TSTP Solution File: SEU173+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU173+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 12:39:02 EDT 2022
% Result : Theorem 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 13 unt; 0 def)
% Number of atoms : 107 ( 11 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 116 ( 49 ~; 32 |; 11 &)
% ( 15 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 66 ( 1 sgn 47 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_zfmisc_1,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ) ).
fof(d2_subset_1,axiom,
! [A,B] :
( ( ~ empty(A)
=> ( element(B,A)
<=> in(B,A) ) )
& ( empty(A)
=> ( element(B,A)
<=> empty(B) ) ) ) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ) ).
fof(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)) ).
fof(l71_subset_1,conjecture,
! [A,B] :
( ! [C] :
( in(C,A)
=> in(C,B) )
=> element(A,powerset(B)) ) ).
fof(subgoal_0,plain,
! [A,B] :
( ! [C] :
( in(C,A)
=> in(C,B) )
=> element(A,powerset(B)) ),
inference(strip,[],[l71_subset_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( ! [C] :
( in(C,A)
=> in(C,B) )
=> element(A,powerset(B)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B] :
( ~ element(A,powerset(B))
& ! [C] :
( ~ in(C,A)
| in(C,B) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(canonicalize,[],[d3_tarski]) ).
fof(normalize_0_2,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
? [A,B] :
( ~ element(A,powerset(B))
& subset(A,B) ),
inference(simplify,[],[normalize_0_0,normalize_0_2]) ).
fof(normalize_0_4,plain,
( ~ element(skolemFOFtoCNF_A_2,powerset(skolemFOFtoCNF_B_3))
& subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3) ),
inference(skolemize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B] :
( B != powerset(A)
<=> ? [C] :
( ~ in(C,B)
<=> subset(C,A) ) ),
inference(canonicalize,[],[d1_zfmisc_1]) ).
fof(normalize_0_7,plain,
! [A,B] :
( B != powerset(A)
<=> ? [C] :
( ~ in(C,B)
<=> subset(C,A) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B,C] :
( ( B != powerset(A)
| ~ in(C,B)
| subset(C,A) )
& ( B != powerset(A)
| ~ subset(C,A)
| in(C,B) )
& ( ~ in(skolemFOFtoCNF_C(A,B),B)
| ~ subset(skolemFOFtoCNF_C(A,B),A)
| B = powerset(A) )
& ( B = powerset(A)
| in(skolemFOFtoCNF_C(A,B),B)
| subset(skolemFOFtoCNF_C(A,B),A) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B,C] :
( B != powerset(A)
| ~ subset(C,A)
| in(C,B) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
( ! [A] :
( ~ empty(A)
| ! [B] :
( ~ element(B,A)
<=> ~ empty(B) ) )
& ! [A] :
( empty(A)
| ! [B] :
( ~ element(B,A)
<=> ~ in(B,A) ) ) ),
inference(canonicalize,[],[d2_subset_1]) ).
fof(normalize_0_11,plain,
! [A] :
( empty(A)
| ! [B] :
( ~ element(B,A)
<=> ~ in(B,A) ) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A] :
( empty(A)
| ! [B] :
( ~ element(B,A)
<=> ~ in(B,A) ) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A,B] :
( ( ~ element(B,A)
| empty(A)
| in(B,A) )
& ( ~ in(B,A)
| element(B,A)
| empty(A) ) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A,B] :
( ~ in(B,A)
| element(B,A)
| empty(A) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
~ element(skolemFOFtoCNF_A_2,powerset(skolemFOFtoCNF_B_3)),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_16,plain,
! [A] : ~ empty(powerset(A)),
inference(canonicalize,[],[fc1_subset_1]) ).
fof(normalize_0_17,plain,
! [A] : ~ empty(powerset(A)),
inference(specialize,[],[normalize_0_16]) ).
cnf(refute_0_0,plain,
subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_1,plain,
( B != powerset(A)
| ~ subset(C,A)
| in(C,B) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_2,plain,
( powerset(A) != powerset(A)
| ~ subset(C,A)
| in(C,powerset(A)) ),
inference(subst,[],[refute_0_1:[bind(B,$fot(powerset(A)))]]) ).
cnf(refute_0_3,plain,
powerset(A) = powerset(A),
introduced(tautology,[refl,[$fot(powerset(A))]]) ).
cnf(refute_0_4,plain,
( ~ subset(C,A)
| in(C,powerset(A)) ),
inference(resolve,[$cnf( $equal(powerset(A),powerset(A)) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
( ~ subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)
| in(skolemFOFtoCNF_A_2,powerset(skolemFOFtoCNF_B_3)) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_B_3)),bind(C,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_6,plain,
in(skolemFOFtoCNF_A_2,powerset(skolemFOFtoCNF_B_3)),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3) )],[refute_0_0,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ in(B,A)
| element(B,A)
| empty(A) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_8,plain,
( ~ in(skolemFOFtoCNF_A_2,powerset(skolemFOFtoCNF_B_3))
| element(skolemFOFtoCNF_A_2,powerset(skolemFOFtoCNF_B_3))
| empty(powerset(skolemFOFtoCNF_B_3)) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(powerset(skolemFOFtoCNF_B_3))),bind(B,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_9,plain,
( element(skolemFOFtoCNF_A_2,powerset(skolemFOFtoCNF_B_3))
| empty(powerset(skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,powerset(skolemFOFtoCNF_B_3)) )],[refute_0_6,refute_0_8]) ).
cnf(refute_0_10,plain,
~ element(skolemFOFtoCNF_A_2,powerset(skolemFOFtoCNF_B_3)),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_11,plain,
empty(powerset(skolemFOFtoCNF_B_3)),
inference(resolve,[$cnf( element(skolemFOFtoCNF_A_2,powerset(skolemFOFtoCNF_B_3)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
~ empty(powerset(A)),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_13,plain,
~ empty(powerset(skolemFOFtoCNF_B_3)),
inference(subst,[],[refute_0_12:[bind(A,$fot(skolemFOFtoCNF_B_3))]]) ).
cnf(refute_0_14,plain,
$false,
inference(resolve,[$cnf( empty(powerset(skolemFOFtoCNF_B_3)) )],[refute_0_11,refute_0_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU173+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 19 16:29:39 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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
% 0.13/0.35
%------------------------------------------------------------------------------