TSTP Solution File: SET351+4 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET351+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %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 : 300s
% DateTime : Wed May 31 12:34:27 EDT 2023
% Result : Theorem 0.16s 0.44s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 68 ( 9 unt; 0 def)
% Number of atoms : 179 ( 10 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 183 ( 72 ~; 79 |; 20 &)
% ( 11 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 86 (; 80 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(A,B)
& subset(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,A] :
( member(X,singleton(A))
<=> X = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,A] :
( member(X,sum(A))
<=> ? [Y] :
( member(Y,A)
& member(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A] : equal_set(sum(singleton(A)),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A] : equal_set(sum(singleton(A)),A),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( ~ member(X,A)
| member(X,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f15,plain,
! [A,B] :
( ( ~ subset(A,B)
| ! [X] :
( ~ member(X,A)
| member(X,B) ) )
& ( subset(A,B)
| ? [X] :
( member(X,A)
& ~ member(X,B) ) ) ),
inference(NNF_transformation,[status(esa)],[f14]) ).
fof(f16,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [X] :
( ~ member(X,A)
| member(X,B) ) )
& ! [A,B] :
( subset(A,B)
| ? [X] :
( member(X,A)
& ~ member(X,B) ) ) ),
inference(miniscoping,[status(esa)],[f15]) ).
fof(f17,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [X] :
( ~ member(X,A)
| member(X,B) ) )
& ! [A,B] :
( subset(A,B)
| ( member(sk0_0(B,A),A)
& ~ member(sk0_0(B,A),B) ) ) ),
inference(skolemization,[status(esa)],[f16]) ).
fof(f19,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f20,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f21,plain,
! [A,B] :
( ( ~ equal_set(A,B)
| ( subset(A,B)
& subset(B,A) ) )
& ( equal_set(A,B)
| ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(NNF_transformation,[status(esa)],[f2]) ).
fof(f22,plain,
( ! [A,B] :
( ~ equal_set(A,B)
| ( subset(A,B)
& subset(B,A) ) )
& ! [A,B] :
( equal_set(A,B)
| ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(miniscoping,[status(esa)],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f25,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f46,plain,
! [X,A] :
( ( ~ member(X,singleton(A))
| X = A )
& ( member(X,singleton(A))
| X != A ) ),
inference(NNF_transformation,[status(esa)],[f8]) ).
fof(f47,plain,
( ! [X,A] :
( ~ member(X,singleton(A))
| X = A )
& ! [X,A] :
( member(X,singleton(A))
| X != A ) ),
inference(miniscoping,[status(esa)],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( member(X0,singleton(X1))
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f55,plain,
! [X,A] :
( ( ~ member(X,sum(A))
| ? [Y] :
( member(Y,A)
& member(X,Y) ) )
& ( member(X,sum(A))
| ! [Y] :
( ~ member(Y,A)
| ~ member(X,Y) ) ) ),
inference(NNF_transformation,[status(esa)],[f10]) ).
fof(f56,plain,
( ! [X,A] :
( ~ member(X,sum(A))
| ? [Y] :
( member(Y,A)
& member(X,Y) ) )
& ! [X,A] :
( member(X,sum(A))
| ! [Y] :
( ~ member(Y,A)
| ~ member(X,Y) ) ) ),
inference(miniscoping,[status(esa)],[f55]) ).
fof(f57,plain,
( ! [X,A] :
( ~ member(X,sum(A))
| ( member(sk0_1(A,X),A)
& member(X,sk0_1(A,X)) ) )
& ! [X,A] :
( member(X,sum(A))
| ! [Y] :
( ~ member(Y,A)
| ~ member(X,Y) ) ) ),
inference(skolemization,[status(esa)],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( ~ member(X0,sum(X1))
| member(sk0_1(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f57]) ).
fof(f59,plain,
! [X0,X1] :
( ~ member(X0,sum(X1))
| member(X0,sk0_1(X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f57]) ).
fof(f60,plain,
! [X0,X1,X2] :
( member(X0,sum(X1))
| ~ member(X2,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f57]) ).
fof(f68,plain,
? [A] : ~ equal_set(sum(singleton(A)),A),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f69,plain,
~ equal_set(sum(singleton(sk0_3)),sk0_3),
inference(skolemization,[status(esa)],[f68]) ).
fof(f70,plain,
~ equal_set(sum(singleton(sk0_3)),sk0_3),
inference(cnf_transformation,[status(esa)],[f69]) ).
fof(f71,plain,
! [X0] : member(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(esa)],[f49]) ).
fof(f95,plain,
! [X0,X1] :
( ~ member(X0,sum(singleton(X1)))
| sk0_1(singleton(X1),X0) = X1 ),
inference(resolution,[status(thm)],[f58,f48]) ).
fof(f97,plain,
! [X0,X1] :
( sk0_1(singleton(X0),sk0_0(X1,sum(singleton(X0)))) = X0
| subset(sum(singleton(X0)),X1) ),
inference(resolution,[status(thm)],[f95,f19]) ).
fof(f152,plain,
! [X0,X1,X2] :
( subset(X0,sum(X1))
| ~ member(X2,X1)
| ~ member(sk0_0(sum(X1),X0),X2) ),
inference(resolution,[status(thm)],[f20,f60]) ).
fof(f174,plain,
( spl0_1
<=> subset(sum(singleton(sk0_3)),sk0_3) ),
introduced(split_symbol_definition) ).
fof(f175,plain,
( subset(sum(singleton(sk0_3)),sk0_3)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f174]) ).
fof(f176,plain,
( ~ subset(sum(singleton(sk0_3)),sk0_3)
| spl0_1 ),
inference(component_clause,[status(thm)],[f174]) ).
fof(f180,plain,
( sk0_1(singleton(sk0_3),sk0_0(sk0_3,sum(singleton(sk0_3)))) = sk0_3
| spl0_1 ),
inference(resolution,[status(thm)],[f176,f97]) ).
fof(f182,plain,
( spl0_2
<=> member(sk0_0(sk0_3,sum(singleton(sk0_3))),sum(singleton(sk0_3))) ),
introduced(split_symbol_definition) ).
fof(f184,plain,
( ~ member(sk0_0(sk0_3,sum(singleton(sk0_3))),sum(singleton(sk0_3)))
| spl0_2 ),
inference(component_clause,[status(thm)],[f182]) ).
fof(f185,plain,
( spl0_3
<=> member(sk0_0(sk0_3,sum(singleton(sk0_3))),sk0_3) ),
introduced(split_symbol_definition) ).
fof(f186,plain,
( member(sk0_0(sk0_3,sum(singleton(sk0_3))),sk0_3)
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f185]) ).
fof(f188,plain,
( ~ member(sk0_0(sk0_3,sum(singleton(sk0_3))),sum(singleton(sk0_3)))
| member(sk0_0(sk0_3,sum(singleton(sk0_3))),sk0_3)
| spl0_1 ),
inference(paramodulation,[status(thm)],[f180,f59]) ).
fof(f189,plain,
( ~ spl0_2
| spl0_3
| spl0_1 ),
inference(split_clause,[status(thm)],[f188,f182,f185,f174]) ).
fof(f195,plain,
( subset(sum(singleton(sk0_3)),sk0_3)
| spl0_2 ),
inference(resolution,[status(thm)],[f184,f19]) ).
fof(f199,plain,
( spl0_5
<=> equal_set(sk0_3,sum(singleton(sk0_3))) ),
introduced(split_symbol_definition) ).
fof(f200,plain,
( equal_set(sk0_3,sum(singleton(sk0_3)))
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f202,plain,
( spl0_6
<=> subset(sk0_3,sum(singleton(sk0_3))) ),
introduced(split_symbol_definition) ).
fof(f204,plain,
( ~ subset(sk0_3,sum(singleton(sk0_3)))
| spl0_6 ),
inference(component_clause,[status(thm)],[f202]) ).
fof(f208,plain,
( subset(sk0_3,sum(singleton(sk0_3)))
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f200,f23]) ).
fof(f215,plain,
( spl0_7
<=> equal_set(sum(singleton(sk0_3)),sk0_3) ),
introduced(split_symbol_definition) ).
fof(f216,plain,
( equal_set(sum(singleton(sk0_3)),sk0_3)
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f215]) ).
fof(f218,plain,
( equal_set(sum(singleton(sk0_3)),sk0_3)
| ~ subset(sum(singleton(sk0_3)),sk0_3)
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f208,f25]) ).
fof(f219,plain,
( spl0_7
| ~ spl0_1
| ~ spl0_5 ),
inference(split_clause,[status(thm)],[f218,f215,f174,f199]) ).
fof(f220,plain,
( $false
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f216,f70]) ).
fof(f221,plain,
~ spl0_7,
inference(contradiction_clause,[status(thm)],[f220]) ).
fof(f225,plain,
! [X0] :
( ~ member(X0,singleton(sk0_3))
| ~ member(sk0_0(sum(singleton(sk0_3)),sk0_3),X0)
| spl0_6 ),
inference(resolution,[status(thm)],[f204,f152]) ).
fof(f227,plain,
( $false
| spl0_2
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f176,f195]) ).
fof(f228,plain,
( spl0_2
| spl0_1 ),
inference(contradiction_clause,[status(thm)],[f227]) ).
fof(f252,plain,
( subset(sum(singleton(sk0_3)),sk0_3)
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f186,f20]) ).
fof(f253,plain,
( $false
| spl0_1
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f252,f176]) ).
fof(f254,plain,
( spl0_1
| ~ spl0_3 ),
inference(contradiction_clause,[status(thm)],[f253]) ).
fof(f256,plain,
( equal_set(sk0_3,sum(singleton(sk0_3)))
| ~ subset(sk0_3,sum(singleton(sk0_3)))
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f175,f25]) ).
fof(f257,plain,
( spl0_5
| ~ spl0_6
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f256,f199,f202,f174]) ).
fof(f272,plain,
( ~ member(sk0_0(sum(singleton(sk0_3)),sk0_3),sk0_3)
| spl0_6 ),
inference(resolution,[status(thm)],[f225,f71]) ).
fof(f274,plain,
( subset(sk0_3,sum(singleton(sk0_3)))
| spl0_6 ),
inference(resolution,[status(thm)],[f272,f19]) ).
fof(f275,plain,
( $false
| spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f274,f204]) ).
fof(f276,plain,
spl0_6,
inference(contradiction_clause,[status(thm)],[f275]) ).
fof(f277,plain,
$false,
inference(sat_refutation,[status(thm)],[f189,f219,f221,f228,f254,f257,f276]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET351+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32 % Computer : n022.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 : 300
% 0.11/0.32 % DateTime : Tue May 30 10:19:12 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % Drodi V3.5.1
% 0.16/0.44 % Refutation found
% 0.16/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.47 % Elapsed time: 0.145159 seconds
% 0.16/0.47 % CPU time: 0.436357 seconds
% 0.16/0.47 % Memory used: 49.349 MB
%------------------------------------------------------------------------------