TSTP Solution File: SET696+4 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET696+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n027.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 20:40:12 EDT 2024
% Result : Theorem 0.20s 0.43s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 7 unt; 0 def)
% Number of atoms : 105 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 113 ( 43 ~; 39 |; 23 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 94 ( 90 !; 4 ?)
% 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(f6,axiom,
! [X] : ~ member(X,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [B,A,E] :
( member(B,difference(E,A))
<=> ( member(B,E)
& ~ member(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,E] :
( subset(A,E)
=> equal_set(intersection(difference(E,A),A),empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,E] :
( subset(A,E)
=> equal_set(intersection(difference(E,A),A),empty_set) ),
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(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(f40,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f41,plain,
! [B,A,E] :
( ( ~ member(B,difference(E,A))
| ( member(B,E)
& ~ member(B,A) ) )
& ( member(B,difference(E,A))
| ~ member(B,E)
| member(B,A) ) ),
inference(NNF_transformation,[status(esa)],[f7]) ).
fof(f42,plain,
( ! [B,A,E] :
( ~ member(B,difference(E,A))
| ( member(B,E)
& ~ member(B,A) ) )
& ! [B,A,E] :
( member(B,difference(E,A))
| ~ member(B,E)
| member(B,A) ) ),
inference(miniscoping,[status(esa)],[f41]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ member(X0,difference(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f68,plain,
? [A,E] :
( subset(A,E)
& ~ equal_set(intersection(difference(E,A),A),empty_set) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f69,plain,
( subset(sk0_3,sk0_4)
& ~ equal_set(intersection(difference(sk0_4,sk0_3),sk0_3),empty_set) ),
inference(skolemization,[status(esa)],[f68]) ).
fof(f71,plain,
~ equal_set(intersection(difference(sk0_4,sk0_3),sk0_3),empty_set),
inference(cnf_transformation,[status(esa)],[f69]) ).
fof(f87,plain,
! [X0,X1,X2] :
( subset(intersection(X0,X1),X2)
| member(sk0_0(X2,intersection(X0,X1)),X1) ),
inference(resolution,[status(thm)],[f19,f33]) ).
fof(f88,plain,
! [X0,X1,X2] :
( subset(intersection(X0,X1),X2)
| member(sk0_0(X2,intersection(X0,X1)),X0) ),
inference(resolution,[status(thm)],[f19,f32]) ).
fof(f89,plain,
! [X0] : subset(empty_set,X0),
inference(resolution,[status(thm)],[f19,f40]) ).
fof(f93,plain,
! [X0] :
( equal_set(X0,empty_set)
| ~ subset(X0,empty_set) ),
inference(resolution,[status(thm)],[f89,f25]) ).
fof(f156,plain,
! [X0,X1,X2,X3] :
( subset(intersection(difference(X0,X1),X2),X3)
| ~ member(sk0_0(X3,intersection(difference(X0,X1),X2)),X1) ),
inference(resolution,[status(thm)],[f88,f44]) ).
fof(f182,plain,
! [X0,X1,X2] :
( subset(intersection(difference(X0,X1),X1),X2)
| subset(intersection(difference(X0,X1),X1),X2) ),
inference(resolution,[status(thm)],[f156,f87]) ).
fof(f183,plain,
! [X0,X1,X2] : subset(intersection(difference(X0,X1),X1),X2),
inference(duplicate_literals_removal,[status(esa)],[f182]) ).
fof(f293,plain,
! [X0,X1] : equal_set(intersection(difference(X0,X1),X1),empty_set),
inference(resolution,[status(thm)],[f183,f93]) ).
fof(f295,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f71,f293]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET696+4 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 29 21:55:47 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 0.20/0.43 % Refutation found
% 0.20/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.44 % Elapsed time: 0.085493 seconds
% 0.20/0.44 % CPU time: 0.565462 seconds
% 0.20/0.44 % Total memory used: 56.943 MB
% 0.20/0.44 % Net memory used: 56.562 MB
%------------------------------------------------------------------------------