TSTP Solution File: SET143+3 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET143+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n019.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 12:34:06 EDT 2023
% Result : Theorem 57.81s 7.66s
% Output : CNFRefutation 58.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 79 ( 8 unt; 0 def)
% Number of atoms : 201 ( 13 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 189 ( 67 ~; 92 |; 16 &)
% ( 13 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 13 ( 11 usr; 10 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 90 (; 85 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,B)
& member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,C] :
( B = C
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
! [B,C,D] : intersection(intersection(B,C),D) = intersection(B,intersection(C,D)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [B,C,D] : intersection(intersection(B,C),D) = intersection(B,intersection(C,D)),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
! [B,C,D] :
( ( ~ member(D,intersection(B,C))
| ( member(D,B)
& member(D,C) ) )
& ( member(D,intersection(B,C))
| ~ member(D,B)
| ~ member(D,C) ) ),
inference(NNF_transformation,[status(esa)],[f1]) ).
fof(f10,plain,
( ! [B,C,D] :
( ~ member(D,intersection(B,C))
| ( member(D,B)
& member(D,C) ) )
& ! [B,C,D] :
( member(D,intersection(B,C))
| ~ member(D,B)
| ~ member(D,C) ) ),
inference(miniscoping,[status(esa)],[f9]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f12,plain,
! [X0,X1,X2] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f13,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f14,plain,
! [B,C] :
( ( B != C
| ( subset(B,C)
& subset(C,B) ) )
& ( B = C
| ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(NNF_transformation,[status(esa)],[f2]) ).
fof(f15,plain,
( ! [B,C] :
( B != C
| ( subset(B,C)
& subset(C,B) ) )
& ! [B,C] :
( B = C
| ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(miniscoping,[status(esa)],[f14]) ).
fof(f18,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f19,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f20,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( ~ member(D,B)
| member(D,C) ) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f21,plain,
! [B,C] :
( ( ~ subset(B,C)
| ! [D] :
( ~ member(D,B)
| member(D,C) ) )
& ( subset(B,C)
| ? [D] :
( member(D,B)
& ~ member(D,C) ) ) ),
inference(NNF_transformation,[status(esa)],[f20]) ).
fof(f22,plain,
( ! [B,C] :
( ~ subset(B,C)
| ! [D] :
( ~ member(D,B)
| member(D,C) ) )
& ! [B,C] :
( subset(B,C)
| ? [D] :
( member(D,B)
& ~ member(D,C) ) ) ),
inference(miniscoping,[status(esa)],[f21]) ).
fof(f23,plain,
( ! [B,C] :
( ~ subset(B,C)
| ! [D] :
( ~ member(D,B)
| member(D,C) ) )
& ! [B,C] :
( subset(B,C)
| ( member(sk0_0(C,B),B)
& ~ member(sk0_0(C,B),C) ) ) ),
inference(skolemization,[status(esa)],[f22]) ).
fof(f25,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f26,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f35,plain,
? [B,C,D] : intersection(intersection(B,C),D) != intersection(B,intersection(C,D)),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f36,plain,
intersection(intersection(sk0_2,sk0_3),sk0_4) != intersection(sk0_2,intersection(sk0_3,sk0_4)),
inference(skolemization,[status(esa)],[f35]) ).
fof(f37,plain,
intersection(intersection(sk0_2,sk0_3),sk0_4) != intersection(sk0_2,intersection(sk0_3,sk0_4)),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f48,plain,
! [X0,X1,X2] :
( subset(intersection(X0,X1),X2)
| member(sk0_0(X2,intersection(X0,X1)),X1) ),
inference(resolution,[status(thm)],[f25,f12]) ).
fof(f50,plain,
! [X0,X1,X2,X3] :
( subset(intersection(X0,intersection(X1,X2)),X3)
| member(sk0_0(X3,intersection(X0,intersection(X1,X2))),X2) ),
inference(resolution,[status(thm)],[f48,f12]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( subset(intersection(X0,intersection(X1,X2)),X3)
| member(sk0_0(X3,intersection(X0,intersection(X1,X2))),X1) ),
inference(resolution,[status(thm)],[f48,f11]) ).
fof(f52,plain,
! [X0,X1,X2] :
( subset(intersection(X0,X1),X2)
| member(sk0_0(X2,intersection(X1,X0)),X1) ),
inference(paramodulation,[status(thm)],[f19,f48]) ).
fof(f109,plain,
( spl0_8
<=> subset(intersection(sk0_4,intersection(sk0_2,sk0_3)),intersection(sk0_2,intersection(sk0_3,sk0_4))) ),
introduced(split_symbol_definition) ).
fof(f111,plain,
( ~ subset(intersection(sk0_4,intersection(sk0_2,sk0_3)),intersection(sk0_2,intersection(sk0_3,sk0_4)))
| spl0_8 ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f117,plain,
( spl0_10
<=> subset(intersection(intersection(sk0_2,sk0_3),sk0_4),intersection(sk0_2,intersection(sk0_3,sk0_4))) ),
introduced(split_symbol_definition) ).
fof(f119,plain,
( ~ subset(intersection(intersection(sk0_2,sk0_3),sk0_4),intersection(sk0_2,intersection(sk0_3,sk0_4)))
| spl0_10 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,plain,
( spl0_11
<=> subset(intersection(sk0_2,intersection(sk0_3,sk0_4)),intersection(intersection(sk0_2,sk0_3),sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f122,plain,
( ~ subset(intersection(sk0_2,intersection(sk0_3,sk0_4)),intersection(intersection(sk0_2,sk0_3),sk0_4))
| spl0_11 ),
inference(component_clause,[status(thm)],[f120]) ).
fof(f123,plain,
( ~ subset(intersection(intersection(sk0_2,sk0_3),sk0_4),intersection(sk0_2,intersection(sk0_3,sk0_4)))
| ~ subset(intersection(sk0_2,intersection(sk0_3,sk0_4)),intersection(intersection(sk0_2,sk0_3),sk0_4)) ),
inference(resolution,[status(thm)],[f18,f37]) ).
fof(f124,plain,
( ~ spl0_10
| ~ spl0_11 ),
inference(split_clause,[status(thm)],[f123,f117,f120]) ).
fof(f129,plain,
( ~ subset(intersection(sk0_4,intersection(sk0_2,sk0_3)),intersection(sk0_2,intersection(sk0_3,sk0_4)))
| spl0_10 ),
inference(forward_demodulation,[status(thm)],[f19,f119]) ).
fof(f129_001,plain,
( ~ subset(intersection(sk0_4,intersection(sk0_2,sk0_3)),intersection(sk0_2,intersection(sk0_3,sk0_4)))
| spl0_10 ),
inference(forward_demodulation,[status(thm)],[f19,f119]) ).
fof(f141,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)],[f26,f13]) ).
fof(f269,plain,
! [X0,X1,X2,X3] :
( subset(X0,intersection(X1,intersection(X2,X3)))
| ~ member(sk0_0(intersection(X1,intersection(X2,X3)),X0),X1)
| ~ member(sk0_0(intersection(X1,intersection(X2,X3)),X0),X2)
| ~ member(sk0_0(intersection(X1,intersection(X2,X3)),X0),X3) ),
inference(resolution,[status(thm)],[f141,f13]) ).
fof(f324,plain,
( ~ subset(intersection(sk0_2,intersection(sk0_3,sk0_4)),intersection(sk0_4,intersection(sk0_2,sk0_3)))
| spl0_11 ),
inference(forward_demodulation,[status(thm)],[f19,f122]) ).
fof(f3596,plain,
( spl0_92
<=> member(sk0_0(intersection(sk0_2,intersection(sk0_3,sk0_4)),intersection(sk0_4,intersection(sk0_2,sk0_3))),sk0_2) ),
introduced(split_symbol_definition) ).
fof(f3598,plain,
( ~ member(sk0_0(intersection(sk0_2,intersection(sk0_3,sk0_4)),intersection(sk0_4,intersection(sk0_2,sk0_3))),sk0_2)
| spl0_92 ),
inference(component_clause,[status(thm)],[f3596]) ).
fof(f3599,plain,
( spl0_93
<=> member(sk0_0(intersection(sk0_2,intersection(sk0_3,sk0_4)),intersection(sk0_4,intersection(sk0_2,sk0_3))),sk0_3) ),
introduced(split_symbol_definition) ).
fof(f3601,plain,
( ~ member(sk0_0(intersection(sk0_2,intersection(sk0_3,sk0_4)),intersection(sk0_4,intersection(sk0_2,sk0_3))),sk0_3)
| spl0_93 ),
inference(component_clause,[status(thm)],[f3599]) ).
fof(f3602,plain,
( spl0_94
<=> member(sk0_0(intersection(sk0_2,intersection(sk0_3,sk0_4)),intersection(sk0_4,intersection(sk0_2,sk0_3))),sk0_4) ),
introduced(split_symbol_definition) ).
fof(f3604,plain,
( ~ member(sk0_0(intersection(sk0_2,intersection(sk0_3,sk0_4)),intersection(sk0_4,intersection(sk0_2,sk0_3))),sk0_4)
| spl0_94 ),
inference(component_clause,[status(thm)],[f3602]) ).
fof(f3605,plain,
( ~ member(sk0_0(intersection(sk0_2,intersection(sk0_3,sk0_4)),intersection(sk0_4,intersection(sk0_2,sk0_3))),sk0_2)
| ~ member(sk0_0(intersection(sk0_2,intersection(sk0_3,sk0_4)),intersection(sk0_4,intersection(sk0_2,sk0_3))),sk0_3)
| ~ member(sk0_0(intersection(sk0_2,intersection(sk0_3,sk0_4)),intersection(sk0_4,intersection(sk0_2,sk0_3))),sk0_4)
| spl0_10 ),
inference(resolution,[status(thm)],[f269,f129]) ).
fof(f3606,plain,
( ~ spl0_92
| ~ spl0_93
| ~ spl0_94
| spl0_10 ),
inference(split_clause,[status(thm)],[f3605,f3596,f3599,f3602,f117]) ).
fof(f4388,plain,
( subset(intersection(intersection(sk0_2,sk0_3),sk0_4),intersection(sk0_2,intersection(sk0_3,sk0_4)))
| spl0_94 ),
inference(resolution,[status(thm)],[f3604,f52]) ).
fof(f4389,plain,
( subset(intersection(sk0_4,intersection(sk0_2,sk0_3)),intersection(sk0_2,intersection(sk0_3,sk0_4)))
| spl0_94 ),
inference(forward_demodulation,[status(thm)],[f19,f4388]) ).
fof(f4390,plain,
( $false
| spl0_10
| spl0_94 ),
inference(forward_subsumption_resolution,[status(thm)],[f4389,f129]) ).
fof(f4391,plain,
( spl0_10
| spl0_94 ),
inference(contradiction_clause,[status(thm)],[f4390]) ).
fof(f7285,plain,
( subset(intersection(sk0_4,intersection(sk0_2,sk0_3)),intersection(sk0_2,intersection(sk0_3,sk0_4)))
| spl0_93 ),
inference(resolution,[status(thm)],[f3601,f50]) ).
fof(f7286,plain,
( $false
| spl0_8
| spl0_93 ),
inference(forward_subsumption_resolution,[status(thm)],[f7285,f111]) ).
fof(f7287,plain,
( spl0_8
| spl0_93 ),
inference(contradiction_clause,[status(thm)],[f7286]) ).
fof(f7425,plain,
( subset(intersection(sk0_4,intersection(sk0_2,sk0_3)),intersection(sk0_2,intersection(sk0_3,sk0_4)))
| spl0_92 ),
inference(resolution,[status(thm)],[f3598,f51]) ).
fof(f7426,plain,
( $false
| spl0_8
| spl0_92 ),
inference(forward_subsumption_resolution,[status(thm)],[f7425,f111]) ).
fof(f7427,plain,
( spl0_8
| spl0_92 ),
inference(contradiction_clause,[status(thm)],[f7426]) ).
fof(f7468,plain,
( spl0_112
<=> member(sk0_0(intersection(sk0_4,intersection(sk0_2,sk0_3)),intersection(sk0_2,intersection(sk0_3,sk0_4))),sk0_4) ),
introduced(split_symbol_definition) ).
fof(f7470,plain,
( ~ member(sk0_0(intersection(sk0_4,intersection(sk0_2,sk0_3)),intersection(sk0_2,intersection(sk0_3,sk0_4))),sk0_4)
| spl0_112 ),
inference(component_clause,[status(thm)],[f7468]) ).
fof(f7471,plain,
( spl0_113
<=> member(sk0_0(intersection(sk0_4,intersection(sk0_2,sk0_3)),intersection(sk0_2,intersection(sk0_3,sk0_4))),sk0_2) ),
introduced(split_symbol_definition) ).
fof(f7473,plain,
( ~ member(sk0_0(intersection(sk0_4,intersection(sk0_2,sk0_3)),intersection(sk0_2,intersection(sk0_3,sk0_4))),sk0_2)
| spl0_113 ),
inference(component_clause,[status(thm)],[f7471]) ).
fof(f7474,plain,
( spl0_114
<=> member(sk0_0(intersection(sk0_4,intersection(sk0_2,sk0_3)),intersection(sk0_2,intersection(sk0_3,sk0_4))),sk0_3) ),
introduced(split_symbol_definition) ).
fof(f7476,plain,
( ~ member(sk0_0(intersection(sk0_4,intersection(sk0_2,sk0_3)),intersection(sk0_2,intersection(sk0_3,sk0_4))),sk0_3)
| spl0_114 ),
inference(component_clause,[status(thm)],[f7474]) ).
fof(f7477,plain,
( ~ member(sk0_0(intersection(sk0_4,intersection(sk0_2,sk0_3)),intersection(sk0_2,intersection(sk0_3,sk0_4))),sk0_4)
| ~ member(sk0_0(intersection(sk0_4,intersection(sk0_2,sk0_3)),intersection(sk0_2,intersection(sk0_3,sk0_4))),sk0_2)
| ~ member(sk0_0(intersection(sk0_4,intersection(sk0_2,sk0_3)),intersection(sk0_2,intersection(sk0_3,sk0_4))),sk0_3)
| spl0_11 ),
inference(resolution,[status(thm)],[f324,f269]) ).
fof(f7478,plain,
( ~ spl0_112
| ~ spl0_113
| ~ spl0_114
| spl0_11 ),
inference(split_clause,[status(thm)],[f7477,f7468,f7471,f7474,f120]) ).
fof(f7588,plain,
( subset(intersection(sk0_2,intersection(sk0_3,sk0_4)),intersection(sk0_4,intersection(sk0_2,sk0_3)))
| spl0_114 ),
inference(resolution,[status(thm)],[f7476,f51]) ).
fof(f7589,plain,
( $false
| spl0_11
| spl0_114 ),
inference(forward_subsumption_resolution,[status(thm)],[f7588,f324]) ).
fof(f7590,plain,
( spl0_11
| spl0_114 ),
inference(contradiction_clause,[status(thm)],[f7589]) ).
fof(f7808,plain,
( ~ spl0_8
| spl0_10 ),
inference(split_clause,[status(thm)],[f129,f109,f117]) ).
fof(f8104,plain,
( subset(intersection(intersection(sk0_3,sk0_4),sk0_2),intersection(sk0_4,intersection(sk0_2,sk0_3)))
| spl0_113 ),
inference(resolution,[status(thm)],[f7473,f52]) ).
fof(f8105,plain,
( subset(intersection(sk0_2,intersection(sk0_3,sk0_4)),intersection(sk0_4,intersection(sk0_2,sk0_3)))
| spl0_113 ),
inference(forward_demodulation,[status(thm)],[f19,f8104]) ).
fof(f8106,plain,
( $false
| spl0_11
| spl0_113 ),
inference(forward_subsumption_resolution,[status(thm)],[f8105,f324]) ).
fof(f8107,plain,
( spl0_11
| spl0_113 ),
inference(contradiction_clause,[status(thm)],[f8106]) ).
fof(f12151,plain,
( subset(intersection(sk0_2,intersection(sk0_3,sk0_4)),intersection(sk0_4,intersection(sk0_2,sk0_3)))
| spl0_112 ),
inference(resolution,[status(thm)],[f7470,f50]) ).
fof(f12152,plain,
( $false
| spl0_11
| spl0_112 ),
inference(forward_subsumption_resolution,[status(thm)],[f12151,f324]) ).
fof(f12153,plain,
( spl0_11
| spl0_112 ),
inference(contradiction_clause,[status(thm)],[f12152]) ).
fof(f12154,plain,
$false,
inference(sat_refutation,[status(thm)],[f124,f3606,f4391,f7287,f7427,f7478,f7590,f7808,f8107,f12153]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11 % Problem : SET143+3 : TPTP v8.1.2. Released v2.2.0.
% 0.05/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue May 30 10:21:25 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % Drodi V3.5.1
% 57.81/7.66 % Refutation found
% 57.81/7.66 % SZS status Theorem for theBenchmark: Theorem is valid
% 57.81/7.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 58.46/7.75 % Elapsed time: 7.402497 seconds
% 58.46/7.75 % CPU time: 58.685065 seconds
% 58.46/7.75 % Memory used: 512.884 MB
%------------------------------------------------------------------------------