TSTP Solution File: SEU320+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU320+1 : 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 12:40:17 EDT 2022
% Result : Theorem 0.23s 0.40s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 78 ( 24 unt; 0 def)
% Number of atoms : 195 ( 13 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 210 ( 93 ~; 71 |; 26 &)
% ( 6 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 48 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k3_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> element(subset_complement(A,B),powerset(A)) ) ).
fof(involutiveness_k3_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,subset_complement(A,B)) = B ) ).
fof(t29_tops_1,axiom,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( closed_subset(B,A)
<=> open_subset(subset_complement(the_carrier(A),B),A) ) ) ) ).
fof(t30_tops_1,conjecture,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( open_subset(B,A)
<=> closed_subset(subset_complement(the_carrier(A),B),A) ) ) ) ).
fof(subgoal_0,plain,
! [A] :
( top_str(A)
=> ! [B] :
( ( element(B,powerset(the_carrier(A)))
& open_subset(B,A) )
=> closed_subset(subset_complement(the_carrier(A),B),A) ) ),
inference(strip,[],[t30_tops_1]) ).
fof(subgoal_1,plain,
! [A] :
( top_str(A)
=> ! [B] :
( ( element(B,powerset(the_carrier(A)))
& closed_subset(subset_complement(the_carrier(A),B),A) )
=> open_subset(B,A) ) ),
inference(strip,[],[t30_tops_1]) ).
fof(negate_0_0,plain,
~ ! [A] :
( top_str(A)
=> ! [B] :
( ( element(B,powerset(the_carrier(A)))
& open_subset(B,A) )
=> closed_subset(subset_complement(the_carrier(A),B),A) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A] :
( ~ top_str(A)
| ! [B] :
( ~ element(B,powerset(the_carrier(A)))
| ( ~ closed_subset(B,A)
<=> ~ open_subset(subset_complement(the_carrier(A),B),A) ) ) ),
inference(canonicalize,[],[t29_tops_1]) ).
fof(normalize_0_1,plain,
! [A] :
( ~ top_str(A)
| ! [B] :
( ~ element(B,powerset(the_carrier(A)))
| ( ~ closed_subset(B,A)
<=> ~ open_subset(subset_complement(the_carrier(A),B),A) ) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] :
( ( ~ closed_subset(B,A)
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A)
| open_subset(subset_complement(the_carrier(A),B),A) )
& ( ~ element(B,powerset(the_carrier(A)))
| ~ open_subset(subset_complement(the_carrier(A),B),A)
| ~ top_str(A)
| closed_subset(B,A) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( ~ element(B,powerset(the_carrier(A)))
| ~ open_subset(subset_complement(the_carrier(A),B),A)
| ~ top_str(A)
| closed_subset(B,A) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [A] :
( top_str(A)
& ? [B] :
( ~ closed_subset(subset_complement(the_carrier(A),B),A)
& element(B,powerset(the_carrier(A)))
& open_subset(B,A) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( top_str(skolemFOFtoCNF_A_2)
& ? [B] :
( ~ closed_subset(subset_complement(the_carrier(skolemFOFtoCNF_A_2),B),skolemFOFtoCNF_A_2)
& element(B,powerset(the_carrier(skolemFOFtoCNF_A_2)))
& open_subset(B,skolemFOFtoCNF_A_2) ) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [B] :
( ~ closed_subset(subset_complement(the_carrier(skolemFOFtoCNF_A_2),B),skolemFOFtoCNF_A_2)
& element(B,powerset(the_carrier(skolemFOFtoCNF_A_2)))
& open_subset(B,skolemFOFtoCNF_A_2) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
( ~ closed_subset(subset_complement(the_carrier(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2)
& element(skolemFOFtoCNF_B_1,powerset(the_carrier(skolemFOFtoCNF_A_2)))
& open_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
element(skolemFOFtoCNF_B_1,powerset(the_carrier(skolemFOFtoCNF_A_2))),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B] :
( ~ element(B,powerset(A))
| subset_complement(A,subset_complement(A,B)) = B ),
inference(canonicalize,[],[involutiveness_k3_subset_1]) ).
fof(normalize_0_10,plain,
! [A,B] :
( ~ element(B,powerset(A))
| subset_complement(A,subset_complement(A,B)) = B ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B] :
( ~ element(B,powerset(A))
| element(subset_complement(A,B),powerset(A)) ),
inference(canonicalize,[],[dt_k3_subset_1]) ).
fof(normalize_0_12,plain,
! [A,B] :
( ~ element(B,powerset(A))
| element(subset_complement(A,B),powerset(A)) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
open_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_14,plain,
top_str(skolemFOFtoCNF_A_2),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_15,plain,
~ closed_subset(subset_complement(the_carrier(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2),
inference(conjunct,[],[normalize_0_7]) ).
cnf(refute_0_0,plain,
( ~ element(B,powerset(the_carrier(A)))
| ~ open_subset(subset_complement(the_carrier(A),B),A)
| ~ top_str(A)
| closed_subset(B,A) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ element(subset_complement(the_carrier(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),powerset(the_carrier(skolemFOFtoCNF_A_2)))
| ~ open_subset(subset_complement(the_carrier(skolemFOFtoCNF_A_2),subset_complement(the_carrier(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1)),skolemFOFtoCNF_A_2)
| ~ top_str(skolemFOFtoCNF_A_2)
| closed_subset(subset_complement(the_carrier(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(subset_complement(the_carrier(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1)))]]) ).
cnf(refute_0_2,plain,
element(skolemFOFtoCNF_B_1,powerset(the_carrier(skolemFOFtoCNF_A_2))),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_3,plain,
( ~ element(B,powerset(A))
| subset_complement(A,subset_complement(A,B)) = B ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_4,plain,
( ~ element(skolemFOFtoCNF_B_1,powerset(the_carrier(skolemFOFtoCNF_A_2)))
| subset_complement(the_carrier(skolemFOFtoCNF_A_2),subset_complement(the_carrier(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1)) = skolemFOFtoCNF_B_1 ),
inference(subst,[],[refute_0_3:[bind(A,$fot(the_carrier(skolemFOFtoCNF_A_2))),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_5,plain,
subset_complement(the_carrier(skolemFOFtoCNF_A_2),subset_complement(the_carrier(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1)) = skolemFOFtoCNF_B_1,
inference(resolve,[$cnf( element(skolemFOFtoCNF_B_1,powerset(the_carrier(skolemFOFtoCNF_A_2))) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
( subset_complement(the_carrier(skolemFOFtoCNF_A_2),subset_complement(the_carrier(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1)) != skolemFOFtoCNF_B_1
| ~ open_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)
| open_subset(subset_complement(the_carrier(skolemFOFtoCNF_A_2),subset_complement(the_carrier(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1)),skolemFOFtoCNF_A_2) ),
introduced(tautology,[equality,[$cnf( ~ open_subset(subset_complement(the_carrier(skolemFOFtoCNF_A_2),subset_complement(the_carrier(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1)),skolemFOFtoCNF_A_2) ),[0],$fot(skolemFOFtoCNF_B_1)]]) ).
cnf(refute_0_7,plain,
( ~ open_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)
| open_subset(subset_complement(the_carrier(skolemFOFtoCNF_A_2),subset_complement(the_carrier(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1)),skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( $equal(subset_complement(the_carrier(skolemFOFtoCNF_A_2),subset_complement(the_carrier(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1)),skolemFOFtoCNF_B_1) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ element(subset_complement(the_carrier(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),powerset(the_carrier(skolemFOFtoCNF_A_2)))
| ~ open_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)
| ~ top_str(skolemFOFtoCNF_A_2)
| closed_subset(subset_complement(the_carrier(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( open_subset(subset_complement(the_carrier(skolemFOFtoCNF_A_2),subset_complement(the_carrier(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1)),skolemFOFtoCNF_A_2) )],[refute_0_7,refute_0_1]) ).
cnf(refute_0_9,plain,
( ~ element(B,powerset(A))
| element(subset_complement(A,B),powerset(A)) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_10,plain,
( ~ element(skolemFOFtoCNF_B_1,powerset(the_carrier(skolemFOFtoCNF_A_2)))
| element(subset_complement(the_carrier(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),powerset(the_carrier(skolemFOFtoCNF_A_2))) ),
inference(subst,[],[refute_0_9:[bind(A,$fot(the_carrier(skolemFOFtoCNF_A_2))),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_11,plain,
element(subset_complement(the_carrier(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),powerset(the_carrier(skolemFOFtoCNF_A_2))),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B_1,powerset(the_carrier(skolemFOFtoCNF_A_2))) )],[refute_0_2,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ open_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)
| ~ top_str(skolemFOFtoCNF_A_2)
| closed_subset(subset_complement(the_carrier(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( element(subset_complement(the_carrier(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),powerset(the_carrier(skolemFOFtoCNF_A_2))) )],[refute_0_11,refute_0_8]) ).
cnf(refute_0_13,plain,
open_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_14,plain,
( ~ top_str(skolemFOFtoCNF_A_2)
| closed_subset(subset_complement(the_carrier(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( open_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) )],[refute_0_13,refute_0_12]) ).
cnf(refute_0_15,plain,
top_str(skolemFOFtoCNF_A_2),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_16,plain,
closed_subset(subset_complement(the_carrier(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( top_str(skolemFOFtoCNF_A_2) )],[refute_0_15,refute_0_14]) ).
cnf(refute_0_17,plain,
~ closed_subset(subset_complement(the_carrier(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_18,plain,
$false,
inference(resolve,[$cnf( closed_subset(subset_complement(the_carrier(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2) )],[refute_0_16,refute_0_17]) ).
fof(negate_1_0,plain,
~ ! [A] :
( top_str(A)
=> ! [B] :
( ( element(B,powerset(the_carrier(A)))
& closed_subset(subset_complement(the_carrier(A),B),A) )
=> open_subset(B,A) ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [A] :
( top_str(A)
& ? [B] :
( ~ open_subset(B,A)
& closed_subset(subset_complement(the_carrier(A),B),A)
& element(B,powerset(the_carrier(A))) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( top_str(skolemFOFtoCNF_A_3)
& ? [B] :
( ~ open_subset(B,skolemFOFtoCNF_A_3)
& closed_subset(subset_complement(the_carrier(skolemFOFtoCNF_A_3),B),skolemFOFtoCNF_A_3)
& element(B,powerset(the_carrier(skolemFOFtoCNF_A_3))) ) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
? [B] :
( ~ open_subset(B,skolemFOFtoCNF_A_3)
& closed_subset(subset_complement(the_carrier(skolemFOFtoCNF_A_3),B),skolemFOFtoCNF_A_3)
& element(B,powerset(the_carrier(skolemFOFtoCNF_A_3))) ),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
( ~ open_subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3)
& closed_subset(subset_complement(the_carrier(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2),skolemFOFtoCNF_A_3)
& element(skolemFOFtoCNF_B_2,powerset(the_carrier(skolemFOFtoCNF_A_3))) ),
inference(skolemize,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
element(skolemFOFtoCNF_B_2,powerset(the_carrier(skolemFOFtoCNF_A_3))),
inference(conjunct,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [A,B] :
( ~ element(B,powerset(A))
| element(subset_complement(A,B),powerset(A)) ),
inference(canonicalize,[],[dt_k3_subset_1]) ).
fof(normalize_1_6,plain,
! [A,B] :
( ~ element(B,powerset(A))
| element(subset_complement(A,B),powerset(A)) ),
inference(specialize,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [A] :
( ~ top_str(A)
| ! [B] :
( ~ element(B,powerset(the_carrier(A)))
| ( ~ closed_subset(B,A)
<=> ~ open_subset(subset_complement(the_carrier(A),B),A) ) ) ),
inference(canonicalize,[],[t29_tops_1]) ).
fof(normalize_1_8,plain,
! [A] :
( ~ top_str(A)
| ! [B] :
( ~ element(B,powerset(the_carrier(A)))
| ( ~ closed_subset(B,A)
<=> ~ open_subset(subset_complement(the_carrier(A),B),A) ) ) ),
inference(specialize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [A,B] :
( ( ~ closed_subset(B,A)
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A)
| open_subset(subset_complement(the_carrier(A),B),A) )
& ( ~ element(B,powerset(the_carrier(A)))
| ~ open_subset(subset_complement(the_carrier(A),B),A)
| ~ top_str(A)
| closed_subset(B,A) ) ),
inference(clausify,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
! [A,B] :
( ~ closed_subset(B,A)
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A)
| open_subset(subset_complement(the_carrier(A),B),A) ),
inference(conjunct,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
! [A,B] :
( ~ element(B,powerset(A))
| subset_complement(A,subset_complement(A,B)) = B ),
inference(canonicalize,[],[involutiveness_k3_subset_1]) ).
fof(normalize_1_12,plain,
! [A,B] :
( ~ element(B,powerset(A))
| subset_complement(A,subset_complement(A,B)) = B ),
inference(specialize,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
closed_subset(subset_complement(the_carrier(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2),skolemFOFtoCNF_A_3),
inference(conjunct,[],[normalize_1_3]) ).
fof(normalize_1_14,plain,
top_str(skolemFOFtoCNF_A_3),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_15,plain,
~ open_subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3),
inference(conjunct,[],[normalize_1_3]) ).
cnf(refute_1_0,plain,
element(skolemFOFtoCNF_B_2,powerset(the_carrier(skolemFOFtoCNF_A_3))),
inference(canonicalize,[],[normalize_1_4]) ).
cnf(refute_1_1,plain,
( ~ element(B,powerset(A))
| element(subset_complement(A,B),powerset(A)) ),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_2,plain,
( ~ element(skolemFOFtoCNF_B_2,powerset(the_carrier(skolemFOFtoCNF_A_3)))
| element(subset_complement(the_carrier(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2),powerset(the_carrier(skolemFOFtoCNF_A_3))) ),
inference(subst,[],[refute_1_1:[bind(A,$fot(the_carrier(skolemFOFtoCNF_A_3))),bind(B,$fot(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_1_3,plain,
element(subset_complement(the_carrier(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2),powerset(the_carrier(skolemFOFtoCNF_A_3))),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B_2,powerset(the_carrier(skolemFOFtoCNF_A_3))) )],[refute_1_0,refute_1_2]) ).
cnf(refute_1_4,plain,
( ~ closed_subset(B,A)
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A)
| open_subset(subset_complement(the_carrier(A),B),A) ),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_5,plain,
( ~ closed_subset(subset_complement(the_carrier(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2),skolemFOFtoCNF_A_3)
| ~ element(subset_complement(the_carrier(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2),powerset(the_carrier(skolemFOFtoCNF_A_3)))
| ~ top_str(skolemFOFtoCNF_A_3)
| open_subset(subset_complement(the_carrier(skolemFOFtoCNF_A_3),subset_complement(the_carrier(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2)),skolemFOFtoCNF_A_3) ),
inference(subst,[],[refute_1_4:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(subset_complement(the_carrier(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2)))]]) ).
cnf(refute_1_6,plain,
( ~ closed_subset(subset_complement(the_carrier(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2),skolemFOFtoCNF_A_3)
| ~ top_str(skolemFOFtoCNF_A_3)
| open_subset(subset_complement(the_carrier(skolemFOFtoCNF_A_3),subset_complement(the_carrier(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2)),skolemFOFtoCNF_A_3) ),
inference(resolve,[$cnf( element(subset_complement(the_carrier(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2),powerset(the_carrier(skolemFOFtoCNF_A_3))) )],[refute_1_3,refute_1_5]) ).
cnf(refute_1_7,plain,
( ~ element(B,powerset(A))
| subset_complement(A,subset_complement(A,B)) = B ),
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_8,plain,
( ~ element(skolemFOFtoCNF_B_2,powerset(the_carrier(skolemFOFtoCNF_A_3)))
| subset_complement(the_carrier(skolemFOFtoCNF_A_3),subset_complement(the_carrier(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2)) = skolemFOFtoCNF_B_2 ),
inference(subst,[],[refute_1_7:[bind(A,$fot(the_carrier(skolemFOFtoCNF_A_3))),bind(B,$fot(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_1_9,plain,
subset_complement(the_carrier(skolemFOFtoCNF_A_3),subset_complement(the_carrier(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2)) = skolemFOFtoCNF_B_2,
inference(resolve,[$cnf( element(skolemFOFtoCNF_B_2,powerset(the_carrier(skolemFOFtoCNF_A_3))) )],[refute_1_0,refute_1_8]) ).
cnf(refute_1_10,plain,
( subset_complement(the_carrier(skolemFOFtoCNF_A_3),subset_complement(the_carrier(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2)) != skolemFOFtoCNF_B_2
| ~ open_subset(subset_complement(the_carrier(skolemFOFtoCNF_A_3),subset_complement(the_carrier(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2)),skolemFOFtoCNF_A_3)
| open_subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3) ),
introduced(tautology,[equality,[$cnf( open_subset(subset_complement(the_carrier(skolemFOFtoCNF_A_3),subset_complement(the_carrier(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2)),skolemFOFtoCNF_A_3) ),[0],$fot(skolemFOFtoCNF_B_2)]]) ).
cnf(refute_1_11,plain,
( ~ open_subset(subset_complement(the_carrier(skolemFOFtoCNF_A_3),subset_complement(the_carrier(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2)),skolemFOFtoCNF_A_3)
| open_subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3) ),
inference(resolve,[$cnf( $equal(subset_complement(the_carrier(skolemFOFtoCNF_A_3),subset_complement(the_carrier(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2)),skolemFOFtoCNF_B_2) )],[refute_1_9,refute_1_10]) ).
cnf(refute_1_12,plain,
( ~ closed_subset(subset_complement(the_carrier(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2),skolemFOFtoCNF_A_3)
| ~ top_str(skolemFOFtoCNF_A_3)
| open_subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3) ),
inference(resolve,[$cnf( open_subset(subset_complement(the_carrier(skolemFOFtoCNF_A_3),subset_complement(the_carrier(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2)),skolemFOFtoCNF_A_3) )],[refute_1_6,refute_1_11]) ).
cnf(refute_1_13,plain,
closed_subset(subset_complement(the_carrier(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2),skolemFOFtoCNF_A_3),
inference(canonicalize,[],[normalize_1_13]) ).
cnf(refute_1_14,plain,
( ~ top_str(skolemFOFtoCNF_A_3)
| open_subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3) ),
inference(resolve,[$cnf( closed_subset(subset_complement(the_carrier(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2),skolemFOFtoCNF_A_3) )],[refute_1_13,refute_1_12]) ).
cnf(refute_1_15,plain,
top_str(skolemFOFtoCNF_A_3),
inference(canonicalize,[],[normalize_1_14]) ).
cnf(refute_1_16,plain,
open_subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3),
inference(resolve,[$cnf( top_str(skolemFOFtoCNF_A_3) )],[refute_1_15,refute_1_14]) ).
cnf(refute_1_17,plain,
~ open_subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3),
inference(canonicalize,[],[normalize_1_15]) ).
cnf(refute_1_18,plain,
$false,
inference(resolve,[$cnf( open_subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_3) )],[refute_1_16,refute_1_17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SEU320+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.15 % Command : metis --show proof --show saturation %s
% 0.15/0.36 % Computer : n007.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Mon Jun 20 11:01:59 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.15/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.23/0.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.40
% 0.23/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.23/0.42
%------------------------------------------------------------------------------