TSTP Solution File: SET692+4 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET692+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n006.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 20:40:11 EDT 2024
% Result : Theorem 0.16s 0.39s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 57 ( 3 unt; 0 def)
% Number of atoms : 163 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 170 ( 64 ~; 76 |; 18 &)
% ( 10 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 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(f4,axiom,
! [X,A,B] :
( member(X,intersection(A,B))
<=> ( member(X,A)
& member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,B] :
( equal_set(A,intersection(A,B))
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,B] :
( equal_set(A,intersection(A,B))
<=> subset(A,B) ),
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(f18,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
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(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(A,intersection(A,B))
<~> subset(A,B) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f69,plain,
? [A,B] :
( ( equal_set(A,intersection(A,B))
| subset(A,B) )
& ( ~ equal_set(A,intersection(A,B))
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(esa)],[f68]) ).
fof(f70,plain,
( ( equal_set(sk0_3,intersection(sk0_3,sk0_4))
| subset(sk0_3,sk0_4) )
& ( ~ equal_set(sk0_3,intersection(sk0_3,sk0_4))
| ~ subset(sk0_3,sk0_4) ) ),
inference(skolemization,[status(esa)],[f69]) ).
fof(f71,plain,
( equal_set(sk0_3,intersection(sk0_3,sk0_4))
| subset(sk0_3,sk0_4) ),
inference(cnf_transformation,[status(esa)],[f70]) ).
fof(f72,plain,
( ~ equal_set(sk0_3,intersection(sk0_3,sk0_4))
| ~ subset(sk0_3,sk0_4) ),
inference(cnf_transformation,[status(esa)],[f70]) ).
fof(f73,plain,
( spl0_0
<=> equal_set(sk0_3,intersection(sk0_3,sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f74,plain,
( equal_set(sk0_3,intersection(sk0_3,sk0_4))
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,plain,
( spl0_1
<=> subset(sk0_3,sk0_4) ),
introduced(split_symbol_definition) ).
fof(f77,plain,
( subset(sk0_3,sk0_4)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f76]) ).
fof(f79,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f71,f73,f76]) ).
fof(f80,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f72,f73,f76]) ).
fof(f86,plain,
! [X0,X1,X2] :
( subset(intersection(X0,X1),X2)
| member(sk0_0(X2,intersection(X0,X1)),X0) ),
inference(resolution,[status(thm)],[f19,f32]) ).
fof(f87,plain,
! [X0,X1,X2] :
( subset(X0,X1)
| member(sk0_0(X1,X0),intersection(X0,X2))
| ~ member(sk0_0(X1,X0),X2) ),
inference(resolution,[status(thm)],[f19,f34]) ).
fof(f130,plain,
! [X0,X1] :
( subset(intersection(X0,X1),X0)
| subset(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[f20,f86]) ).
fof(f131,plain,
! [X0,X1] : subset(intersection(X0,X1),X0),
inference(duplicate_literals_removal,[status(esa)],[f130]) ).
fof(f203,plain,
! [X0] :
( ~ member(X0,sk0_3)
| member(X0,sk0_4)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f77,f18]) ).
fof(f207,plain,
! [X0] :
( member(sk0_0(X0,sk0_3),sk0_4)
| subset(sk0_3,X0)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f203,f19]) ).
fof(f226,plain,
! [X0] :
( subset(sk0_3,X0)
| subset(sk0_3,X0)
| member(sk0_0(X0,sk0_3),intersection(sk0_3,sk0_4))
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f207,f87]) ).
fof(f227,plain,
! [X0] :
( subset(sk0_3,X0)
| member(sk0_0(X0,sk0_3),intersection(sk0_3,sk0_4))
| ~ spl0_1 ),
inference(duplicate_literals_removal,[status(esa)],[f226]) ).
fof(f244,plain,
( spl0_4
<=> subset(sk0_3,intersection(sk0_3,sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f245,plain,
( subset(sk0_3,intersection(sk0_3,sk0_4))
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f244]) ).
fof(f247,plain,
( subset(sk0_3,intersection(sk0_3,sk0_4))
| subset(sk0_3,intersection(sk0_3,sk0_4))
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f227,f20]) ).
fof(f248,plain,
( spl0_4
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f247,f244,f76]) ).
fof(f256,plain,
( subset(sk0_3,intersection(sk0_3,sk0_4))
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f74,f23]) ).
fof(f259,plain,
( spl0_5
<=> subset(intersection(sk0_3,sk0_4),sk0_3) ),
introduced(split_symbol_definition) ).
fof(f261,plain,
( ~ subset(intersection(sk0_3,sk0_4),sk0_3)
| spl0_5 ),
inference(component_clause,[status(thm)],[f259]) ).
fof(f264,plain,
! [X0] :
( ~ member(X0,sk0_3)
| member(X0,intersection(sk0_3,sk0_4))
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f256,f18]) ).
fof(f274,plain,
( equal_set(sk0_3,intersection(sk0_3,sk0_4))
| ~ subset(intersection(sk0_3,sk0_4),sk0_3)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f245,f25]) ).
fof(f275,plain,
( spl0_0
| ~ spl0_5
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f274,f73,f259,f244]) ).
fof(f277,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f261,f131]) ).
fof(f278,plain,
spl0_5,
inference(contradiction_clause,[status(thm)],[f277]) ).
fof(f293,plain,
! [X0] :
( member(sk0_0(X0,sk0_3),intersection(sk0_3,sk0_4))
| subset(sk0_3,X0)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f264,f19]) ).
fof(f298,plain,
! [X0] :
( subset(sk0_3,X0)
| member(sk0_0(X0,sk0_3),sk0_4)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f293,f33]) ).
fof(f301,plain,
( subset(sk0_3,sk0_4)
| subset(sk0_3,sk0_4)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f298,f20]) ).
fof(f302,plain,
( spl0_1
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f301,f76,f73]) ).
fof(f306,plain,
$false,
inference(sat_refutation,[status(thm)],[f79,f80,f248,f275,f278,f302]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SET692+4 : TPTP v8.1.2. Released v2.2.0.
% 0.02/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32 % Computer : n006.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Mon Apr 29 21:30:35 EDT 2024
% 0.10/0.33 % CPUTime :
% 0.10/0.33 % Drodi V3.6.0
% 0.16/0.39 % Refutation found
% 0.16/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.39 % Elapsed time: 0.061065 seconds
% 0.16/0.39 % CPU time: 0.360396 seconds
% 0.16/0.39 % Total memory used: 54.709 MB
% 0.16/0.39 % Net memory used: 54.279 MB
%------------------------------------------------------------------------------