%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU153+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 12:38:49 EDT 2022
% Result : Theorem 0.79s 0.94s
% Output : CNFRefutation 0.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 34
% Syntax : Number of formulae : 166 ( 94 unt; 0 def)
% Number of atoms : 264 ( 219 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 199 ( 101 ~; 84 |; 5 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 239 ( 12 sgn 74 !; 2 ?)
% 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(d7_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ) ).
fof(l1_zfmisc_1,lemma,
! [A] : singleton(A) != empty_set ).
fof(l25_zfmisc_1,conjecture,
! [A,B] :
~ ( disjoint(singleton(A),B)
& in(A,B) ) ).
fof(l2_zfmisc_1,lemma,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ) ).
fof(t12_xboole_1,lemma,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ) ).
fof(t1_boole,axiom,
! [A] : set_union2(A,empty_set) = A ).
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] :
( disjoint(singleton(A),B)
=> ~ in(A,B) ),
inference(strip,[],[l25_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( disjoint(singleton(A),B)
=> ~ in(A,B) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B] :
( disjoint(singleton(A),B)
& in(A,B) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( disjoint(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1)
& in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
disjoint(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( set_intersection2(A,B) != empty_set
<=> ~ disjoint(A,B) ),
inference(canonicalize,[],[d7_xboole_0]) ).
fof(normalize_0_4,plain,
! [A,B] :
( set_intersection2(A,B) != empty_set
<=> ~ disjoint(A,B) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B] :
( ( set_intersection2(A,B) != empty_set
| disjoint(A,B) )
& ( ~ disjoint(A,B)
| set_intersection2(A,B) = empty_set ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B] :
( ~ disjoint(A,B)
| set_intersection2(A,B) = empty_set ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(canonicalize,[],[t48_xboole_1]) ).
fof(normalize_0_8,plain,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
inference(canonicalize,[],[t40_xboole_1]) ).
fof(normalize_0_10,plain,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(canonicalize,[],[commutativity_k3_xboole_0]) ).
fof(normalize_0_12,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
inference(canonicalize,[],[t39_xboole_1]) ).
fof(normalize_0_14,plain,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[commutativity_k2_xboole_0]) ).
fof(normalize_0_16,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [A] : set_union2(A,empty_set) = A,
inference(canonicalize,[],[t1_boole]) ).
fof(normalize_0_18,plain,
! [A] : set_union2(A,empty_set) = A,
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(canonicalize,[],[t4_boole]) ).
fof(normalize_0_20,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [A] : set_difference(A,empty_set) = A,
inference(canonicalize,[],[t3_boole]) ).
fof(normalize_0_22,plain,
! [A] : set_difference(A,empty_set) = A,
inference(specialize,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [A,B] :
( ~ subset(A,B)
| set_union2(A,B) = B ),
inference(canonicalize,[],[t12_xboole_1]) ).
fof(normalize_0_24,plain,
! [A,B] :
( ~ subset(A,B)
| set_union2(A,B) = B ),
inference(specialize,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_26,plain,
! [A,B] :
( ~ in(A,B)
<=> ~ subset(singleton(A),B) ),
inference(canonicalize,[],[l2_zfmisc_1]) ).
fof(normalize_0_27,plain,
! [A,B] :
( ~ in(A,B)
<=> ~ subset(singleton(A),B) ),
inference(specialize,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [A,B] :
( ( ~ in(A,B)
| subset(singleton(A),B) )
& ( ~ subset(singleton(A),B)
| in(A,B) ) ),
inference(clausify,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
! [A,B] :
( ~ in(A,B)
| subset(singleton(A),B) ),
inference(conjunct,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
! [A] : singleton(A) != empty_set,
inference(canonicalize,[],[l1_zfmisc_1]) ).
fof(normalize_0_31,plain,
! [A] : singleton(A) != empty_set,
inference(specialize,[],[normalize_0_30]) ).
cnf(refute_0_0,plain,
disjoint(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ disjoint(A,B)
| set_intersection2(A,B) = empty_set ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( ~ disjoint(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1)
| set_intersection2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) = empty_set ),
inference(subst,[],[refute_0_1:[bind(A,$fot(singleton(skolemFOFtoCNF_A_2))),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_3,plain,
set_intersection2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) = empty_set,
inference(resolve,[$cnf( disjoint(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
set_difference(set_union2(A,X_57),set_difference(set_union2(A,X_57),X_57)) = set_intersection2(set_union2(A,X_57),X_57),
inference(subst,[],[refute_0_4:[bind(A,$fot(set_union2(A,X_57))),bind(B,$fot(X_57))]]) ).
cnf(refute_0_6,plain,
set_difference(set_union2(A,B),B) = set_difference(A,B),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_7,plain,
set_difference(set_union2(A,X_57),X_57) = set_difference(A,X_57),
inference(subst,[],[refute_0_6:[bind(B,$fot(X_57))]]) ).
cnf(refute_0_8,plain,
( set_difference(set_union2(A,X_57),X_57) != set_difference(A,X_57)
| set_difference(set_union2(A,X_57),set_difference(set_union2(A,X_57),X_57)) != set_intersection2(set_union2(A,X_57),X_57)
| set_difference(set_union2(A,X_57),set_difference(A,X_57)) = set_intersection2(set_union2(A,X_57),X_57) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(A,X_57),set_difference(set_union2(A,X_57),X_57)),set_intersection2(set_union2(A,X_57),X_57)) ),[0,1],$fot(set_difference(A,X_57))]]) ).
cnf(refute_0_9,plain,
( set_difference(set_union2(A,X_57),set_difference(set_union2(A,X_57),X_57)) != set_intersection2(set_union2(A,X_57),X_57)
| set_difference(set_union2(A,X_57),set_difference(A,X_57)) = set_intersection2(set_union2(A,X_57),X_57) ),
inference(resolve,[$cnf( $equal(set_difference(set_union2(A,X_57),X_57),set_difference(A,X_57)) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
set_difference(set_union2(A,X_57),set_difference(A,X_57)) = set_intersection2(set_union2(A,X_57),X_57),
inference(resolve,[$cnf( $equal(set_difference(set_union2(A,X_57),set_difference(set_union2(A,X_57),X_57)),set_intersection2(set_union2(A,X_57),X_57)) )],[refute_0_5,refute_0_9]) ).
cnf(refute_0_11,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_12,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_13,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_14,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( set_intersection2(A,B) != set_intersection2(B,A)
| set_intersection2(B,A) = set_intersection2(A,B) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(set_intersection2(A,B))),bind(Y,$fot(set_intersection2(B,A)))]]) ).
cnf(refute_0_16,plain,
set_intersection2(B,A) = set_intersection2(A,B),
inference(resolve,[$cnf( $equal(set_intersection2(A,B),set_intersection2(B,A)) )],[refute_0_11,refute_0_15]) ).
cnf(refute_0_17,plain,
set_intersection2(set_union2(A,X_57),X_57) = set_intersection2(X_57,set_union2(A,X_57)),
inference(subst,[],[refute_0_16:[bind(A,$fot(X_57)),bind(B,$fot(set_union2(A,X_57)))]]) ).
cnf(refute_0_18,plain,
( set_difference(set_union2(A,X_57),set_difference(A,X_57)) != set_intersection2(set_union2(A,X_57),X_57)
| set_intersection2(set_union2(A,X_57),X_57) != set_intersection2(X_57,set_union2(A,X_57))
| set_difference(set_union2(A,X_57),set_difference(A,X_57)) = set_intersection2(X_57,set_union2(A,X_57)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(set_union2(A,X_57),set_difference(A,X_57)),set_intersection2(X_57,set_union2(A,X_57))) ),[0],$fot(set_intersection2(set_union2(A,X_57),X_57))]]) ).
cnf(refute_0_19,plain,
( set_difference(set_union2(A,X_57),set_difference(A,X_57)) != set_intersection2(set_union2(A,X_57),X_57)
| set_difference(set_union2(A,X_57),set_difference(A,X_57)) = set_intersection2(X_57,set_union2(A,X_57)) ),
inference(resolve,[$cnf( $equal(set_intersection2(set_union2(A,X_57),X_57),set_intersection2(X_57,set_union2(A,X_57))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
set_difference(set_union2(A,X_57),set_difference(A,X_57)) = set_intersection2(X_57,set_union2(A,X_57)),
inference(resolve,[$cnf( $equal(set_difference(set_union2(A,X_57),set_difference(A,X_57)),set_intersection2(set_union2(A,X_57),X_57)) )],[refute_0_10,refute_0_19]) ).
cnf(refute_0_21,plain,
set_difference(X_56,set_difference(X_56,set_union2(X_53,X_56))) = set_intersection2(X_56,set_union2(X_53,X_56)),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_56)),bind(B,$fot(set_union2(X_53,X_56)))]]) ).
cnf(refute_0_22,plain,
set_difference(set_union2(A,set_union2(A,X_50)),set_union2(A,X_50)) = set_difference(A,set_union2(A,X_50)),
inference(subst,[],[refute_0_6:[bind(B,$fot(set_union2(A,X_50)))]]) ).
cnf(refute_0_23,plain,
set_union2(A,set_difference(B,A)) = set_union2(A,B),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_24,plain,
set_union2(X_48,set_difference(set_union2(X_48,A),X_48)) = set_union2(X_48,set_union2(X_48,A)),
inference(subst,[],[refute_0_23:[bind(A,$fot(X_48)),bind(B,$fot(set_union2(X_48,A)))]]) ).
cnf(refute_0_25,plain,
set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_26,plain,
( set_difference(set_union2(A,B),B) != set_difference(A,B)
| set_union2(A,B) != set_union2(B,A)
| set_difference(set_union2(B,A),B) = set_difference(A,B) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(A,B),B),set_difference(A,B)) ),[0,0],$fot(set_union2(B,A))]]) ).
cnf(refute_0_27,plain,
( set_difference(set_union2(A,B),B) != set_difference(A,B)
| set_difference(set_union2(B,A),B) = set_difference(A,B) ),
inference(resolve,[$cnf( $equal(set_union2(A,B),set_union2(B,A)) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
set_difference(set_union2(B,A),B) = set_difference(A,B),
inference(resolve,[$cnf( $equal(set_difference(set_union2(A,B),B),set_difference(A,B)) )],[refute_0_6,refute_0_27]) ).
cnf(refute_0_29,plain,
set_difference(set_union2(X_48,A),X_48) = set_difference(A,X_48),
inference(subst,[],[refute_0_28:[bind(B,$fot(X_48))]]) ).
cnf(refute_0_30,plain,
( set_difference(set_union2(X_48,A),X_48) != set_difference(A,X_48)
| set_union2(X_48,set_difference(set_union2(X_48,A),X_48)) != set_union2(X_48,set_union2(X_48,A))
| set_union2(X_48,set_difference(A,X_48)) = set_union2(X_48,set_union2(X_48,A)) ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(X_48,set_difference(set_union2(X_48,A),X_48)),set_union2(X_48,set_union2(X_48,A))) ),[0,1],$fot(set_difference(A,X_48))]]) ).
cnf(refute_0_31,plain,
( set_union2(X_48,set_difference(set_union2(X_48,A),X_48)) != set_union2(X_48,set_union2(X_48,A))
| set_union2(X_48,set_difference(A,X_48)) = set_union2(X_48,set_union2(X_48,A)) ),
inference(resolve,[$cnf( $equal(set_difference(set_union2(X_48,A),X_48),set_difference(A,X_48)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
set_union2(X_48,set_difference(A,X_48)) = set_union2(X_48,set_union2(X_48,A)),
inference(resolve,[$cnf( $equal(set_union2(X_48,set_difference(set_union2(X_48,A),X_48)),set_union2(X_48,set_union2(X_48,A))) )],[refute_0_24,refute_0_31]) ).
cnf(refute_0_33,plain,
set_union2(X_48,set_difference(A,X_48)) = set_union2(X_48,A),
inference(subst,[],[refute_0_23:[bind(A,$fot(X_48)),bind(B,$fot(A))]]) ).
cnf(refute_0_34,plain,
( set_union2(X_48,set_difference(A,X_48)) != set_union2(X_48,A)
| set_union2(X_48,set_difference(A,X_48)) != set_union2(X_48,set_union2(X_48,A))
| set_union2(X_48,A) = set_union2(X_48,set_union2(X_48,A)) ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(X_48,set_difference(A,X_48)),set_union2(X_48,set_union2(X_48,A))) ),[0],$fot(set_union2(X_48,A))]]) ).
cnf(refute_0_35,plain,
( set_union2(X_48,set_difference(A,X_48)) != set_union2(X_48,set_union2(X_48,A))
| set_union2(X_48,A) = set_union2(X_48,set_union2(X_48,A)) ),
inference(resolve,[$cnf( $equal(set_union2(X_48,set_difference(A,X_48)),set_union2(X_48,A)) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
set_union2(X_48,A) = set_union2(X_48,set_union2(X_48,A)),
inference(resolve,[$cnf( $equal(set_union2(X_48,set_difference(A,X_48)),set_union2(X_48,set_union2(X_48,A))) )],[refute_0_32,refute_0_35]) ).
cnf(refute_0_37,plain,
set_union2(A,X_50) = set_union2(A,set_union2(A,X_50)),
inference(subst,[],[refute_0_36:[bind(A,$fot(X_50)),bind(X_48,$fot(A))]]) ).
cnf(refute_0_38,plain,
( set_union2(A,X_50) != set_union2(A,set_union2(A,X_50))
| set_union2(A,set_union2(A,X_50)) = set_union2(A,X_50) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(set_union2(A,X_50))),bind(Y,$fot(set_union2(A,set_union2(A,X_50))))]]) ).
cnf(refute_0_39,plain,
set_union2(A,set_union2(A,X_50)) = set_union2(A,X_50),
inference(resolve,[$cnf( $equal(set_union2(A,X_50),set_union2(A,set_union2(A,X_50))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( set_difference(set_union2(A,set_union2(A,X_50)),set_union2(A,X_50)) != set_difference(A,set_union2(A,X_50))
| set_union2(A,set_union2(A,X_50)) != set_union2(A,X_50)
| set_difference(set_union2(A,X_50),set_union2(A,X_50)) = set_difference(A,set_union2(A,X_50)) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(A,set_union2(A,X_50)),set_union2(A,X_50)),set_difference(A,set_union2(A,X_50))) ),[0,0],$fot(set_union2(A,X_50))]]) ).
cnf(refute_0_41,plain,
( set_difference(set_union2(A,set_union2(A,X_50)),set_union2(A,X_50)) != set_difference(A,set_union2(A,X_50))
| set_difference(set_union2(A,X_50),set_union2(A,X_50)) = set_difference(A,set_union2(A,X_50)) ),
inference(resolve,[$cnf( $equal(set_union2(A,set_union2(A,X_50)),set_union2(A,X_50)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
set_difference(set_union2(A,X_50),set_union2(A,X_50)) = set_difference(A,set_union2(A,X_50)),
inference(resolve,[$cnf( $equal(set_difference(set_union2(A,set_union2(A,X_50)),set_union2(A,X_50)),set_difference(A,set_union2(A,X_50))) )],[refute_0_22,refute_0_41]) ).
cnf(refute_0_43,plain,
set_difference(set_union2(empty_set,B),B) = set_difference(empty_set,B),
inference(subst,[],[refute_0_6:[bind(A,$fot(empty_set))]]) ).
cnf(refute_0_44,plain,
set_union2(A,empty_set) = A,
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_45,plain,
set_union2(A,empty_set) = set_union2(empty_set,A),
inference(subst,[],[refute_0_25:[bind(B,$fot(empty_set))]]) ).
cnf(refute_0_46,plain,
( set_union2(A,empty_set) != A
| set_union2(A,empty_set) != set_union2(empty_set,A)
| set_union2(empty_set,A) = A ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(A,empty_set),A) ),[0],$fot(set_union2(empty_set,A))]]) ).
cnf(refute_0_47,plain,
( set_union2(A,empty_set) != A
| set_union2(empty_set,A) = A ),
inference(resolve,[$cnf( $equal(set_union2(A,empty_set),set_union2(empty_set,A)) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
set_union2(empty_set,A) = A,
inference(resolve,[$cnf( $equal(set_union2(A,empty_set),A) )],[refute_0_44,refute_0_47]) ).
cnf(refute_0_49,plain,
set_union2(empty_set,B) = B,
inference(subst,[],[refute_0_48:[bind(A,$fot(B))]]) ).
cnf(refute_0_50,plain,
( set_difference(set_union2(empty_set,B),B) != set_difference(empty_set,B)
| set_union2(empty_set,B) != B
| set_difference(B,B) = set_difference(empty_set,B) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(empty_set,B),B),set_difference(empty_set,B)) ),[0,0],$fot(B)]]) ).
cnf(refute_0_51,plain,
( set_difference(set_union2(empty_set,B),B) != set_difference(empty_set,B)
| set_difference(B,B) = set_difference(empty_set,B) ),
inference(resolve,[$cnf( $equal(set_union2(empty_set,B),B) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
set_difference(B,B) = set_difference(empty_set,B),
inference(resolve,[$cnf( $equal(set_difference(set_union2(empty_set,B),B),set_difference(empty_set,B)) )],[refute_0_43,refute_0_51]) ).
cnf(refute_0_53,plain,
set_difference(empty_set,A) = empty_set,
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_54,plain,
set_difference(empty_set,B) = empty_set,
inference(subst,[],[refute_0_53:[bind(A,$fot(B))]]) ).
cnf(refute_0_55,plain,
( set_difference(B,B) != set_difference(empty_set,B)
| set_difference(empty_set,B) != empty_set
| set_difference(B,B) = empty_set ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(B,B),empty_set) ),[0],$fot(set_difference(empty_set,B))]]) ).
cnf(refute_0_56,plain,
( set_difference(B,B) != set_difference(empty_set,B)
| set_difference(B,B) = empty_set ),
inference(resolve,[$cnf( $equal(set_difference(empty_set,B),empty_set) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
set_difference(B,B) = empty_set,
inference(resolve,[$cnf( $equal(set_difference(B,B),set_difference(empty_set,B)) )],[refute_0_52,refute_0_56]) ).
cnf(refute_0_58,plain,
set_difference(set_union2(A,X_50),set_union2(A,X_50)) = empty_set,
inference(subst,[],[refute_0_57:[bind(B,$fot(set_union2(A,X_50)))]]) ).
cnf(refute_0_59,plain,
( set_difference(set_union2(A,X_50),set_union2(A,X_50)) != empty_set
| set_difference(set_union2(A,X_50),set_union2(A,X_50)) != set_difference(A,set_union2(A,X_50))
| empty_set = set_difference(A,set_union2(A,X_50)) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(A,X_50),set_union2(A,X_50)),set_difference(A,set_union2(A,X_50))) ),[0],$fot(empty_set)]]) ).
cnf(refute_0_60,plain,
( set_difference(set_union2(A,X_50),set_union2(A,X_50)) != set_difference(A,set_union2(A,X_50))
| empty_set = set_difference(A,set_union2(A,X_50)) ),
inference(resolve,[$cnf( $equal(set_difference(set_union2(A,X_50),set_union2(A,X_50)),empty_set) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
empty_set = set_difference(A,set_union2(A,X_50)),
inference(resolve,[$cnf( $equal(set_difference(set_union2(A,X_50),set_union2(A,X_50)),set_difference(A,set_union2(A,X_50))) )],[refute_0_42,refute_0_60]) ).
cnf(refute_0_62,plain,
empty_set = set_difference(X_52,set_union2(X_52,X_53)),
inference(subst,[],[refute_0_61:[bind(A,$fot(X_52)),bind(X_50,$fot(X_53))]]) ).
cnf(refute_0_63,plain,
set_union2(X_53,X_52) = set_union2(X_52,X_53),
inference(subst,[],[refute_0_25:[bind(A,$fot(X_53)),bind(B,$fot(X_52))]]) ).
cnf(refute_0_64,plain,
( set_union2(X_53,X_52) != set_union2(X_52,X_53)
| set_union2(X_52,X_53) = set_union2(X_53,X_52) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(set_union2(X_53,X_52))),bind(Y,$fot(set_union2(X_52,X_53)))]]) ).
cnf(refute_0_65,plain,
set_union2(X_52,X_53) = set_union2(X_53,X_52),
inference(resolve,[$cnf( $equal(set_union2(X_53,X_52),set_union2(X_52,X_53)) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
( empty_set != set_difference(X_52,set_union2(X_52,X_53))
| set_union2(X_52,X_53) != set_union2(X_53,X_52)
| empty_set = set_difference(X_52,set_union2(X_53,X_52)) ),
introduced(tautology,[equality,[$cnf( $equal(empty_set,set_difference(X_52,set_union2(X_52,X_53))) ),[1,1],$fot(set_union2(X_53,X_52))]]) ).
cnf(refute_0_67,plain,
( empty_set != set_difference(X_52,set_union2(X_52,X_53))
| empty_set = set_difference(X_52,set_union2(X_53,X_52)) ),
inference(resolve,[$cnf( $equal(set_union2(X_52,X_53),set_union2(X_53,X_52)) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
empty_set = set_difference(X_52,set_union2(X_53,X_52)),
inference(resolve,[$cnf( $equal(empty_set,set_difference(X_52,set_union2(X_52,X_53))) )],[refute_0_62,refute_0_67]) ).
cnf(refute_0_69,plain,
empty_set = set_difference(X_56,set_union2(X_53,X_56)),
inference(subst,[],[refute_0_68:[bind(X_52,$fot(X_56))]]) ).
cnf(refute_0_70,plain,
( empty_set != set_difference(X_56,set_union2(X_53,X_56))
| set_difference(X_56,set_union2(X_53,X_56)) = empty_set ),
inference(subst,[],[refute_0_14:[bind(X,$fot(empty_set)),bind(Y,$fot(set_difference(X_56,set_union2(X_53,X_56))))]]) ).
cnf(refute_0_71,plain,
set_difference(X_56,set_union2(X_53,X_56)) = empty_set,
inference(resolve,[$cnf( $equal(empty_set,set_difference(X_56,set_union2(X_53,X_56))) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
( set_difference(X_56,set_difference(X_56,set_union2(X_53,X_56))) != set_intersection2(X_56,set_union2(X_53,X_56))
| set_difference(X_56,set_union2(X_53,X_56)) != empty_set
| set_difference(X_56,empty_set) = set_intersection2(X_56,set_union2(X_53,X_56)) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(X_56,set_difference(X_56,set_union2(X_53,X_56))),set_intersection2(X_56,set_union2(X_53,X_56))) ),[0,1],$fot(empty_set)]]) ).
cnf(refute_0_73,plain,
( set_difference(X_56,set_difference(X_56,set_union2(X_53,X_56))) != set_intersection2(X_56,set_union2(X_53,X_56))
| set_difference(X_56,empty_set) = set_intersection2(X_56,set_union2(X_53,X_56)) ),
inference(resolve,[$cnf( $equal(set_difference(X_56,set_union2(X_53,X_56)),empty_set) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
set_difference(X_56,empty_set) = set_intersection2(X_56,set_union2(X_53,X_56)),
inference(resolve,[$cnf( $equal(set_difference(X_56,set_difference(X_56,set_union2(X_53,X_56))),set_intersection2(X_56,set_union2(X_53,X_56))) )],[refute_0_21,refute_0_73]) ).
cnf(refute_0_75,plain,
set_difference(A,empty_set) = A,
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_76,plain,
set_difference(X_56,empty_set) = X_56,
inference(subst,[],[refute_0_75:[bind(A,$fot(X_56))]]) ).
cnf(refute_0_77,plain,
( set_difference(X_56,empty_set) != X_56
| set_difference(X_56,empty_set) != set_intersection2(X_56,set_union2(X_53,X_56))
| X_56 = set_intersection2(X_56,set_union2(X_53,X_56)) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(X_56,empty_set),set_intersection2(X_56,set_union2(X_53,X_56))) ),[0],$fot(X_56)]]) ).
cnf(refute_0_78,plain,
( set_difference(X_56,empty_set) != set_intersection2(X_56,set_union2(X_53,X_56))
| X_56 = set_intersection2(X_56,set_union2(X_53,X_56)) ),
inference(resolve,[$cnf( $equal(set_difference(X_56,empty_set),X_56) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
X_56 = set_intersection2(X_56,set_union2(X_53,X_56)),
inference(resolve,[$cnf( $equal(set_difference(X_56,empty_set),set_intersection2(X_56,set_union2(X_53,X_56))) )],[refute_0_74,refute_0_78]) ).
cnf(refute_0_80,plain,
( X_56 != set_intersection2(X_56,set_union2(X_53,X_56))
| set_intersection2(X_56,set_union2(X_53,X_56)) = X_56 ),
inference(subst,[],[refute_0_14:[bind(X,$fot(X_56)),bind(Y,$fot(set_intersection2(X_56,set_union2(X_53,X_56))))]]) ).
cnf(refute_0_81,plain,
set_intersection2(X_56,set_union2(X_53,X_56)) = X_56,
inference(resolve,[$cnf( $equal(X_56,set_intersection2(X_56,set_union2(X_53,X_56))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
set_intersection2(X_57,set_union2(A,X_57)) = X_57,
inference(subst,[],[refute_0_81:[bind(X_53,$fot(A)),bind(X_56,$fot(X_57))]]) ).
cnf(refute_0_83,plain,
( set_difference(set_union2(A,X_57),set_difference(A,X_57)) != set_intersection2(X_57,set_union2(A,X_57))
| set_intersection2(X_57,set_union2(A,X_57)) != X_57
| set_difference(set_union2(A,X_57),set_difference(A,X_57)) = X_57 ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(set_union2(A,X_57),set_difference(A,X_57)),X_57) ),[0],$fot(set_intersection2(X_57,set_union2(A,X_57)))]]) ).
cnf(refute_0_84,plain,
( set_difference(set_union2(A,X_57),set_difference(A,X_57)) != set_intersection2(X_57,set_union2(A,X_57))
| set_difference(set_union2(A,X_57),set_difference(A,X_57)) = X_57 ),
inference(resolve,[$cnf( $equal(set_intersection2(X_57,set_union2(A,X_57)),X_57) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
set_difference(set_union2(A,X_57),set_difference(A,X_57)) = X_57,
inference(resolve,[$cnf( $equal(set_difference(set_union2(A,X_57),set_difference(A,X_57)),set_intersection2(X_57,set_union2(A,X_57))) )],[refute_0_20,refute_0_84]) ).
cnf(refute_0_86,plain,
set_difference(set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)),set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))) = singleton(skolemFOFtoCNF_A_2),
inference(subst,[],[refute_0_85:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(X_57,$fot(singleton(skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_87,plain,
( ~ subset(A,B)
| set_union2(A,B) = B ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_88,plain,
( ~ subset(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1)
| set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) = skolemFOFtoCNF_B_1 ),
inference(subst,[],[refute_0_87:[bind(A,$fot(singleton(skolemFOFtoCNF_A_2))),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_89,plain,
in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_90,plain,
( ~ in(A,B)
| subset(singleton(A),B) ),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_91,plain,
( ~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| subset(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_90:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_92,plain,
subset(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) )],[refute_0_89,refute_0_91]) ).
cnf(refute_0_93,plain,
set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) = skolemFOFtoCNF_B_1,
inference(resolve,[$cnf( subset(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) )],[refute_0_92,refute_0_88]) ).
cnf(refute_0_94,plain,
( set_union2(A,B) != set_union2(B,A)
| set_union2(B,A) = set_union2(A,B) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(set_union2(A,B))),bind(Y,$fot(set_union2(B,A)))]]) ).
cnf(refute_0_95,plain,
set_union2(B,A) = set_union2(A,B),
inference(resolve,[$cnf( $equal(set_union2(A,B),set_union2(B,A)) )],[refute_0_25,refute_0_94]) ).
cnf(refute_0_96,plain,
set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) = set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)),
inference(subst,[],[refute_0_95:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(singleton(skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_97,plain,
( set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) != set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))
| set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) != skolemFOFtoCNF_B_1
| set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)) = skolemFOFtoCNF_B_1 ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),skolemFOFtoCNF_B_1) ),[0],$fot(set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_98,plain,
( set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) != skolemFOFtoCNF_B_1
| set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)) = skolemFOFtoCNF_B_1 ),
inference(resolve,[$cnf( $equal(set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)) = skolemFOFtoCNF_B_1,
inference(resolve,[$cnf( $equal(set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),skolemFOFtoCNF_B_1) )],[refute_0_93,refute_0_98]) ).
cnf(refute_0_100,plain,
( set_difference(set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)),set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))) != singleton(skolemFOFtoCNF_A_2)
| set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)) != skolemFOFtoCNF_B_1
| set_difference(skolemFOFtoCNF_B_1,set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))) = singleton(skolemFOFtoCNF_A_2) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)),set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))),singleton(skolemFOFtoCNF_A_2)) ),[0,0],$fot(skolemFOFtoCNF_B_1)]]) ).
cnf(refute_0_101,plain,
( set_difference(set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)),set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))) != singleton(skolemFOFtoCNF_A_2)
| set_difference(skolemFOFtoCNF_B_1,set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))) = singleton(skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( $equal(set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)),skolemFOFtoCNF_B_1) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
set_difference(skolemFOFtoCNF_B_1,set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))) = singleton(skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( $equal(set_difference(set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)),set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_86,refute_0_101]) ).
cnf(refute_0_103,plain,
set_difference(skolemFOFtoCNF_B_1,set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))) = set_intersection2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(singleton(skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_104,plain,
( set_difference(skolemFOFtoCNF_B_1,set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))) != set_intersection2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))
| set_difference(skolemFOFtoCNF_B_1,set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))) != singleton(skolemFOFtoCNF_A_2)
| set_intersection2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)) = singleton(skolemFOFtoCNF_A_2) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(skolemFOFtoCNF_B_1,set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))),singleton(skolemFOFtoCNF_A_2)) ),[0],$fot(set_intersection2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_105,plain,
( set_difference(skolemFOFtoCNF_B_1,set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))) != singleton(skolemFOFtoCNF_A_2)
| set_intersection2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)) = singleton(skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_B_1,set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))),set_intersection2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
set_intersection2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)) = singleton(skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_B_1,set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_102,refute_0_105]) ).
cnf(refute_0_107,plain,
set_intersection2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) = set_intersection2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(singleton(skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_108,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_109,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_14,refute_0_108]) ).
cnf(refute_0_110,plain,
( set_intersection2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) != set_intersection2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))
| set_intersection2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)) != singleton(skolemFOFtoCNF_A_2)
| set_intersection2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) = singleton(skolemFOFtoCNF_A_2) ),
inference(subst,[],[refute_0_109:[bind(X,$fot(set_intersection2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1))),bind(Y,$fot(set_intersection2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)))),bind(Z,$fot(singleton(skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_111,plain,
( set_intersection2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)) != singleton(skolemFOFtoCNF_A_2)
| set_intersection2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) = singleton(skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( $equal(set_intersection2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),set_intersection2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))) )],[refute_0_107,refute_0_110]) ).
cnf(refute_0_112,plain,
set_intersection2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) = singleton(skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_106,refute_0_111]) ).
cnf(refute_0_113,plain,
( set_intersection2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) != empty_set
| set_intersection2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) != singleton(skolemFOFtoCNF_A_2)
| singleton(skolemFOFtoCNF_A_2) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(set_intersection2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),empty_set) ),[0],$fot(singleton(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_114,plain,
( set_intersection2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) != empty_set
| singleton(skolemFOFtoCNF_A_2) = empty_set ),
inference(resolve,[$cnf( $equal(set_intersection2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
singleton(skolemFOFtoCNF_A_2) = empty_set,
inference(resolve,[$cnf( $equal(set_intersection2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),empty_set) )],[refute_0_3,refute_0_114]) ).
cnf(refute_0_116,plain,
singleton(A) != empty_set,
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_117,plain,
singleton(skolemFOFtoCNF_A_2) != empty_set,
inference(subst,[],[refute_0_116:[bind(A,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_118,plain,
$false,
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_A_2),empty_set) )],[refute_0_115,refute_0_117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU153+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jun 19 15:32:52 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.79/0.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.79/0.94
% 0.79/0.94 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.81/0.95
%------------------------------------------------------------------------------