TSTP Solution File: SEV517+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEV517+1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n014.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 : 300s
% DateTime : Tue Apr 30 20:43:42 EDT 2024
% Result : Theorem 2.39s 0.60s
% Output : CNFRefutation 2.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 61 ( 8 unt; 0 def)
% Number of atoms : 238 ( 16 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 283 ( 106 ~; 100 |; 61 &)
% ( 10 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 146 ( 120 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [B,A,E] :
( member(B,difference(E,A))
<=> ( member(B,E)
& ~ member(B,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,A] :
( member(X,singleton(A))
<=> X = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,E] :
( partition(A,E)
<=> ( ! [X] :
( member(X,A)
=> subset(X,E) )
& ! [X] :
( member(X,E)
=> ? [Y] :
( member(Y,A)
& member(X,Y) ) )
& ! [X,Y] :
( ( member(X,A)
& member(Y,A) )
=> ( ? [Z] :
( member(Z,X)
& member(Z,Y) )
=> X = Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,conjecture,
! [X,A,B,P] :
( ( member(X,difference(A,B))
& partition(P,A) )
=> ? [S] :
( member(S,difference(P,singleton(B)))
& member(X,S) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
~ ! [X,A,B,P] :
( ( member(X,difference(A,B))
& partition(P,A) )
=> ? [S] :
( member(S,difference(P,singleton(B)))
& member(X,S) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f49,plain,
! [B,A,E] :
( ( ~ member(B,difference(E,A))
| ( member(B,E)
& ~ member(B,A) ) )
& ( member(B,difference(E,A))
| ~ member(B,E)
| member(B,A) ) ),
inference(NNF_transformation,[status(esa)],[f7]) ).
fof(f50,plain,
( ! [B,A,E] :
( ~ member(B,difference(E,A))
| ( member(B,E)
& ~ member(B,A) ) )
& ! [B,A,E] :
( member(B,difference(E,A))
| ~ member(B,E)
| member(B,A) ) ),
inference(miniscoping,[status(esa)],[f49]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ~ member(X0,difference(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ~ member(X0,difference(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f53,plain,
! [X0,X1,X2] :
( member(X0,difference(X1,X2))
| ~ member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f54,plain,
! [X,A] :
( ( ~ member(X,singleton(A))
| X = A )
& ( member(X,singleton(A))
| X != A ) ),
inference(NNF_transformation,[status(esa)],[f8]) ).
fof(f55,plain,
( ! [X,A] :
( ~ member(X,singleton(A))
| X = A )
& ! [X,A] :
( member(X,singleton(A))
| X != A ) ),
inference(miniscoping,[status(esa)],[f54]) ).
fof(f56,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f55]) ).
fof(f83,plain,
! [A,E] :
( partition(A,E)
<=> ( ! [X] :
( ~ member(X,A)
| subset(X,E) )
& ! [X] :
( ~ member(X,E)
| ? [Y] :
( member(Y,A)
& member(X,Y) ) )
& ! [X,Y] :
( ~ member(X,A)
| ~ member(Y,A)
| ! [Z] :
( ~ member(Z,X)
| ~ member(Z,Y) )
| X = Y ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f84,plain,
! [A,E] :
( pd0_0(E,A)
<=> ( ! [X] :
( ~ member(X,A)
| subset(X,E) )
& ! [X] :
( ~ member(X,E)
| ? [Y] :
( member(Y,A)
& member(X,Y) ) ) ) ),
introduced(predicate_definition,[f83]) ).
fof(f85,plain,
! [A,E] :
( partition(A,E)
<=> ( pd0_0(E,A)
& ! [X,Y] :
( ~ member(X,A)
| ~ member(Y,A)
| ! [Z] :
( ~ member(Z,X)
| ~ member(Z,Y) )
| X = Y ) ) ),
inference(formula_renaming,[status(thm)],[f83,f84]) ).
fof(f86,plain,
! [A,E] :
( ( ~ partition(A,E)
| ( pd0_0(E,A)
& ! [X,Y] :
( ~ member(X,A)
| ~ member(Y,A)
| ! [Z] :
( ~ member(Z,X)
| ~ member(Z,Y) )
| X = Y ) ) )
& ( partition(A,E)
| ~ pd0_0(E,A)
| ? [X,Y] :
( member(X,A)
& member(Y,A)
& ? [Z] :
( member(Z,X)
& member(Z,Y) )
& X != Y ) ) ),
inference(NNF_transformation,[status(esa)],[f85]) ).
fof(f87,plain,
( ! [A,E] :
( ~ partition(A,E)
| ( pd0_0(E,A)
& ! [X,Y] :
( ~ member(X,A)
| ~ member(Y,A)
| ! [Z] :
( ~ member(Z,X)
| ~ member(Z,Y) )
| X = Y ) ) )
& ! [A,E] :
( partition(A,E)
| ~ pd0_0(E,A)
| ? [X,Y] :
( member(X,A)
& member(Y,A)
& ? [Z] :
( member(Z,X)
& member(Z,Y) )
& X != Y ) ) ),
inference(miniscoping,[status(esa)],[f86]) ).
fof(f88,plain,
( ! [A,E] :
( ~ partition(A,E)
| ( pd0_0(E,A)
& ! [X,Y] :
( ~ member(X,A)
| ~ member(Y,A)
| ! [Z] :
( ~ member(Z,X)
| ~ member(Z,Y) )
| X = Y ) ) )
& ! [A,E] :
( partition(A,E)
| ~ pd0_0(E,A)
| ( member(sk0_4(E,A),A)
& member(sk0_5(E,A),A)
& member(sk0_6(E,A),sk0_4(E,A))
& member(sk0_6(E,A),sk0_5(E,A))
& sk0_4(E,A) != sk0_5(E,A) ) ) ),
inference(skolemization,[status(esa)],[f87]) ).
fof(f89,plain,
! [X0,X1] :
( ~ partition(X0,X1)
| pd0_0(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f88]) ).
fof(f144,plain,
? [X,A,B,P] :
( member(X,difference(A,B))
& partition(P,A)
& ! [S] :
( ~ member(S,difference(P,singleton(B)))
| ~ member(X,S) ) ),
inference(pre_NNF_transformation,[status(esa)],[f21]) ).
fof(f145,plain,
? [X,B,P] :
( ? [A] :
( member(X,difference(A,B))
& partition(P,A) )
& ! [S] :
( ~ member(S,difference(P,singleton(B)))
| ~ member(X,S) ) ),
inference(miniscoping,[status(esa)],[f144]) ).
fof(f146,plain,
( member(sk0_18,difference(sk0_21,sk0_19))
& partition(sk0_20,sk0_21)
& ! [S] :
( ~ member(S,difference(sk0_20,singleton(sk0_19)))
| ~ member(sk0_18,S) ) ),
inference(skolemization,[status(esa)],[f145]) ).
fof(f147,plain,
member(sk0_18,difference(sk0_21,sk0_19)),
inference(cnf_transformation,[status(esa)],[f146]) ).
fof(f148,plain,
partition(sk0_20,sk0_21),
inference(cnf_transformation,[status(esa)],[f146]) ).
fof(f149,plain,
! [X0] :
( ~ member(X0,difference(sk0_20,singleton(sk0_19)))
| ~ member(sk0_18,X0) ),
inference(cnf_transformation,[status(esa)],[f146]) ).
fof(f150,plain,
! [A,E] :
( ( ~ pd0_0(E,A)
| ( ! [X] :
( ~ member(X,A)
| subset(X,E) )
& ! [X] :
( ~ member(X,E)
| ? [Y] :
( member(Y,A)
& member(X,Y) ) ) ) )
& ( pd0_0(E,A)
| ? [X] :
( member(X,A)
& ~ subset(X,E) )
| ? [X] :
( member(X,E)
& ! [Y] :
( ~ member(Y,A)
| ~ member(X,Y) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f84]) ).
fof(f151,plain,
( ! [A,E] :
( ~ pd0_0(E,A)
| ( ! [X] :
( ~ member(X,A)
| subset(X,E) )
& ! [X] :
( ~ member(X,E)
| ? [Y] :
( member(Y,A)
& member(X,Y) ) ) ) )
& ! [A,E] :
( pd0_0(E,A)
| ? [X] :
( member(X,A)
& ~ subset(X,E) )
| ? [X] :
( member(X,E)
& ! [Y] :
( ~ member(Y,A)
| ~ member(X,Y) ) ) ) ),
inference(miniscoping,[status(esa)],[f150]) ).
fof(f152,plain,
( ! [A,E] :
( ~ pd0_0(E,A)
| ( ! [X] :
( ~ member(X,A)
| subset(X,E) )
& ! [X] :
( ~ member(X,E)
| ( member(sk0_22(X,E,A),A)
& member(X,sk0_22(X,E,A)) ) ) ) )
& ! [A,E] :
( pd0_0(E,A)
| ( member(sk0_23(E,A),A)
& ~ subset(sk0_23(E,A),E) )
| ( member(sk0_24(E,A),E)
& ! [Y] :
( ~ member(Y,A)
| ~ member(sk0_24(E,A),Y) ) ) ) ),
inference(skolemization,[status(esa)],[f151]) ).
fof(f154,plain,
! [X0,X1,X2] :
( ~ pd0_0(X0,X1)
| ~ member(X2,X0)
| member(sk0_22(X2,X0,X1),X1) ),
inference(cnf_transformation,[status(esa)],[f152]) ).
fof(f155,plain,
! [X0,X1,X2] :
( ~ pd0_0(X0,X1)
| ~ member(X2,X0)
| member(X2,sk0_22(X2,X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f152]) ).
fof(f187,plain,
member(sk0_18,sk0_21),
inference(resolution,[status(thm)],[f51,f147]) ).
fof(f189,plain,
~ member(sk0_18,sk0_19),
inference(resolution,[status(thm)],[f52,f147]) ).
fof(f190,plain,
! [X0] :
( ~ member(X0,sk0_20)
| member(X0,singleton(sk0_19))
| ~ member(sk0_18,X0) ),
inference(resolution,[status(thm)],[f53,f149]) ).
fof(f198,plain,
! [X0,X1,X2] :
( ~ member(X0,X1)
| member(sk0_22(X0,X1,X2),X2)
| ~ partition(X2,X1) ),
inference(resolution,[status(thm)],[f154,f89]) ).
fof(f199,plain,
! [X0] :
( ~ member(X0,sk0_21)
| member(sk0_22(X0,sk0_21,sk0_20),sk0_20) ),
inference(resolution,[status(thm)],[f198,f148]) ).
fof(f200,plain,
member(sk0_22(sk0_18,sk0_21,sk0_20),sk0_20),
inference(resolution,[status(thm)],[f199,f187]) ).
fof(f202,plain,
( spl0_0
<=> member(sk0_22(sk0_18,sk0_21,sk0_20),singleton(sk0_19)) ),
introduced(split_symbol_definition) ).
fof(f203,plain,
( member(sk0_22(sk0_18,sk0_21,sk0_20),singleton(sk0_19))
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f202]) ).
fof(f205,plain,
( spl0_1
<=> member(sk0_18,sk0_22(sk0_18,sk0_21,sk0_20)) ),
introduced(split_symbol_definition) ).
fof(f206,plain,
( member(sk0_18,sk0_22(sk0_18,sk0_21,sk0_20))
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f207,plain,
( ~ member(sk0_18,sk0_22(sk0_18,sk0_21,sk0_20))
| spl0_1 ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,plain,
( member(sk0_22(sk0_18,sk0_21,sk0_20),singleton(sk0_19))
| ~ member(sk0_18,sk0_22(sk0_18,sk0_21,sk0_20)) ),
inference(resolution,[status(thm)],[f200,f190]) ).
fof(f209,plain,
( spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f208,f202,f205]) ).
fof(f252,plain,
( spl0_3
<=> member(sk0_18,sk0_21) ),
introduced(split_symbol_definition) ).
fof(f254,plain,
( ~ member(sk0_18,sk0_21)
| spl0_3 ),
inference(component_clause,[status(thm)],[f252]) ).
fof(f257,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f254,f187]) ).
fof(f258,plain,
spl0_3,
inference(contradiction_clause,[status(thm)],[f257]) ).
fof(f268,plain,
( spl0_4
<=> member(sk0_18,difference(sk0_21,sk0_19)) ),
introduced(split_symbol_definition) ).
fof(f270,plain,
( ~ member(sk0_18,difference(sk0_21,sk0_19))
| spl0_4 ),
inference(component_clause,[status(thm)],[f268]) ).
fof(f655,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f270,f147]) ).
fof(f656,plain,
spl0_4,
inference(contradiction_clause,[status(thm)],[f655]) ).
fof(f1108,plain,
! [X0,X1,X2] :
( ~ member(X0,X1)
| member(X0,sk0_22(X0,X1,X2))
| ~ partition(X2,X1) ),
inference(resolution,[status(thm)],[f155,f89]) ).
fof(f1110,plain,
! [X0] :
( ~ member(X0,sk0_21)
| member(X0,sk0_22(X0,sk0_21,sk0_20)) ),
inference(resolution,[status(thm)],[f1108,f148]) ).
fof(f1111,plain,
( ~ member(sk0_18,sk0_21)
| spl0_1 ),
inference(resolution,[status(thm)],[f1110,f207]) ).
fof(f1112,plain,
( ~ spl0_3
| spl0_1 ),
inference(split_clause,[status(thm)],[f1111,f252,f205]) ).
fof(f1161,plain,
( sk0_22(sk0_18,sk0_21,sk0_20) = sk0_19
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f203,f56]) ).
fof(f1171,plain,
( member(sk0_18,sk0_19)
| ~ spl0_0
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f1161,f206]) ).
fof(f1172,plain,
( $false
| ~ spl0_0
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f1171,f189]) ).
fof(f1173,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(contradiction_clause,[status(thm)],[f1172]) ).
fof(f1174,plain,
$false,
inference(sat_refutation,[status(thm)],[f209,f258,f656,f1112,f1173]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.07 % Problem : SEV517+1 : TPTP v8.1.2. Released v7.3.0.
% 0.02/0.07 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.26 % Computer : n014.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Mon Apr 29 19:45:49 EDT 2024
% 0.07/0.26 % CPUTime :
% 0.11/0.27 % Drodi V3.6.0
% 2.39/0.60 % Refutation found
% 2.39/0.60 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.39/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.39/0.62 % Elapsed time: 0.352325 seconds
% 2.39/0.62 % CPU time: 2.689003 seconds
% 2.39/0.62 % Total memory used: 95.950 MB
% 2.39/0.62 % Net memory used: 93.013 MB
%------------------------------------------------------------------------------