TSTP Solution File: SEU152+2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU152+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n005.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 0.77s 0.96s
% Output : CNFRefutation 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 32
% Syntax : Number of formulae : 148 ( 82 unt; 0 def)
% Number of atoms : 238 ( 204 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 180 ( 90 ~; 76 |; 4 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 234 ( 9 sgn 64 !; 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(l23_zfmisc_1,conjecture,
! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ) ).
fof(l2_zfmisc_1,lemma,
! [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(t2_boole,axiom,
! [A] : set_intersection2(A,empty_set) = empty_set ).
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(subgoal_0,plain,
! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
inference(strip,[],[l23_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(canonicalize,[],[t48_xboole_1]) ).
fof(normalize_0_1,plain,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
inference(canonicalize,[],[t40_xboole_1]) ).
fof(normalize_0_3,plain,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[commutativity_k2_xboole_0]) ).
fof(normalize_0_5,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(canonicalize,[],[commutativity_k3_xboole_0]) ).
fof(normalize_0_7,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
inference(canonicalize,[],[t39_xboole_1]) ).
fof(normalize_0_9,plain,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A] : set_difference(A,empty_set) = A,
inference(canonicalize,[],[t3_boole]) ).
fof(normalize_0_11,plain,
! [A] : set_difference(A,empty_set) = A,
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(canonicalize,[],[t2_boole]) ).
fof(normalize_0_13,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
? [A,B] :
( set_union2(singleton(A),B) != B
& in(A,B) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_15,plain,
( set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) != skolemFOFtoCNF_B_1
& in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) ),
inference(skolemize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [A,B] :
( ~ in(A,B)
<=> ~ subset(singleton(A),B) ),
inference(canonicalize,[],[l2_zfmisc_1]) ).
fof(normalize_0_18,plain,
! [A,B] :
( ~ in(A,B)
<=> ~ subset(singleton(A),B) ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [A,B] :
( ( ~ in(A,B)
| subset(singleton(A),B) )
& ( ~ subset(singleton(A),B)
| in(A,B) ) ),
inference(clausify,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [A,B] :
( ~ in(A,B)
| subset(singleton(A),B) ),
inference(conjunct,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [A,B] :
( set_difference(A,B) != empty_set
<=> ~ subset(A,B) ),
inference(canonicalize,[],[t37_xboole_1]) ).
fof(normalize_0_22,plain,
! [A,B] :
( set_difference(A,B) != empty_set
<=> ~ subset(A,B) ),
inference(specialize,[],[normalize_0_21]) ).
fof(normalize_0_23,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_22]) ).
fof(normalize_0_24,plain,
! [A,B] :
( ~ subset(A,B)
| set_difference(A,B) = empty_set ),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) != skolemFOFtoCNF_B_1,
inference(conjunct,[],[normalize_0_15]) ).
cnf(refute_0_0,plain,
set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
set_difference(set_union2(B,X_40),set_difference(set_union2(B,X_40),B)) = set_intersection2(set_union2(B,X_40),B),
inference(subst,[],[refute_0_0:[bind(A,$fot(set_union2(B,X_40)))]]) ).
cnf(refute_0_2,plain,
set_difference(set_union2(A,B),B) = set_difference(A,B),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
( set_difference(set_union2(A,B),B) != set_difference(A,B)
| set_union2(A,B) != set_union2(B,A)
| set_difference(set_union2(B,A),B) = set_difference(A,B) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(A,B),B),set_difference(A,B)) ),[0,0],$fot(set_union2(B,A))]]) ).
cnf(refute_0_5,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( $equal(set_union2(A,B),set_union2(B,A)) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
set_difference(set_union2(B,A),B) = set_difference(A,B),
inference(resolve,[$cnf( $equal(set_difference(set_union2(A,B),B),set_difference(A,B)) )],[refute_0_2,refute_0_5]) ).
cnf(refute_0_7,plain,
set_difference(set_union2(B,X_40),B) = set_difference(X_40,B),
inference(subst,[],[refute_0_6:[bind(A,$fot(X_40))]]) ).
cnf(refute_0_8,plain,
( set_difference(set_union2(B,X_40),B) != set_difference(X_40,B)
| set_difference(set_union2(B,X_40),set_difference(set_union2(B,X_40),B)) != set_intersection2(set_union2(B,X_40),B)
| set_difference(set_union2(B,X_40),set_difference(X_40,B)) = set_intersection2(set_union2(B,X_40),B) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(B,X_40),set_difference(set_union2(B,X_40),B)),set_intersection2(set_union2(B,X_40),B)) ),[0,1],$fot(set_difference(X_40,B))]]) ).
cnf(refute_0_9,plain,
( set_difference(set_union2(B,X_40),set_difference(set_union2(B,X_40),B)) != set_intersection2(set_union2(B,X_40),B)
| set_difference(set_union2(B,X_40),set_difference(X_40,B)) = set_intersection2(set_union2(B,X_40),B) ),
inference(resolve,[$cnf( $equal(set_difference(set_union2(B,X_40),B),set_difference(X_40,B)) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
set_difference(set_union2(B,X_40),set_difference(X_40,B)) = set_intersection2(set_union2(B,X_40),B),
inference(resolve,[$cnf( $equal(set_difference(set_union2(B,X_40),set_difference(set_union2(B,X_40),B)),set_intersection2(set_union2(B,X_40),B)) )],[refute_0_1,refute_0_9]) ).
cnf(refute_0_11,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_12,plain,
X = X,
introduced(tautology,[refl,[$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( $equal(set_intersection2(A,B),set_intersection2(B,A)) )],[refute_0_11,refute_0_15]) ).
cnf(refute_0_17,plain,
set_intersection2(set_union2(B,X_40),B) = set_intersection2(B,set_union2(B,X_40)),
inference(subst,[],[refute_0_16:[bind(A,$fot(B)),bind(B,$fot(set_union2(B,X_40)))]]) ).
cnf(refute_0_18,plain,
( set_difference(set_union2(B,X_40),set_difference(X_40,B)) != set_intersection2(set_union2(B,X_40),B)
| set_intersection2(set_union2(B,X_40),B) != set_intersection2(B,set_union2(B,X_40))
| set_difference(set_union2(B,X_40),set_difference(X_40,B)) = set_intersection2(B,set_union2(B,X_40)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(set_union2(B,X_40),set_difference(X_40,B)),set_intersection2(B,set_union2(B,X_40))) ),[0],$fot(set_intersection2(set_union2(B,X_40),B))]]) ).
cnf(refute_0_19,plain,
( set_difference(set_union2(B,X_40),set_difference(X_40,B)) != set_intersection2(set_union2(B,X_40),B)
| set_difference(set_union2(B,X_40),set_difference(X_40,B)) = set_intersection2(B,set_union2(B,X_40)) ),
inference(resolve,[$cnf( $equal(set_intersection2(set_union2(B,X_40),B),set_intersection2(B,set_union2(B,X_40))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
set_difference(set_union2(B,X_40),set_difference(X_40,B)) = set_intersection2(B,set_union2(B,X_40)),
inference(resolve,[$cnf( $equal(set_difference(set_union2(B,X_40),set_difference(X_40,B)),set_intersection2(set_union2(B,X_40),B)) )],[refute_0_10,refute_0_19]) ).
cnf(refute_0_21,plain,
set_difference(set_union2(A,set_difference(X_56,A)),set_difference(X_56,A)) = set_difference(A,set_difference(X_56,A)),
inference(subst,[],[refute_0_2:[bind(B,$fot(set_difference(X_56,A)))]]) ).
cnf(refute_0_22,plain,
set_union2(A,set_difference(B,A)) = set_union2(A,B),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_23,plain,
set_union2(A,set_difference(X_56,A)) = set_union2(A,X_56),
inference(subst,[],[refute_0_22:[bind(B,$fot(X_56))]]) ).
cnf(refute_0_24,plain,
( set_difference(set_union2(A,set_difference(X_56,A)),set_difference(X_56,A)) != set_difference(A,set_difference(X_56,A))
| set_union2(A,set_difference(X_56,A)) != set_union2(A,X_56)
| set_difference(set_union2(A,X_56),set_difference(X_56,A)) = set_difference(A,set_difference(X_56,A)) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(A,set_difference(X_56,A)),set_difference(X_56,A)),set_difference(A,set_difference(X_56,A))) ),[0,0],$fot(set_union2(A,X_56))]]) ).
cnf(refute_0_25,plain,
( set_difference(set_union2(A,set_difference(X_56,A)),set_difference(X_56,A)) != set_difference(A,set_difference(X_56,A))
| set_difference(set_union2(A,X_56),set_difference(X_56,A)) = set_difference(A,set_difference(X_56,A)) ),
inference(resolve,[$cnf( $equal(set_union2(A,set_difference(X_56,A)),set_union2(A,X_56)) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
set_difference(set_union2(A,X_56),set_difference(X_56,A)) = set_difference(A,set_difference(X_56,A)),
inference(resolve,[$cnf( $equal(set_difference(set_union2(A,set_difference(X_56,A)),set_difference(X_56,A)),set_difference(A,set_difference(X_56,A))) )],[refute_0_21,refute_0_25]) ).
cnf(refute_0_27,plain,
set_difference(set_union2(A,X_56),set_difference(X_56,A)) = set_intersection2(A,set_union2(A,X_56)),
inference(subst,[],[refute_0_20:[bind(B,$fot(A)),bind(X_40,$fot(X_56))]]) ).
cnf(refute_0_28,plain,
( set_difference(set_union2(A,X_56),set_difference(X_56,A)) != set_difference(A,set_difference(X_56,A))
| set_difference(set_union2(A,X_56),set_difference(X_56,A)) != set_intersection2(A,set_union2(A,X_56))
| set_intersection2(A,set_union2(A,X_56)) = set_difference(A,set_difference(X_56,A)) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(A,X_56),set_difference(X_56,A)),set_difference(A,set_difference(X_56,A))) ),[0],$fot(set_intersection2(A,set_union2(A,X_56)))]]) ).
cnf(refute_0_29,plain,
( set_difference(set_union2(A,X_56),set_difference(X_56,A)) != set_difference(A,set_difference(X_56,A))
| set_intersection2(A,set_union2(A,X_56)) = set_difference(A,set_difference(X_56,A)) ),
inference(resolve,[$cnf( $equal(set_difference(set_union2(A,X_56),set_difference(X_56,A)),set_intersection2(A,set_union2(A,X_56))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
set_intersection2(A,set_union2(A,X_56)) = set_difference(A,set_difference(X_56,A)),
inference(resolve,[$cnf( $equal(set_difference(set_union2(A,X_56),set_difference(X_56,A)),set_difference(A,set_difference(X_56,A))) )],[refute_0_26,refute_0_29]) ).
cnf(refute_0_31,plain,
set_intersection2(B,set_union2(B,X_40)) = set_difference(B,set_difference(X_40,B)),
inference(subst,[],[refute_0_30:[bind(A,$fot(B)),bind(X_56,$fot(X_40))]]) ).
cnf(refute_0_32,plain,
( set_difference(set_union2(B,X_40),set_difference(X_40,B)) != set_intersection2(B,set_union2(B,X_40))
| set_intersection2(B,set_union2(B,X_40)) != set_difference(B,set_difference(X_40,B))
| set_difference(set_union2(B,X_40),set_difference(X_40,B)) = set_difference(B,set_difference(X_40,B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(set_union2(B,X_40),set_difference(X_40,B)),set_difference(B,set_difference(X_40,B))) ),[0],$fot(set_intersection2(B,set_union2(B,X_40)))]]) ).
cnf(refute_0_33,plain,
( set_difference(set_union2(B,X_40),set_difference(X_40,B)) != set_intersection2(B,set_union2(B,X_40))
| set_difference(set_union2(B,X_40),set_difference(X_40,B)) = set_difference(B,set_difference(X_40,B)) ),
inference(resolve,[$cnf( $equal(set_intersection2(B,set_union2(B,X_40)),set_difference(B,set_difference(X_40,B))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
set_difference(set_union2(B,X_40),set_difference(X_40,B)) = set_difference(B,set_difference(X_40,B)),
inference(resolve,[$cnf( $equal(set_difference(set_union2(B,X_40),set_difference(X_40,B)),set_intersection2(B,set_union2(B,X_40))) )],[refute_0_20,refute_0_33]) ).
cnf(refute_0_35,plain,
set_difference(A,set_difference(A,set_union2(A,X_98))) = set_intersection2(A,set_union2(A,X_98)),
inference(subst,[],[refute_0_0:[bind(B,$fot(set_union2(A,X_98)))]]) ).
cnf(refute_0_36,plain,
set_difference(set_union2(A,set_union2(A,X_67)),set_union2(A,X_67)) = set_difference(A,set_union2(A,X_67)),
inference(subst,[],[refute_0_2:[bind(B,$fot(set_union2(A,X_67)))]]) ).
cnf(refute_0_37,plain,
set_union2(X_55,set_difference(set_union2(X_55,A),X_55)) = set_union2(X_55,set_union2(X_55,A)),
inference(subst,[],[refute_0_22:[bind(A,$fot(X_55)),bind(B,$fot(set_union2(X_55,A)))]]) ).
cnf(refute_0_38,plain,
set_difference(set_union2(X_55,A),X_55) = set_difference(A,X_55),
inference(subst,[],[refute_0_6:[bind(B,$fot(X_55))]]) ).
cnf(refute_0_39,plain,
( set_difference(set_union2(X_55,A),X_55) != set_difference(A,X_55)
| set_union2(X_55,set_difference(set_union2(X_55,A),X_55)) != set_union2(X_55,set_union2(X_55,A))
| set_union2(X_55,set_difference(A,X_55)) = set_union2(X_55,set_union2(X_55,A)) ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(X_55,set_difference(set_union2(X_55,A),X_55)),set_union2(X_55,set_union2(X_55,A))) ),[0,1],$fot(set_difference(A,X_55))]]) ).
cnf(refute_0_40,plain,
( set_union2(X_55,set_difference(set_union2(X_55,A),X_55)) != set_union2(X_55,set_union2(X_55,A))
| set_union2(X_55,set_difference(A,X_55)) = set_union2(X_55,set_union2(X_55,A)) ),
inference(resolve,[$cnf( $equal(set_difference(set_union2(X_55,A),X_55),set_difference(A,X_55)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
set_union2(X_55,set_difference(A,X_55)) = set_union2(X_55,set_union2(X_55,A)),
inference(resolve,[$cnf( $equal(set_union2(X_55,set_difference(set_union2(X_55,A),X_55)),set_union2(X_55,set_union2(X_55,A))) )],[refute_0_37,refute_0_40]) ).
cnf(refute_0_42,plain,
set_union2(X_55,set_difference(A,X_55)) = set_union2(X_55,A),
inference(subst,[],[refute_0_22:[bind(A,$fot(X_55)),bind(B,$fot(A))]]) ).
cnf(refute_0_43,plain,
( set_union2(X_55,set_difference(A,X_55)) != set_union2(X_55,A)
| set_union2(X_55,set_difference(A,X_55)) != set_union2(X_55,set_union2(X_55,A))
| set_union2(X_55,A) = set_union2(X_55,set_union2(X_55,A)) ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(X_55,set_difference(A,X_55)),set_union2(X_55,set_union2(X_55,A))) ),[0],$fot(set_union2(X_55,A))]]) ).
cnf(refute_0_44,plain,
( set_union2(X_55,set_difference(A,X_55)) != set_union2(X_55,set_union2(X_55,A))
| set_union2(X_55,A) = set_union2(X_55,set_union2(X_55,A)) ),
inference(resolve,[$cnf( $equal(set_union2(X_55,set_difference(A,X_55)),set_union2(X_55,A)) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
set_union2(X_55,A) = set_union2(X_55,set_union2(X_55,A)),
inference(resolve,[$cnf( $equal(set_union2(X_55,set_difference(A,X_55)),set_union2(X_55,set_union2(X_55,A))) )],[refute_0_41,refute_0_44]) ).
cnf(refute_0_46,plain,
set_union2(A,X_67) = set_union2(A,set_union2(A,X_67)),
inference(subst,[],[refute_0_45:[bind(A,$fot(X_67)),bind(X_55,$fot(A))]]) ).
cnf(refute_0_47,plain,
( set_union2(A,X_67) != set_union2(A,set_union2(A,X_67))
| set_union2(A,set_union2(A,X_67)) = set_union2(A,X_67) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(set_union2(A,X_67))),bind(Y,$fot(set_union2(A,set_union2(A,X_67))))]]) ).
cnf(refute_0_48,plain,
set_union2(A,set_union2(A,X_67)) = set_union2(A,X_67),
inference(resolve,[$cnf( $equal(set_union2(A,X_67),set_union2(A,set_union2(A,X_67))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( set_difference(set_union2(A,set_union2(A,X_67)),set_union2(A,X_67)) != set_difference(A,set_union2(A,X_67))
| set_union2(A,set_union2(A,X_67)) != set_union2(A,X_67)
| set_difference(set_union2(A,X_67),set_union2(A,X_67)) = set_difference(A,set_union2(A,X_67)) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(A,set_union2(A,X_67)),set_union2(A,X_67)),set_difference(A,set_union2(A,X_67))) ),[0,0],$fot(set_union2(A,X_67))]]) ).
cnf(refute_0_50,plain,
( set_difference(set_union2(A,set_union2(A,X_67)),set_union2(A,X_67)) != set_difference(A,set_union2(A,X_67))
| set_difference(set_union2(A,X_67),set_union2(A,X_67)) = set_difference(A,set_union2(A,X_67)) ),
inference(resolve,[$cnf( $equal(set_union2(A,set_union2(A,X_67)),set_union2(A,X_67)) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
set_difference(set_union2(A,X_67),set_union2(A,X_67)) = set_difference(A,set_union2(A,X_67)),
inference(resolve,[$cnf( $equal(set_difference(set_union2(A,set_union2(A,X_67)),set_union2(A,X_67)),set_difference(A,set_union2(A,X_67))) )],[refute_0_36,refute_0_50]) ).
cnf(refute_0_52,plain,
set_difference(X_14,set_difference(X_14,empty_set)) = set_intersection2(X_14,empty_set),
inference(subst,[],[refute_0_0:[bind(A,$fot(X_14)),bind(B,$fot(empty_set))]]) ).
cnf(refute_0_53,plain,
set_difference(A,empty_set) = A,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_54,plain,
set_difference(X_14,empty_set) = X_14,
inference(subst,[],[refute_0_53:[bind(A,$fot(X_14))]]) ).
cnf(refute_0_55,plain,
( set_difference(X_14,empty_set) != X_14
| set_difference(X_14,set_difference(X_14,empty_set)) != set_intersection2(X_14,empty_set)
| set_difference(X_14,X_14) = set_intersection2(X_14,empty_set) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(X_14,set_difference(X_14,empty_set)),set_intersection2(X_14,empty_set)) ),[0,1],$fot(X_14)]]) ).
cnf(refute_0_56,plain,
( set_difference(X_14,set_difference(X_14,empty_set)) != set_intersection2(X_14,empty_set)
| set_difference(X_14,X_14) = set_intersection2(X_14,empty_set) ),
inference(resolve,[$cnf( $equal(set_difference(X_14,empty_set),X_14) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
set_difference(X_14,X_14) = set_intersection2(X_14,empty_set),
inference(resolve,[$cnf( $equal(set_difference(X_14,set_difference(X_14,empty_set)),set_intersection2(X_14,empty_set)) )],[refute_0_52,refute_0_56]) ).
cnf(refute_0_58,plain,
set_intersection2(A,empty_set) = empty_set,
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_59,plain,
set_intersection2(X_14,empty_set) = empty_set,
inference(subst,[],[refute_0_58:[bind(A,$fot(X_14))]]) ).
cnf(refute_0_60,plain,
( set_difference(X_14,X_14) != set_intersection2(X_14,empty_set)
| set_intersection2(X_14,empty_set) != empty_set
| set_difference(X_14,X_14) = empty_set ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(X_14,X_14),empty_set) ),[0],$fot(set_intersection2(X_14,empty_set))]]) ).
cnf(refute_0_61,plain,
( set_difference(X_14,X_14) != set_intersection2(X_14,empty_set)
| set_difference(X_14,X_14) = empty_set ),
inference(resolve,[$cnf( $equal(set_intersection2(X_14,empty_set),empty_set) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
set_difference(X_14,X_14) = empty_set,
inference(resolve,[$cnf( $equal(set_difference(X_14,X_14),set_intersection2(X_14,empty_set)) )],[refute_0_57,refute_0_61]) ).
cnf(refute_0_63,plain,
set_difference(set_union2(A,X_67),set_union2(A,X_67)) = empty_set,
inference(subst,[],[refute_0_62:[bind(X_14,$fot(set_union2(A,X_67)))]]) ).
cnf(refute_0_64,plain,
( set_difference(set_union2(A,X_67),set_union2(A,X_67)) != empty_set
| set_difference(set_union2(A,X_67),set_union2(A,X_67)) != set_difference(A,set_union2(A,X_67))
| empty_set = set_difference(A,set_union2(A,X_67)) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(A,X_67),set_union2(A,X_67)),set_difference(A,set_union2(A,X_67))) ),[0],$fot(empty_set)]]) ).
cnf(refute_0_65,plain,
( set_difference(set_union2(A,X_67),set_union2(A,X_67)) != set_difference(A,set_union2(A,X_67))
| empty_set = set_difference(A,set_union2(A,X_67)) ),
inference(resolve,[$cnf( $equal(set_difference(set_union2(A,X_67),set_union2(A,X_67)),empty_set) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
empty_set = set_difference(A,set_union2(A,X_67)),
inference(resolve,[$cnf( $equal(set_difference(set_union2(A,X_67),set_union2(A,X_67)),set_difference(A,set_union2(A,X_67))) )],[refute_0_51,refute_0_65]) ).
cnf(refute_0_67,plain,
empty_set = set_difference(A,set_union2(A,X_98)),
inference(subst,[],[refute_0_66:[bind(X_67,$fot(X_98))]]) ).
cnf(refute_0_68,plain,
( empty_set != set_difference(A,set_union2(A,X_98))
| set_difference(A,set_union2(A,X_98)) = empty_set ),
inference(subst,[],[refute_0_14:[bind(X,$fot(empty_set)),bind(Y,$fot(set_difference(A,set_union2(A,X_98))))]]) ).
cnf(refute_0_69,plain,
set_difference(A,set_union2(A,X_98)) = empty_set,
inference(resolve,[$cnf( $equal(empty_set,set_difference(A,set_union2(A,X_98))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
( set_difference(A,set_difference(A,set_union2(A,X_98))) != set_intersection2(A,set_union2(A,X_98))
| set_difference(A,set_union2(A,X_98)) != empty_set
| set_difference(A,empty_set) = set_intersection2(A,set_union2(A,X_98)) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(A,set_difference(A,set_union2(A,X_98))),set_intersection2(A,set_union2(A,X_98))) ),[0,1],$fot(empty_set)]]) ).
cnf(refute_0_71,plain,
( set_difference(A,set_difference(A,set_union2(A,X_98))) != set_intersection2(A,set_union2(A,X_98))
| set_difference(A,empty_set) = set_intersection2(A,set_union2(A,X_98)) ),
inference(resolve,[$cnf( $equal(set_difference(A,set_union2(A,X_98)),empty_set) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
set_difference(A,empty_set) = set_intersection2(A,set_union2(A,X_98)),
inference(resolve,[$cnf( $equal(set_difference(A,set_difference(A,set_union2(A,X_98))),set_intersection2(A,set_union2(A,X_98))) )],[refute_0_35,refute_0_71]) ).
cnf(refute_0_73,plain,
( set_difference(A,empty_set) != A
| set_difference(A,empty_set) != set_intersection2(A,set_union2(A,X_98))
| A = set_intersection2(A,set_union2(A,X_98)) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(A,empty_set),set_intersection2(A,set_union2(A,X_98))) ),[0],$fot(A)]]) ).
cnf(refute_0_74,plain,
( set_difference(A,empty_set) != set_intersection2(A,set_union2(A,X_98))
| A = set_intersection2(A,set_union2(A,X_98)) ),
inference(resolve,[$cnf( $equal(set_difference(A,empty_set),A) )],[refute_0_53,refute_0_73]) ).
cnf(refute_0_75,plain,
set_intersection2(A,set_union2(A,X_98)) = set_difference(A,set_difference(X_98,A)),
inference(subst,[],[refute_0_30:[bind(X_56,$fot(X_98))]]) ).
cnf(refute_0_76,plain,
( A != set_intersection2(A,set_union2(A,X_98))
| set_intersection2(A,set_union2(A,X_98)) != set_difference(A,set_difference(X_98,A))
| A = set_difference(A,set_difference(X_98,A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(A,set_difference(A,set_difference(X_98,A))) ),[0],$fot(set_intersection2(A,set_union2(A,X_98)))]]) ).
cnf(refute_0_77,plain,
( A != set_intersection2(A,set_union2(A,X_98))
| A = set_difference(A,set_difference(X_98,A)) ),
inference(resolve,[$cnf( $equal(set_intersection2(A,set_union2(A,X_98)),set_difference(A,set_difference(X_98,A))) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
( set_difference(A,empty_set) != set_intersection2(A,set_union2(A,X_98))
| A = set_difference(A,set_difference(X_98,A)) ),
inference(resolve,[$cnf( $equal(A,set_intersection2(A,set_union2(A,X_98))) )],[refute_0_74,refute_0_77]) ).
cnf(refute_0_79,plain,
A = set_difference(A,set_difference(X_98,A)),
inference(resolve,[$cnf( $equal(set_difference(A,empty_set),set_intersection2(A,set_union2(A,X_98))) )],[refute_0_72,refute_0_78]) ).
cnf(refute_0_80,plain,
( A != set_difference(A,set_difference(X_98,A))
| set_difference(A,set_difference(X_98,A)) = A ),
inference(subst,[],[refute_0_14:[bind(X,$fot(A)),bind(Y,$fot(set_difference(A,set_difference(X_98,A))))]]) ).
cnf(refute_0_81,plain,
set_difference(A,set_difference(X_98,A)) = A,
inference(resolve,[$cnf( $equal(A,set_difference(A,set_difference(X_98,A))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
set_difference(B,set_difference(X_40,B)) = B,
inference(subst,[],[refute_0_81:[bind(A,$fot(B)),bind(X_98,$fot(X_40))]]) ).
cnf(refute_0_83,plain,
( set_difference(B,set_difference(X_40,B)) != B
| set_difference(set_union2(B,X_40),set_difference(X_40,B)) != set_difference(B,set_difference(X_40,B))
| set_difference(set_union2(B,X_40),set_difference(X_40,B)) = B ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(B,X_40),set_difference(X_40,B)),set_difference(B,set_difference(X_40,B))) ),[1],$fot(B)]]) ).
cnf(refute_0_84,plain,
( set_difference(set_union2(B,X_40),set_difference(X_40,B)) != set_difference(B,set_difference(X_40,B))
| set_difference(set_union2(B,X_40),set_difference(X_40,B)) = B ),
inference(resolve,[$cnf( $equal(set_difference(B,set_difference(X_40,B)),B) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
set_difference(set_union2(B,X_40),set_difference(X_40,B)) = B,
inference(resolve,[$cnf( $equal(set_difference(set_union2(B,X_40),set_difference(X_40,B)),set_difference(B,set_difference(X_40,B))) )],[refute_0_34,refute_0_84]) ).
cnf(refute_0_86,plain,
set_difference(set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)),set_difference(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1)) = skolemFOFtoCNF_B_1,
inference(subst,[],[refute_0_85:[bind(B,$fot(skolemFOFtoCNF_B_1)),bind(X_40,$fot(singleton(skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_87,plain,
in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_88,plain,
( ~ in(A,B)
| subset(singleton(A),B) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_89,plain,
( ~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| subset(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_88:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_90,plain,
subset(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) )],[refute_0_87,refute_0_89]) ).
cnf(refute_0_91,plain,
( ~ subset(A,B)
| set_difference(A,B) = empty_set ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_92,plain,
( ~ subset(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1)
| set_difference(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) = empty_set ),
inference(subst,[],[refute_0_91:[bind(A,$fot(singleton(skolemFOFtoCNF_A_2))),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_93,plain,
set_difference(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) = empty_set,
inference(resolve,[$cnf( subset(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) )],[refute_0_90,refute_0_92]) ).
cnf(refute_0_94,plain,
( set_difference(set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)),set_difference(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1)) != skolemFOFtoCNF_B_1
| set_difference(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) != empty_set
| set_difference(set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)),empty_set) = skolemFOFtoCNF_B_1 ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)),set_difference(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1)),skolemFOFtoCNF_B_1) ),[0,1],$fot(empty_set)]]) ).
cnf(refute_0_95,plain,
( set_difference(set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)),set_difference(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1)) != skolemFOFtoCNF_B_1
| set_difference(set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)),empty_set) = skolemFOFtoCNF_B_1 ),
inference(resolve,[$cnf( $equal(set_difference(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),empty_set) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
set_difference(set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)),empty_set) = skolemFOFtoCNF_B_1,
inference(resolve,[$cnf( $equal(set_difference(set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)),set_difference(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1)),skolemFOFtoCNF_B_1) )],[refute_0_86,refute_0_95]) ).
cnf(refute_0_97,plain,
set_difference(set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)),empty_set) = set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)),
inference(subst,[],[refute_0_53:[bind(A,$fot(set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))))]]) ).
cnf(refute_0_98,plain,
( set_difference(set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)),empty_set) != set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))
| set_difference(set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)),empty_set) != skolemFOFtoCNF_B_1
| set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)) = skolemFOFtoCNF_B_1 ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)),empty_set),skolemFOFtoCNF_B_1) ),[0],$fot(set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_99,plain,
( set_difference(set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)),empty_set) != skolemFOFtoCNF_B_1
| set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)) = skolemFOFtoCNF_B_1 ),
inference(resolve,[$cnf( $equal(set_difference(set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)),empty_set),set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)) = skolemFOFtoCNF_B_1,
inference(resolve,[$cnf( $equal(set_difference(set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)),empty_set),skolemFOFtoCNF_B_1) )],[refute_0_96,refute_0_99]) ).
cnf(refute_0_101,plain,
set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) != skolemFOFtoCNF_B_1,
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_102,plain,
( set_union2(A,B) != set_union2(B,A)
| set_union2(B,A) = set_union2(A,B) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(set_union2(A,B))),bind(Y,$fot(set_union2(B,A)))]]) ).
cnf(refute_0_103,plain,
set_union2(B,A) = set_union2(A,B),
inference(resolve,[$cnf( $equal(set_union2(A,B),set_union2(B,A)) )],[refute_0_3,refute_0_102]) ).
cnf(refute_0_104,plain,
set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) = set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)),
inference(subst,[],[refute_0_103:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(singleton(skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_105,plain,
( set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) != set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))
| set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)) != skolemFOFtoCNF_B_1
| set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) = skolemFOFtoCNF_B_1 ),
introduced(tautology,[equality,[$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_106,plain,
( set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)) != skolemFOFtoCNF_B_1
| set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) = skolemFOFtoCNF_B_1 ),
inference(resolve,[$cnf( $equal(set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)) != skolemFOFtoCNF_B_1,
inference(resolve,[$cnf( $equal(set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),skolemFOFtoCNF_B_1) )],[refute_0_106,refute_0_101]) ).
cnf(refute_0_108,plain,
$false,
inference(resolve,[$cnf( $equal(set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)),skolemFOFtoCNF_B_1) )],[refute_0_100,refute_0_107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU152+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n005.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 : Sun Jun 19 14:53:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.77/0.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.77/0.96
% 0.77/0.96 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.77/0.96
%------------------------------------------------------------------------------