TSTP Solution File: SEU155+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU155+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 12:38:50 EDT 2022
% Result : Theorem 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 7 unt; 0 def)
% Number of atoms : 103 ( 13 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 112 ( 44 ~; 41 |; 14 &)
% ( 9 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 35 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ) ).
fof(d4_tarski,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(C,D)
& in(D,A) ) ) ) ).
fof(l50_zfmisc_1,conjecture,
! [A,B] :
( in(A,B)
=> subset(A,union(B)) ) ).
fof(subgoal_0,plain,
! [A,B] :
( in(A,B)
=> subset(A,union(B)) ),
inference(strip,[],[l50_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( in(A,B)
=> subset(A,union(B)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(canonicalize,[],[d3_tarski]) ).
fof(normalize_0_1,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B,C] :
( ( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) )
& ( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) )
& ( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B] :
( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_5,plain,
? [A,B] :
( ~ subset(A,union(B))
& in(A,B) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_6,plain,
( ~ subset(skolemFOFtoCNF_A,union(skolemFOFtoCNF_B))
& in(skolemFOFtoCNF_A,skolemFOFtoCNF_B) ),
inference(skolemize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
in(skolemFOFtoCNF_A,skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B] :
( B != union(A)
<=> ? [C] :
( ~ in(C,B)
<=> ? [D] :
( in(C,D)
& in(D,A) ) ) ),
inference(canonicalize,[],[d4_tarski]) ).
fof(normalize_0_9,plain,
! [A,B] :
( B != union(A)
<=> ? [C] :
( ~ in(C,B)
<=> ? [D] :
( in(C,D)
& in(D,A) ) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B,C,D] :
( ( B != union(A)
| ~ in(C,B)
| in(C,skolemFOFtoCNF_D_1(A,C)) )
& ( B != union(A)
| ~ in(C,B)
| in(skolemFOFtoCNF_D_1(A,C),A) )
& ( B = union(A)
| in(skolemFOFtoCNF_C_1(A,B),B)
| in(skolemFOFtoCNF_C_1(A,B),skolemFOFtoCNF_D(A,B)) )
& ( B = union(A)
| in(skolemFOFtoCNF_C_1(A,B),B)
| in(skolemFOFtoCNF_D(A,B),A) )
& ( B != union(A)
| ~ in(C,D)
| ~ in(D,A)
| in(C,B) )
& ( ~ in(D,A)
| ~ in(skolemFOFtoCNF_C_1(A,B),B)
| ~ in(skolemFOFtoCNF_C_1(A,B),D)
| B = union(A) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B,C,D] :
( B != union(A)
| ~ in(C,D)
| ~ in(D,A)
| in(C,B) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
~ subset(skolemFOFtoCNF_A,union(skolemFOFtoCNF_B)),
inference(conjunct,[],[normalize_0_6]) ).
cnf(refute_0_0,plain,
( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ in(skolemFOFtoCNF_C(skolemFOFtoCNF_A,union(skolemFOFtoCNF_B)),union(skolemFOFtoCNF_B))
| subset(skolemFOFtoCNF_A,union(skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(union(skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_2,plain,
( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
( in(skolemFOFtoCNF_C(skolemFOFtoCNF_A,B),skolemFOFtoCNF_A)
| subset(skolemFOFtoCNF_A,B) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_4,plain,
in(skolemFOFtoCNF_A,skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( B != union(A)
| ~ in(C,D)
| ~ in(D,A)
| in(C,B) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_6,plain,
( union(A) != union(A)
| ~ in(C,D)
| ~ in(D,A)
| in(C,union(A)) ),
inference(subst,[],[refute_0_5:[bind(B,$fot(union(A)))]]) ).
cnf(refute_0_7,plain,
union(A) = union(A),
introduced(tautology,[refl,[$fot(union(A))]]) ).
cnf(refute_0_8,plain,
( ~ in(C,D)
| ~ in(D,A)
| in(C,union(A)) ),
inference(resolve,[$cnf( $equal(union(A),union(A)) )],[refute_0_7,refute_0_6]) ).
cnf(refute_0_9,plain,
( ~ in(X_26,skolemFOFtoCNF_A)
| ~ in(skolemFOFtoCNF_A,skolemFOFtoCNF_B)
| in(X_26,union(skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_B)),bind(C,$fot(X_26)),bind(D,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_10,plain,
( ~ in(X_26,skolemFOFtoCNF_A)
| in(X_26,union(skolemFOFtoCNF_B)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A,skolemFOFtoCNF_B) )],[refute_0_4,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ in(skolemFOFtoCNF_C(skolemFOFtoCNF_A,B),skolemFOFtoCNF_A)
| in(skolemFOFtoCNF_C(skolemFOFtoCNF_A,B),union(skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_10:[bind(X_26,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_A,B)))]]) ).
cnf(refute_0_12,plain,
( in(skolemFOFtoCNF_C(skolemFOFtoCNF_A,B),union(skolemFOFtoCNF_B))
| subset(skolemFOFtoCNF_A,B) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(skolemFOFtoCNF_A,B),skolemFOFtoCNF_A) )],[refute_0_3,refute_0_11]) ).
cnf(refute_0_13,plain,
( in(skolemFOFtoCNF_C(skolemFOFtoCNF_A,union(skolemFOFtoCNF_B)),union(skolemFOFtoCNF_B))
| subset(skolemFOFtoCNF_A,union(skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_12:[bind(B,$fot(union(skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_14,plain,
subset(skolemFOFtoCNF_A,union(skolemFOFtoCNF_B)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(skolemFOFtoCNF_A,union(skolemFOFtoCNF_B)),union(skolemFOFtoCNF_B)) )],[refute_0_13,refute_0_1]) ).
cnf(refute_0_15,plain,
~ subset(skolemFOFtoCNF_A,union(skolemFOFtoCNF_B)),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_16,plain,
$false,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A,union(skolemFOFtoCNF_B)) )],[refute_0_14,refute_0_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU155+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n017.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 : Mon Jun 20 11:18:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35
% 0.13/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.36
%------------------------------------------------------------------------------