TSTP Solution File: SET355+4 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET355+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 03:34:22 EDT 2022
% Result : Theorem 138.76s 139.00s
% Output : CNFRefutation 138.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 6 unt; 0 def)
% Number of atoms : 77 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 78 ( 33 ~; 26 |; 9 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 34 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ) ).
fof(sum,axiom,
! [X,A] :
( member(X,sum(A))
<=> ? [Y] :
( member(Y,A)
& member(X,Y) ) ) ).
fof(thI43,conjecture,
! [A,X] :
( member(X,A)
=> subset(X,sum(A)) ) ).
fof(subgoal_0,plain,
! [A,X] :
( member(X,A)
=> subset(X,sum(A)) ),
inference(strip,[],[thI43]) ).
fof(negate_0_0,plain,
~ ! [A,X] :
( member(X,A)
=> subset(X,sum(A)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [X] :
( ~ member(X,B)
& member(X,A) ) ),
inference(canonicalize,[],[subset]) ).
fof(normalize_0_1,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [X] :
( ~ member(X,B)
& member(X,A) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,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_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( ~ member(skolemFOFtoCNF_X(A,B),B)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B] :
( member(skolemFOFtoCNF_X(A,B),A)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_5,plain,
? [A,X] :
( ~ subset(X,sum(A))
& member(X,A) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_6,plain,
( ~ subset(skolemFOFtoCNF_X_1,sum(skolemFOFtoCNF_A))
& member(skolemFOFtoCNF_X_1,skolemFOFtoCNF_A) ),
inference(skolemize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
member(skolemFOFtoCNF_X_1,skolemFOFtoCNF_A),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,X] :
( ~ member(X,sum(A))
<=> ! [Y] :
( ~ member(X,Y)
| ~ member(Y,A) ) ),
inference(canonicalize,[],[sum]) ).
fof(normalize_0_9,plain,
! [A,X] :
( ~ member(X,sum(A))
<=> ! [Y] :
( ~ member(X,Y)
| ~ member(Y,A) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,X,Y] :
( ( ~ member(X,sum(A))
| member(X,skolemFOFtoCNF_Y(A,X)) )
& ( ~ member(X,sum(A))
| member(skolemFOFtoCNF_Y(A,X),A) )
& ( ~ member(X,Y)
| ~ member(Y,A)
| member(X,sum(A)) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,X,Y] :
( ~ member(X,Y)
| ~ member(Y,A)
| member(X,sum(A)) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
~ subset(skolemFOFtoCNF_X_1,sum(skolemFOFtoCNF_A)),
inference(conjunct,[],[normalize_0_6]) ).
cnf(refute_0_0,plain,
( ~ member(skolemFOFtoCNF_X(A,B),B)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ member(skolemFOFtoCNF_X(skolemFOFtoCNF_X_1,sum(skolemFOFtoCNF_A)),sum(skolemFOFtoCNF_A))
| subset(skolemFOFtoCNF_X_1,sum(skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_X_1)),bind(B,$fot(sum(skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_2,plain,
( member(skolemFOFtoCNF_X(A,B),A)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
( member(skolemFOFtoCNF_X(skolemFOFtoCNF_X_1,B),skolemFOFtoCNF_X_1)
| subset(skolemFOFtoCNF_X_1,B) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_X_1))]]) ).
cnf(refute_0_4,plain,
member(skolemFOFtoCNF_X_1,skolemFOFtoCNF_A),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ member(X,Y)
| ~ member(Y,A)
| member(X,sum(A)) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_6,plain,
( ~ member(X_5274,skolemFOFtoCNF_X_1)
| ~ member(skolemFOFtoCNF_X_1,skolemFOFtoCNF_A)
| member(X_5274,sum(skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(skolemFOFtoCNF_A)),bind(X,$fot(X_5274)),bind(Y,$fot(skolemFOFtoCNF_X_1))]]) ).
cnf(refute_0_7,plain,
( ~ member(X_5274,skolemFOFtoCNF_X_1)
| member(X_5274,sum(skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_X_1,skolemFOFtoCNF_A) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ member(skolemFOFtoCNF_X(skolemFOFtoCNF_X_1,B),skolemFOFtoCNF_X_1)
| member(skolemFOFtoCNF_X(skolemFOFtoCNF_X_1,B),sum(skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_7:[bind(X_5274,$fot(skolemFOFtoCNF_X(skolemFOFtoCNF_X_1,B)))]]) ).
cnf(refute_0_9,plain,
( member(skolemFOFtoCNF_X(skolemFOFtoCNF_X_1,B),sum(skolemFOFtoCNF_A))
| subset(skolemFOFtoCNF_X_1,B) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_X(skolemFOFtoCNF_X_1,B),skolemFOFtoCNF_X_1) )],[refute_0_3,refute_0_8]) ).
cnf(refute_0_10,plain,
( member(skolemFOFtoCNF_X(skolemFOFtoCNF_X_1,sum(skolemFOFtoCNF_A)),sum(skolemFOFtoCNF_A))
| subset(skolemFOFtoCNF_X_1,sum(skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_9:[bind(B,$fot(sum(skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_11,plain,
subset(skolemFOFtoCNF_X_1,sum(skolemFOFtoCNF_A)),
inference(resolve,[$cnf( member(skolemFOFtoCNF_X(skolemFOFtoCNF_X_1,sum(skolemFOFtoCNF_A)),sum(skolemFOFtoCNF_A)) )],[refute_0_10,refute_0_1]) ).
cnf(refute_0_12,plain,
~ subset(skolemFOFtoCNF_X_1,sum(skolemFOFtoCNF_A)),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_13,plain,
$false,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_X_1,sum(skolemFOFtoCNF_A)) )],[refute_0_11,refute_0_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET355+4 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n022.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 Jul 10 03:10:25 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 138.76/139.00 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 138.76/139.00
% 138.76/139.00 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 138.76/139.00
%------------------------------------------------------------------------------