%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU139+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.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 12:38:40 EDT 2022
% Result : Theorem 0.19s 0.47s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 17
% Syntax : Number of formulae : 81 ( 39 unt; 0 def)
% Number of atoms : 143 ( 90 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 124 ( 62 ~; 46 |; 7 &)
% ( 7 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 74 ( 1 sgn 47 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ).
fof(d8_xboole_0,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( subset(A,B)
& A != B ) ) ).
fof(irreflexivity_r2_xboole_0,axiom,
! [A,B] : ~ proper_subset(A,A) ).
fof(l32_xboole_1,lemma,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ) ).
fof(t37_xboole_1,lemma,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ) ).
fof(t3_boole,axiom,
! [A] : set_difference(A,empty_set) = A ).
fof(t48_xboole_1,lemma,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B) ).
fof(t60_xboole_1,conjecture,
! [A,B] :
~ ( subset(A,B)
& proper_subset(B,A) ) ).
fof(subgoal_0,plain,
! [A,B] :
( subset(A,B)
=> ~ proper_subset(B,A) ),
inference(strip,[],[t60_xboole_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( subset(A,B)
=> ~ proper_subset(B,A) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B] :
( proper_subset(B,A)
& subset(A,B) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( proper_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)
& subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
proper_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(canonicalize,[],[t48_xboole_1]) ).
fof(normalize_0_4,plain,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B] :
( ~ proper_subset(A,B)
<=> ( ~ subset(A,B)
| A = B ) ),
inference(canonicalize,[],[d8_xboole_0]) ).
fof(normalize_0_6,plain,
! [A,B] :
( ~ proper_subset(A,B)
<=> ( ~ subset(A,B)
| A = B ) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B] :
( ( A != B
| ~ proper_subset(A,B) )
& ( ~ proper_subset(A,B)
| subset(A,B) )
& ( ~ subset(A,B)
| A = B
| proper_subset(A,B) ) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B] :
( ~ proper_subset(A,B)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B] :
( set_difference(A,B) != empty_set
<=> ~ subset(A,B) ),
inference(canonicalize,[],[t37_xboole_1]) ).
fof(normalize_0_10,plain,
! [A,B] :
( set_difference(A,B) != empty_set
<=> ~ subset(A,B) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,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_10]) ).
fof(normalize_0_12,plain,
! [A,B] :
( ~ subset(A,B)
| set_difference(A,B) = empty_set ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A] : set_difference(A,empty_set) = A,
inference(canonicalize,[],[t3_boole]) ).
fof(normalize_0_14,plain,
! [A] : set_difference(A,empty_set) = A,
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_16,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(canonicalize,[],[commutativity_k3_xboole_0]) ).
fof(normalize_0_17,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [A] : ~ proper_subset(A,A),
inference(canonicalize,[],[irreflexivity_r2_xboole_0]) ).
fof(normalize_0_19,plain,
! [A] : ~ proper_subset(A,A),
inference(specialize,[],[normalize_0_18]) ).
cnf(refute_0_0,plain,
proper_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
set_difference(skolemFOFtoCNF_B_1,set_difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)) = set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2),
inference(subst,[],[refute_0_1:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_3,plain,
( ~ proper_subset(A,B)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_4,plain,
( ~ proper_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)
| subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_5,plain,
subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( proper_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) )],[refute_0_0,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ subset(A,B)
| set_difference(A,B) = empty_set ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_7,plain,
( ~ subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)
| set_difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) = empty_set ),
inference(subst,[],[refute_0_6:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_8,plain,
set_difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) = empty_set,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
( set_difference(skolemFOFtoCNF_B_1,set_difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)) != set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)
| set_difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) != empty_set
| set_difference(skolemFOFtoCNF_B_1,empty_set) = set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(skolemFOFtoCNF_B_1,set_difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)) ),[0,1],$fot(empty_set)]]) ).
cnf(refute_0_10,plain,
( set_difference(skolemFOFtoCNF_B_1,set_difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)) != set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)
| set_difference(skolemFOFtoCNF_B_1,empty_set) = set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2),empty_set) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
set_difference(skolemFOFtoCNF_B_1,empty_set) = set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_B_1,set_difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)) )],[refute_0_2,refute_0_10]) ).
cnf(refute_0_12,plain,
set_difference(A,empty_set) = A,
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_13,plain,
set_difference(skolemFOFtoCNF_B_1,empty_set) = skolemFOFtoCNF_B_1,
inference(subst,[],[refute_0_12:[bind(A,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_14,plain,
( set_difference(skolemFOFtoCNF_B_1,empty_set) != set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)
| set_difference(skolemFOFtoCNF_B_1,empty_set) != skolemFOFtoCNF_B_1
| skolemFOFtoCNF_B_1 = set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(skolemFOFtoCNF_B_1,empty_set),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)) ),[0],$fot(skolemFOFtoCNF_B_1)]]) ).
cnf(refute_0_15,plain,
( set_difference(skolemFOFtoCNF_B_1,empty_set) != set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)
| skolemFOFtoCNF_B_1 = set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_B_1,empty_set),skolemFOFtoCNF_B_1) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) = set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_1:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_17,plain,
subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_18,plain,
( ~ subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = empty_set ),
inference(subst,[],[refute_0_6:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_19,plain,
set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = empty_set,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) != set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) != empty_set
| set_difference(skolemFOFtoCNF_A_2,empty_set) = set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)),set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) ),[0,1],$fot(empty_set)]]) ).
cnf(refute_0_21,plain,
( set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) != set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| set_difference(skolemFOFtoCNF_A_2,empty_set) = set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),empty_set) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
set_difference(skolemFOFtoCNF_A_2,empty_set) = set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)),set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) )],[refute_0_16,refute_0_21]) ).
cnf(refute_0_23,plain,
set_difference(skolemFOFtoCNF_A_2,empty_set) = skolemFOFtoCNF_A_2,
inference(subst,[],[refute_0_12:[bind(A,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_24,plain,
( set_difference(skolemFOFtoCNF_A_2,empty_set) != set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| set_difference(skolemFOFtoCNF_A_2,empty_set) != skolemFOFtoCNF_A_2
| skolemFOFtoCNF_A_2 = set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(skolemFOFtoCNF_A_2,empty_set),set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) ),[0],$fot(skolemFOFtoCNF_A_2)]]) ).
cnf(refute_0_25,plain,
( set_difference(skolemFOFtoCNF_A_2,empty_set) != set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| skolemFOFtoCNF_A_2 = set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_A_2,empty_set),skolemFOFtoCNF_A_2) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
skolemFOFtoCNF_A_2 = set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_A_2,empty_set),set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) )],[refute_0_22,refute_0_25]) ).
cnf(refute_0_27,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_28,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_29,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( skolemFOFtoCNF_A_2 != set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = skolemFOFtoCNF_A_2 ),
inference(subst,[],[refute_0_29:[bind(X,$fot(skolemFOFtoCNF_A_2)),bind(Y,$fot(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)))]]) ).
cnf(refute_0_31,plain,
set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = skolemFOFtoCNF_A_2,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) )],[refute_0_26,refute_0_30]) ).
cnf(refute_0_32,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_33,plain,
( set_intersection2(A,B) != set_intersection2(B,A)
| set_intersection2(B,A) = set_intersection2(A,B) ),
inference(subst,[],[refute_0_29:[bind(X,$fot(set_intersection2(A,B))),bind(Y,$fot(set_intersection2(B,A)))]]) ).
cnf(refute_0_34,plain,
set_intersection2(B,A) = set_intersection2(A,B),
inference(resolve,[$cnf( $equal(set_intersection2(A,B),set_intersection2(B,A)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) = set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_34:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_36,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_37,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_29,refute_0_36]) ).
cnf(refute_0_38,plain,
( set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) != skolemFOFtoCNF_A_2
| set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) != set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) = skolemFOFtoCNF_A_2 ),
inference(subst,[],[refute_0_37:[bind(X,$fot(set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2))),bind(Y,$fot(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1))),bind(Z,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_39,plain,
( set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) != skolemFOFtoCNF_A_2
| set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) = skolemFOFtoCNF_A_2 ),
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2),set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) )],[refute_0_35,refute_0_38]) ).
cnf(refute_0_40,plain,
set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) = skolemFOFtoCNF_A_2,
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2) )],[refute_0_31,refute_0_39]) ).
cnf(refute_0_41,plain,
( set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) != skolemFOFtoCNF_A_2
| skolemFOFtoCNF_B_1 != set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)
| skolemFOFtoCNF_B_1 = skolemFOFtoCNF_A_2 ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_B_1,set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)) ),[1],$fot(skolemFOFtoCNF_A_2)]]) ).
cnf(refute_0_42,plain,
( skolemFOFtoCNF_B_1 != set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)
| skolemFOFtoCNF_B_1 = skolemFOFtoCNF_A_2 ),
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2),skolemFOFtoCNF_A_2) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
( set_difference(skolemFOFtoCNF_B_1,empty_set) != set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)
| skolemFOFtoCNF_B_1 = skolemFOFtoCNF_A_2 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_1,set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)) )],[refute_0_15,refute_0_42]) ).
cnf(refute_0_44,plain,
skolemFOFtoCNF_B_1 = skolemFOFtoCNF_A_2,
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_B_1,empty_set),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)) )],[refute_0_11,refute_0_43]) ).
cnf(refute_0_45,plain,
( skolemFOFtoCNF_B_1 != skolemFOFtoCNF_A_2
| ~ proper_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)
| proper_subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2) ),
introduced(tautology,[equality,[$cnf( proper_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) ),[0],$fot(skolemFOFtoCNF_A_2)]]) ).
cnf(refute_0_46,plain,
( ~ proper_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)
| proper_subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
proper_subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( proper_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) )],[refute_0_0,refute_0_46]) ).
cnf(refute_0_48,plain,
~ proper_subset(A,A),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_49,plain,
~ proper_subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),
inference(subst,[],[refute_0_48:[bind(A,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_50,plain,
$false,
inference(resolve,[$cnf( proper_subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2) )],[refute_0_47,refute_0_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU139+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n007.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 01:05:13 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.47
% 0.19/0.47 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.48
%------------------------------------------------------------------------------