TSTP Solution File: SEU355+2 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU355+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n029.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 20:42:03 EDT 2024
% Result : Theorem 185.23s 23.72s
% Output : CNFRefutation 185.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 49 ( 7 unt; 0 def)
% Number of atoms : 179 ( 8 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 212 ( 82 ~; 81 |; 27 &)
% ( 10 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 6 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 79 ( 71 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f89,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f145,axiom,
! [A] :
( rel_str(A)
=> ! [B,C] :
( element(C,the_carrier(A))
=> ( relstr_element_smaller(A,B,C)
<=> ! [D] :
( element(D,the_carrier(A))
=> ( in(D,B)
=> related(A,C,D) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f153,axiom,
! [A] :
( rel_str(A)
=> ! [B,C] :
( element(C,the_carrier(A))
=> ( relstr_set_smaller(A,B,C)
<=> ! [D] :
( element(D,the_carrier(A))
=> ( in(D,B)
=> related(A,D,C) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f643,conjecture,
! [A] :
( rel_str(A)
=> ! [B] :
( element(B,the_carrier(A))
=> ( relstr_set_smaller(A,empty_set,B)
& relstr_element_smaller(A,empty_set,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f644,negated_conjecture,
~ ! [A] :
( rel_str(A)
=> ! [B] :
( element(B,the_carrier(A))
=> ( relstr_set_smaller(A,empty_set,B)
& relstr_element_smaller(A,empty_set,B) ) ) ),
inference(negated_conjecture,[status(cth)],[f643]) ).
fof(f1117,plain,
! [A] :
( ( A != empty_set
| ! [B] : ~ in(B,A) )
& ( A = empty_set
| ? [B] : in(B,A) ) ),
inference(NNF_transformation,[status(esa)],[f89]) ).
fof(f1118,plain,
( ! [A] :
( A != empty_set
| ! [B] : ~ in(B,A) )
& ! [A] :
( A = empty_set
| ? [B] : in(B,A) ) ),
inference(miniscoping,[status(esa)],[f1117]) ).
fof(f1119,plain,
( ! [A] :
( A != empty_set
| ! [B] : ~ in(B,A) )
& ! [A] :
( A = empty_set
| in(sk0_48(A),A) ) ),
inference(skolemization,[status(esa)],[f1118]) ).
fof(f1120,plain,
! [X0,X1] :
( X0 != empty_set
| ~ in(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f1119]) ).
fof(f1470,plain,
! [A] :
( ~ rel_str(A)
| ! [B,C] :
( ~ element(C,the_carrier(A))
| ( relstr_element_smaller(A,B,C)
<=> ! [D] :
( ~ element(D,the_carrier(A))
| ~ in(D,B)
| related(A,C,D) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f145]) ).
fof(f1471,plain,
! [A] :
( ~ rel_str(A)
| ! [B,C] :
( ~ element(C,the_carrier(A))
| ( ( ~ relstr_element_smaller(A,B,C)
| ! [D] :
( ~ element(D,the_carrier(A))
| ~ in(D,B)
| related(A,C,D) ) )
& ( relstr_element_smaller(A,B,C)
| ? [D] :
( element(D,the_carrier(A))
& in(D,B)
& ~ related(A,C,D) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f1470]) ).
fof(f1472,plain,
! [A] :
( ~ rel_str(A)
| ! [C] :
( ~ element(C,the_carrier(A))
| ( ! [B] :
( ~ relstr_element_smaller(A,B,C)
| ! [D] :
( ~ element(D,the_carrier(A))
| ~ in(D,B)
| related(A,C,D) ) )
& ! [B] :
( relstr_element_smaller(A,B,C)
| ? [D] :
( element(D,the_carrier(A))
& in(D,B)
& ~ related(A,C,D) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f1471]) ).
fof(f1473,plain,
! [A] :
( ~ rel_str(A)
| ! [C] :
( ~ element(C,the_carrier(A))
| ( ! [B] :
( ~ relstr_element_smaller(A,B,C)
| ! [D] :
( ~ element(D,the_carrier(A))
| ~ in(D,B)
| related(A,C,D) ) )
& ! [B] :
( relstr_element_smaller(A,B,C)
| ( element(sk0_102(B,C,A),the_carrier(A))
& in(sk0_102(B,C,A),B)
& ~ related(A,C,sk0_102(B,C,A)) ) ) ) ) ),
inference(skolemization,[status(esa)],[f1472]) ).
fof(f1476,plain,
! [X0,X1,X2] :
( ~ rel_str(X0)
| ~ element(X1,the_carrier(X0))
| relstr_element_smaller(X0,X2,X1)
| in(sk0_102(X2,X1,X0),X2) ),
inference(cnf_transformation,[status(esa)],[f1473]) ).
fof(f1525,plain,
! [A] :
( ~ rel_str(A)
| ! [B,C] :
( ~ element(C,the_carrier(A))
| ( relstr_set_smaller(A,B,C)
<=> ! [D] :
( ~ element(D,the_carrier(A))
| ~ in(D,B)
| related(A,D,C) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f153]) ).
fof(f1526,plain,
! [A] :
( ~ rel_str(A)
| ! [B,C] :
( ~ element(C,the_carrier(A))
| ( ( ~ relstr_set_smaller(A,B,C)
| ! [D] :
( ~ element(D,the_carrier(A))
| ~ in(D,B)
| related(A,D,C) ) )
& ( relstr_set_smaller(A,B,C)
| ? [D] :
( element(D,the_carrier(A))
& in(D,B)
& ~ related(A,D,C) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f1525]) ).
fof(f1527,plain,
! [A] :
( ~ rel_str(A)
| ! [C] :
( ~ element(C,the_carrier(A))
| ( ! [B] :
( ~ relstr_set_smaller(A,B,C)
| ! [D] :
( ~ element(D,the_carrier(A))
| ~ in(D,B)
| related(A,D,C) ) )
& ! [B] :
( relstr_set_smaller(A,B,C)
| ? [D] :
( element(D,the_carrier(A))
& in(D,B)
& ~ related(A,D,C) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f1526]) ).
fof(f1528,plain,
! [A] :
( ~ rel_str(A)
| ! [C] :
( ~ element(C,the_carrier(A))
| ( ! [B] :
( ~ relstr_set_smaller(A,B,C)
| ! [D] :
( ~ element(D,the_carrier(A))
| ~ in(D,B)
| related(A,D,C) ) )
& ! [B] :
( relstr_set_smaller(A,B,C)
| ( element(sk0_113(B,C,A),the_carrier(A))
& in(sk0_113(B,C,A),B)
& ~ related(A,sk0_113(B,C,A),C) ) ) ) ) ),
inference(skolemization,[status(esa)],[f1527]) ).
fof(f1531,plain,
! [X0,X1,X2] :
( ~ rel_str(X0)
| ~ element(X1,the_carrier(X0))
| relstr_set_smaller(X0,X2,X1)
| in(sk0_113(X2,X1,X0),X2) ),
inference(cnf_transformation,[status(esa)],[f1528]) ).
fof(f3422,plain,
? [A] :
( rel_str(A)
& ? [B] :
( element(B,the_carrier(A))
& ( ~ relstr_set_smaller(A,empty_set,B)
| ~ relstr_element_smaller(A,empty_set,B) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f644]) ).
fof(f3423,plain,
( rel_str(sk0_386)
& element(sk0_387,the_carrier(sk0_386))
& ( ~ relstr_set_smaller(sk0_386,empty_set,sk0_387)
| ~ relstr_element_smaller(sk0_386,empty_set,sk0_387) ) ),
inference(skolemization,[status(esa)],[f3422]) ).
fof(f3424,plain,
rel_str(sk0_386),
inference(cnf_transformation,[status(esa)],[f3423]) ).
fof(f3425,plain,
element(sk0_387,the_carrier(sk0_386)),
inference(cnf_transformation,[status(esa)],[f3423]) ).
fof(f3426,plain,
( ~ relstr_set_smaller(sk0_386,empty_set,sk0_387)
| ~ relstr_element_smaller(sk0_386,empty_set,sk0_387) ),
inference(cnf_transformation,[status(esa)],[f3423]) ).
fof(f3972,plain,
( spl0_35
<=> relstr_set_smaller(sk0_386,empty_set,sk0_387) ),
introduced(split_symbol_definition) ).
fof(f3974,plain,
( ~ relstr_set_smaller(sk0_386,empty_set,sk0_387)
| spl0_35 ),
inference(component_clause,[status(thm)],[f3972]) ).
fof(f3975,plain,
( spl0_36
<=> relstr_element_smaller(sk0_386,empty_set,sk0_387) ),
introduced(split_symbol_definition) ).
fof(f3977,plain,
( ~ relstr_element_smaller(sk0_386,empty_set,sk0_387)
| spl0_36 ),
inference(component_clause,[status(thm)],[f3975]) ).
fof(f3978,plain,
( ~ spl0_35
| ~ spl0_36 ),
inference(split_clause,[status(thm)],[f3426,f3972,f3975]) ).
fof(f4100,plain,
! [X0] : ~ in(X0,empty_set),
inference(destructive_equality_resolution,[status(esa)],[f1120]) ).
fof(f62505,plain,
! [X0,X1] :
( ~ element(X0,the_carrier(sk0_386))
| relstr_element_smaller(sk0_386,X1,X0)
| in(sk0_102(X1,X0,sk0_386),X1) ),
inference(resolution,[status(thm)],[f1476,f3424]) ).
fof(f62590,plain,
( spl0_1407
<=> in(sk0_102(empty_set,sk0_387,sk0_386),empty_set) ),
introduced(split_symbol_definition) ).
fof(f62591,plain,
( in(sk0_102(empty_set,sk0_387,sk0_386),empty_set)
| ~ spl0_1407 ),
inference(component_clause,[status(thm)],[f62590]) ).
fof(f62659,plain,
( $false
| ~ spl0_1407 ),
inference(forward_subsumption_resolution,[status(thm)],[f62591,f4100]) ).
fof(f62660,plain,
~ spl0_1407,
inference(contradiction_clause,[status(thm)],[f62659]) ).
fof(f68223,plain,
! [X0,X1] :
( ~ element(X0,the_carrier(sk0_386))
| relstr_set_smaller(sk0_386,X1,X0)
| in(sk0_113(X1,X0,sk0_386),X1) ),
inference(resolution,[status(thm)],[f1531,f3424]) ).
fof(f68535,plain,
( spl0_1532
<=> in(sk0_113(empty_set,sk0_387,sk0_386),empty_set) ),
introduced(split_symbol_definition) ).
fof(f68536,plain,
( in(sk0_113(empty_set,sk0_387,sk0_386),empty_set)
| ~ spl0_1532 ),
inference(component_clause,[status(thm)],[f68535]) ).
fof(f68540,plain,
( $false
| ~ spl0_1532 ),
inference(forward_subsumption_resolution,[status(thm)],[f68536,f4100]) ).
fof(f68541,plain,
~ spl0_1532,
inference(contradiction_clause,[status(thm)],[f68540]) ).
fof(f69250,plain,
( spl0_1554
<=> element(sk0_387,the_carrier(sk0_386)) ),
introduced(split_symbol_definition) ).
fof(f69252,plain,
( ~ element(sk0_387,the_carrier(sk0_386))
| spl0_1554 ),
inference(component_clause,[status(thm)],[f69250]) ).
fof(f69308,plain,
( $false
| spl0_1554 ),
inference(forward_subsumption_resolution,[status(thm)],[f69252,f3425]) ).
fof(f69309,plain,
spl0_1554,
inference(contradiction_clause,[status(thm)],[f69308]) ).
fof(f69320,plain,
( ~ element(sk0_387,the_carrier(sk0_386))
| in(sk0_113(empty_set,sk0_387,sk0_386),empty_set)
| spl0_35 ),
inference(resolution,[status(thm)],[f68223,f3974]) ).
fof(f69321,plain,
( ~ spl0_1554
| spl0_1532
| spl0_35 ),
inference(split_clause,[status(thm)],[f69320,f69250,f68535,f3972]) ).
fof(f70900,plain,
( ~ element(sk0_387,the_carrier(sk0_386))
| in(sk0_102(empty_set,sk0_387,sk0_386),empty_set)
| spl0_36 ),
inference(resolution,[status(thm)],[f62505,f3977]) ).
fof(f70901,plain,
( ~ spl0_1554
| spl0_1407
| spl0_36 ),
inference(split_clause,[status(thm)],[f70900,f69250,f62590,f3975]) ).
fof(f70942,plain,
$false,
inference(sat_refutation,[status(thm)],[f3978,f62660,f68541,f69309,f69321,f70901]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : SEU355+2 : TPTP v8.1.2. Released v3.3.0.
% 0.09/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.33 % Computer : n029.cluster.edu
% 0.10/0.33 % Model : x86_64 x86_64
% 0.10/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.33 % Memory : 8042.1875MB
% 0.10/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.33 % CPULimit : 300
% 0.10/0.33 % WCLimit : 300
% 0.10/0.33 % DateTime : Mon Apr 29 20:06:04 EDT 2024
% 0.10/0.33 % CPUTime :
% 0.10/0.39 % Drodi V3.6.0
% 185.23/23.72 % Refutation found
% 185.23/23.72 % SZS status Theorem for theBenchmark: Theorem is valid
% 185.23/23.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 185.98/23.88 % Elapsed time: 23.524458 seconds
% 185.98/23.88 % CPU time: 185.948438 seconds
% 185.98/23.88 % Total memory used: 739.838 MB
% 185.98/23.88 % Net memory used: 707.547 MB
%------------------------------------------------------------------------------