TSTP Solution File: SET693+4 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET693+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n003.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 12:35:02 EDT 2023
% Result : Theorem 0.20s 0.44s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 84 ( 5 unt; 0 def)
% Number of atoms : 226 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 232 ( 90 ~; 109 |; 17 &)
% ( 14 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 100 (; 94 !; 6 ?)
% 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] :
( equal_set(A,union(A,B))
<=> subset(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,B] :
( equal_set(A,union(A,B))
<=> subset(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(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(f24,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| subset(X1,X0) ),
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(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] :
( equal_set(A,union(A,B))
<~> subset(B,A) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f69,plain,
? [A,B] :
( ( equal_set(A,union(A,B))
| subset(B,A) )
& ( ~ equal_set(A,union(A,B))
| ~ subset(B,A) ) ),
inference(NNF_transformation,[status(esa)],[f68]) ).
fof(f70,plain,
( ( equal_set(sk0_3,union(sk0_3,sk0_4))
| subset(sk0_4,sk0_3) )
& ( ~ equal_set(sk0_3,union(sk0_3,sk0_4))
| ~ subset(sk0_4,sk0_3) ) ),
inference(skolemization,[status(esa)],[f69]) ).
fof(f71,plain,
( equal_set(sk0_3,union(sk0_3,sk0_4))
| subset(sk0_4,sk0_3) ),
inference(cnf_transformation,[status(esa)],[f70]) ).
fof(f72,plain,
( ~ equal_set(sk0_3,union(sk0_3,sk0_4))
| ~ subset(sk0_4,sk0_3) ),
inference(cnf_transformation,[status(esa)],[f70]) ).
fof(f73,plain,
( spl0_0
<=> equal_set(sk0_3,union(sk0_3,sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f74,plain,
( equal_set(sk0_3,union(sk0_3,sk0_4))
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,plain,
( spl0_1
<=> subset(sk0_4,sk0_3) ),
introduced(split_symbol_definition) ).
fof(f77,plain,
( subset(sk0_4,sk0_3)
| ~ 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(f91,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(f103,plain,
! [X0,X1,X2] :
( subset(X0,union(X1,X2))
| ~ member(sk0_0(union(X1,X2),X0),X2) ),
inference(resolution,[status(thm)],[f20,f39]) ).
fof(f104,plain,
! [X0,X1,X2] :
( subset(X0,union(X1,X2))
| ~ member(sk0_0(union(X1,X2),X0),X1) ),
inference(resolution,[status(thm)],[f20,f38]) ).
fof(f105,plain,
! [X0,X1,X2] :
( subset(X0,X1)
| ~ subset(X2,X1)
| ~ member(sk0_0(X1,X0),X2) ),
inference(resolution,[status(thm)],[f20,f18]) ).
fof(f149,plain,
! [X0] :
( subset(X0,sk0_3)
| ~ member(sk0_0(sk0_3,X0),sk0_4)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f105,f77]) ).
fof(f167,plain,
! [X0,X1] :
( subset(X0,union(X1,X0))
| subset(X0,union(X1,X0)) ),
inference(resolution,[status(thm)],[f103,f19]) ).
fof(f168,plain,
! [X0,X1] : subset(X0,union(X1,X0)),
inference(duplicate_literals_removal,[status(esa)],[f167]) ).
fof(f178,plain,
! [X0,X1] :
( subset(X0,union(X0,X1))
| subset(X0,union(X0,X1)) ),
inference(resolution,[status(thm)],[f104,f19]) ).
fof(f179,plain,
! [X0,X1] : subset(X0,union(X0,X1)),
inference(duplicate_literals_removal,[status(esa)],[f178]) ).
fof(f197,plain,
( spl0_4
<=> subset(union(sk0_4,sk0_4),sk0_3) ),
introduced(split_symbol_definition) ).
fof(f198,plain,
( subset(union(sk0_4,sk0_4),sk0_3)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f197]) ).
fof(f202,plain,
! [X0] :
( subset(union(sk0_4,X0),sk0_3)
| member(sk0_0(sk0_3,union(sk0_4,X0)),X0)
| subset(union(sk0_4,X0),sk0_3)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f91,f149]) ).
fof(f203,plain,
! [X0] :
( subset(union(sk0_4,X0),sk0_3)
| member(sk0_0(sk0_3,union(sk0_4,X0)),X0)
| ~ spl0_1 ),
inference(duplicate_literals_removal,[status(esa)],[f202]) ).
fof(f232,plain,
! [X0] :
( subset(union(X0,sk0_4),sk0_3)
| member(sk0_0(sk0_3,union(X0,sk0_4)),X0)
| subset(union(X0,sk0_4),sk0_3)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f91,f149]) ).
fof(f233,plain,
! [X0] :
( subset(union(X0,sk0_4),sk0_3)
| member(sk0_0(sk0_3,union(X0,sk0_4)),X0)
| ~ spl0_1 ),
inference(duplicate_literals_removal,[status(esa)],[f232]) ).
fof(f247,plain,
( subset(union(sk0_3,sk0_4),sk0_3)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f74,f24]) ).
fof(f249,plain,
! [X0] :
( subset(X0,sk0_3)
| ~ member(sk0_0(sk0_3,X0),union(sk0_3,sk0_4))
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f247,f105]) ).
fof(f250,plain,
( spl0_5
<=> subset(sk0_3,union(sk0_3,sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f252,plain,
( ~ subset(sk0_3,union(sk0_3,sk0_4))
| spl0_5 ),
inference(component_clause,[status(thm)],[f250]) ).
fof(f258,plain,
! [X0] :
( subset(X0,sk0_3)
| ~ member(sk0_0(sk0_3,X0),union(sk0_4,sk0_4))
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f198,f105]) ).
fof(f299,plain,
! [X0] :
( subset(X0,sk0_3)
| ~ member(sk0_0(sk0_3,X0),sk0_4)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f258,f38]) ).
fof(f541,plain,
( subset(sk0_4,sk0_3)
| subset(sk0_4,sk0_3)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f299,f19]) ).
fof(f542,plain,
( spl0_1
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f541,f76,f197]) ).
fof(f603,plain,
( spl0_12
<=> subset(union(sk0_4,sk0_3),sk0_3) ),
introduced(split_symbol_definition) ).
fof(f604,plain,
( subset(union(sk0_4,sk0_3),sk0_3)
| ~ spl0_12 ),
inference(component_clause,[status(thm)],[f603]) ).
fof(f606,plain,
( subset(union(sk0_4,sk0_3),sk0_3)
| subset(union(sk0_4,sk0_3),sk0_3)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f203,f20]) ).
fof(f607,plain,
( spl0_12
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f606,f603,f76]) ).
fof(f635,plain,
( spl0_13
<=> equal_set(sk0_3,union(sk0_4,sk0_3)) ),
introduced(split_symbol_definition) ).
fof(f636,plain,
( equal_set(sk0_3,union(sk0_4,sk0_3))
| ~ spl0_13 ),
inference(component_clause,[status(thm)],[f635]) ).
fof(f638,plain,
( spl0_14
<=> subset(sk0_3,union(sk0_4,sk0_3)) ),
introduced(split_symbol_definition) ).
fof(f640,plain,
( ~ subset(sk0_3,union(sk0_4,sk0_3))
| spl0_14 ),
inference(component_clause,[status(thm)],[f638]) ).
fof(f641,plain,
( equal_set(sk0_3,union(sk0_4,sk0_3))
| ~ subset(sk0_3,union(sk0_4,sk0_3))
| ~ spl0_12 ),
inference(resolution,[status(thm)],[f604,f25]) ).
fof(f642,plain,
( spl0_13
| ~ spl0_14
| ~ spl0_12 ),
inference(split_clause,[status(thm)],[f641,f635,f638,f603]) ).
fof(f643,plain,
( $false
| spl0_14 ),
inference(forward_subsumption_resolution,[status(thm)],[f640,f168]) ).
fof(f644,plain,
spl0_14,
inference(contradiction_clause,[status(thm)],[f643]) ).
fof(f994,plain,
( spl0_19
<=> subset(union(sk0_3,sk0_4),sk0_3) ),
introduced(split_symbol_definition) ).
fof(f995,plain,
( subset(union(sk0_3,sk0_4),sk0_3)
| ~ spl0_19 ),
inference(component_clause,[status(thm)],[f994]) ).
fof(f997,plain,
( subset(union(sk0_3,sk0_4),sk0_3)
| subset(union(sk0_3,sk0_4),sk0_3)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f233,f20]) ).
fof(f998,plain,
( spl0_19
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f997,f994,f76]) ).
fof(f1016,plain,
( subset(union(sk0_4,sk0_3),sk0_3)
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f636,f24]) ).
fof(f1031,plain,
! [X0] :
( subset(X0,sk0_3)
| ~ member(sk0_0(sk0_3,X0),union(sk0_4,sk0_3))
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f1016,f105]) ).
fof(f1051,plain,
( equal_set(sk0_3,union(sk0_3,sk0_4))
| ~ subset(sk0_3,union(sk0_3,sk0_4))
| ~ spl0_19 ),
inference(resolution,[status(thm)],[f995,f25]) ).
fof(f1052,plain,
( spl0_0
| ~ spl0_5
| ~ spl0_19 ),
inference(split_clause,[status(thm)],[f1051,f73,f250,f994]) ).
fof(f1053,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f252,f179]) ).
fof(f1054,plain,
spl0_5,
inference(contradiction_clause,[status(thm)],[f1053]) ).
fof(f1082,plain,
! [X0] :
( subset(X0,sk0_3)
| ~ member(sk0_0(sk0_3,X0),sk0_4)
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f1031,f38]) ).
fof(f1105,plain,
! [X0] :
( subset(X0,sk0_3)
| ~ member(sk0_0(sk0_3,X0),sk0_4)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f249,f39]) ).
fof(f1501,plain,
( subset(union(sk0_4,sk0_4),sk0_3)
| subset(union(sk0_4,sk0_4),sk0_3)
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f1082,f91]) ).
fof(f1502,plain,
( spl0_4
| ~ spl0_13 ),
inference(split_clause,[status(thm)],[f1501,f197,f635]) ).
fof(f1526,plain,
( subset(sk0_4,sk0_3)
| subset(sk0_4,sk0_3)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f1105,f19]) ).
fof(f1527,plain,
( spl0_1
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f1526,f76,f73]) ).
fof(f1529,plain,
$false,
inference(sat_refutation,[status(thm)],[f79,f80,f542,f607,f642,f644,f998,f1052,f1054,f1502,f1527]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET693+4 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue May 30 10:24:08 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % Drodi V3.5.1
% 0.20/0.44 % Refutation found
% 0.20/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.46 % Elapsed time: 0.111052 seconds
% 0.20/0.46 % CPU time: 0.753954 seconds
% 0.20/0.46 % Memory used: 52.715 MB
%------------------------------------------------------------------------------