TSTP Solution File: SET691+4 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET691+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 03:36:40 EDT 2022
% Result : Theorem 0.17s 0.53s
% Output : CNFRefutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 49 ( 19 unt; 0 def)
% Number of atoms : 105 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 108 ( 52 ~; 29 |; 13 &)
% ( 9 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 52 ( 3 sgn 38 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ) ).
fof(equal_set,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(A,B)
& subset(B,A) ) ) ).
fof(empty_set,axiom,
! [X] : ~ member(X,empty_set) ).
fof(thI16,conjecture,
! [A] :
( subset(A,empty_set)
<=> equal_set(A,empty_set) ) ).
fof(subgoal_0,plain,
! [A] :
( subset(A,empty_set)
=> equal_set(A,empty_set) ),
inference(strip,[],[thI16]) ).
fof(subgoal_1,plain,
! [A] :
( equal_set(A,empty_set)
=> subset(A,empty_set) ),
inference(strip,[],[thI16]) ).
fof(negate_0_0,plain,
~ ! [A] :
( subset(A,empty_set)
=> equal_set(A,empty_set) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A] :
( ~ equal_set(A,empty_set)
& subset(A,empty_set) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ equal_set(skolemFOFtoCNF_A,empty_set)
& subset(skolemFOFtoCNF_A,empty_set) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
subset(skolemFOFtoCNF_A,empty_set),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( ~ equal_set(A,B)
<=> ( ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(canonicalize,[],[equal_set]) ).
fof(normalize_0_4,plain,
! [A,B] :
( ~ equal_set(A,B)
<=> ( ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B] :
( ( ~ equal_set(A,B)
| subset(A,B) )
& ( ~ equal_set(A,B)
| subset(B,A) )
& ( ~ subset(A,B)
| ~ subset(B,A)
| equal_set(A,B) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B] :
( ~ subset(A,B)
| ~ subset(B,A)
| equal_set(A,B) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X] : ~ member(X,empty_set),
inference(canonicalize,[],[empty_set]) ).
fof(normalize_0_8,plain,
! [X] : ~ member(X,empty_set),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [X] :
( ~ member(X,B)
& member(X,A) ) ),
inference(canonicalize,[],[subset]) ).
fof(normalize_0_10,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [X] :
( ~ member(X,B)
& member(X,A) ) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B,X] :
( ( ~ member(skolemFOFtoCNF_X(A,B),B)
| subset(A,B) )
& ( member(skolemFOFtoCNF_X(A,B),A)
| subset(A,B) )
& ( ~ member(X,A)
| ~ subset(A,B)
| member(X,B) ) ),
inference(clausify,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B] :
( member(skolemFOFtoCNF_X(A,B),A)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
~ equal_set(skolemFOFtoCNF_A,empty_set),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
subset(skolemFOFtoCNF_A,empty_set),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ subset(A,B)
| ~ subset(B,A)
| equal_set(A,B) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( ~ subset(empty_set,skolemFOFtoCNF_A)
| ~ subset(skolemFOFtoCNF_A,empty_set)
| equal_set(skolemFOFtoCNF_A,empty_set) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(empty_set))]]) ).
cnf(refute_0_3,plain,
( ~ subset(empty_set,skolemFOFtoCNF_A)
| equal_set(skolemFOFtoCNF_A,empty_set) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A,empty_set) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
~ member(X,empty_set),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
~ member(skolemFOFtoCNF_X(empty_set,X_21),empty_set),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_X(empty_set,X_21)))]]) ).
cnf(refute_0_6,plain,
( member(skolemFOFtoCNF_X(A,B),A)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_7,plain,
( member(skolemFOFtoCNF_X(empty_set,X_21),empty_set)
| subset(empty_set,X_21) ),
inference(subst,[],[refute_0_6:[bind(A,$fot(empty_set)),bind(B,$fot(X_21))]]) ).
cnf(refute_0_8,plain,
subset(empty_set,X_21),
inference(resolve,[$cnf( member(skolemFOFtoCNF_X(empty_set,X_21),empty_set) )],[refute_0_7,refute_0_5]) ).
cnf(refute_0_9,plain,
subset(empty_set,skolemFOFtoCNF_A),
inference(subst,[],[refute_0_8:[bind(X_21,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_10,plain,
equal_set(skolemFOFtoCNF_A,empty_set),
inference(resolve,[$cnf( subset(empty_set,skolemFOFtoCNF_A) )],[refute_0_9,refute_0_3]) ).
cnf(refute_0_11,plain,
~ equal_set(skolemFOFtoCNF_A,empty_set),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_12,plain,
$false,
inference(resolve,[$cnf( equal_set(skolemFOFtoCNF_A,empty_set) )],[refute_0_10,refute_0_11]) ).
fof(negate_1_0,plain,
~ ! [A] :
( equal_set(A,empty_set)
=> subset(A,empty_set) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [A] :
( ~ subset(A,empty_set)
& equal_set(A,empty_set) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( ~ subset(skolemFOFtoCNF_A_1,empty_set)
& equal_set(skolemFOFtoCNF_A_1,empty_set) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
equal_set(skolemFOFtoCNF_A_1,empty_set),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [A,B] :
( ~ equal_set(A,B)
<=> ( ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(canonicalize,[],[equal_set]) ).
fof(normalize_1_4,plain,
! [A,B] :
( ~ equal_set(A,B)
<=> ( ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(specialize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [A,B] :
( ( ~ equal_set(A,B)
| subset(A,B) )
& ( ~ equal_set(A,B)
| subset(B,A) )
& ( ~ subset(A,B)
| ~ subset(B,A)
| equal_set(A,B) ) ),
inference(clausify,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [A,B] :
( ~ equal_set(A,B)
| subset(A,B) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
~ subset(skolemFOFtoCNF_A_1,empty_set),
inference(conjunct,[],[normalize_1_1]) ).
cnf(refute_1_0,plain,
equal_set(skolemFOFtoCNF_A_1,empty_set),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
( ~ equal_set(A,B)
| subset(A,B) ),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_2,plain,
( ~ equal_set(skolemFOFtoCNF_A_1,empty_set)
| subset(skolemFOFtoCNF_A_1,empty_set) ),
inference(subst,[],[refute_1_1:[bind(A,$fot(skolemFOFtoCNF_A_1)),bind(B,$fot(empty_set))]]) ).
cnf(refute_1_3,plain,
subset(skolemFOFtoCNF_A_1,empty_set),
inference(resolve,[$cnf( equal_set(skolemFOFtoCNF_A_1,empty_set) )],[refute_1_0,refute_1_2]) ).
cnf(refute_1_4,plain,
~ subset(skolemFOFtoCNF_A_1,empty_set),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_5,plain,
$false,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_1,empty_set) )],[refute_1_3,refute_1_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET691+4 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Sun Jul 10 06:21:45 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.32 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.17/0.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.53
% 0.17/0.53 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.37/0.54
%------------------------------------------------------------------------------