TSTP Solution File: SEU094+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU094+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 12:38:24 EDT 2022
% Result : Theorem 80.42s 80.66s
% Output : CNFRefutation 80.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 64 ( 23 unt; 0 def)
% Number of atoms : 138 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 125 ( 51 ~; 33 |; 22 &)
% ( 4 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 60 ( 0 sgn 41 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l22_finset_1,axiom,
! [A] :
( ( finite(A)
& ! [B] :
( in(B,A)
=> finite(B) ) )
=> finite(union(A)) ) ).
fof(t100_zfmisc_1,axiom,
! [A] : subset(A,powerset(union(A))) ).
fof(t13_finset_1,axiom,
! [A,B] :
( ( subset(A,B)
& finite(B) )
=> finite(A) ) ).
fof(t24_finset_1,axiom,
! [A] :
( finite(A)
<=> finite(powerset(A)) ) ).
fof(t25_finset_1,conjecture,
! [A] :
( ( finite(A)
& ! [B] :
( in(B,A)
=> finite(B) ) )
<=> finite(union(A)) ) ).
fof(t92_zfmisc_1,axiom,
! [A,B] :
( in(A,B)
=> subset(A,union(B)) ) ).
fof(subgoal_0,plain,
! [A] :
( ( finite(A)
& ! [B] :
( in(B,A)
=> finite(B) ) )
=> finite(union(A)) ),
inference(strip,[],[t25_finset_1]) ).
fof(subgoal_1,plain,
! [A] :
( finite(union(A))
=> finite(A) ),
inference(strip,[],[t25_finset_1]) ).
fof(subgoal_2,plain,
! [A] :
( ( finite(union(A))
& finite(A) )
=> ! [B] :
( in(B,A)
=> finite(B) ) ),
inference(strip,[],[t25_finset_1]) ).
fof(negate_0_0,plain,
~ ! [A] :
( ( finite(A)
& ! [B] :
( in(B,A)
=> finite(B) ) )
=> finite(union(A)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A] :
( ~ finite(union(A))
& finite(A)
& ! [B] :
( ~ in(B,A)
| finite(B) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [A] :
( ~ finite(A)
| finite(union(A))
| ? [B] :
( ~ finite(B)
& in(B,A) ) ),
inference(canonicalize,[],[l22_finset_1]) ).
fof(normalize_0_2,plain,
! [A] :
( ~ finite(A)
| finite(union(A))
| ? [B] :
( ~ finite(B)
& in(B,A) ) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
$false,
inference(simplify,[],[normalize_0_0,normalize_0_2]) ).
cnf(refute_0_0,plain,
$false,
inference(canonicalize,[],[normalize_0_3]) ).
fof(negate_1_0,plain,
~ ! [A] :
( finite(union(A))
=> finite(A) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [A] :
( ~ finite(A)
& finite(union(A)) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( ~ finite(skolemFOFtoCNF_A_21)
& finite(union(skolemFOFtoCNF_A_21)) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
finite(union(skolemFOFtoCNF_A_21)),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [A] :
( ~ finite(A)
<=> ~ finite(powerset(A)) ),
inference(canonicalize,[],[t24_finset_1]) ).
fof(normalize_1_4,plain,
! [A] :
( ~ finite(A)
<=> ~ finite(powerset(A)) ),
inference(specialize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [A] :
( ( ~ finite(A)
| finite(powerset(A)) )
& ( ~ finite(powerset(A))
| finite(A) ) ),
inference(clausify,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [A] :
( ~ finite(A)
| finite(powerset(A)) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [A] : subset(A,powerset(union(A))),
inference(canonicalize,[],[t100_zfmisc_1]) ).
fof(normalize_1_8,plain,
! [A] : subset(A,powerset(union(A))),
inference(specialize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [A,B] :
( ~ finite(B)
| ~ subset(A,B)
| finite(A) ),
inference(canonicalize,[],[t13_finset_1]) ).
fof(normalize_1_10,plain,
! [A,B] :
( ~ finite(B)
| ~ subset(A,B)
| finite(A) ),
inference(specialize,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
~ finite(skolemFOFtoCNF_A_21),
inference(conjunct,[],[normalize_1_1]) ).
cnf(refute_1_0,plain,
finite(union(skolemFOFtoCNF_A_21)),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
( ~ finite(A)
| finite(powerset(A)) ),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_2,plain,
( ~ finite(union(skolemFOFtoCNF_A_21))
| finite(powerset(union(skolemFOFtoCNF_A_21))) ),
inference(subst,[],[refute_1_1:[bind(A,$fot(union(skolemFOFtoCNF_A_21)))]]) ).
cnf(refute_1_3,plain,
finite(powerset(union(skolemFOFtoCNF_A_21))),
inference(resolve,[$cnf( finite(union(skolemFOFtoCNF_A_21)) )],[refute_1_0,refute_1_2]) ).
cnf(refute_1_4,plain,
subset(A,powerset(union(A))),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_5,plain,
subset(X_108,powerset(union(X_108))),
inference(subst,[],[refute_1_4:[bind(A,$fot(X_108))]]) ).
cnf(refute_1_6,plain,
( ~ finite(B)
| ~ subset(A,B)
| finite(A) ),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_7,plain,
( ~ finite(powerset(union(X_108)))
| ~ subset(X_108,powerset(union(X_108)))
| finite(X_108) ),
inference(subst,[],[refute_1_6:[bind(A,$fot(X_108)),bind(B,$fot(powerset(union(X_108))))]]) ).
cnf(refute_1_8,plain,
( ~ finite(powerset(union(X_108)))
| finite(X_108) ),
inference(resolve,[$cnf( subset(X_108,powerset(union(X_108))) )],[refute_1_5,refute_1_7]) ).
cnf(refute_1_9,plain,
( ~ finite(powerset(union(skolemFOFtoCNF_A_21)))
| finite(skolemFOFtoCNF_A_21) ),
inference(subst,[],[refute_1_8:[bind(X_108,$fot(skolemFOFtoCNF_A_21))]]) ).
cnf(refute_1_10,plain,
finite(skolemFOFtoCNF_A_21),
inference(resolve,[$cnf( finite(powerset(union(skolemFOFtoCNF_A_21))) )],[refute_1_3,refute_1_9]) ).
cnf(refute_1_11,plain,
~ finite(skolemFOFtoCNF_A_21),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_12,plain,
$false,
inference(resolve,[$cnf( finite(skolemFOFtoCNF_A_21) )],[refute_1_10,refute_1_11]) ).
fof(negate_2_0,plain,
~ ! [A] :
( ( finite(union(A))
& finite(A) )
=> ! [B] :
( in(B,A)
=> finite(B) ) ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
? [A] :
( finite(A)
& finite(union(A))
& ? [B] :
( ~ finite(B)
& in(B,A) ) ),
inference(canonicalize,[],[negate_2_0]) ).
fof(normalize_2_1,plain,
( finite(skolemFOFtoCNF_A_22)
& finite(union(skolemFOFtoCNF_A_22))
& ? [B] :
( ~ finite(B)
& in(B,skolemFOFtoCNF_A_22) ) ),
inference(skolemize,[],[normalize_2_0]) ).
fof(normalize_2_2,plain,
? [B] :
( ~ finite(B)
& in(B,skolemFOFtoCNF_A_22) ),
inference(conjunct,[],[normalize_2_1]) ).
fof(normalize_2_3,plain,
( ~ finite(skolemFOFtoCNF_B_6)
& in(skolemFOFtoCNF_B_6,skolemFOFtoCNF_A_22) ),
inference(skolemize,[],[normalize_2_2]) ).
fof(normalize_2_4,plain,
in(skolemFOFtoCNF_B_6,skolemFOFtoCNF_A_22),
inference(conjunct,[],[normalize_2_3]) ).
fof(normalize_2_5,plain,
! [A,B] :
( ~ in(A,B)
| subset(A,union(B)) ),
inference(canonicalize,[],[t92_zfmisc_1]) ).
fof(normalize_2_6,plain,
! [A,B] :
( ~ in(A,B)
| subset(A,union(B)) ),
inference(specialize,[],[normalize_2_5]) ).
fof(normalize_2_7,plain,
! [A,B] :
( ~ finite(B)
| ~ subset(A,B)
| finite(A) ),
inference(canonicalize,[],[t13_finset_1]) ).
fof(normalize_2_8,plain,
! [A,B] :
( ~ finite(B)
| ~ subset(A,B)
| finite(A) ),
inference(specialize,[],[normalize_2_7]) ).
fof(normalize_2_9,plain,
finite(union(skolemFOFtoCNF_A_22)),
inference(conjunct,[],[normalize_2_1]) ).
fof(normalize_2_10,plain,
~ finite(skolemFOFtoCNF_B_6),
inference(conjunct,[],[normalize_2_3]) ).
cnf(refute_2_0,plain,
in(skolemFOFtoCNF_B_6,skolemFOFtoCNF_A_22),
inference(canonicalize,[],[normalize_2_4]) ).
cnf(refute_2_1,plain,
( ~ in(A,B)
| subset(A,union(B)) ),
inference(canonicalize,[],[normalize_2_6]) ).
cnf(refute_2_2,plain,
( ~ in(skolemFOFtoCNF_B_6,skolemFOFtoCNF_A_22)
| subset(skolemFOFtoCNF_B_6,union(skolemFOFtoCNF_A_22)) ),
inference(subst,[],[refute_2_1:[bind(A,$fot(skolemFOFtoCNF_B_6)),bind(B,$fot(skolemFOFtoCNF_A_22))]]) ).
cnf(refute_2_3,plain,
subset(skolemFOFtoCNF_B_6,union(skolemFOFtoCNF_A_22)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_6,skolemFOFtoCNF_A_22) )],[refute_2_0,refute_2_2]) ).
cnf(refute_2_4,plain,
( ~ finite(B)
| ~ subset(A,B)
| finite(A) ),
inference(canonicalize,[],[normalize_2_8]) ).
cnf(refute_2_5,plain,
( ~ finite(union(skolemFOFtoCNF_A_22))
| ~ subset(skolemFOFtoCNF_B_6,union(skolemFOFtoCNF_A_22))
| finite(skolemFOFtoCNF_B_6) ),
inference(subst,[],[refute_2_4:[bind(A,$fot(skolemFOFtoCNF_B_6)),bind(B,$fot(union(skolemFOFtoCNF_A_22)))]]) ).
cnf(refute_2_6,plain,
( ~ finite(union(skolemFOFtoCNF_A_22))
| finite(skolemFOFtoCNF_B_6) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B_6,union(skolemFOFtoCNF_A_22)) )],[refute_2_3,refute_2_5]) ).
cnf(refute_2_7,plain,
finite(union(skolemFOFtoCNF_A_22)),
inference(canonicalize,[],[normalize_2_9]) ).
cnf(refute_2_8,plain,
finite(skolemFOFtoCNF_B_6),
inference(resolve,[$cnf( finite(union(skolemFOFtoCNF_A_22)) )],[refute_2_7,refute_2_6]) ).
cnf(refute_2_9,plain,
~ finite(skolemFOFtoCNF_B_6),
inference(canonicalize,[],[normalize_2_10]) ).
cnf(refute_2_10,plain,
$false,
inference(resolve,[$cnf( finite(skolemFOFtoCNF_B_6) )],[refute_2_8,refute_2_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU094+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 22:50:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 80.42/80.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 80.42/80.66
% 80.42/80.66 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 80.42/80.66
%------------------------------------------------------------------------------