TSTP Solution File: SET694+4 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET694+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n013.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 0.18s 0.61s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 57 ( 10 unt; 0 def)
% Number of atoms : 137 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 136 ( 56 ~; 58 |; 12 &)
% ( 9 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 8 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 81 (; 77 !; 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(f3,axiom,
! [X,A] :
( member(X,power_set(A))
<=> subset(X,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] : subset(union(power_set(A),power_set(B)),power_set(union(A,B))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,B] : subset(union(power_set(A),power_set(B)),power_set(union(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(f26,plain,
! [X,A] :
( ( ~ member(X,power_set(A))
| subset(X,A) )
& ( member(X,power_set(A))
| ~ subset(X,A) ) ),
inference(NNF_transformation,[status(esa)],[f3]) ).
fof(f27,plain,
( ! [X,A] :
( ~ member(X,power_set(A))
| subset(X,A) )
& ! [X,A] :
( member(X,power_set(A))
| ~ subset(X,A) ) ),
inference(miniscoping,[status(esa)],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( ~ member(X0,power_set(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f27]) ).
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] : ~ subset(union(power_set(A),power_set(B)),power_set(union(A,B))),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f69,plain,
~ subset(union(power_set(sk0_3),power_set(sk0_4)),power_set(union(sk0_3,sk0_4))),
inference(skolemization,[status(esa)],[f68]) ).
fof(f70,plain,
~ subset(union(power_set(sk0_3),power_set(sk0_4)),power_set(union(sk0_3,sk0_4))),
inference(cnf_transformation,[status(esa)],[f69]) ).
fof(f115,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(f119,plain,
! [X0,X1,X2] :
( subset(X0,X1)
| ~ subset(X0,X2)
| member(sk0_0(X1,X0),X2) ),
inference(resolution,[status(thm)],[f19,f18]) ).
fof(f148,plain,
! [X0,X1,X2] :
( subset(X0,union(X1,X2))
| ~ member(sk0_0(union(X1,X2),X0),X2) ),
inference(resolution,[status(thm)],[f20,f39]) ).
fof(f149,plain,
! [X0,X1,X2] :
( subset(X0,union(X1,X2))
| ~ member(sk0_0(union(X1,X2),X0),X1) ),
inference(resolution,[status(thm)],[f20,f38]) ).
fof(f150,plain,
! [X0,X1] :
( subset(X0,power_set(X1))
| ~ subset(sk0_0(power_set(X1),X0),X1) ),
inference(resolution,[status(thm)],[f20,f29]) ).
fof(f195,plain,
( spl0_2
<=> member(sk0_0(power_set(union(sk0_3,sk0_4)),union(power_set(sk0_3),power_set(sk0_4))),power_set(sk0_3)) ),
introduced(split_symbol_definition) ).
fof(f196,plain,
( member(sk0_0(power_set(union(sk0_3,sk0_4)),union(power_set(sk0_3),power_set(sk0_4))),power_set(sk0_3))
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f195]) ).
fof(f198,plain,
( spl0_3
<=> member(sk0_0(power_set(union(sk0_3,sk0_4)),union(power_set(sk0_3),power_set(sk0_4))),power_set(sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f199,plain,
( member(sk0_0(power_set(union(sk0_3,sk0_4)),union(power_set(sk0_3),power_set(sk0_4))),power_set(sk0_4))
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f198]) ).
fof(f201,plain,
( member(sk0_0(power_set(union(sk0_3,sk0_4)),union(power_set(sk0_3),power_set(sk0_4))),power_set(sk0_3))
| member(sk0_0(power_set(union(sk0_3,sk0_4)),union(power_set(sk0_3),power_set(sk0_4))),power_set(sk0_4)) ),
inference(resolution,[status(thm)],[f115,f70]) ).
fof(f202,plain,
( spl0_2
| spl0_3 ),
inference(split_clause,[status(thm)],[f201,f195,f198]) ).
fof(f217,plain,
( subset(sk0_0(power_set(union(sk0_3,sk0_4)),union(power_set(sk0_3),power_set(sk0_4))),sk0_3)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f196,f28]) ).
fof(f299,plain,
( subset(sk0_0(power_set(union(sk0_3,sk0_4)),union(power_set(sk0_3),power_set(sk0_4))),sk0_4)
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f199,f28]) ).
fof(f492,plain,
~ subset(sk0_0(power_set(union(sk0_3,sk0_4)),union(power_set(sk0_3),power_set(sk0_4))),union(sk0_3,sk0_4)),
inference(resolution,[status(thm)],[f150,f70]) ).
fof(f502,plain,
~ member(sk0_0(union(sk0_3,sk0_4),sk0_0(power_set(union(sk0_3,sk0_4)),union(power_set(sk0_3),power_set(sk0_4)))),sk0_4),
inference(resolution,[status(thm)],[f148,f492]) ).
fof(f597,plain,
~ member(sk0_0(union(sk0_3,sk0_4),sk0_0(power_set(union(sk0_3,sk0_4)),union(power_set(sk0_3),power_set(sk0_4)))),sk0_3),
inference(resolution,[status(thm)],[f149,f492]) ).
fof(f1109,plain,
( spl0_59
<=> subset(sk0_0(power_set(union(sk0_3,sk0_4)),union(power_set(sk0_3),power_set(sk0_4))),union(sk0_3,sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f1110,plain,
( subset(sk0_0(power_set(union(sk0_3,sk0_4)),union(power_set(sk0_3),power_set(sk0_4))),union(sk0_3,sk0_4))
| ~ spl0_59 ),
inference(component_clause,[status(thm)],[f1109]) ).
fof(f1112,plain,
( spl0_60
<=> subset(sk0_0(power_set(union(sk0_3,sk0_4)),union(power_set(sk0_3),power_set(sk0_4))),sk0_4) ),
introduced(split_symbol_definition) ).
fof(f1114,plain,
( ~ subset(sk0_0(power_set(union(sk0_3,sk0_4)),union(power_set(sk0_3),power_set(sk0_4))),sk0_4)
| spl0_60 ),
inference(component_clause,[status(thm)],[f1112]) ).
fof(f1115,plain,
( subset(sk0_0(power_set(union(sk0_3,sk0_4)),union(power_set(sk0_3),power_set(sk0_4))),union(sk0_3,sk0_4))
| ~ subset(sk0_0(power_set(union(sk0_3,sk0_4)),union(power_set(sk0_3),power_set(sk0_4))),sk0_4) ),
inference(resolution,[status(thm)],[f502,f119]) ).
fof(f1116,plain,
( spl0_59
| ~ spl0_60 ),
inference(split_clause,[status(thm)],[f1115,f1109,f1112]) ).
fof(f1121,plain,
( $false
| ~ spl0_3
| spl0_60 ),
inference(forward_subsumption_resolution,[status(thm)],[f1114,f299]) ).
fof(f1122,plain,
( ~ spl0_3
| spl0_60 ),
inference(contradiction_clause,[status(thm)],[f1121]) ).
fof(f1123,plain,
( $false
| ~ spl0_59 ),
inference(forward_subsumption_resolution,[status(thm)],[f1110,f492]) ).
fof(f1124,plain,
~ spl0_59,
inference(contradiction_clause,[status(thm)],[f1123]) ).
fof(f1125,plain,
( spl0_61
<=> subset(sk0_0(power_set(union(sk0_3,sk0_4)),union(power_set(sk0_3),power_set(sk0_4))),sk0_3) ),
introduced(split_symbol_definition) ).
fof(f1127,plain,
( ~ subset(sk0_0(power_set(union(sk0_3,sk0_4)),union(power_set(sk0_3),power_set(sk0_4))),sk0_3)
| spl0_61 ),
inference(component_clause,[status(thm)],[f1125]) ).
fof(f1128,plain,
( subset(sk0_0(power_set(union(sk0_3,sk0_4)),union(power_set(sk0_3),power_set(sk0_4))),union(sk0_3,sk0_4))
| ~ subset(sk0_0(power_set(union(sk0_3,sk0_4)),union(power_set(sk0_3),power_set(sk0_4))),sk0_3) ),
inference(resolution,[status(thm)],[f597,f119]) ).
fof(f1129,plain,
( spl0_59
| ~ spl0_61 ),
inference(split_clause,[status(thm)],[f1128,f1109,f1125]) ).
fof(f1134,plain,
( $false
| ~ spl0_2
| spl0_61 ),
inference(forward_subsumption_resolution,[status(thm)],[f1127,f217]) ).
fof(f1135,plain,
( ~ spl0_2
| spl0_61 ),
inference(contradiction_clause,[status(thm)],[f1134]) ).
fof(f1136,plain,
$false,
inference(sat_refutation,[status(thm)],[f202,f1116,f1122,f1124,f1129,f1135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET694+4 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33 % Computer : n013.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 10:11:05 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % Drodi V3.5.1
% 0.18/0.61 % Refutation found
% 0.18/0.61 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.62 % Elapsed time: 0.283932 seconds
% 0.18/0.62 % CPU time: 2.149503 seconds
% 0.18/0.62 % Memory used: 65.663 MB
%------------------------------------------------------------------------------