TSTP Solution File: SET813+4 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET813+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 03:37:22 EDT 2022
% Result : Theorem 0.41s 0.60s
% Output : CNFRefutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 10 unt; 0 def)
% Number of atoms : 74 ( 9 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 73 ( 35 ~; 18 |; 8 &)
% ( 9 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 57 ( 3 sgn 38 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(union,axiom,
! [X,A,B] :
( member(X,union(A,B))
<=> ( member(X,A)
| member(X,B) ) ) ).
fof(singleton,axiom,
! [X,A] :
( member(X,singleton(A))
<=> X = A ) ).
fof(successor,axiom,
! [A,X] :
( member(X,suc(A))
<=> member(X,union(A,singleton(A))) ) ).
fof(thV12,conjecture,
! [A] :
( member(A,on)
=> member(A,suc(A)) ) ).
fof(subgoal_0,plain,
! [A] :
( member(A,on)
=> member(A,suc(A)) ),
inference(strip,[],[thV12]) ).
fof(negate_0_0,plain,
~ ! [A] :
( member(A,on)
=> member(A,suc(A)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A] :
( ~ member(A,suc(A))
& member(A,on) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ member(skolemFOFtoCNF_A_1,suc(skolemFOFtoCNF_A_1))
& member(skolemFOFtoCNF_A_1,on) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ member(skolemFOFtoCNF_A_1,suc(skolemFOFtoCNF_A_1)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,X] :
( ~ member(X,suc(A))
<=> ~ member(X,union(A,singleton(A))) ),
inference(canonicalize,[],[successor]) ).
fof(normalize_0_4,plain,
! [A,X] :
( ~ member(X,suc(A))
<=> ~ member(X,union(A,singleton(A))) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,X] :
( ( ~ member(X,suc(A))
| member(X,union(A,singleton(A))) )
& ( ~ member(X,union(A,singleton(A)))
| member(X,suc(A)) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,X] :
( ~ member(X,union(A,singleton(A)))
| member(X,suc(A)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,X] :
( X != A
<=> ~ member(X,singleton(A)) ),
inference(canonicalize,[],[singleton]) ).
fof(normalize_0_8,plain,
! [A,X] :
( X != A
<=> ~ member(X,singleton(A)) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,X] :
( ( X != A
| member(X,singleton(A)) )
& ( ~ member(X,singleton(A))
| X = A ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,X] :
( X != A
| member(X,singleton(A)) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B,X] :
( ~ member(X,union(A,B))
<=> ( ~ member(X,A)
& ~ member(X,B) ) ),
inference(canonicalize,[],[union]) ).
fof(normalize_0_12,plain,
! [A,B,X] :
( ~ member(X,union(A,B))
<=> ( ~ member(X,A)
& ~ member(X,B) ) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A,B,X] :
( ( ~ member(X,A)
| member(X,union(A,B)) )
& ( ~ member(X,B)
| member(X,union(A,B)) )
& ( ~ member(X,union(A,B))
| member(X,A)
| member(X,B) ) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A,B,X] :
( ~ member(X,B)
| member(X,union(A,B)) ),
inference(conjunct,[],[normalize_0_13]) ).
cnf(refute_0_0,plain,
~ member(skolemFOFtoCNF_A_1,suc(skolemFOFtoCNF_A_1)),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ member(X,union(A,singleton(A)))
| member(X,suc(A)) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( ~ member(X_636,union(X_636,singleton(X_636)))
| member(X_636,suc(X_636)) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_636)),bind(X,$fot(X_636))]]) ).
cnf(refute_0_3,plain,
( X != A
| member(X,singleton(A)) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_4,plain,
( A != A
| member(A,singleton(A)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(A))]]) ).
cnf(refute_0_5,plain,
A = A,
introduced(tautology,[refl,[$fot(A)]]) ).
cnf(refute_0_6,plain,
member(A,singleton(A)),
inference(resolve,[$cnf( $equal(A,A) )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
member(X_591,singleton(X_591)),
inference(subst,[],[refute_0_6:[bind(A,$fot(X_591))]]) ).
cnf(refute_0_8,plain,
( ~ member(X,B)
| member(X,union(A,B)) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_9,plain,
( ~ member(X_591,singleton(X_591))
| member(X_591,union(X_589,singleton(X_591))) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(X_589)),bind(B,$fot(singleton(X_591))),bind(X,$fot(X_591))]]) ).
cnf(refute_0_10,plain,
member(X_591,union(X_589,singleton(X_591))),
inference(resolve,[$cnf( member(X_591,singleton(X_591)) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
member(X_636,union(X_636,singleton(X_636))),
inference(subst,[],[refute_0_10:[bind(X_589,$fot(X_636)),bind(X_591,$fot(X_636))]]) ).
cnf(refute_0_12,plain,
member(X_636,suc(X_636)),
inference(resolve,[$cnf( member(X_636,union(X_636,singleton(X_636))) )],[refute_0_11,refute_0_2]) ).
cnf(refute_0_13,plain,
member(skolemFOFtoCNF_A_1,suc(skolemFOFtoCNF_A_1)),
inference(subst,[],[refute_0_12:[bind(X_636,$fot(skolemFOFtoCNF_A_1))]]) ).
cnf(refute_0_14,plain,
$false,
inference(resolve,[$cnf( member(skolemFOFtoCNF_A_1,suc(skolemFOFtoCNF_A_1)) )],[refute_0_13,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET813+4 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 16:36:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.41/0.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.41/0.60
% 0.41/0.60 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.41/0.60
%------------------------------------------------------------------------------