TSTP Solution File: SET159+4 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET159+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n015.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 20:39:18 EDT 2024
% Result : Theorem 0.19s 0.40s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 76 ( 6 unt; 0 def)
% Number of atoms : 195 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 191 ( 72 ~; 89 |; 15 &)
% ( 14 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 14 ( 13 usr; 11 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 74 ( 69 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(A,B)
& subset(B,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,A,B] :
( member(X,union(A,B))
<=> ( member(X,A)
| member(X,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,B,C] : equal_set(union(union(A,B),C),union(A,union(B,C))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,B,C] : equal_set(union(union(A,B),C),union(A,union(B,C))),
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(f25,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f35,plain,
! [X,A,B] :
( ( ~ member(X,union(A,B))
| member(X,A)
| member(X,B) )
& ( member(X,union(A,B))
| ( ~ member(X,A)
& ~ member(X,B) ) ) ),
inference(NNF_transformation,[status(esa)],[f5]) ).
fof(f36,plain,
( ! [X,A,B] :
( ~ member(X,union(A,B))
| member(X,A)
| member(X,B) )
& ! [X,A,B] :
( member(X,union(A,B))
| ( ~ member(X,A)
& ~ member(X,B) ) ) ),
inference(miniscoping,[status(esa)],[f35]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f38,plain,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f39,plain,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f68,plain,
? [A,B,C] : ~ equal_set(union(union(A,B),C),union(A,union(B,C))),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f69,plain,
~ equal_set(union(union(sk0_3,sk0_4),sk0_5),union(sk0_3,union(sk0_4,sk0_5))),
inference(skolemization,[status(esa)],[f68]) ).
fof(f70,plain,
~ equal_set(union(union(sk0_3,sk0_4),sk0_5),union(sk0_3,union(sk0_4,sk0_5))),
inference(cnf_transformation,[status(esa)],[f69]) ).
fof(f74,plain,
( spl0_0
<=> subset(union(union(sk0_3,sk0_4),sk0_5),union(sk0_3,union(sk0_4,sk0_5))) ),
introduced(split_symbol_definition) ).
fof(f76,plain,
( ~ subset(union(union(sk0_3,sk0_4),sk0_5),union(sk0_3,union(sk0_4,sk0_5)))
| spl0_0 ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f77,plain,
( spl0_1
<=> subset(union(sk0_3,union(sk0_4,sk0_5)),union(union(sk0_3,sk0_4),sk0_5)) ),
introduced(split_symbol_definition) ).
fof(f79,plain,
( ~ subset(union(sk0_3,union(sk0_4,sk0_5)),union(union(sk0_3,sk0_4),sk0_5))
| spl0_1 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,plain,
( ~ subset(union(union(sk0_3,sk0_4),sk0_5),union(sk0_3,union(sk0_4,sk0_5)))
| ~ subset(union(sk0_3,union(sk0_4,sk0_5)),union(union(sk0_3,sk0_4),sk0_5)) ),
inference(resolution,[status(thm)],[f25,f70]) ).
fof(f81,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f80,f74,f77]) ).
fof(f83,plain,
! [X0,X1,X2] :
( subset(union(X0,X1),X2)
| member(sk0_0(X2,union(X0,X1)),X0)
| member(sk0_0(X2,union(X0,X1)),X1) ),
inference(resolution,[status(thm)],[f19,f37]) ).
fof(f84,plain,
( spl0_2
<=> member(sk0_0(union(sk0_3,union(sk0_4,sk0_5)),union(union(sk0_3,sk0_4),sk0_5)),union(sk0_3,sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f85,plain,
( member(sk0_0(union(sk0_3,union(sk0_4,sk0_5)),union(union(sk0_3,sk0_4),sk0_5)),union(sk0_3,sk0_4))
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f84]) ).
fof(f87,plain,
( spl0_3
<=> member(sk0_0(union(sk0_3,union(sk0_4,sk0_5)),union(union(sk0_3,sk0_4),sk0_5)),sk0_5) ),
introduced(split_symbol_definition) ).
fof(f88,plain,
( member(sk0_0(union(sk0_3,union(sk0_4,sk0_5)),union(union(sk0_3,sk0_4),sk0_5)),sk0_5)
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f87]) ).
fof(f90,plain,
( member(sk0_0(union(sk0_3,union(sk0_4,sk0_5)),union(union(sk0_3,sk0_4),sk0_5)),union(sk0_3,sk0_4))
| member(sk0_0(union(sk0_3,union(sk0_4,sk0_5)),union(union(sk0_3,sk0_4),sk0_5)),sk0_5)
| spl0_0 ),
inference(resolution,[status(thm)],[f83,f76]) ).
fof(f91,plain,
( spl0_2
| spl0_3
| spl0_0 ),
inference(split_clause,[status(thm)],[f90,f84,f87,f74]) ).
fof(f92,plain,
( spl0_4
<=> member(sk0_0(union(union(sk0_3,sk0_4),sk0_5),union(sk0_3,union(sk0_4,sk0_5))),sk0_3) ),
introduced(split_symbol_definition) ).
fof(f93,plain,
( member(sk0_0(union(union(sk0_3,sk0_4),sk0_5),union(sk0_3,union(sk0_4,sk0_5))),sk0_3)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f92]) ).
fof(f95,plain,
( spl0_5
<=> member(sk0_0(union(union(sk0_3,sk0_4),sk0_5),union(sk0_3,union(sk0_4,sk0_5))),union(sk0_4,sk0_5)) ),
introduced(split_symbol_definition) ).
fof(f96,plain,
( member(sk0_0(union(union(sk0_3,sk0_4),sk0_5),union(sk0_3,union(sk0_4,sk0_5))),union(sk0_4,sk0_5))
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f95]) ).
fof(f98,plain,
( member(sk0_0(union(union(sk0_3,sk0_4),sk0_5),union(sk0_3,union(sk0_4,sk0_5))),sk0_3)
| member(sk0_0(union(union(sk0_3,sk0_4),sk0_5),union(sk0_3,union(sk0_4,sk0_5))),union(sk0_4,sk0_5))
| spl0_1 ),
inference(resolution,[status(thm)],[f79,f83]) ).
fof(f99,plain,
( spl0_4
| spl0_5
| spl0_1 ),
inference(split_clause,[status(thm)],[f98,f92,f95,f77]) ).
fof(f102,plain,
( spl0_6
<=> member(sk0_0(union(sk0_3,union(sk0_4,sk0_5)),union(union(sk0_3,sk0_4),sk0_5)),sk0_3) ),
introduced(split_symbol_definition) ).
fof(f103,plain,
( member(sk0_0(union(sk0_3,union(sk0_4,sk0_5)),union(union(sk0_3,sk0_4),sk0_5)),sk0_3)
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f102]) ).
fof(f105,plain,
( spl0_7
<=> member(sk0_0(union(sk0_3,union(sk0_4,sk0_5)),union(union(sk0_3,sk0_4),sk0_5)),sk0_4) ),
introduced(split_symbol_definition) ).
fof(f106,plain,
( member(sk0_0(union(sk0_3,union(sk0_4,sk0_5)),union(union(sk0_3,sk0_4),sk0_5)),sk0_4)
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f108,plain,
( member(sk0_0(union(sk0_3,union(sk0_4,sk0_5)),union(union(sk0_3,sk0_4),sk0_5)),sk0_3)
| member(sk0_0(union(sk0_3,union(sk0_4,sk0_5)),union(union(sk0_3,sk0_4),sk0_5)),sk0_4)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f85,f37]) ).
fof(f109,plain,
( spl0_6
| spl0_7
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f108,f102,f105,f84]) ).
fof(f110,plain,
( spl0_8
<=> member(sk0_0(union(union(sk0_3,sk0_4),sk0_5),union(sk0_3,union(sk0_4,sk0_5))),sk0_4) ),
introduced(split_symbol_definition) ).
fof(f111,plain,
( member(sk0_0(union(union(sk0_3,sk0_4),sk0_5),union(sk0_3,union(sk0_4,sk0_5))),sk0_4)
| ~ spl0_8 ),
inference(component_clause,[status(thm)],[f110]) ).
fof(f113,plain,
( spl0_9
<=> member(sk0_0(union(union(sk0_3,sk0_4),sk0_5),union(sk0_3,union(sk0_4,sk0_5))),sk0_5) ),
introduced(split_symbol_definition) ).
fof(f114,plain,
( member(sk0_0(union(union(sk0_3,sk0_4),sk0_5),union(sk0_3,union(sk0_4,sk0_5))),sk0_5)
| ~ spl0_9 ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f116,plain,
( member(sk0_0(union(union(sk0_3,sk0_4),sk0_5),union(sk0_3,union(sk0_4,sk0_5))),sk0_4)
| member(sk0_0(union(union(sk0_3,sk0_4),sk0_5),union(sk0_3,union(sk0_4,sk0_5))),sk0_5)
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f96,f37]) ).
fof(f117,plain,
( spl0_8
| spl0_9
| ~ spl0_5 ),
inference(split_clause,[status(thm)],[f116,f110,f113,f95]) ).
fof(f120,plain,
! [X0,X1,X2] :
( subset(X0,union(X1,X2))
| ~ member(sk0_0(union(X1,X2),X0),X2) ),
inference(resolution,[status(thm)],[f20,f39]) ).
fof(f121,plain,
! [X0,X1,X2] :
( subset(X0,union(X1,X2))
| ~ member(sk0_0(union(X1,X2),X0),X1) ),
inference(resolution,[status(thm)],[f20,f38]) ).
fof(f122,plain,
( ~ member(sk0_0(union(sk0_3,union(sk0_4,sk0_5)),union(union(sk0_3,sk0_4),sk0_5)),union(sk0_4,sk0_5))
| spl0_0 ),
inference(resolution,[status(thm)],[f120,f76]) ).
fof(f123,plain,
( ~ member(sk0_0(union(sk0_3,union(sk0_4,sk0_5)),union(union(sk0_3,sk0_4),sk0_5)),sk0_5)
| spl0_0 ),
inference(resolution,[status(thm)],[f122,f39]) ).
fof(f124,plain,
( $false
| ~ spl0_3
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f123,f88]) ).
fof(f125,plain,
( ~ spl0_3
| spl0_0 ),
inference(contradiction_clause,[status(thm)],[f124]) ).
fof(f128,plain,
( ~ member(sk0_0(union(union(sk0_3,sk0_4),sk0_5),union(sk0_3,union(sk0_4,sk0_5))),sk0_5)
| spl0_1 ),
inference(resolution,[status(thm)],[f79,f120]) ).
fof(f129,plain,
( $false
| ~ spl0_9
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f128,f114]) ).
fof(f130,plain,
( ~ spl0_9
| spl0_1 ),
inference(contradiction_clause,[status(thm)],[f129]) ).
fof(f131,plain,
( ~ member(sk0_0(union(sk0_3,union(sk0_4,sk0_5)),union(union(sk0_3,sk0_4),sk0_5)),sk0_4)
| spl0_0 ),
inference(resolution,[status(thm)],[f122,f38]) ).
fof(f139,plain,
( ~ member(sk0_0(union(sk0_3,union(sk0_4,sk0_5)),union(union(sk0_3,sk0_4),sk0_5)),sk0_3)
| spl0_0 ),
inference(resolution,[status(thm)],[f121,f76]) ).
fof(f140,plain,
( $false
| ~ spl0_6
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f139,f103]) ).
fof(f141,plain,
( ~ spl0_6
| spl0_0 ),
inference(contradiction_clause,[status(thm)],[f140]) ).
fof(f144,plain,
( ~ member(sk0_0(union(union(sk0_3,sk0_4),sk0_5),union(sk0_3,union(sk0_4,sk0_5))),union(sk0_3,sk0_4))
| spl0_1 ),
inference(resolution,[status(thm)],[f79,f121]) ).
fof(f146,plain,
( $false
| ~ spl0_7
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f131,f106]) ).
fof(f147,plain,
( ~ spl0_7
| spl0_0 ),
inference(contradiction_clause,[status(thm)],[f146]) ).
fof(f152,plain,
( ~ member(sk0_0(union(union(sk0_3,sk0_4),sk0_5),union(sk0_3,union(sk0_4,sk0_5))),sk0_4)
| spl0_1 ),
inference(resolution,[status(thm)],[f144,f39]) ).
fof(f153,plain,
( $false
| ~ spl0_8
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f152,f111]) ).
fof(f154,plain,
( ~ spl0_8
| spl0_1 ),
inference(contradiction_clause,[status(thm)],[f153]) ).
fof(f155,plain,
( ~ member(sk0_0(union(union(sk0_3,sk0_4),sk0_5),union(sk0_3,union(sk0_4,sk0_5))),sk0_3)
| spl0_1 ),
inference(resolution,[status(thm)],[f144,f38]) ).
fof(f156,plain,
( $false
| ~ spl0_4
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f155,f93]) ).
fof(f157,plain,
( ~ spl0_4
| spl0_1 ),
inference(contradiction_clause,[status(thm)],[f156]) ).
fof(f158,plain,
$false,
inference(sat_refutation,[status(thm)],[f81,f91,f99,f109,f117,f125,f130,f141,f147,f154,f157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET159+4 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 29 22:10:17 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.19/0.35 % Drodi V3.6.0
% 0.19/0.40 % Refutation found
% 0.19/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.42 % Elapsed time: 0.069986 seconds
% 0.19/0.42 % CPU time: 0.445865 seconds
% 0.19/0.42 % Total memory used: 56.732 MB
% 0.19/0.42 % Net memory used: 56.476 MB
%------------------------------------------------------------------------------