TSTP Solution File: SEU179+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU179+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n031.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 12:36:09 EDT 2023
% Result : Theorem 0.15s 0.52s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 53 ( 6 unt; 0 def)
% Number of atoms : 201 ( 20 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 239 ( 91 ~; 95 |; 32 &)
% ( 12 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-3 aty)
% Number of variables : 139 (; 119 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,conjecture,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(A,B)
=> ( subset(relation_dom(A),relation_dom(B))
& subset(relation_rng(A),relation_rng(B)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ ! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(A,B)
=> ( subset(relation_dom(A),relation_dom(B))
& subset(relation_rng(A),relation_rng(B)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f40,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( ~ in(C,A)
| in(C,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f3]) ).
fof(f41,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)],[f40]) ).
fof(f42,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)],[f41]) ).
fof(f43,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ! [A,B] :
( subset(A,B)
| ( in(sk0_0(B,A),A)
& ~ in(sk0_0(B,A),B) ) ) ),
inference(skolemization,[status(esa)],[f42]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ in(X2,X0)
| in(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f43]) ).
fof(f46,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f43]) ).
fof(f47,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)],[f4]) ).
fof(f48,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)],[f47]) ).
fof(f49,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)],[f48]) ).
fof(f50,plain,
! [A] :
( ~ relation(A)
| ( ! [B] :
( B != relation_dom(A)
| ( ! [C] :
( ~ in(C,B)
| in(ordered_pair(C,sk0_1(C,B,A)),A) )
& ! [C] :
( in(C,B)
| ! [D] : ~ in(ordered_pair(C,D),A) ) ) )
& ! [B] :
( B = relation_dom(A)
| ( ( ~ in(sk0_2(B,A),B)
| ! [D] : ~ in(ordered_pair(sk0_2(B,A),D),A) )
& ( in(sk0_2(B,A),B)
| in(ordered_pair(sk0_2(B,A),sk0_3(B,A)),A) ) ) ) ) ),
inference(skolemization,[status(esa)],[f49]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| X1 != relation_dom(X0)
| ~ in(X2,X1)
| in(ordered_pair(X2,sk0_1(X2,X1,X0)),X0) ),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f52,plain,
! [X0,X1,X2,X3] :
( ~ relation(X0)
| X1 != relation_dom(X0)
| in(X2,X1)
| ~ in(ordered_pair(X2,X3),X0) ),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f55,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)],[f5]) ).
fof(f56,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)],[f55]) ).
fof(f57,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)],[f56]) ).
fof(f58,plain,
! [A] :
( ~ relation(A)
| ( ! [B] :
( B != relation_rng(A)
| ( ! [C] :
( ~ in(C,B)
| in(ordered_pair(sk0_4(C,B,A),C),A) )
& ! [C] :
( in(C,B)
| ! [D] : ~ in(ordered_pair(D,C),A) ) ) )
& ! [B] :
( B = relation_rng(A)
| ( ( ~ in(sk0_5(B,A),B)
| ! [D] : ~ in(ordered_pair(D,sk0_5(B,A)),A) )
& ( in(sk0_5(B,A),B)
| in(ordered_pair(sk0_6(B,A),sk0_5(B,A)),A) ) ) ) ) ),
inference(skolemization,[status(esa)],[f57]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| X1 != relation_rng(X0)
| ~ in(X2,X1)
| in(ordered_pair(sk0_4(X2,X1,X0),X2),X0) ),
inference(cnf_transformation,[status(esa)],[f58]) ).
fof(f60,plain,
! [X0,X1,X2,X3] :
( ~ relation(X0)
| X1 != relation_rng(X0)
| in(X2,X1)
| ~ in(ordered_pair(X3,X2),X0) ),
inference(cnf_transformation,[status(esa)],[f58]) ).
fof(f89,plain,
? [A] :
( relation(A)
& ? [B] :
( relation(B)
& subset(A,B)
& ( ~ subset(relation_dom(A),relation_dom(B))
| ~ subset(relation_rng(A),relation_rng(B)) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f29]) ).
fof(f90,plain,
( relation(sk0_13)
& relation(sk0_14)
& subset(sk0_13,sk0_14)
& ( ~ subset(relation_dom(sk0_13),relation_dom(sk0_14))
| ~ subset(relation_rng(sk0_13),relation_rng(sk0_14)) ) ),
inference(skolemization,[status(esa)],[f89]) ).
fof(f91,plain,
relation(sk0_13),
inference(cnf_transformation,[status(esa)],[f90]) ).
fof(f92,plain,
relation(sk0_14),
inference(cnf_transformation,[status(esa)],[f90]) ).
fof(f93,plain,
subset(sk0_13,sk0_14),
inference(cnf_transformation,[status(esa)],[f90]) ).
fof(f94,plain,
( ~ subset(relation_dom(sk0_13),relation_dom(sk0_14))
| ~ subset(relation_rng(sk0_13),relation_rng(sk0_14)) ),
inference(cnf_transformation,[status(esa)],[f90]) ).
fof(f115,plain,
( spl0_0
<=> subset(relation_dom(sk0_13),relation_dom(sk0_14)) ),
introduced(split_symbol_definition) ).
fof(f118,plain,
( spl0_1
<=> subset(relation_rng(sk0_13),relation_rng(sk0_14)) ),
introduced(split_symbol_definition) ).
fof(f121,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f94,f115,f118]) ).
fof(f122,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| in(ordered_pair(X1,sk0_1(X1,relation_dom(X0),X0)),X0) ),
inference(destructive_equality_resolution,[status(esa)],[f51]) ).
fof(f123,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| in(X1,relation_dom(X0))
| ~ in(ordered_pair(X1,X2),X0) ),
inference(destructive_equality_resolution,[status(esa)],[f52]) ).
fof(f124,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(X1,relation_rng(X0))
| in(ordered_pair(sk0_4(X1,relation_rng(X0),X0),X1),X0) ),
inference(destructive_equality_resolution,[status(esa)],[f59]) ).
fof(f125,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| in(X1,relation_rng(X0))
| ~ in(ordered_pair(X2,X1),X0) ),
inference(destructive_equality_resolution,[status(esa)],[f60]) ).
fof(f127,plain,
! [X0,X1] :
( in(X0,relation_dom(sk0_14))
| ~ in(ordered_pair(X0,X1),sk0_14) ),
inference(resolution,[status(thm)],[f123,f92]) ).
fof(f129,plain,
! [X0,X1] :
( in(X0,relation_rng(sk0_14))
| ~ in(ordered_pair(X1,X0),sk0_14) ),
inference(resolution,[status(thm)],[f125,f92]) ).
fof(f131,plain,
! [X0] :
( ~ in(X0,sk0_13)
| in(X0,sk0_14) ),
inference(resolution,[status(thm)],[f44,f93]) ).
fof(f132,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),sk0_13)
| in(X0,relation_dom(sk0_14)) ),
inference(resolution,[status(thm)],[f131,f127]) ).
fof(f133,plain,
! [X0,X1] :
( in(X0,relation_rng(sk0_14))
| ~ in(ordered_pair(X1,X0),sk0_13) ),
inference(resolution,[status(thm)],[f129,f131]) ).
fof(f175,plain,
! [X0] :
( ~ in(X0,relation_dom(sk0_13))
| in(ordered_pair(X0,sk0_1(X0,relation_dom(sk0_13),sk0_13)),sk0_13) ),
inference(resolution,[status(thm)],[f122,f91]) ).
fof(f180,plain,
! [X0] :
( ~ in(X0,relation_dom(sk0_13))
| in(X0,relation_dom(sk0_14)) ),
inference(resolution,[status(thm)],[f175,f132]) ).
fof(f191,plain,
! [X0] :
( ~ in(sk0_0(relation_dom(sk0_14),X0),relation_dom(sk0_13))
| subset(X0,relation_dom(sk0_14)) ),
inference(resolution,[status(thm)],[f180,f46]) ).
fof(f200,plain,
( subset(relation_dom(sk0_13),relation_dom(sk0_14))
| subset(relation_dom(sk0_13),relation_dom(sk0_14)) ),
inference(resolution,[status(thm)],[f191,f45]) ).
fof(f201,plain,
spl0_0,
inference(split_clause,[status(thm)],[f200,f115]) ).
fof(f280,plain,
! [X0] :
( ~ in(X0,relation_rng(sk0_13))
| in(ordered_pair(sk0_4(X0,relation_rng(sk0_13),sk0_13),X0),sk0_13) ),
inference(resolution,[status(thm)],[f124,f91]) ).
fof(f287,plain,
! [X0] :
( ~ in(X0,relation_rng(sk0_13))
| in(X0,relation_rng(sk0_14)) ),
inference(resolution,[status(thm)],[f280,f133]) ).
fof(f307,plain,
! [X0] :
( ~ in(sk0_0(relation_rng(sk0_14),X0),relation_rng(sk0_13))
| subset(X0,relation_rng(sk0_14)) ),
inference(resolution,[status(thm)],[f287,f46]) ).
fof(f318,plain,
( subset(relation_rng(sk0_13),relation_rng(sk0_14))
| subset(relation_rng(sk0_13),relation_rng(sk0_14)) ),
inference(resolution,[status(thm)],[f307,f45]) ).
fof(f319,plain,
spl0_1,
inference(split_clause,[status(thm)],[f318,f118]) ).
fof(f320,plain,
$false,
inference(sat_refutation,[status(thm)],[f121,f201,f319]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.10 % Problem : SEU179+1 : TPTP v8.1.2. Released v3.3.0.
% 0.04/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n031.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 09:33:37 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.09/0.31 % Drodi V3.5.1
% 0.15/0.52 % Refutation found
% 0.15/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.55 % Elapsed time: 0.237500 seconds
% 0.15/0.55 % CPU time: 0.921762 seconds
% 0.15/0.55 % Memory used: 67.592 MB
%------------------------------------------------------------------------------