TSTP Solution File: SET598+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET598+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 0.19s 0.54s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 18
% Syntax : Number of formulae : 133 ( 65 unt; 0 def)
% Number of atoms : 276 ( 84 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 249 ( 106 ~; 78 |; 47 &)
% ( 4 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 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 : 160 ( 6 sgn 85 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection_is_subset,axiom,
! [B,C] : subset(intersection(B,C),B) ).
fof(intersection_of_subsets,axiom,
! [B,C,D] :
( ( subset(B,C)
& subset(B,D) )
=> subset(B,intersection(C,D)) ) ).
fof(equal_defn,axiom,
! [B,C] :
( B = C
<=> ( subset(B,C)
& subset(C,B) ) ) ).
fof(commutativity_of_intersection,axiom,
! [B,C] : intersection(B,C) = intersection(C,B) ).
fof(prove_th57,conjecture,
! [B,C,D] :
( B = intersection(C,D)
<=> ( subset(B,C)
& subset(B,D)
& ! [E] :
( ( subset(E,C)
& subset(E,D) )
=> subset(E,B) ) ) ) ).
fof(subgoal_0,plain,
! [B,C,D] :
( B = intersection(C,D)
=> subset(B,C) ),
inference(strip,[],[prove_th57]) ).
fof(subgoal_1,plain,
! [B,C,D] :
( ( B = intersection(C,D)
& subset(B,C) )
=> subset(B,D) ),
inference(strip,[],[prove_th57]) ).
fof(subgoal_2,plain,
! [B,C,D] :
( ( B = intersection(C,D)
& subset(B,C)
& subset(B,D) )
=> ! [E] :
( ( subset(E,C)
& subset(E,D) )
=> subset(E,B) ) ),
inference(strip,[],[prove_th57]) ).
fof(subgoal_3,plain,
! [B,C,D] :
( ( subset(B,C)
& subset(B,D)
& ! [E] :
( ( subset(E,C)
& subset(E,D) )
=> subset(E,B) ) )
=> B = intersection(C,D) ),
inference(strip,[],[prove_th57]) ).
fof(negate_0_0,plain,
~ ! [B,C,D] :
( B = intersection(C,D)
=> subset(B,C) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [B,C] : subset(intersection(B,C),B),
inference(canonicalize,[],[intersection_is_subset]) ).
fof(normalize_0_1,plain,
! [B,C] : subset(intersection(B,C),B),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [B,C] :
( ~ subset(B,C)
& ? [D] : B = intersection(C,D) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_3,plain,
( ~ subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
& ? [D] : skolemFOFtoCNF_B = intersection(skolemFOFtoCNF_C,D) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [D] : skolemFOFtoCNF_B = intersection(skolemFOFtoCNF_C,D),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
skolemFOFtoCNF_B = intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
~ subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_3]) ).
cnf(refute_0_0,plain,
subset(intersection(B,C),B),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
subset(intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_C),
inference(subst,[],[refute_0_0:[bind(B,$fot(skolemFOFtoCNF_C)),bind(C,$fot(skolemFOFtoCNF_D_2))]]) ).
cnf(refute_0_2,plain,
skolemFOFtoCNF_B = intersection(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( $equal(X,X) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( skolemFOFtoCNF_B != intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)
| intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2) = skolemFOFtoCNF_B ),
inference(subst,[],[refute_0_5:[bind(X,$fot(skolemFOFtoCNF_B)),bind(Y,$fot(intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)))]]) ).
cnf(refute_0_7,plain,
intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2) = skolemFOFtoCNF_B,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) )],[refute_0_2,refute_0_6]) ).
cnf(refute_0_8,plain,
( intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2) != skolemFOFtoCNF_B
| ~ subset(intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_C)
| subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C) ),
introduced(tautology,[equality,[$cnf( subset(intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_C) ),[0],$fot(skolemFOFtoCNF_B)]]) ).
cnf(refute_0_9,plain,
( ~ subset(intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_C)
| subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_B) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(resolve,[$cnf( subset(intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),skolemFOFtoCNF_C) )],[refute_0_1,refute_0_9]) ).
cnf(refute_0_11,plain,
~ subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_12,plain,
$false,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_10,refute_0_11]) ).
fof(negate_1_0,plain,
~ ! [B,C,D] :
( ( B = intersection(C,D)
& subset(B,C) )
=> subset(B,D) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [B,C] : subset(intersection(B,C),B),
inference(canonicalize,[],[intersection_is_subset]) ).
fof(normalize_1_1,plain,
! [B,C] : subset(intersection(B,C),B),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(canonicalize,[],[commutativity_of_intersection]) ).
fof(normalize_1_3,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(specialize,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
? [B,C,D] :
( ~ subset(B,D)
& B = intersection(C,D)
& subset(B,C) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_5,plain,
( ~ subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3)
& skolemFOFtoCNF_B_1 = intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3)
& subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) ),
inference(skolemize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
skolemFOFtoCNF_B_1 = intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
~ subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3),
inference(conjunct,[],[normalize_1_5]) ).
cnf(refute_1_0,plain,
subset(intersection(B,C),B),
inference(canonicalize,[],[normalize_1_1]) ).
cnf(refute_1_1,plain,
intersection(B,C) = intersection(C,B),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_2,plain,
( intersection(B,C) != intersection(C,B)
| ~ subset(intersection(B,C),B)
| subset(intersection(C,B),B) ),
introduced(tautology,[equality,[$cnf( subset(intersection(B,C),B) ),[0],$fot(intersection(C,B))]]) ).
cnf(refute_1_3,plain,
( ~ subset(intersection(B,C),B)
| subset(intersection(C,B),B) ),
inference(resolve,[$cnf( $equal(intersection(B,C),intersection(C,B)) )],[refute_1_1,refute_1_2]) ).
cnf(refute_1_4,plain,
subset(intersection(C,B),B),
inference(resolve,[$cnf( subset(intersection(B,C),B) )],[refute_1_0,refute_1_3]) ).
cnf(refute_1_5,plain,
subset(intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3),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 = intersection(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( $equal(X,X) )],[refute_1_7,refute_1_8]) ).
cnf(refute_1_10,plain,
( skolemFOFtoCNF_B_1 != intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3)
| intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3) = skolemFOFtoCNF_B_1 ),
inference(subst,[],[refute_1_9:[bind(X,$fot(skolemFOFtoCNF_B_1)),bind(Y,$fot(intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3)))]]) ).
cnf(refute_1_11,plain,
intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3) = skolemFOFtoCNF_B_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_1,intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3)) )],[refute_1_6,refute_1_10]) ).
cnf(refute_1_12,plain,
( intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3) != skolemFOFtoCNF_B_1
| ~ subset(intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3),skolemFOFtoCNF_D_3)
| subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3) ),
introduced(tautology,[equality,[$cnf( subset(intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3),skolemFOFtoCNF_D_3) ),[0],$fot(skolemFOFtoCNF_B_1)]]) ).
cnf(refute_1_13,plain,
( ~ subset(intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3),skolemFOFtoCNF_D_3)
| subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3) ),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3),skolemFOFtoCNF_B_1) )],[refute_1_11,refute_1_12]) ).
cnf(refute_1_14,plain,
subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3),
inference(resolve,[$cnf( subset(intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3),skolemFOFtoCNF_D_3) )],[refute_1_5,refute_1_13]) ).
cnf(refute_1_15,plain,
~ subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_16,plain,
$false,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3) )],[refute_1_14,refute_1_15]) ).
fof(negate_2_0,plain,
~ ! [B,C,D] :
( ( B = intersection(C,D)
& subset(B,C)
& subset(B,D) )
=> ! [E] :
( ( subset(E,C)
& subset(E,D) )
=> subset(E,B) ) ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
? [B,C,D] :
( B = intersection(C,D)
& subset(B,C)
& subset(B,D)
& ? [E] :
( ~ subset(E,B)
& subset(E,C)
& subset(E,D) ) ),
inference(canonicalize,[],[negate_2_0]) ).
fof(normalize_2_1,plain,
( skolemFOFtoCNF_B_2 = intersection(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_4)
& subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_2)
& subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_4)
& ? [E] :
( ~ subset(E,skolemFOFtoCNF_B_2)
& subset(E,skolemFOFtoCNF_C_2)
& subset(E,skolemFOFtoCNF_D_4) ) ),
inference(skolemize,[],[normalize_2_0]) ).
fof(normalize_2_2,plain,
? [E] :
( ~ subset(E,skolemFOFtoCNF_B_2)
& subset(E,skolemFOFtoCNF_C_2)
& subset(E,skolemFOFtoCNF_D_4) ),
inference(conjunct,[],[normalize_2_1]) ).
fof(normalize_2_3,plain,
( ~ subset(skolemFOFtoCNF_E,skolemFOFtoCNF_B_2)
& subset(skolemFOFtoCNF_E,skolemFOFtoCNF_C_2)
& subset(skolemFOFtoCNF_E,skolemFOFtoCNF_D_4) ),
inference(skolemize,[],[normalize_2_2]) ).
fof(normalize_2_4,plain,
subset(skolemFOFtoCNF_E,skolemFOFtoCNF_D_4),
inference(conjunct,[],[normalize_2_3]) ).
fof(normalize_2_5,plain,
subset(skolemFOFtoCNF_E,skolemFOFtoCNF_C_2),
inference(conjunct,[],[normalize_2_3]) ).
fof(normalize_2_6,plain,
! [B,C,D] :
( ~ subset(B,C)
| ~ subset(B,D)
| subset(B,intersection(C,D)) ),
inference(canonicalize,[],[intersection_of_subsets]) ).
fof(normalize_2_7,plain,
! [B,C,D] :
( ~ subset(B,C)
| ~ subset(B,D)
| subset(B,intersection(C,D)) ),
inference(specialize,[],[normalize_2_6]) ).
fof(normalize_2_8,plain,
skolemFOFtoCNF_B_2 = intersection(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_4),
inference(conjunct,[],[normalize_2_1]) ).
fof(normalize_2_9,plain,
~ subset(skolemFOFtoCNF_E,skolemFOFtoCNF_B_2),
inference(conjunct,[],[normalize_2_3]) ).
cnf(refute_2_0,plain,
subset(skolemFOFtoCNF_E,skolemFOFtoCNF_D_4),
inference(canonicalize,[],[normalize_2_4]) ).
cnf(refute_2_1,plain,
subset(skolemFOFtoCNF_E,skolemFOFtoCNF_C_2),
inference(canonicalize,[],[normalize_2_5]) ).
cnf(refute_2_2,plain,
( ~ subset(B,C)
| ~ subset(B,D)
| subset(B,intersection(C,D)) ),
inference(canonicalize,[],[normalize_2_7]) ).
cnf(refute_2_3,plain,
( ~ subset(skolemFOFtoCNF_E,X_134)
| ~ subset(skolemFOFtoCNF_E,skolemFOFtoCNF_C_2)
| subset(skolemFOFtoCNF_E,intersection(skolemFOFtoCNF_C_2,X_134)) ),
inference(subst,[],[refute_2_2:[bind(B,$fot(skolemFOFtoCNF_E)),bind(C,$fot(skolemFOFtoCNF_C_2)),bind(D,$fot(X_134))]]) ).
cnf(refute_2_4,plain,
( ~ subset(skolemFOFtoCNF_E,X_134)
| subset(skolemFOFtoCNF_E,intersection(skolemFOFtoCNF_C_2,X_134)) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_E,skolemFOFtoCNF_C_2) )],[refute_2_1,refute_2_3]) ).
cnf(refute_2_5,plain,
( ~ subset(skolemFOFtoCNF_E,skolemFOFtoCNF_D_4)
| subset(skolemFOFtoCNF_E,intersection(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_4)) ),
inference(subst,[],[refute_2_4:[bind(X_134,$fot(skolemFOFtoCNF_D_4))]]) ).
cnf(refute_2_6,plain,
subset(skolemFOFtoCNF_E,intersection(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_4)),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_E,skolemFOFtoCNF_D_4) )],[refute_2_0,refute_2_5]) ).
cnf(refute_2_7,plain,
skolemFOFtoCNF_B_2 = intersection(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( $equal(X,X) )],[refute_2_8,refute_2_9]) ).
cnf(refute_2_11,plain,
( skolemFOFtoCNF_B_2 != intersection(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_4)
| intersection(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_4) = skolemFOFtoCNF_B_2 ),
inference(subst,[],[refute_2_10:[bind(X,$fot(skolemFOFtoCNF_B_2)),bind(Y,$fot(intersection(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_4)))]]) ).
cnf(refute_2_12,plain,
intersection(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_4) = skolemFOFtoCNF_B_2,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_2,intersection(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_4)) )],[refute_2_7,refute_2_11]) ).
cnf(refute_2_13,plain,
( intersection(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_4) != skolemFOFtoCNF_B_2
| ~ subset(skolemFOFtoCNF_E,intersection(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_4))
| subset(skolemFOFtoCNF_E,skolemFOFtoCNF_B_2) ),
introduced(tautology,[equality,[$cnf( subset(skolemFOFtoCNF_E,intersection(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_4)) ),[1],$fot(skolemFOFtoCNF_B_2)]]) ).
cnf(refute_2_14,plain,
( ~ subset(skolemFOFtoCNF_E,intersection(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_4))
| subset(skolemFOFtoCNF_E,skolemFOFtoCNF_B_2) ),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_4),skolemFOFtoCNF_B_2) )],[refute_2_12,refute_2_13]) ).
cnf(refute_2_15,plain,
subset(skolemFOFtoCNF_E,skolemFOFtoCNF_B_2),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_E,intersection(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_4)) )],[refute_2_6,refute_2_14]) ).
cnf(refute_2_16,plain,
~ subset(skolemFOFtoCNF_E,skolemFOFtoCNF_B_2),
inference(canonicalize,[],[normalize_2_9]) ).
cnf(refute_2_17,plain,
$false,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_E,skolemFOFtoCNF_B_2) )],[refute_2_15,refute_2_16]) ).
fof(negate_3_0,plain,
~ ! [B,C,D] :
( ( subset(B,C)
& subset(B,D)
& ! [E] :
( ( subset(E,C)
& subset(E,D) )
=> subset(E,B) ) )
=> B = intersection(C,D) ),
inference(negate,[],[subgoal_3]) ).
fof(normalize_3_0,plain,
? [B,C,D] :
( B != intersection(C,D)
& subset(B,C)
& subset(B,D)
& ! [E] :
( ~ subset(E,C)
| ~ subset(E,D)
| subset(E,B) ) ),
inference(canonicalize,[],[negate_3_0]) ).
fof(normalize_3_1,plain,
( skolemFOFtoCNF_B_3 != intersection(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5)
& subset(skolemFOFtoCNF_B_3,skolemFOFtoCNF_C_3)
& subset(skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_5)
& ! [E] :
( ~ subset(E,skolemFOFtoCNF_C_3)
| ~ subset(E,skolemFOFtoCNF_D_5)
| subset(E,skolemFOFtoCNF_B_3) ) ),
inference(skolemize,[],[normalize_3_0]) ).
fof(normalize_3_2,plain,
subset(skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_5),
inference(conjunct,[],[normalize_3_1]) ).
fof(normalize_3_3,plain,
subset(skolemFOFtoCNF_B_3,skolemFOFtoCNF_C_3),
inference(conjunct,[],[normalize_3_1]) ).
fof(normalize_3_4,plain,
! [B,C,D] :
( ~ subset(B,C)
| ~ subset(B,D)
| subset(B,intersection(C,D)) ),
inference(canonicalize,[],[intersection_of_subsets]) ).
fof(normalize_3_5,plain,
! [B,C,D] :
( ~ subset(B,C)
| ~ subset(B,D)
| subset(B,intersection(C,D)) ),
inference(specialize,[],[normalize_3_4]) ).
fof(normalize_3_6,plain,
! [B,C] : subset(intersection(B,C),B),
inference(canonicalize,[],[intersection_is_subset]) ).
fof(normalize_3_7,plain,
! [B,C] : subset(intersection(B,C),B),
inference(specialize,[],[normalize_3_6]) ).
fof(normalize_3_8,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(canonicalize,[],[commutativity_of_intersection]) ).
fof(normalize_3_9,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(specialize,[],[normalize_3_8]) ).
fof(normalize_3_10,plain,
! [E] :
( ~ subset(E,skolemFOFtoCNF_C_3)
| ~ subset(E,skolemFOFtoCNF_D_5)
| subset(E,skolemFOFtoCNF_B_3) ),
inference(conjunct,[],[normalize_3_1]) ).
fof(normalize_3_11,plain,
! [E] :
( ~ subset(E,skolemFOFtoCNF_C_3)
| ~ subset(E,skolemFOFtoCNF_D_5)
| subset(E,skolemFOFtoCNF_B_3) ),
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,
skolemFOFtoCNF_B_3 != intersection(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5),
inference(conjunct,[],[normalize_3_1]) ).
cnf(refute_3_0,plain,
subset(skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_5),
inference(canonicalize,[],[normalize_3_2]) ).
cnf(refute_3_1,plain,
subset(skolemFOFtoCNF_B_3,skolemFOFtoCNF_C_3),
inference(canonicalize,[],[normalize_3_3]) ).
cnf(refute_3_2,plain,
( ~ subset(B,C)
| ~ subset(B,D)
| subset(B,intersection(C,D)) ),
inference(canonicalize,[],[normalize_3_5]) ).
cnf(refute_3_3,plain,
( ~ subset(skolemFOFtoCNF_B_3,X_237)
| ~ subset(skolemFOFtoCNF_B_3,skolemFOFtoCNF_C_3)
| subset(skolemFOFtoCNF_B_3,intersection(skolemFOFtoCNF_C_3,X_237)) ),
inference(subst,[],[refute_3_2:[bind(B,$fot(skolemFOFtoCNF_B_3)),bind(C,$fot(skolemFOFtoCNF_C_3)),bind(D,$fot(X_237))]]) ).
cnf(refute_3_4,plain,
( ~ subset(skolemFOFtoCNF_B_3,X_237)
| subset(skolemFOFtoCNF_B_3,intersection(skolemFOFtoCNF_C_3,X_237)) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B_3,skolemFOFtoCNF_C_3) )],[refute_3_1,refute_3_3]) ).
cnf(refute_3_5,plain,
( ~ subset(skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_5)
| subset(skolemFOFtoCNF_B_3,intersection(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5)) ),
inference(subst,[],[refute_3_4:[bind(X_237,$fot(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_3_6,plain,
subset(skolemFOFtoCNF_B_3,intersection(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5)),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_5) )],[refute_3_0,refute_3_5]) ).
cnf(refute_3_7,plain,
subset(intersection(B,C),B),
inference(canonicalize,[],[normalize_3_7]) ).
cnf(refute_3_8,plain,
subset(intersection(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5),skolemFOFtoCNF_C_3),
inference(subst,[],[refute_3_7:[bind(B,$fot(skolemFOFtoCNF_C_3)),bind(C,$fot(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_3_9,plain,
intersection(B,C) = intersection(C,B),
inference(canonicalize,[],[normalize_3_9]) ).
cnf(refute_3_10,plain,
( intersection(B,C) != intersection(C,B)
| ~ subset(intersection(B,C),B)
| subset(intersection(C,B),B) ),
introduced(tautology,[equality,[$cnf( subset(intersection(B,C),B) ),[0],$fot(intersection(C,B))]]) ).
cnf(refute_3_11,plain,
( ~ subset(intersection(B,C),B)
| subset(intersection(C,B),B) ),
inference(resolve,[$cnf( $equal(intersection(B,C),intersection(C,B)) )],[refute_3_9,refute_3_10]) ).
cnf(refute_3_12,plain,
subset(intersection(C,B),B),
inference(resolve,[$cnf( subset(intersection(B,C),B) )],[refute_3_7,refute_3_11]) ).
cnf(refute_3_13,plain,
subset(intersection(C,skolemFOFtoCNF_D_5),skolemFOFtoCNF_D_5),
inference(subst,[],[refute_3_12:[bind(B,$fot(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_3_14,plain,
( ~ subset(E,skolemFOFtoCNF_C_3)
| ~ subset(E,skolemFOFtoCNF_D_5)
| subset(E,skolemFOFtoCNF_B_3) ),
inference(canonicalize,[],[normalize_3_11]) ).
cnf(refute_3_15,plain,
( ~ subset(intersection(C,skolemFOFtoCNF_D_5),skolemFOFtoCNF_C_3)
| ~ subset(intersection(C,skolemFOFtoCNF_D_5),skolemFOFtoCNF_D_5)
| subset(intersection(C,skolemFOFtoCNF_D_5),skolemFOFtoCNF_B_3) ),
inference(subst,[],[refute_3_14:[bind(E,$fot(intersection(C,skolemFOFtoCNF_D_5)))]]) ).
cnf(refute_3_16,plain,
( ~ subset(intersection(C,skolemFOFtoCNF_D_5),skolemFOFtoCNF_C_3)
| subset(intersection(C,skolemFOFtoCNF_D_5),skolemFOFtoCNF_B_3) ),
inference(resolve,[$cnf( subset(intersection(C,skolemFOFtoCNF_D_5),skolemFOFtoCNF_D_5) )],[refute_3_13,refute_3_15]) ).
cnf(refute_3_17,plain,
( ~ subset(intersection(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5),skolemFOFtoCNF_C_3)
| subset(intersection(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5),skolemFOFtoCNF_B_3) ),
inference(subst,[],[refute_3_16:[bind(C,$fot(skolemFOFtoCNF_C_3))]]) ).
cnf(refute_3_18,plain,
subset(intersection(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5),skolemFOFtoCNF_B_3),
inference(resolve,[$cnf( subset(intersection(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5),skolemFOFtoCNF_C_3) )],[refute_3_8,refute_3_17]) ).
cnf(refute_3_19,plain,
( ~ subset(B,C)
| ~ subset(C,B)
| B = C ),
inference(canonicalize,[],[normalize_3_15]) ).
cnf(refute_3_20,plain,
( ~ subset(intersection(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5),skolemFOFtoCNF_B_3)
| ~ subset(skolemFOFtoCNF_B_3,intersection(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5))
| intersection(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5) = skolemFOFtoCNF_B_3 ),
inference(subst,[],[refute_3_19:[bind(B,$fot(intersection(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5))),bind(C,$fot(skolemFOFtoCNF_B_3))]]) ).
cnf(refute_3_21,plain,
( ~ subset(skolemFOFtoCNF_B_3,intersection(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5))
| intersection(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5) = skolemFOFtoCNF_B_3 ),
inference(resolve,[$cnf( subset(intersection(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5),skolemFOFtoCNF_B_3) )],[refute_3_18,refute_3_20]) ).
cnf(refute_3_22,plain,
skolemFOFtoCNF_B_3 != intersection(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5),
inference(canonicalize,[],[normalize_3_16]) ).
cnf(refute_3_23,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_3_24,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_3_25,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_3_23,refute_3_24]) ).
cnf(refute_3_26,plain,
( intersection(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5) != skolemFOFtoCNF_B_3
| skolemFOFtoCNF_B_3 = intersection(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5) ),
inference(subst,[],[refute_3_25:[bind(X,$fot(intersection(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5))),bind(Y,$fot(skolemFOFtoCNF_B_3))]]) ).
cnf(refute_3_27,plain,
intersection(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5) != skolemFOFtoCNF_B_3,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_3,intersection(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5)) )],[refute_3_26,refute_3_22]) ).
cnf(refute_3_28,plain,
~ subset(skolemFOFtoCNF_B_3,intersection(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5)),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5),skolemFOFtoCNF_B_3) )],[refute_3_21,refute_3_27]) ).
cnf(refute_3_29,plain,
$false,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B_3,intersection(skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_5)) )],[refute_3_6,refute_3_28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET598+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n021.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 : Mon Jul 11 08:39:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.54
% 0.19/0.54 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.54
%------------------------------------------------------------------------------