TSTP Solution File: SET143+4 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET143+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n008.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 20:39:15 EDT 2024
% Result : Theorem 2.21s 0.71s
% Output : CNFRefutation 2.21s
% 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 : 184 ( 65 ~; 88 |; 16 &)
% ( 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/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,C] : equal_set(intersection(intersection(A,B),C),intersection(A,intersection(B,C))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,B,C] : equal_set(intersection(intersection(A,B),C),intersection(A,intersection(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(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,C] : ~ equal_set(intersection(intersection(A,B),C),intersection(A,intersection(B,C))),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f69,plain,
~ equal_set(intersection(intersection(sk0_3,sk0_4),sk0_5),intersection(sk0_3,intersection(sk0_4,sk0_5))),
inference(skolemization,[status(esa)],[f68]) ).
fof(f70,plain,
~ equal_set(intersection(intersection(sk0_3,sk0_4),sk0_5),intersection(sk0_3,intersection(sk0_4,sk0_5))),
inference(cnf_transformation,[status(esa)],[f69]) ).
fof(f71,plain,
( spl0_0
<=> subset(intersection(intersection(sk0_3,sk0_4),sk0_5),intersection(sk0_3,intersection(sk0_4,sk0_5))) ),
introduced(split_symbol_definition) ).
fof(f73,plain,
( ~ subset(intersection(intersection(sk0_3,sk0_4),sk0_5),intersection(sk0_3,intersection(sk0_4,sk0_5)))
| spl0_0 ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f74,plain,
( spl0_1
<=> subset(intersection(sk0_3,intersection(sk0_4,sk0_5)),intersection(intersection(sk0_3,sk0_4),sk0_5)) ),
introduced(split_symbol_definition) ).
fof(f76,plain,
( ~ subset(intersection(sk0_3,intersection(sk0_4,sk0_5)),intersection(intersection(sk0_3,sk0_4),sk0_5))
| spl0_1 ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f77,plain,
( ~ subset(intersection(intersection(sk0_3,sk0_4),sk0_5),intersection(sk0_3,intersection(sk0_4,sk0_5)))
| ~ subset(intersection(sk0_3,intersection(sk0_4,sk0_5)),intersection(intersection(sk0_3,sk0_4),sk0_5)) ),
inference(resolution,[status(thm)],[f25,f70]) ).
fof(f78,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f77,f71,f74]) ).
fof(f94,plain,
! [X0,X1,X2] :
( subset(intersection(X0,X1),X2)
| member(sk0_0(X2,intersection(X0,X1)),X1) ),
inference(resolution,[status(thm)],[f19,f33]) ).
fof(f95,plain,
! [X0,X1,X2] :
( subset(intersection(X0,X1),X2)
| member(sk0_0(X2,intersection(X0,X1)),X0) ),
inference(resolution,[status(thm)],[f19,f32]) ).
fof(f178,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(f188,plain,
( member(sk0_0(intersection(sk0_3,intersection(sk0_4,sk0_5)),intersection(intersection(sk0_3,sk0_4),sk0_5)),intersection(sk0_3,sk0_4))
| spl0_0 ),
inference(resolution,[status(thm)],[f73,f95]) ).
fof(f189,plain,
( member(sk0_0(intersection(sk0_3,intersection(sk0_4,sk0_5)),intersection(intersection(sk0_3,sk0_4),sk0_5)),sk0_5)
| spl0_0 ),
inference(resolution,[status(thm)],[f73,f94]) ).
fof(f194,plain,
( member(sk0_0(intersection(sk0_3,intersection(sk0_4,sk0_5)),intersection(intersection(sk0_3,sk0_4),sk0_5)),sk0_4)
| spl0_0 ),
inference(resolution,[status(thm)],[f188,f33]) ).
fof(f195,plain,
( member(sk0_0(intersection(sk0_3,intersection(sk0_4,sk0_5)),intersection(intersection(sk0_3,sk0_4),sk0_5)),sk0_3)
| spl0_0 ),
inference(resolution,[status(thm)],[f188,f32]) ).
fof(f224,plain,
( member(sk0_0(intersection(intersection(sk0_3,sk0_4),sk0_5),intersection(sk0_3,intersection(sk0_4,sk0_5))),sk0_3)
| spl0_1 ),
inference(resolution,[status(thm)],[f76,f95]) ).
fof(f225,plain,
( member(sk0_0(intersection(intersection(sk0_3,sk0_4),sk0_5),intersection(sk0_3,intersection(sk0_4,sk0_5))),intersection(sk0_4,sk0_5))
| spl0_1 ),
inference(resolution,[status(thm)],[f76,f94]) ).
fof(f230,plain,
( member(sk0_0(intersection(intersection(sk0_3,sk0_4),sk0_5),intersection(sk0_3,intersection(sk0_4,sk0_5))),sk0_5)
| spl0_1 ),
inference(resolution,[status(thm)],[f225,f33]) ).
fof(f231,plain,
( member(sk0_0(intersection(intersection(sk0_3,sk0_4),sk0_5),intersection(sk0_3,intersection(sk0_4,sk0_5))),sk0_4)
| spl0_1 ),
inference(resolution,[status(thm)],[f225,f32]) ).
fof(f663,plain,
( spl0_9
<=> member(sk0_0(intersection(sk0_3,intersection(sk0_4,sk0_5)),intersection(intersection(sk0_3,sk0_4),sk0_5)),sk0_3) ),
introduced(split_symbol_definition) ).
fof(f665,plain,
( ~ member(sk0_0(intersection(sk0_3,intersection(sk0_4,sk0_5)),intersection(intersection(sk0_3,sk0_4),sk0_5)),sk0_3)
| spl0_9 ),
inference(component_clause,[status(thm)],[f663]) ).
fof(f666,plain,
( spl0_10
<=> member(sk0_0(intersection(sk0_3,intersection(sk0_4,sk0_5)),intersection(intersection(sk0_3,sk0_4),sk0_5)),intersection(sk0_4,sk0_5)) ),
introduced(split_symbol_definition) ).
fof(f668,plain,
( ~ member(sk0_0(intersection(sk0_3,intersection(sk0_4,sk0_5)),intersection(intersection(sk0_3,sk0_4),sk0_5)),intersection(sk0_4,sk0_5))
| spl0_10 ),
inference(component_clause,[status(thm)],[f666]) ).
fof(f669,plain,
( ~ member(sk0_0(intersection(sk0_3,intersection(sk0_4,sk0_5)),intersection(intersection(sk0_3,sk0_4),sk0_5)),sk0_3)
| ~ member(sk0_0(intersection(sk0_3,intersection(sk0_4,sk0_5)),intersection(intersection(sk0_3,sk0_4),sk0_5)),intersection(sk0_4,sk0_5))
| spl0_0 ),
inference(resolution,[status(thm)],[f73,f178]) ).
fof(f670,plain,
( ~ spl0_9
| ~ spl0_10
| spl0_0 ),
inference(split_clause,[status(thm)],[f669,f663,f666,f71]) ).
fof(f671,plain,
( $false
| spl0_0
| spl0_9 ),
inference(forward_subsumption_resolution,[status(thm)],[f665,f195]) ).
fof(f672,plain,
( spl0_0
| spl0_9 ),
inference(contradiction_clause,[status(thm)],[f671]) ).
fof(f682,plain,
( spl0_11
<=> member(sk0_0(intersection(intersection(sk0_3,sk0_4),sk0_5),intersection(sk0_3,intersection(sk0_4,sk0_5))),intersection(sk0_3,sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f684,plain,
( ~ member(sk0_0(intersection(intersection(sk0_3,sk0_4),sk0_5),intersection(sk0_3,intersection(sk0_4,sk0_5))),intersection(sk0_3,sk0_4))
| spl0_11 ),
inference(component_clause,[status(thm)],[f682]) ).
fof(f685,plain,
( spl0_12
<=> member(sk0_0(intersection(intersection(sk0_3,sk0_4),sk0_5),intersection(sk0_3,intersection(sk0_4,sk0_5))),sk0_5) ),
introduced(split_symbol_definition) ).
fof(f687,plain,
( ~ member(sk0_0(intersection(intersection(sk0_3,sk0_4),sk0_5),intersection(sk0_3,intersection(sk0_4,sk0_5))),sk0_5)
| spl0_12 ),
inference(component_clause,[status(thm)],[f685]) ).
fof(f688,plain,
( ~ member(sk0_0(intersection(intersection(sk0_3,sk0_4),sk0_5),intersection(sk0_3,intersection(sk0_4,sk0_5))),intersection(sk0_3,sk0_4))
| ~ member(sk0_0(intersection(intersection(sk0_3,sk0_4),sk0_5),intersection(sk0_3,intersection(sk0_4,sk0_5))),sk0_5)
| spl0_1 ),
inference(resolution,[status(thm)],[f76,f178]) ).
fof(f689,plain,
( ~ spl0_11
| ~ spl0_12
| spl0_1 ),
inference(split_clause,[status(thm)],[f688,f682,f685,f74]) ).
fof(f701,plain,
( spl0_13
<=> member(sk0_0(intersection(sk0_3,intersection(sk0_4,sk0_5)),intersection(intersection(sk0_3,sk0_4),sk0_5)),sk0_4) ),
introduced(split_symbol_definition) ).
fof(f703,plain,
( ~ member(sk0_0(intersection(sk0_3,intersection(sk0_4,sk0_5)),intersection(intersection(sk0_3,sk0_4),sk0_5)),sk0_4)
| spl0_13 ),
inference(component_clause,[status(thm)],[f701]) ).
fof(f704,plain,
( spl0_14
<=> member(sk0_0(intersection(sk0_3,intersection(sk0_4,sk0_5)),intersection(intersection(sk0_3,sk0_4),sk0_5)),sk0_5) ),
introduced(split_symbol_definition) ).
fof(f706,plain,
( ~ member(sk0_0(intersection(sk0_3,intersection(sk0_4,sk0_5)),intersection(intersection(sk0_3,sk0_4),sk0_5)),sk0_5)
| spl0_14 ),
inference(component_clause,[status(thm)],[f704]) ).
fof(f707,plain,
( ~ member(sk0_0(intersection(sk0_3,intersection(sk0_4,sk0_5)),intersection(intersection(sk0_3,sk0_4),sk0_5)),sk0_4)
| ~ member(sk0_0(intersection(sk0_3,intersection(sk0_4,sk0_5)),intersection(intersection(sk0_3,sk0_4),sk0_5)),sk0_5)
| spl0_10 ),
inference(resolution,[status(thm)],[f668,f34]) ).
fof(f708,plain,
( ~ spl0_13
| ~ spl0_14
| spl0_10 ),
inference(split_clause,[status(thm)],[f707,f701,f704,f666]) ).
fof(f711,plain,
( $false
| spl0_0
| spl0_13 ),
inference(forward_subsumption_resolution,[status(thm)],[f703,f194]) ).
fof(f712,plain,
( spl0_0
| spl0_13 ),
inference(contradiction_clause,[status(thm)],[f711]) ).
fof(f724,plain,
( $false
| spl0_14
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f189,f706]) ).
fof(f725,plain,
( spl0_14
| spl0_0 ),
inference(contradiction_clause,[status(thm)],[f724]) ).
fof(f726,plain,
( $false
| spl0_12
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f230,f687]) ).
fof(f727,plain,
( spl0_12
| spl0_1 ),
inference(contradiction_clause,[status(thm)],[f726]) ).
fof(f773,plain,
( spl0_17
<=> member(sk0_0(intersection(intersection(sk0_3,sk0_4),sk0_5),intersection(sk0_3,intersection(sk0_4,sk0_5))),sk0_3) ),
introduced(split_symbol_definition) ).
fof(f775,plain,
( ~ member(sk0_0(intersection(intersection(sk0_3,sk0_4),sk0_5),intersection(sk0_3,intersection(sk0_4,sk0_5))),sk0_3)
| spl0_17 ),
inference(component_clause,[status(thm)],[f773]) ).
fof(f776,plain,
( spl0_18
<=> member(sk0_0(intersection(intersection(sk0_3,sk0_4),sk0_5),intersection(sk0_3,intersection(sk0_4,sk0_5))),sk0_4) ),
introduced(split_symbol_definition) ).
fof(f778,plain,
( ~ member(sk0_0(intersection(intersection(sk0_3,sk0_4),sk0_5),intersection(sk0_3,intersection(sk0_4,sk0_5))),sk0_4)
| spl0_18 ),
inference(component_clause,[status(thm)],[f776]) ).
fof(f779,plain,
( ~ member(sk0_0(intersection(intersection(sk0_3,sk0_4),sk0_5),intersection(sk0_3,intersection(sk0_4,sk0_5))),sk0_3)
| ~ member(sk0_0(intersection(intersection(sk0_3,sk0_4),sk0_5),intersection(sk0_3,intersection(sk0_4,sk0_5))),sk0_4)
| spl0_11 ),
inference(resolution,[status(thm)],[f684,f34]) ).
fof(f780,plain,
( ~ spl0_17
| ~ spl0_18
| spl0_11 ),
inference(split_clause,[status(thm)],[f779,f773,f776,f682]) ).
fof(f783,plain,
( $false
| spl0_1
| spl0_17 ),
inference(forward_subsumption_resolution,[status(thm)],[f775,f224]) ).
fof(f784,plain,
( spl0_1
| spl0_17 ),
inference(contradiction_clause,[status(thm)],[f783]) ).
fof(f785,plain,
( $false
| spl0_1
| spl0_18 ),
inference(forward_subsumption_resolution,[status(thm)],[f778,f231]) ).
fof(f786,plain,
( spl0_1
| spl0_18 ),
inference(contradiction_clause,[status(thm)],[f785]) ).
fof(f787,plain,
$false,
inference(sat_refutation,[status(thm)],[f78,f670,f672,f689,f708,f712,f725,f727,f780,f784,f786]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET143+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 : n008.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 : Mon Apr 29 21:30:12 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % Drodi V3.6.0
% 2.21/0.71 % Refutation found
% 2.21/0.71 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.21/0.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.21/0.72 % Elapsed time: 0.375518 seconds
% 2.21/0.72 % CPU time: 2.886179 seconds
% 2.21/0.72 % Total memory used: 88.617 MB
% 2.21/0.72 % Net memory used: 86.967 MB
%------------------------------------------------------------------------------