TSTP Solution File: SET013+4 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET013+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n011.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 20:38:37 EDT 2024
% Result : Theorem 0.22s 0.39s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 56 ( 6 unt; 0 def)
% Number of atoms : 149 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 146 ( 53 ~; 66 |; 16 &)
% ( 10 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 71 ( 67 !; 4 ?)
% 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(f4,axiom,
! [X,A,B] :
( member(X,intersection(A,B))
<=> ( member(X,A)
& member(X,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,B] : equal_set(intersection(A,B),intersection(B,A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,B] : equal_set(intersection(A,B),intersection(B,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(f25,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f30,plain,
! [X,A,B] :
( ( ~ member(X,intersection(A,B))
| ( member(X,A)
& member(X,B) ) )
& ( member(X,intersection(A,B))
| ~ member(X,A)
| ~ member(X,B) ) ),
inference(NNF_transformation,[status(esa)],[f4]) ).
fof(f31,plain,
( ! [X,A,B] :
( ~ member(X,intersection(A,B))
| ( member(X,A)
& member(X,B) ) )
& ! [X,A,B] :
( member(X,intersection(A,B))
| ~ member(X,A)
| ~ member(X,B) ) ),
inference(miniscoping,[status(esa)],[f30]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f34,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f68,plain,
? [A,B] : ~ equal_set(intersection(A,B),intersection(B,A)),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f69,plain,
~ equal_set(intersection(sk0_3,sk0_4),intersection(sk0_4,sk0_3)),
inference(skolemization,[status(esa)],[f68]) ).
fof(f70,plain,
~ equal_set(intersection(sk0_3,sk0_4),intersection(sk0_4,sk0_3)),
inference(cnf_transformation,[status(esa)],[f69]) ).
fof(f74,plain,
( spl0_0
<=> subset(intersection(sk0_3,sk0_4),intersection(sk0_4,sk0_3)) ),
introduced(split_symbol_definition) ).
fof(f76,plain,
( ~ subset(intersection(sk0_3,sk0_4),intersection(sk0_4,sk0_3))
| spl0_0 ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f77,plain,
( spl0_1
<=> subset(intersection(sk0_4,sk0_3),intersection(sk0_3,sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f79,plain,
( ~ subset(intersection(sk0_4,sk0_3),intersection(sk0_3,sk0_4))
| spl0_1 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,plain,
( ~ subset(intersection(sk0_3,sk0_4),intersection(sk0_4,sk0_3))
| ~ subset(intersection(sk0_4,sk0_3),intersection(sk0_3,sk0_4)) ),
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(intersection(X0,X1),X2)
| member(sk0_0(X2,intersection(X0,X1)),X1) ),
inference(resolution,[status(thm)],[f19,f33]) ).
fof(f84,plain,
! [X0,X1,X2] :
( subset(intersection(X0,X1),X2)
| member(sk0_0(X2,intersection(X0,X1)),X0) ),
inference(resolution,[status(thm)],[f19,f32]) ).
fof(f85,plain,
( member(sk0_0(intersection(sk0_4,sk0_3),intersection(sk0_3,sk0_4)),sk0_4)
| spl0_0 ),
inference(resolution,[status(thm)],[f83,f76]) ).
fof(f86,plain,
( member(sk0_0(intersection(sk0_4,sk0_3),intersection(sk0_3,sk0_4)),sk0_3)
| spl0_0 ),
inference(resolution,[status(thm)],[f84,f76]) ).
fof(f89,plain,
! [X0,X1,X2] :
( subset(X0,intersection(X1,X2))
| ~ member(sk0_0(intersection(X1,X2),X0),X1)
| ~ member(sk0_0(intersection(X1,X2),X0),X2) ),
inference(resolution,[status(thm)],[f20,f34]) ).
fof(f90,plain,
( spl0_2
<=> member(sk0_0(intersection(sk0_4,sk0_3),intersection(sk0_3,sk0_4)),sk0_4) ),
introduced(split_symbol_definition) ).
fof(f92,plain,
( ~ member(sk0_0(intersection(sk0_4,sk0_3),intersection(sk0_3,sk0_4)),sk0_4)
| spl0_2 ),
inference(component_clause,[status(thm)],[f90]) ).
fof(f93,plain,
( spl0_3
<=> member(sk0_0(intersection(sk0_4,sk0_3),intersection(sk0_3,sk0_4)),sk0_3) ),
introduced(split_symbol_definition) ).
fof(f95,plain,
( ~ member(sk0_0(intersection(sk0_4,sk0_3),intersection(sk0_3,sk0_4)),sk0_3)
| spl0_3 ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( ~ member(sk0_0(intersection(sk0_4,sk0_3),intersection(sk0_3,sk0_4)),sk0_4)
| ~ member(sk0_0(intersection(sk0_4,sk0_3),intersection(sk0_3,sk0_4)),sk0_3)
| spl0_0 ),
inference(resolution,[status(thm)],[f89,f76]) ).
fof(f97,plain,
( ~ spl0_2
| ~ spl0_3
| spl0_0 ),
inference(split_clause,[status(thm)],[f96,f90,f93,f74]) ).
fof(f98,plain,
( member(sk0_0(intersection(sk0_3,sk0_4),intersection(sk0_4,sk0_3)),sk0_4)
| spl0_1 ),
inference(resolution,[status(thm)],[f79,f84]) ).
fof(f99,plain,
( member(sk0_0(intersection(sk0_3,sk0_4),intersection(sk0_4,sk0_3)),sk0_3)
| spl0_1 ),
inference(resolution,[status(thm)],[f79,f83]) ).
fof(f100,plain,
( spl0_4
<=> member(sk0_0(intersection(sk0_3,sk0_4),intersection(sk0_4,sk0_3)),sk0_3) ),
introduced(split_symbol_definition) ).
fof(f102,plain,
( ~ member(sk0_0(intersection(sk0_3,sk0_4),intersection(sk0_4,sk0_3)),sk0_3)
| spl0_4 ),
inference(component_clause,[status(thm)],[f100]) ).
fof(f103,plain,
( spl0_5
<=> member(sk0_0(intersection(sk0_3,sk0_4),intersection(sk0_4,sk0_3)),sk0_4) ),
introduced(split_symbol_definition) ).
fof(f105,plain,
( ~ member(sk0_0(intersection(sk0_3,sk0_4),intersection(sk0_4,sk0_3)),sk0_4)
| spl0_5 ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,plain,
( ~ member(sk0_0(intersection(sk0_3,sk0_4),intersection(sk0_4,sk0_3)),sk0_3)
| ~ member(sk0_0(intersection(sk0_3,sk0_4),intersection(sk0_4,sk0_3)),sk0_4)
| spl0_1 ),
inference(resolution,[status(thm)],[f79,f89]) ).
fof(f107,plain,
( ~ spl0_4
| ~ spl0_5
| spl0_1 ),
inference(split_clause,[status(thm)],[f106,f100,f103,f77]) ).
fof(f108,plain,
( $false
| spl0_2
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f85,f92]) ).
fof(f109,plain,
( spl0_2
| spl0_0 ),
inference(contradiction_clause,[status(thm)],[f108]) ).
fof(f110,plain,
( $false
| spl0_4
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f99,f102]) ).
fof(f111,plain,
( spl0_4
| spl0_1 ),
inference(contradiction_clause,[status(thm)],[f110]) ).
fof(f112,plain,
( $false
| spl0_3
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f86,f95]) ).
fof(f113,plain,
( spl0_3
| spl0_0 ),
inference(contradiction_clause,[status(thm)],[f112]) ).
fof(f114,plain,
( $false
| spl0_5
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f98,f105]) ).
fof(f115,plain,
( spl0_5
| spl0_1 ),
inference(contradiction_clause,[status(thm)],[f114]) ).
fof(f116,plain,
$false,
inference(sat_refutation,[status(thm)],[f81,f97,f107,f109,f111,f113,f115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET013+4 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.15/0.35 % Computer : n011.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon Apr 29 21:32:01 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % Drodi V3.6.0
% 0.22/0.39 % Refutation found
% 0.22/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.22/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.42 % Elapsed time: 0.050744 seconds
% 0.22/0.42 % CPU time: 0.265509 seconds
% 0.22/0.42 % Total memory used: 44.650 MB
% 0.22/0.42 % Net memory used: 44.551 MB
%------------------------------------------------------------------------------