TSTP Solution File: SET947+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET947+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n024.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 12:35:35 EDT 2023
% Result : Theorem 0.16s 0.54s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 7 unt; 0 def)
% Number of atoms : 85 ( 8 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 96 ( 37 ~; 38 |; 15 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 65 (; 60 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( in(A,B)
=> subset(A,union(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,conjecture,
! [A] : subset(A,powerset(union(A))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ ! [A] : subset(A,powerset(union(A))),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f12,plain,
! [A,B] :
( ( B != powerset(A)
| ! [C] :
( ( ~ in(C,B)
| subset(C,A) )
& ( in(C,B)
| ~ subset(C,A) ) ) )
& ( B = powerset(A)
| ? [C] :
( ( ~ in(C,B)
| ~ subset(C,A) )
& ( in(C,B)
| subset(C,A) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f2]) ).
fof(f13,plain,
( ! [A,B] :
( B != powerset(A)
| ( ! [C] :
( ~ in(C,B)
| subset(C,A) )
& ! [C] :
( in(C,B)
| ~ subset(C,A) ) ) )
& ! [A,B] :
( B = powerset(A)
| ? [C] :
( ( ~ in(C,B)
| ~ subset(C,A) )
& ( in(C,B)
| subset(C,A) ) ) ) ),
inference(miniscoping,[status(esa)],[f12]) ).
fof(f14,plain,
( ! [A,B] :
( B != powerset(A)
| ( ! [C] :
( ~ in(C,B)
| subset(C,A) )
& ! [C] :
( in(C,B)
| ~ subset(C,A) ) ) )
& ! [A,B] :
( B = powerset(A)
| ( ( ~ in(sk0_0(B,A),B)
| ~ subset(sk0_0(B,A),A) )
& ( in(sk0_0(B,A),B)
| subset(sk0_0(B,A),A) ) ) ) ),
inference(skolemization,[status(esa)],[f13]) ).
fof(f16,plain,
! [X0,X1,X2] :
( X0 != powerset(X1)
| in(X2,X0)
| ~ subset(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f19,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( ~ in(C,A)
| in(C,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f3]) ).
fof(f20,plain,
! [A,B] :
( ( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ( subset(A,B)
| ? [C] :
( in(C,A)
& ~ in(C,B) ) ) ),
inference(NNF_transformation,[status(esa)],[f19]) ).
fof(f21,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ! [A,B] :
( subset(A,B)
| ? [C] :
( in(C,A)
& ~ in(C,B) ) ) ),
inference(miniscoping,[status(esa)],[f20]) ).
fof(f22,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ! [A,B] :
( subset(A,B)
| ( in(sk0_1(B,A),A)
& ~ in(sk0_1(B,A),B) ) ) ),
inference(skolemization,[status(esa)],[f21]) ).
fof(f24,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sk0_1(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f25,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sk0_1(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f26,plain,
! [A,B] :
( ~ in(A,B)
| subset(A,union(B)) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f27,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(X0,union(X1)) ),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f34,plain,
? [A] : ~ subset(A,powerset(union(A))),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f35,plain,
~ subset(sk0_4,powerset(union(sk0_4))),
inference(skolemization,[status(esa)],[f34]) ).
fof(f36,plain,
~ subset(sk0_4,powerset(union(sk0_4))),
inference(cnf_transformation,[status(esa)],[f35]) ).
fof(f38,plain,
! [X0,X1] :
( in(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(destructive_equality_resolution,[status(esa)],[f16]) ).
fof(f64,plain,
! [X0,X1] :
( subset(X0,powerset(X1))
| ~ subset(sk0_1(powerset(X1),X0),X1) ),
inference(resolution,[status(thm)],[f25,f38]) ).
fof(f81,plain,
! [X0,X1] :
( subset(X0,powerset(union(X1)))
| ~ in(sk0_1(powerset(union(X1)),X0),X1) ),
inference(resolution,[status(thm)],[f64,f27]) ).
fof(f189,plain,
! [X0] :
( subset(X0,powerset(union(X0)))
| subset(X0,powerset(union(X0))) ),
inference(resolution,[status(thm)],[f81,f24]) ).
fof(f190,plain,
! [X0] : subset(X0,powerset(union(X0))),
inference(duplicate_literals_removal,[status(esa)],[f189]) ).
fof(f200,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f36,f190]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SET947+1 : TPTP v8.1.2. Released v3.2.0.
% 0.05/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.31 % Computer : n024.cluster.edu
% 0.09/0.31 % Model : x86_64 x86_64
% 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31 % Memory : 8042.1875MB
% 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31 % CPULimit : 300
% 0.09/0.31 % WCLimit : 300
% 0.09/0.31 % DateTime : Tue May 30 10:18:48 EDT 2023
% 0.09/0.31 % CPUTime :
% 0.15/0.32 % Drodi V3.5.1
% 0.16/0.54 % Refutation found
% 0.16/0.54 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.54 % Elapsed time: 0.017583 seconds
% 0.16/0.54 % CPU time: 0.025168 seconds
% 0.16/0.54 % Memory used: 3.018 MB
%------------------------------------------------------------------------------