TSTP Solution File: SEU187+2 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU187+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n019.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 20:41:24 EDT 2024
% Result : Theorem 1.76s 0.60s
% Output : CNFRefutation 2.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 7 unt; 0 def)
% Number of atoms : 149 ( 45 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 168 ( 60 ~; 71 |; 24 &)
% ( 11 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 1 con; 0-3 aty)
% Number of variables : 89 ( 71 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f64,axiom,
( empty(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f151,conjecture,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f152,negated_conjecture,
~ ( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
inference(negated_conjecture,[status(cth)],[f151]) ).
fof(f209,plain,
! [A] :
( ( A != empty_set
| ! [B] : ~ in(B,A) )
& ( A = empty_set
| ? [B] : in(B,A) ) ),
inference(NNF_transformation,[status(esa)],[f11]) ).
fof(f210,plain,
( ! [A] :
( A != empty_set
| ! [B] : ~ in(B,A) )
& ! [A] :
( A = empty_set
| ? [B] : in(B,A) ) ),
inference(miniscoping,[status(esa)],[f209]) ).
fof(f211,plain,
( ! [A] :
( A != empty_set
| ! [B] : ~ in(B,A) )
& ! [A] :
( A = empty_set
| in(sk0_7(A),A) ) ),
inference(skolemization,[status(esa)],[f210]) ).
fof(f212,plain,
! [X0,X1] :
( X0 != empty_set
| ~ in(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f211]) ).
fof(f271,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f19]) ).
fof(f272,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( ( B != relation_dom(A)
| ! [C] :
( ( ~ in(C,B)
| ? [D] : in(ordered_pair(C,D),A) )
& ( in(C,B)
| ! [D] : ~ in(ordered_pair(C,D),A) ) ) )
& ( B = relation_dom(A)
| ? [C] :
( ( ~ in(C,B)
| ! [D] : ~ in(ordered_pair(C,D),A) )
& ( in(C,B)
| ? [D] : in(ordered_pair(C,D),A) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f271]) ).
fof(f273,plain,
! [A] :
( ~ relation(A)
| ( ! [B] :
( B != relation_dom(A)
| ( ! [C] :
( ~ in(C,B)
| ? [D] : in(ordered_pair(C,D),A) )
& ! [C] :
( in(C,B)
| ! [D] : ~ in(ordered_pair(C,D),A) ) ) )
& ! [B] :
( B = relation_dom(A)
| ? [C] :
( ( ~ in(C,B)
| ! [D] : ~ in(ordered_pair(C,D),A) )
& ( in(C,B)
| ? [D] : in(ordered_pair(C,D),A) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f272]) ).
fof(f274,plain,
! [A] :
( ~ relation(A)
| ( ! [B] :
( B != relation_dom(A)
| ( ! [C] :
( ~ in(C,B)
| in(ordered_pair(C,sk0_18(C,B,A)),A) )
& ! [C] :
( in(C,B)
| ! [D] : ~ in(ordered_pair(C,D),A) ) ) )
& ! [B] :
( B = relation_dom(A)
| ( ( ~ in(sk0_19(B,A),B)
| ! [D] : ~ in(ordered_pair(sk0_19(B,A),D),A) )
& ( in(sk0_19(B,A),B)
| in(ordered_pair(sk0_19(B,A),sk0_20(B,A)),A) ) ) ) ) ),
inference(skolemization,[status(esa)],[f273]) ).
fof(f278,plain,
! [X0,X1] :
( ~ relation(X0)
| X1 = relation_dom(X0)
| in(sk0_19(X1,X0),X1)
| in(ordered_pair(sk0_19(X1,X0),sk0_20(X1,X0)),X0) ),
inference(cnf_transformation,[status(esa)],[f274]) ).
fof(f298,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f23]) ).
fof(f299,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( ( B != relation_rng(A)
| ! [C] :
( ( ~ in(C,B)
| ? [D] : in(ordered_pair(D,C),A) )
& ( in(C,B)
| ! [D] : ~ in(ordered_pair(D,C),A) ) ) )
& ( B = relation_rng(A)
| ? [C] :
( ( ~ in(C,B)
| ! [D] : ~ in(ordered_pair(D,C),A) )
& ( in(C,B)
| ? [D] : in(ordered_pair(D,C),A) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f298]) ).
fof(f300,plain,
! [A] :
( ~ relation(A)
| ( ! [B] :
( B != relation_rng(A)
| ( ! [C] :
( ~ in(C,B)
| ? [D] : in(ordered_pair(D,C),A) )
& ! [C] :
( in(C,B)
| ! [D] : ~ in(ordered_pair(D,C),A) ) ) )
& ! [B] :
( B = relation_rng(A)
| ? [C] :
( ( ~ in(C,B)
| ! [D] : ~ in(ordered_pair(D,C),A) )
& ( in(C,B)
| ? [D] : in(ordered_pair(D,C),A) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f299]) ).
fof(f301,plain,
! [A] :
( ~ relation(A)
| ( ! [B] :
( B != relation_rng(A)
| ( ! [C] :
( ~ in(C,B)
| in(ordered_pair(sk0_25(C,B,A),C),A) )
& ! [C] :
( in(C,B)
| ! [D] : ~ in(ordered_pair(D,C),A) ) ) )
& ! [B] :
( B = relation_rng(A)
| ( ( ~ in(sk0_26(B,A),B)
| ! [D] : ~ in(ordered_pair(D,sk0_26(B,A)),A) )
& ( in(sk0_26(B,A),B)
| in(ordered_pair(sk0_27(B,A),sk0_26(B,A)),A) ) ) ) ) ),
inference(skolemization,[status(esa)],[f300]) ).
fof(f305,plain,
! [X0,X1] :
( ~ relation(X0)
| X1 = relation_rng(X0)
| in(sk0_26(X1,X0),X1)
| in(ordered_pair(sk0_27(X1,X0),sk0_26(X1,X0)),X0) ),
inference(cnf_transformation,[status(esa)],[f301]) ).
fof(f377,plain,
relation(empty_set),
inference(cnf_transformation,[status(esa)],[f64]) ).
fof(f605,plain,
( relation_dom(empty_set) != empty_set
| relation_rng(empty_set) != empty_set ),
inference(pre_NNF_transformation,[status(esa)],[f152]) ).
fof(f606,plain,
( relation_dom(empty_set) != empty_set
| relation_rng(empty_set) != empty_set ),
inference(cnf_transformation,[status(esa)],[f605]) ).
fof(f657,plain,
( spl0_0
<=> relation_dom(empty_set) = empty_set ),
introduced(split_symbol_definition) ).
fof(f659,plain,
( relation_dom(empty_set) != empty_set
| spl0_0 ),
inference(component_clause,[status(thm)],[f657]) ).
fof(f660,plain,
( spl0_1
<=> relation_rng(empty_set) = empty_set ),
introduced(split_symbol_definition) ).
fof(f662,plain,
( relation_rng(empty_set) != empty_set
| spl0_1 ),
inference(component_clause,[status(thm)],[f660]) ).
fof(f663,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f606,f657,f660]) ).
fof(f672,plain,
! [X0] : ~ in(X0,empty_set),
inference(equality_resolution,[status(esa)],[f212]) ).
fof(f1054,plain,
! [X0] :
( X0 = relation_dom(empty_set)
| in(sk0_19(X0,empty_set),X0)
| in(ordered_pair(sk0_19(X0,empty_set),sk0_20(X0,empty_set)),empty_set) ),
inference(resolution,[status(thm)],[f278,f377]) ).
fof(f1055,plain,
! [X0] :
( X0 = relation_dom(empty_set)
| in(sk0_19(X0,empty_set),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1054,f672]) ).
fof(f1059,plain,
! [X0] :
( X0 = relation_rng(empty_set)
| in(sk0_26(X0,empty_set),X0)
| in(ordered_pair(sk0_27(X0,empty_set),sk0_26(X0,empty_set)),empty_set) ),
inference(resolution,[status(thm)],[f305,f377]) ).
fof(f1060,plain,
! [X0] :
( X0 = relation_rng(empty_set)
| in(sk0_26(X0,empty_set),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1059,f672]) ).
fof(f1563,plain,
empty_set = relation_dom(empty_set),
inference(resolution,[status(thm)],[f1055,f672]) ).
fof(f1564,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f1563,f659]) ).
fof(f1565,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f1564]) ).
fof(f1627,plain,
empty_set = relation_rng(empty_set),
inference(resolution,[status(thm)],[f1060,f672]) ).
fof(f1867,plain,
( empty_set != empty_set
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f1627,f662]) ).
fof(f1868,plain,
( $false
| spl0_1 ),
inference(trivial_equality_resolution,[status(esa)],[f1867]) ).
fof(f1869,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f1868]) ).
fof(f1870,plain,
$false,
inference(sat_refutation,[status(thm)],[f663,f1565,f1869]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SEU187+2 : TPTP v8.1.2. Released v3.3.0.
% 0.02/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.31 % Computer : n019.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 : Mon Apr 29 19:42:59 EDT 2024
% 0.09/0.32 % CPUTime :
% 0.09/0.33 % Drodi V3.6.0
% 1.76/0.60 % Refutation found
% 1.76/0.60 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.76/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.00/0.62 % Elapsed time: 0.304020 seconds
% 2.00/0.62 % CPU time: 2.172681 seconds
% 2.00/0.62 % Total memory used: 98.116 MB
% 2.00/0.62 % Net memory used: 97.178 MB
%------------------------------------------------------------------------------