TSTP Solution File: SET148+4 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET148+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n005.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 12:34:07 EDT 2023
% Result : Theorem 0.16s 0.33s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 9 unt; 0 def)
% Number of atoms : 91 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 96 ( 37 ~; 38 |; 16 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 74 (; 71 !; 3 ?)
% 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] : equal_set(intersection(A,A),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A] : equal_set(intersection(A,A),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(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(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] : ~ equal_set(intersection(A,A),A),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f69,plain,
~ equal_set(intersection(sk0_3,sk0_3),sk0_3),
inference(skolemization,[status(esa)],[f68]) ).
fof(f70,plain,
~ equal_set(intersection(sk0_3,sk0_3),sk0_3),
inference(cnf_transformation,[status(esa)],[f69]) ).
fof(f77,plain,
! [X0,X1,X2] :
( subset(intersection(X0,X1),X2)
| member(sk0_0(X2,intersection(X0,X1)),X1) ),
inference(resolution,[status(thm)],[f19,f33]) ).
fof(f105,plain,
! [X0,X1] :
( subset(intersection(X0,X1),X1)
| subset(intersection(X0,X1),X1) ),
inference(resolution,[status(thm)],[f20,f77]) ).
fof(f106,plain,
! [X0,X1] : subset(intersection(X0,X1),X1),
inference(duplicate_literals_removal,[status(esa)],[f105]) ).
fof(f110,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(f157,plain,
! [X0,X1] :
( subset(X0,intersection(X1,X0))
| ~ member(sk0_0(intersection(X1,X0),X0),X1)
| subset(X0,intersection(X1,X0)) ),
inference(resolution,[status(thm)],[f110,f19]) ).
fof(f158,plain,
! [X0,X1] :
( subset(X0,intersection(X1,X0))
| ~ member(sk0_0(intersection(X1,X0),X0),X1) ),
inference(duplicate_literals_removal,[status(esa)],[f157]) ).
fof(f232,plain,
! [X0] :
( subset(X0,intersection(X0,X0))
| subset(X0,intersection(X0,X0)) ),
inference(resolution,[status(thm)],[f158,f19]) ).
fof(f233,plain,
! [X0] : subset(X0,intersection(X0,X0)),
inference(duplicate_literals_removal,[status(esa)],[f232]) ).
fof(f245,plain,
! [X0] :
( equal_set(intersection(X0,X0),X0)
| ~ subset(intersection(X0,X0),X0) ),
inference(resolution,[status(thm)],[f233,f25]) ).
fof(f246,plain,
! [X0] : equal_set(intersection(X0,X0),X0),
inference(forward_subsumption_resolution,[status(thm)],[f245,f106]) ).
fof(f249,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f70,f246]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SET148+4 : TPTP v8.1.2. Released v2.2.0.
% 0.05/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31 % Computer : n005.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue May 30 10:13:06 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.16/0.31 % Drodi V3.5.1
% 0.16/0.33 % Refutation found
% 0.16/0.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.36 % Elapsed time: 0.049996 seconds
% 0.16/0.36 % CPU time: 0.049065 seconds
% 0.16/0.36 % Memory used: 7.835 MB
%------------------------------------------------------------------------------