TSTP Solution File: SET679+3 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET679+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n032.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 12:35:00 EDT 2023
% Result : Theorem 0.09s 0.31s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 9 unt; 0 def)
% Number of atoms : 103 ( 8 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 122 ( 54 ~; 41 |; 12 &)
% ( 6 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 45 (; 43 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(C,B)
<=> member(ordered_pair(C,C),identity_relation_of(B)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ~ member(B,empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( not_equal(B,C)
<=> B != C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( empty(B)
<=> ! [C] :
( ilf_type(C,set_type)
=> ~ member(C,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,conjecture,
! [B] :
( ( ~ empty(B)
& ilf_type(B,set_type) )
=> not_equal(identity_relation_of(B),empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
~ ! [B] :
( ( ~ empty(B)
& ilf_type(B,set_type) )
=> not_equal(identity_relation_of(B),empty_set) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f26,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( member(C,B)
<=> member(ordered_pair(C,C),identity_relation_of(B)) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f27,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ member(C,B)
| member(ordered_pair(C,C),identity_relation_of(B)) )
& ( member(C,B)
| ~ member(ordered_pair(C,C),identity_relation_of(B)) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X1,X0)
| member(ordered_pair(X1,X1),identity_relation_of(X0)) ),
inference(cnf_transformation,[status(esa)],[f27]) ).
fof(f30,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ~ member(B,empty_set) ),
inference(pre_NNF_transformation,[status(esa)],[f2]) ).
fof(f31,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ member(X0,empty_set) ),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f49,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( not_equal(B,C)
<=> B != C ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f50,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ not_equal(B,C)
| B != C )
& ( not_equal(B,C)
| B = C ) ) ) ),
inference(NNF_transformation,[status(esa)],[f49]) ).
fof(f52,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| not_equal(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f53,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( empty(B)
<=> ! [C] :
( ~ ilf_type(C,set_type)
| ~ member(C,B) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f54,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ( ~ empty(B)
| ! [C] :
( ~ ilf_type(C,set_type)
| ~ member(C,B) ) )
& ( empty(B)
| ? [C] :
( ilf_type(C,set_type)
& member(C,B) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f53]) ).
fof(f55,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ( ~ empty(B)
| ! [C] :
( ~ ilf_type(C,set_type)
| ~ member(C,B) ) )
& ( empty(B)
| ( ilf_type(sk0_1(B),set_type)
& member(sk0_1(B),B) ) ) ) ),
inference(skolemization,[status(esa)],[f54]) ).
fof(f58,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| empty(X0)
| member(sk0_1(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f55]) ).
fof(f107,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f108,plain,
? [B] :
( ~ empty(B)
& ilf_type(B,set_type)
& ~ not_equal(identity_relation_of(B),empty_set) ),
inference(pre_NNF_transformation,[status(esa)],[f25]) ).
fof(f109,plain,
( ~ empty(sk0_9)
& ilf_type(sk0_9,set_type)
& ~ not_equal(identity_relation_of(sk0_9),empty_set) ),
inference(skolemization,[status(esa)],[f108]) ).
fof(f110,plain,
~ empty(sk0_9),
inference(cnf_transformation,[status(esa)],[f109]) ).
fof(f112,plain,
~ not_equal(identity_relation_of(sk0_9),empty_set),
inference(cnf_transformation,[status(esa)],[f109]) ).
fof(f118,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ member(X0,X1)
| member(ordered_pair(X0,X0),identity_relation_of(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f28,f107]) ).
fof(f120,plain,
! [X0] : ~ member(X0,empty_set),
inference(forward_subsumption_resolution,[status(thm)],[f31,f107]) ).
fof(f122,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| not_equal(X1,X0)
| X1 = X0 ),
inference(forward_subsumption_resolution,[status(thm)],[f52,f107]) ).
fof(f123,plain,
! [X0,X1] :
( not_equal(X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f122,f107]) ).
fof(f124,plain,
identity_relation_of(sk0_9) = empty_set,
inference(resolution,[status(thm)],[f123,f112]) ).
fof(f126,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ member(X0,sk0_9)
| member(ordered_pair(X0,X0),empty_set) ),
inference(paramodulation,[status(thm)],[f124,f118]) ).
fof(f127,plain,
! [X0] :
( ~ member(X0,sk0_9)
| member(ordered_pair(X0,X0),empty_set) ),
inference(forward_subsumption_resolution,[status(thm)],[f126,f107]) ).
fof(f128,plain,
! [X0] : ~ member(X0,sk0_9),
inference(forward_subsumption_resolution,[status(thm)],[f127,f120]) ).
fof(f152,plain,
! [X0] :
( empty(X0)
| member(sk0_1(X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f58,f107]) ).
fof(f153,plain,
empty(sk0_9),
inference(resolution,[status(thm)],[f152,f128]) ).
fof(f154,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f153,f110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.09 % Problem : SET679+3 : TPTP v8.1.2. Released v2.2.0.
% 0.09/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n032.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue May 30 10:19:15 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.09/0.30 % Drodi V3.5.1
% 0.09/0.31 % Refutation found
% 0.09/0.31 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.53 % Elapsed time: 0.012791 seconds
% 0.14/0.53 % CPU time: 0.012175 seconds
% 0.14/0.53 % Memory used: 2.970 MB
%------------------------------------------------------------------------------