%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET597+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n014.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 03:35:46 EDT 2022
% Result : Theorem 0.42s 0.58s
% Output : CNFRefutation 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 22
% Syntax : Number of formulae : 162 ( 79 unt; 0 def)
% Number of atoms : 326 ( 109 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 291 ( 127 ~; 99 |; 47 &)
% ( 4 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 13 con; 0-2 aty)
% Number of variables : 178 ( 6 sgn 88 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset_of_union,axiom,
! [B,C] : subset(B,union(B,C)) ).
fof(union_subset,axiom,
! [B,C,D] :
( ( subset(B,C)
& subset(D,C) )
=> subset(union(B,D),C) ) ).
fof(equal_defn,axiom,
! [B,C] :
( B = C
<=> ( subset(B,C)
& subset(C,B) ) ) ).
fof(commutativity_of_union,axiom,
! [B,C] : union(B,C) = union(C,B) ).
fof(reflexivity_of_subset,axiom,
! [B] : subset(B,B) ).
fof(prove_th56,conjecture,
! [B,C,D] :
( B = union(C,D)
<=> ( subset(C,B)
& subset(D,B)
& ! [E] :
( ( subset(C,E)
& subset(D,E) )
=> subset(B,E) ) ) ) ).
fof(subgoal_0,plain,
! [B,C,D] :
( B = union(C,D)
=> subset(C,B) ),
inference(strip,[],[prove_th56]) ).
fof(subgoal_1,plain,
! [B,C,D] :
( ( B = union(C,D)
& subset(C,B) )
=> subset(D,B) ),
inference(strip,[],[prove_th56]) ).
fof(subgoal_2,plain,
! [B,C,D] :
( ( B = union(C,D)
& subset(C,B)
& subset(D,B) )
=> ! [E] :
( ( subset(C,E)
& subset(D,E) )
=> subset(B,E) ) ),
inference(strip,[],[prove_th56]) ).
fof(subgoal_3,plain,
! [B,C,D] :
( ( subset(C,B)
& subset(D,B)
& ! [E] :
( ( subset(C,E)
& subset(D,E) )
=> subset(B,E) ) )
=> B = union(C,D) ),
inference(strip,[],[prove_th56]) ).
fof(negate_0_0,plain,
~ ! [B,C,D] :
( B = union(C,D)
=> subset(C,B) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [B,C] : subset(B,union(B,C)),
inference(canonicalize,[],[subset_of_union]) ).
fof(normalize_0_1,plain,
! [B,C] : subset(B,union(B,C)),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [B,C] :
( ~ subset(C,B)
& ? [D] : B = union(C,D) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_3,plain,
( ~ subset(skolemFOFtoCNF_C,skolemFOFtoCNF_B)
& ? [D] : skolemFOFtoCNF_B = union(skolemFOFtoCNF_C,D) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [D] : skolemFOFtoCNF_B = union(skolemFOFtoCNF_C,D),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
skolemFOFtoCNF_B = union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
~ subset(skolemFOFtoCNF_C,skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_3]) ).
cnf(refute_0_0,plain,
subset(B,union(B,C)),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
subset(skolemFOFtoCNF_C,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),
inference(subst,[],[refute_0_0:[bind(B,$fot(skolemFOFtoCNF_C)),bind(C,$fot(skolemFOFtoCNF_D_2))]]) ).
cnf(refute_0_2,plain,
skolemFOFtoCNF_B = union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_4,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_5,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( skolemFOFtoCNF_B != union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)
| union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2) = skolemFOFtoCNF_B ),
inference(subst,[],[refute_0_5:[bind(X,$fot(skolemFOFtoCNF_B)),bind(Y,$fot(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)))]]) ).
cnf(refute_0_7,plain,
union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2) = skolemFOFtoCNF_B,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) )],[refute_0_2,refute_0_6]) ).
cnf(refute_0_8,plain,
( union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2) != skolemFOFtoCNF_B
| ~ subset(skolemFOFtoCNF_C,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))
| subset(skolemFOFtoCNF_C,skolemFOFtoCNF_B) ),
introduced(tautology,[equality,[$cnf( subset(skolemFOFtoCNF_C,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) ),[1],$fot(skolemFOFtoCNF_B)]]) ).
cnf(refute_0_9,plain,
( ~ subset(skolemFOFtoCNF_C,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))
| subset(skolemFOFtoCNF_C,skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( $equal(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_B) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
subset(skolemFOFtoCNF_C,skolemFOFtoCNF_B),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_C,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) )],[refute_0_1,refute_0_9]) ).
cnf(refute_0_11,plain,
~ subset(skolemFOFtoCNF_C,skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_12,plain,
$false,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_C,skolemFOFtoCNF_B) )],[refute_0_10,refute_0_11]) ).
fof(negate_1_0,plain,
~ ! [B,C,D] :
( ( B = union(C,D)
& subset(C,B) )
=> subset(D,B) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [B,C] : subset(B,union(B,C)),
inference(canonicalize,[],[subset_of_union]) ).
fof(normalize_1_1,plain,
! [B,C] : subset(B,union(B,C)),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
! [B,C] : union(B,C) = union(C,B),
inference(canonicalize,[],[commutativity_of_union]) ).
fof(normalize_1_3,plain,
! [B,C] : union(B,C) = union(C,B),
inference(specialize,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
? [B,C,D] :
( ~ subset(D,B)
& B = union(C,D)
& subset(C,B) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_5,plain,
( ~ subset(skolemFOFtoCNF_D_3,skolemFOFtoCNF_B_1)
& skolemFOFtoCNF_B_1 = union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3)
& subset(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) ),
inference(skolemize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
skolemFOFtoCNF_B_1 = union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
~ subset(skolemFOFtoCNF_D_3,skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_1_5]) ).
cnf(refute_1_0,plain,
subset(B,union(B,C)),
inference(canonicalize,[],[normalize_1_1]) ).
cnf(refute_1_1,plain,
union(B,C) = union(C,B),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_2,plain,
( union(B,C) != union(C,B)
| ~ subset(B,union(B,C))
| subset(B,union(C,B)) ),
introduced(tautology,[equality,[$cnf( subset(B,union(B,C)) ),[1],$fot(union(C,B))]]) ).
cnf(refute_1_3,plain,
( ~ subset(B,union(B,C))
| subset(B,union(C,B)) ),
inference(resolve,[$cnf( $equal(union(B,C),union(C,B)) )],[refute_1_1,refute_1_2]) ).
cnf(refute_1_4,plain,
subset(B,union(C,B)),
inference(resolve,[$cnf( subset(B,union(B,C)) )],[refute_1_0,refute_1_3]) ).
cnf(refute_1_5,plain,
subset(skolemFOFtoCNF_D_3,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3)),
inference(subst,[],[refute_1_4:[bind(B,$fot(skolemFOFtoCNF_D_3)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_1_6,plain,
skolemFOFtoCNF_B_1 = union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_7,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_8,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_9,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_7,refute_1_8]) ).
cnf(refute_1_10,plain,
( skolemFOFtoCNF_B_1 != union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3)
| union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3) = skolemFOFtoCNF_B_1 ),
inference(subst,[],[refute_1_9:[bind(X,$fot(skolemFOFtoCNF_B_1)),bind(Y,$fot(union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3)))]]) ).
cnf(refute_1_11,plain,
union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3) = skolemFOFtoCNF_B_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_1,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3)) )],[refute_1_6,refute_1_10]) ).
cnf(refute_1_12,plain,
( union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3) != skolemFOFtoCNF_B_1
| ~ subset(skolemFOFtoCNF_D_3,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3))
| subset(skolemFOFtoCNF_D_3,skolemFOFtoCNF_B_1) ),
introduced(tautology,[equality,[$cnf( subset(skolemFOFtoCNF_D_3,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3)) ),[1],$fot(skolemFOFtoCNF_B_1)]]) ).
cnf(refute_1_13,plain,
( ~ subset(skolemFOFtoCNF_D_3,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3))
| subset(skolemFOFtoCNF_D_3,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( $equal(union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3),skolemFOFtoCNF_B_1) )],[refute_1_11,refute_1_12]) ).
cnf(refute_1_14,plain,
subset(skolemFOFtoCNF_D_3,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_D_3,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3)) )],[refute_1_5,refute_1_13]) ).
cnf(refute_1_15,plain,
~ subset(skolemFOFtoCNF_D_3,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_16,plain,
$false,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_D_3,skolemFOFtoCNF_B_1) )],[refute_1_14,refute_1_15]) ).
fof(negate_2_0,plain,
~ ! [B,C,D] :
( ( B = union(C,D)
& subset(C,B)
& subset(D,B) )
=> ! [E] :
( ( subset(C,E)
& subset(D,E) )
=> subset(B,E) ) ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
? [B,C,D] :
( B = union(C,D)
& subset(C,B)
& subset(D,B)
& ? [E] :
( ~ subset(B,E)
& subset(C,E)
& subset(D,E) ) ),
inference(canonicalize,[],[negate_2_0]) ).
fof(normalize_2_1,plain,
( skolemFOFtoCNF_B_2 = union(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_4)
& subset(skolemFOFtoCNF_C_2,skolemFOFtoCNF_B_2)
& subset(skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_2)
& ? [E] :
( ~ subset(skolemFOFtoCNF_B_2,E)
& subset(skolemFOFtoCNF_C_2,E)
& subset(skolemFOFtoCNF_D_4,E) ) ),
inference(skolemize,[],[normalize_2_0]) ).
fof(normalize_2_2,plain,
? [E] :
( ~ subset(skolemFOFtoCNF_B_2,E)
& subset(skolemFOFtoCNF_C_2,E)
& subset(skolemFOFtoCNF_D_4,E) ),
inference(conjunct,[],[normalize_2_1]) ).
fof(normalize_2_3,plain,
( ~ subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_E)
& subset(skolemFOFtoCNF_C_2,skolemFOFtoCNF_E)
& subset(skolemFOFtoCNF_D_4,skolemFOFtoCNF_E) ),
inference(skolemize,[],[normalize_2_2]) ).
fof(normalize_2_4,plain,
subset(skolemFOFtoCNF_D_4,skolemFOFtoCNF_E),
inference(conjunct,[],[normalize_2_3]) ).
fof(normalize_2_5,plain,
subset(skolemFOFtoCNF_C_2,skolemFOFtoCNF_E),
inference(conjunct,[],[normalize_2_3]) ).
fof(normalize_2_6,plain,
! [B,C,D] :
( ~ subset(B,C)
| ~ subset(D,C)
| subset(union(B,D),C) ),
inference(canonicalize,[],[union_subset]) ).
fof(normalize_2_7,plain,
! [B,C,D] :
( ~ subset(B,C)
| ~ subset(D,C)
| subset(union(B,D),C) ),
inference(specialize,[],[normalize_2_6]) ).
fof(normalize_2_8,plain,
skolemFOFtoCNF_B_2 = union(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_4),
inference(conjunct,[],[normalize_2_1]) ).
fof(normalize_2_9,plain,
~ subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_E),
inference(conjunct,[],[normalize_2_3]) ).
cnf(refute_2_0,plain,
subset(skolemFOFtoCNF_D_4,skolemFOFtoCNF_E),
inference(canonicalize,[],[normalize_2_4]) ).
cnf(refute_2_1,plain,
subset(skolemFOFtoCNF_C_2,skolemFOFtoCNF_E),
inference(canonicalize,[],[normalize_2_5]) ).
cnf(refute_2_2,plain,
( ~ subset(B,C)
| ~ subset(D,C)
| subset(union(B,D),C) ),
inference(canonicalize,[],[normalize_2_7]) ).
cnf(refute_2_3,plain,
( ~ subset(X_118,skolemFOFtoCNF_E)
| ~ subset(skolemFOFtoCNF_C_2,skolemFOFtoCNF_E)
| subset(union(skolemFOFtoCNF_C_2,X_118),skolemFOFtoCNF_E) ),
inference(subst,[],[refute_2_2:[bind(B,$fot(skolemFOFtoCNF_C_2)),bind(C,$fot(skolemFOFtoCNF_E)),bind(D,$fot(X_118))]]) ).
cnf(refute_2_4,plain,
( ~ subset(X_118,skolemFOFtoCNF_E)
| subset(union(skolemFOFtoCNF_C_2,X_118),skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_C_2,skolemFOFtoCNF_E) )],[refute_2_1,refute_2_3]) ).
cnf(refute_2_5,plain,
( ~ subset(skolemFOFtoCNF_D_4,skolemFOFtoCNF_E)
| subset(union(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_4),skolemFOFtoCNF_E) ),
inference(subst,[],[refute_2_4:[bind(X_118,$fot(skolemFOFtoCNF_D_4))]]) ).
cnf(refute_2_6,plain,
subset(union(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_4),skolemFOFtoCNF_E),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_D_4,skolemFOFtoCNF_E) )],[refute_2_0,refute_2_5]) ).
cnf(refute_2_7,plain,
skolemFOFtoCNF_B_2 = union(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_4),
inference(canonicalize,[],[normalize_2_8]) ).
cnf(refute_2_8,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_2_9,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_2_10,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_2_8,refute_2_9]) ).
cnf(refute_2_11,plain,
( skolemFOFtoCNF_B_2 != union(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_4)
| union(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_4) = skolemFOFtoCNF_B_2 ),
inference(subst,[],[refute_2_10:[bind(X,$fot(skolemFOFtoCNF_B_2)),bind(Y,$fot(union(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_4)))]]) ).
cnf(refute_2_12,plain,
union(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_4) = skolemFOFtoCNF_B_2,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_2,union(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_4)) )],[refute_2_7,refute_2_11]) ).
cnf(refute_2_13,plain,
( union(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_4) != skolemFOFtoCNF_B_2
| ~ subset(union(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_4),skolemFOFtoCNF_E)
| subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_E) ),
introduced(tautology,[equality,[$cnf( subset(union(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_4),skolemFOFtoCNF_E) ),[0],$fot(skolemFOFtoCNF_B_2)]]) ).
cnf(refute_2_14,plain,
( ~ subset(union(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_4),skolemFOFtoCNF_E)
| subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( $equal(union(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_4),skolemFOFtoCNF_B_2) )],[refute_2_12,refute_2_13]) ).
cnf(refute_2_15,plain,
subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_E),
inference(resolve,[$cnf( subset(union(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_4),skolemFOFtoCNF_E) )],[refute_2_6,refute_2_14]) ).
cnf(refute_2_16,plain,
~ subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_E),
inference(canonicalize,[],[normalize_2_9]) ).
cnf(refute_2_17,plain,
$false,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_E) )],[refute_2_15,refute_2_16]) ).
fof(negate_3_0,plain,
~ ! [B,C,D] :
( ( subset(C,B)
& subset(D,B)
& ! [E] :
( ( subset(C,E)
& subset(D,E) )
=> subset(B,E) ) )
=> B = union(C,D) ),
inference(negate,[],[subgoal_3]) ).
fof(normalize_3_0,plain,
? [B,C,D] :
( B != union(C,D)
& subset(C,B)
& subset(D,B)
& ! [E] :
( ~ subset(C,E)
| ~ subset(D,E)
| subset(B,E) ) ),
inference(canonicalize,[],[negate_3_0]) ).
fof(normalize_3_1,plain,
( skolemFOFtoCNF_B_3 != union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5)
& subset(skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)
& subset(skolemFOFtoCNF_D_5,skolemFOFtoCNF_B_3)
& ! [E] :
( ~ subset(skolemFOFtoCNF_C_3,E)
| ~ subset(skolemFOFtoCNF_D_5,E)
| subset(skolemFOFtoCNF_B_3,E) ) ),
inference(skolemize,[],[normalize_3_0]) ).
fof(normalize_3_2,plain,
subset(skolemFOFtoCNF_D_5,skolemFOFtoCNF_B_3),
inference(conjunct,[],[normalize_3_1]) ).
fof(normalize_3_3,plain,
subset(skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3),
inference(conjunct,[],[normalize_3_1]) ).
fof(normalize_3_4,plain,
! [B,C,D] :
( ~ subset(B,C)
| ~ subset(D,C)
| subset(union(B,D),C) ),
inference(canonicalize,[],[union_subset]) ).
fof(normalize_3_5,plain,
! [B,C,D] :
( ~ subset(B,C)
| ~ subset(D,C)
| subset(union(B,D),C) ),
inference(specialize,[],[normalize_3_4]) ).
fof(normalize_3_6,plain,
! [B,C] : subset(B,union(B,C)),
inference(canonicalize,[],[subset_of_union]) ).
fof(normalize_3_7,plain,
! [B,C] : subset(B,union(B,C)),
inference(specialize,[],[normalize_3_6]) ).
fof(normalize_3_8,plain,
! [B,C] : union(B,C) = union(C,B),
inference(canonicalize,[],[commutativity_of_union]) ).
fof(normalize_3_9,plain,
! [B,C] : union(B,C) = union(C,B),
inference(specialize,[],[normalize_3_8]) ).
fof(normalize_3_10,plain,
! [E] :
( ~ subset(skolemFOFtoCNF_C_3,E)
| ~ subset(skolemFOFtoCNF_D_5,E)
| subset(skolemFOFtoCNF_B_3,E) ),
inference(conjunct,[],[normalize_3_1]) ).
fof(normalize_3_11,plain,
! [E] :
( ~ subset(skolemFOFtoCNF_C_3,E)
| ~ subset(skolemFOFtoCNF_D_5,E)
| subset(skolemFOFtoCNF_B_3,E) ),
inference(specialize,[],[normalize_3_10]) ).
fof(normalize_3_12,plain,
! [B,C] :
( B != C
<=> ( ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(canonicalize,[],[equal_defn]) ).
fof(normalize_3_13,plain,
! [B,C] :
( B != C
<=> ( ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(specialize,[],[normalize_3_12]) ).
fof(normalize_3_14,plain,
! [B,C] :
( ( B != C
| subset(B,C) )
& ( B != C
| subset(C,B) )
& ( ~ subset(B,C)
| ~ subset(C,B)
| B = C ) ),
inference(clausify,[],[normalize_3_13]) ).
fof(normalize_3_15,plain,
! [B,C] :
( ~ subset(B,C)
| ~ subset(C,B)
| B = C ),
inference(conjunct,[],[normalize_3_14]) ).
fof(normalize_3_16,plain,
! [B] : subset(B,B),
inference(canonicalize,[],[reflexivity_of_subset]) ).
fof(normalize_3_17,plain,
! [B] : subset(B,B),
inference(specialize,[],[normalize_3_16]) ).
fof(normalize_3_18,plain,
skolemFOFtoCNF_B_3 != union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5),
inference(conjunct,[],[normalize_3_1]) ).
cnf(refute_3_0,plain,
subset(skolemFOFtoCNF_D_5,skolemFOFtoCNF_B_3),
inference(canonicalize,[],[normalize_3_2]) ).
cnf(refute_3_1,plain,
subset(skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3),
inference(canonicalize,[],[normalize_3_3]) ).
cnf(refute_3_2,plain,
( ~ subset(B,C)
| ~ subset(D,C)
| subset(union(B,D),C) ),
inference(canonicalize,[],[normalize_3_5]) ).
cnf(refute_3_3,plain,
( ~ subset(X_307,skolemFOFtoCNF_B_3)
| ~ subset(skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)
| subset(union(skolemFOFtoCNF_C_3,X_307),skolemFOFtoCNF_B_3) ),
inference(subst,[],[refute_3_2:[bind(B,$fot(skolemFOFtoCNF_C_3)),bind(C,$fot(skolemFOFtoCNF_B_3)),bind(D,$fot(X_307))]]) ).
cnf(refute_3_4,plain,
( ~ subset(X_307,skolemFOFtoCNF_B_3)
| subset(union(skolemFOFtoCNF_C_3,X_307),skolemFOFtoCNF_B_3) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3) )],[refute_3_1,refute_3_3]) ).
cnf(refute_3_5,plain,
( ~ subset(skolemFOFtoCNF_D_5,skolemFOFtoCNF_B_3)
| subset(union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5),skolemFOFtoCNF_B_3) ),
inference(subst,[],[refute_3_4:[bind(X_307,$fot(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_3_6,plain,
subset(union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5),skolemFOFtoCNF_B_3),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_D_5,skolemFOFtoCNF_B_3) )],[refute_3_0,refute_3_5]) ).
cnf(refute_3_7,plain,
( ~ subset(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5))
| subset(union(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)),union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5)) ),
inference(subst,[],[refute_3_2:[bind(B,$fot(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3))),bind(C,$fot(union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5))),bind(D,$fot(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)))]]) ).
cnf(refute_3_8,plain,
( ~ subset(skolemFOFtoCNF_B_3,union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5))
| subset(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5)) ),
inference(subst,[],[refute_3_2:[bind(B,$fot(skolemFOFtoCNF_B_3)),bind(C,$fot(union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5))),bind(D,$fot(skolemFOFtoCNF_B_3))]]) ).
cnf(refute_3_9,plain,
subset(B,union(B,C)),
inference(canonicalize,[],[normalize_3_7]) ).
cnf(refute_3_10,plain,
subset(skolemFOFtoCNF_C_3,union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5)),
inference(subst,[],[refute_3_9:[bind(B,$fot(skolemFOFtoCNF_C_3)),bind(C,$fot(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_3_11,plain,
union(B,C) = union(C,B),
inference(canonicalize,[],[normalize_3_9]) ).
cnf(refute_3_12,plain,
( union(B,C) != union(C,B)
| ~ subset(B,union(B,C))
| subset(B,union(C,B)) ),
introduced(tautology,[equality,[$cnf( subset(B,union(B,C)) ),[1],$fot(union(C,B))]]) ).
cnf(refute_3_13,plain,
( ~ subset(B,union(B,C))
| subset(B,union(C,B)) ),
inference(resolve,[$cnf( $equal(union(B,C),union(C,B)) )],[refute_3_11,refute_3_12]) ).
cnf(refute_3_14,plain,
subset(B,union(C,B)),
inference(resolve,[$cnf( subset(B,union(B,C)) )],[refute_3_9,refute_3_13]) ).
cnf(refute_3_15,plain,
subset(skolemFOFtoCNF_D_5,union(C,skolemFOFtoCNF_D_5)),
inference(subst,[],[refute_3_14:[bind(B,$fot(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_3_16,plain,
( ~ subset(skolemFOFtoCNF_C_3,E)
| ~ subset(skolemFOFtoCNF_D_5,E)
| subset(skolemFOFtoCNF_B_3,E) ),
inference(canonicalize,[],[normalize_3_11]) ).
cnf(refute_3_17,plain,
( ~ subset(skolemFOFtoCNF_C_3,union(C,skolemFOFtoCNF_D_5))
| ~ subset(skolemFOFtoCNF_D_5,union(C,skolemFOFtoCNF_D_5))
| subset(skolemFOFtoCNF_B_3,union(C,skolemFOFtoCNF_D_5)) ),
inference(subst,[],[refute_3_16:[bind(E,$fot(union(C,skolemFOFtoCNF_D_5)))]]) ).
cnf(refute_3_18,plain,
( ~ subset(skolemFOFtoCNF_C_3,union(C,skolemFOFtoCNF_D_5))
| subset(skolemFOFtoCNF_B_3,union(C,skolemFOFtoCNF_D_5)) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_D_5,union(C,skolemFOFtoCNF_D_5)) )],[refute_3_15,refute_3_17]) ).
cnf(refute_3_19,plain,
( ~ subset(skolemFOFtoCNF_C_3,union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5))
| subset(skolemFOFtoCNF_B_3,union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5)) ),
inference(subst,[],[refute_3_18:[bind(C,$fot(skolemFOFtoCNF_C_3))]]) ).
cnf(refute_3_20,plain,
subset(skolemFOFtoCNF_B_3,union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5)),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_C_3,union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5)) )],[refute_3_10,refute_3_19]) ).
cnf(refute_3_21,plain,
subset(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5)),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B_3,union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5)) )],[refute_3_20,refute_3_8]) ).
cnf(refute_3_22,plain,
subset(union(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)),union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5)),
inference(resolve,[$cnf( subset(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5)) )],[refute_3_21,refute_3_7]) ).
cnf(refute_3_23,plain,
( ~ subset(B,C)
| ~ subset(C,B)
| B = C ),
inference(canonicalize,[],[normalize_3_15]) ).
cnf(refute_3_24,plain,
( ~ subset(union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5),union(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)))
| ~ subset(union(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)),union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5))
| union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5) = union(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)) ),
inference(subst,[],[refute_3_23:[bind(B,$fot(union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5))),bind(C,$fot(union(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3))))]]) ).
cnf(refute_3_25,plain,
( ~ subset(union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5),union(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)))
| union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5) = union(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( subset(union(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)),union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5)) )],[refute_3_22,refute_3_24]) ).
cnf(refute_3_26,plain,
subset(B,B),
inference(canonicalize,[],[normalize_3_17]) ).
cnf(refute_3_27,plain,
subset(X_132,X_132),
inference(subst,[],[refute_3_26:[bind(B,$fot(X_132))]]) ).
cnf(refute_3_28,plain,
( ~ subset(X_132,X_132)
| subset(union(X_132,X_132),X_132) ),
inference(subst,[],[refute_3_2:[bind(B,$fot(X_132)),bind(C,$fot(X_132)),bind(D,$fot(X_132))]]) ).
cnf(refute_3_29,plain,
subset(union(X_132,X_132),X_132),
inference(resolve,[$cnf( subset(X_132,X_132) )],[refute_3_27,refute_3_28]) ).
cnf(refute_3_30,plain,
subset(union(X_163,X_163),X_163),
inference(subst,[],[refute_3_29:[bind(X_132,$fot(X_163))]]) ).
cnf(refute_3_31,plain,
( ~ subset(X_163,union(X_163,X_163))
| ~ subset(union(X_163,X_163),X_163)
| union(X_163,X_163) = X_163 ),
inference(subst,[],[refute_3_23:[bind(B,$fot(union(X_163,X_163))),bind(C,$fot(X_163))]]) ).
cnf(refute_3_32,plain,
( ~ subset(X_163,union(X_163,X_163))
| union(X_163,X_163) = X_163 ),
inference(resolve,[$cnf( subset(union(X_163,X_163),X_163) )],[refute_3_30,refute_3_31]) ).
cnf(refute_3_33,plain,
subset(X_163,union(X_163,X_163)),
inference(subst,[],[refute_3_14:[bind(B,$fot(X_163)),bind(C,$fot(X_163))]]) ).
cnf(refute_3_34,plain,
union(X_163,X_163) = X_163,
inference(resolve,[$cnf( subset(X_163,union(X_163,X_163)) )],[refute_3_33,refute_3_32]) ).
cnf(refute_3_35,plain,
union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3) = skolemFOFtoCNF_B_3,
inference(subst,[],[refute_3_34:[bind(X_163,$fot(skolemFOFtoCNF_B_3))]]) ).
cnf(refute_3_36,plain,
union(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)) = union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),
inference(subst,[],[refute_3_34:[bind(X_163,$fot(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)))]]) ).
cnf(refute_3_37,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_3_38,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_3_39,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_3_37,refute_3_38]) ).
cnf(refute_3_40,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_3_41,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_3_39,refute_3_40]) ).
cnf(refute_3_42,plain,
( union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3) != skolemFOFtoCNF_B_3
| union(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)) != union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)
| union(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)) = skolemFOFtoCNF_B_3 ),
inference(subst,[],[refute_3_41:[bind(X,$fot(union(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)))),bind(Y,$fot(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3))),bind(Z,$fot(skolemFOFtoCNF_B_3))]]) ).
cnf(refute_3_43,plain,
( union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3) != skolemFOFtoCNF_B_3
| union(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)) = skolemFOFtoCNF_B_3 ),
inference(resolve,[$cnf( $equal(union(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)),union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)) )],[refute_3_36,refute_3_42]) ).
cnf(refute_3_44,plain,
union(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)) = skolemFOFtoCNF_B_3,
inference(resolve,[$cnf( $equal(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),skolemFOFtoCNF_B_3) )],[refute_3_35,refute_3_43]) ).
cnf(refute_3_45,plain,
( union(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)) != skolemFOFtoCNF_B_3
| ~ subset(union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5),skolemFOFtoCNF_B_3)
| subset(union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5),union(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3))) ),
introduced(tautology,[equality,[$cnf( ~ subset(union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5),union(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3))) ),[1],$fot(skolemFOFtoCNF_B_3)]]) ).
cnf(refute_3_46,plain,
( ~ subset(union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5),skolemFOFtoCNF_B_3)
| subset(union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5),union(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3))) ),
inference(resolve,[$cnf( $equal(union(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_B_3) )],[refute_3_44,refute_3_45]) ).
cnf(refute_3_47,plain,
( ~ subset(union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5),skolemFOFtoCNF_B_3)
| union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5) = union(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( subset(union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5),union(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3))) )],[refute_3_46,refute_3_25]) ).
cnf(refute_3_48,plain,
( union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5) != union(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3))
| union(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)) != skolemFOFtoCNF_B_3
| union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5) = skolemFOFtoCNF_B_3 ),
introduced(tautology,[equality,[$cnf( ~ $equal(union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5),skolemFOFtoCNF_B_3) ),[0],$fot(union(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)))]]) ).
cnf(refute_3_49,plain,
( union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5) != union(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3))
| union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5) = skolemFOFtoCNF_B_3 ),
inference(resolve,[$cnf( $equal(union(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)),skolemFOFtoCNF_B_3) )],[refute_3_44,refute_3_48]) ).
cnf(refute_3_50,plain,
( ~ subset(union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5),skolemFOFtoCNF_B_3)
| union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5) = skolemFOFtoCNF_B_3 ),
inference(resolve,[$cnf( $equal(union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5),union(union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3),union(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3))) )],[refute_3_47,refute_3_49]) ).
cnf(refute_3_51,plain,
skolemFOFtoCNF_B_3 != union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5),
inference(canonicalize,[],[normalize_3_18]) ).
cnf(refute_3_52,plain,
( union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5) != skolemFOFtoCNF_B_3
| skolemFOFtoCNF_B_3 = union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5) ),
inference(subst,[],[refute_3_39:[bind(X,$fot(union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5))),bind(Y,$fot(skolemFOFtoCNF_B_3))]]) ).
cnf(refute_3_53,plain,
union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5) != skolemFOFtoCNF_B_3,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_3,union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5)) )],[refute_3_52,refute_3_51]) ).
cnf(refute_3_54,plain,
~ subset(union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5),skolemFOFtoCNF_B_3),
inference(resolve,[$cnf( $equal(union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5),skolemFOFtoCNF_B_3) )],[refute_3_50,refute_3_53]) ).
cnf(refute_3_55,plain,
$false,
inference(resolve,[$cnf( subset(union(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5),skolemFOFtoCNF_B_3) )],[refute_3_6,refute_3_54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET597+3 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n014.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 Jul 10 15:43:35 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.42/0.58 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.42/0.58
% 0.42/0.58 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.42/0.59
%------------------------------------------------------------------------------