24:[bind(X,$fot(empty_set)),bind(Y,$fot(set_difference(A,set_union2(X_76,A))))]]) ).
cnf(refute_0_85,plain,
set_difference(A,set_union2(X_76,A)) = empty_set,
inference(resolve,[$cnf( $equal(empty_set,set_difference(A,set_union2(X_76,A))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
( set_difference(A,set_difference(A,set_union2(X_76,A))) != set_intersection2(A,set_union2(X_76,A))
| set_difference(A,set_union2(X_76,A)) != empty_set
| set_difference(A,empty_set) = set_intersection2(A,set_union2(X_76,A)) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(A,set_difference(A,set_union2(X_76,A))),set_intersection2(A,set_union2(X_76,A))) ),[0,1],$fot(empty_set)]]) ).
cnf(refute_0_87,plain,
( set_difference(A,set_difference(A,set_union2(X_76,A))) != set_intersection2(A,set_union2(X_76,A))
| set_difference(A,empty_set) = set_intersection2(A,set_union2(X_76,A)) ),
inference(resolve,[$cnf( $equal(set_difference(A,set_union2(X_76,A)),empty_set) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
set_difference(A,empty_set) = set_intersection2(A,set_union2(X_76,A)),
inference(resolve,[$cnf( $equal(set_difference(A,set_difference(A,set_union2(X_76,A))),set_intersection2(A,set_union2(X_76,A))) )],[refute_0_31,refute_0_87]) ).
cnf(refute_0_89,plain,
set_difference(A,empty_set) = A,
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_90,plain,
( set_difference(A,empty_set) != A
| set_difference(A,empty_set) != set_intersection2(A,set_union2(X_76,A))
| A = set_intersection2(A,set_union2(X_76,A)) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(A,empty_set),set_intersection2(A,set_union2(X_76,A))) ),[0],$fot(A)]]) ).
cnf(refute_0_91,plain,
( set_difference(A,empty_set) != set_intersection2(A,set_union2(X_76,A))
| A = set_intersection2(A,set_union2(X_76,A)) ),
inference(resolve,[$cnf( $equal(set_difference(A,empty_set),A) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
A = set_intersection2(A,set_union2(X_76,A)),
inference(resolve,[$cnf( $equal(set_difference(A,empty_set),set_intersection2(A,set_union2(X_76,A))) )],[refute_0_88,refute_0_91]) ).
cnf(refute_0_93,plain,
( A != set_intersection2(A,set_union2(X_76,A))
| set_intersection2(A,set_union2(X_76,A)) = A ),
inference(subst,[],[refute_0_24:[bind(X,$fot(A)),bind(Y,$fot(set_intersection2(A,set_union2(X_76,A))))]]) ).
cnf(refute_0_94,plain,
set_intersection2(A,set_union2(X_76,A)) = A,
inference(resolve,[$cnf( $equal(A,set_intersection2(A,set_union2(X_76,A))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
set_intersection2(X_53,set_union2(A,X_53)) = X_53,
inference(subst,[],[refute_0_94:[bind(A,$fot(X_53)),bind(X_76,$fot(A))]]) ).
cnf(refute_0_96,plain,
( set_difference(set_union2(A,X_53),set_difference(A,X_53)) != set_intersection2(X_53,set_union2(A,X_53))
| set_intersection2(X_53,set_union2(A,X_53)) != X_53
| set_difference(set_union2(A,X_53),set_difference(A,X_53)) = X_53 ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(set_union2(A,X_53),set_difference(A,X_53)),X_53) ),[0],$fot(set_intersection2(X_53,set_union2(A,X_53)))]]) ).
cnf(refute_0_97,plain,
( set_difference(set_union2(A,X_53),set_difference(A,X_53)) != set_intersection2(X_53,set_union2(A,X_53))
| set_difference(set_union2(A,X_53),set_difference(A,X_53)) = X_53 ),
inference(resolve,[$cnf( $equal(set_intersection2(X_53,set_union2(A,X_53)),X_53) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
set_difference(set_union2(A,X_53),set_difference(A,X_53)) = X_53,
inference(resolve,[$cnf( $equal(set_difference(set_union2(A,X_53),set_difference(A,X_53)),set_intersection2(X_53,set_union2(A,X_53))) )],[refute_0_30,refute_0_97]) ).
cnf(refute_0_99,plain,
set_difference(set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),set_difference(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1)) = skolemFOFtoCNF_B_1,
inference(subst,[],[refute_0_98:[bind(A,$fot(singleton(skolemFOFtoCNF_A_2))),bind(X_53,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_100,plain,
subset(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_101,plain,
( ~ subset(A,B)
| set_difference(A,B) = empty_set ),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_102,plain,
( ~ subset(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1)
| set_difference(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) = empty_set ),
inference(subst,[],[refute_0_101:[bind(A,$fot(singleton(skolemFOFtoCNF_A_2))),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_103,plain,
set_difference(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) = empty_set,
inference(resolve,[$cnf( subset(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) )],[refute_0_100,refute_0_102]) ).
cnf(refute_0_104,plain,
( set_difference(set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),set_difference(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1)) != skolemFOFtoCNF_B_1
| set_difference(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) != empty_set
| set_difference(set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),empty_set) = skolemFOFtoCNF_B_1 ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),set_difference(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1)),skolemFOFtoCNF_B_1) ),[0,1],$fot(empty_set)]]) ).
cnf(refute_0_105,plain,
( set_difference(set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),set_difference(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1)) != skolemFOFtoCNF_B_1
| set_difference(set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),empty_set) = skolemFOFtoCNF_B_1 ),
inference(resolve,[$cnf( $equal(set_difference(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),empty_set) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
set_difference(set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),empty_set) = skolemFOFtoCNF_B_1,
inference(resolve,[$cnf( $equal(set_difference(set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),set_difference(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1)),skolemFOFtoCNF_B_1) )],[refute_0_99,refute_0_105]) ).
cnf(refute_0_107,plain,
( set_union2(A,B) != set_union2(B,A)
| set_union2(B,A) = set_union2(A,B) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(set_union2(A,B))),bind(Y,$fot(set_union2(B,A)))]]) ).
cnf(refute_0_108,plain,
set_union2(B,A) = set_union2(A,B),
inference(resolve,[$cnf( $equal(set_union2(A,B),set_union2(B,A)) )],[refute_0_44,refute_0_107]) ).
cnf(refute_0_109,plain,
set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) = set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)),
inference(subst,[],[refute_0_108:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(singleton(skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_110,plain,
set_difference(set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),empty_set) = set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_89:[bind(A,$fot(set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1)))]]) ).
cnf(refute_0_111,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_112,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_24,refute_0_111]) ).
cnf(refute_0_113,plain,
( set_difference(set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),empty_set) != set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1)
| set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) != set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))
| set_difference(set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),empty_set) = set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)) ),
inference(subst,[],[refute_0_112:[bind(X,$fot(set_difference(set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),empty_set))),bind(Y,$fot(set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1))),bind(Z,$fot(set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))))]]) ).
cnf(refute_0_114,plain,
( set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) != set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))
| set_difference(set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),empty_set) = set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)) ),
inference(resolve,[$cnf( $equal(set_difference(set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),empty_set),set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1)) )],[refute_0_110,refute_0_113]) ).
cnf(refute_0_115,plain,
set_difference(set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),empty_set) = set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)),
inference(resolve,[$cnf( $equal(set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))) )],[refute_0_109,refute_0_114]) ).
cnf(refute_0_116,plain,
( set_difference(set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),empty_set) != set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))
| set_difference(set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),empty_set) != skolemFOFtoCNF_B_1
| set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)) = skolemFOFtoCNF_B_1 ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),empty_set),skolemFOFtoCNF_B_1) ),[0],$fot(set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_117,plain,
( set_difference(set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),empty_set) != skolemFOFtoCNF_B_1
| set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)) = skolemFOFtoCNF_B_1 ),
inference(resolve,[$cnf( $equal(set_difference(set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),empty_set),set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)) = skolemFOFtoCNF_B_1,
inference(resolve,[$cnf( $equal(set_difference(set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),empty_set),skolemFOFtoCNF_B_1) )],[refute_0_106,refute_0_117]) ).
cnf(refute_0_119,plain,
( set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)) != skolemFOFtoCNF_B_1
| ~ in(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)))
| in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) ),
introduced(tautology,[equality,[$cnf( in(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))) ),[1],$fot(skolemFOFtoCNF_B_1)]]) ).
cnf(refute_0_120,plain,
( ~ in(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)))
| in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( $equal(set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)),skolemFOFtoCNF_B_1) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))) )],[refute_0_13,refute_0_120]) ).
cnf(refute_0_122,plain,
~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_123,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) )],[refute_0_121,refute_0_122]) ).
fof(negate_1_0,plain,
~ ! [A,B] :
( in(A,B)
=> subset(singleton(A),B) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(canonicalize,[],[d3_tarski]) ).
fof(normalize_1_1,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
! [A,B,C] :
( ( ~ in(skolemFOFtoCNF_C_1(A,B),B)
| subset(A,B) )
& ( in(skolemFOFtoCNF_C_1(A,B),A)
| subset(A,B) )
& ( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ) ),
inference(clausify,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [A,B] :
( ~ in(skolemFOFtoCNF_C_1(A,B),B)
| subset(A,B) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
? [A,B] :
( ~ subset(singleton(A),B)
& in(A,B) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_5,plain,
( ~ subset(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2)
& in(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2) ),
inference(skolemize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
~ subset(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(canonicalize,[],[d1_tarski]) ).
fof(normalize_1_8,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(specialize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [A,B,C] :
( ( B != singleton(A)
| C != A
| in(C,B) )
& ( B != singleton(A)
| ~ in(C,B)
| C = A )
& ( skolemFOFtoCNF_C(A,B) != A
| ~ in(skolemFOFtoCNF_C(A,B),B)
| B = singleton(A) )
& ( B = singleton(A)
| skolemFOFtoCNF_C(A,B) = A
| in(skolemFOFtoCNF_C(A,B),B) ) ),
inference(clausify,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
! [A,B,C] :
( B != singleton(A)
| ~ in(C,B)
| C = A ),
inference(conjunct,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
! [A,B] :
( in(skolemFOFtoCNF_C_1(A,B),A)
| subset(A,B) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_12,plain,
in(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2),
inference(conjunct,[],[normalize_1_5]) ).
cnf(refute_1_0,plain,
( ~ in(skolemFOFtoCNF_C_1(A,B),B)
| subset(A,B) ),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_1,plain,
( ~ in(skolemFOFtoCNF_C_1(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2),skolemFOFtoCNF_B_2)
| subset(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2) ),
inference(subst,[],[refute_1_0:[bind(A,$fot(singleton(skolemFOFtoCNF_A_3))),bind(B,$fot(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_1_2,plain,
~ subset(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_3,plain,
( B != singleton(A)
| ~ in(C,B)
| C = A ),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_4,plain,
( singleton(A) != singleton(A)
| ~ in(C,singleton(A))
| C = A ),
inference(subst,[],[refute_1_3:[bind(B,$fot(singleton(A)))]]) ).
cnf(refute_1_5,plain,
singleton(A) = singleton(A),
introduced(tautology,[refl,[$fot(singleton(A))]]) ).
cnf(refute_1_6,plain,
( ~ in(C,singleton(A))
| C = A ),
inference(resolve,[$cnf( $equal(singleton(A),singleton(A)) )],[refute_1_5,refute_1_4]) ).
cnf(refute_1_7,plain,
( ~ in(skolemFOFtoCNF_C_1(singleton(A),X_633),singleton(A))
| skolemFOFtoCNF_C_1(singleton(A),X_633) = A ),
inference(subst,[],[refute_1_6:[bind(C,$fot(skolemFOFtoCNF_C_1(singleton(A),X_633)))]]) ).
cnf(refute_1_8,plain,
( in(skolemFOFtoCNF_C_1(A,B),A)
| subset(A,B) ),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_9,plain,
( in(skolemFOFtoCNF_C_1(singleton(A),X_633),singleton(A))
| subset(singleton(A),X_633) ),
inference(subst,[],[refute_1_8:[bind(A,$fot(singleton(A))),bind(B,$fot(X_633))]]) ).
cnf(refute_1_10,plain,
( skolemFOFtoCNF_C_1(singleton(A),X_633) = A
| subset(singleton(A),X_633) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(singleton(A),X_633),singleton(A)) )],[refute_1_9,refute_1_7]) ).
cnf(refute_1_11,plain,
( skolemFOFtoCNF_C_1(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2) = skolemFOFtoCNF_A_3
| subset(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2) ),
inference(subst,[],[refute_1_10:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(X_633,$fot(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_1_12,plain,
skolemFOFtoCNF_C_1(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2) = skolemFOFtoCNF_A_3,
inference(resolve,[$cnf( subset(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2) )],[refute_1_11,refute_1_2]) ).
cnf(refute_1_13,plain,
( skolemFOFtoCNF_C_1(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2) != skolemFOFtoCNF_A_3
| ~ in(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2)
| in(skolemFOFtoCNF_C_1(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2),skolemFOFtoCNF_B_2) ),
introduced(tautology,[equality,[$cnf( ~ in(skolemFOFtoCNF_C_1(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2),skolemFOFtoCNF_B_2) ),[0],$fot(skolemFOFtoCNF_A_3)]]) ).
cnf(refute_1_14,plain,
( ~ in(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2)
| in(skolemFOFtoCNF_C_1(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2),skolemFOFtoCNF_B_2) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C_1(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2),skolemFOFtoCNF_A_3) )],[refute_1_12,refute_1_13]) ).
cnf(refute_1_15,plain,
( ~ in(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2)
| subset(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2),skolemFOFtoCNF_B_2) )],[refute_1_14,refute_1_1]) ).
cnf(refute_1_16,plain,
in(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2),
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_17,plain,
subset(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2) )],[refute_1_16,refute_1_15]) ).
cnf(refute_1_18,plain,
$false,
inference(resolve,[$cnf( subset(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2) )],[refute_1_17,refute_1_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU144+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 19 17:03:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.45/1.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.45/1.63
% 1.45/1.63 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.45/1.64
%------------------------------------------------------------------------------