TSTP Solution File: SEU254+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU254+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n022.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 12:36:29 EDT 2023
% Result : Theorem 0.20s 0.48s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 66 ( 6 unt; 0 def)
% Number of atoms : 238 ( 0 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 289 ( 117 ~; 130 |; 27 &)
% ( 7 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 146 (; 136 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [A,B] :
( relation(A)
=> relation(relation_restriction(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A] :
( relation(A)
=> ( transitive(A)
<=> ! [B,C,D] :
( ( in(ordered_pair(B,C),A)
& in(ordered_pair(C,D),A) )
=> in(ordered_pair(B,D),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(A,C)
& in(B,D) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_restriction(C,B))
<=> ( in(A,C)
& in(A,cartesian_product2(B,B)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
! [A,B] :
( relation(B)
=> ( transitive(B)
=> transitive(relation_restriction(B,A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> ( transitive(B)
=> transitive(relation_restriction(B,A)) ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f49,plain,
! [A,B] :
( ~ relation(A)
| relation(relation_restriction(A,B)) ),
inference(pre_NNF_transformation,[status(esa)],[f11]) ).
fof(f50,plain,
! [A] :
( ~ relation(A)
| ! [B] : relation(relation_restriction(A,B)) ),
inference(miniscoping,[status(esa)],[f49]) ).
fof(f51,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_restriction(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f58,plain,
! [A] :
( ~ relation(A)
| ( transitive(A)
<=> ! [B,C,D] :
( ~ in(ordered_pair(B,C),A)
| ~ in(ordered_pair(C,D),A)
| in(ordered_pair(B,D),A) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f59,plain,
! [A] :
( ~ relation(A)
| ( ( ~ transitive(A)
| ! [B,C,D] :
( ~ in(ordered_pair(B,C),A)
| ~ in(ordered_pair(C,D),A)
| in(ordered_pair(B,D),A) ) )
& ( transitive(A)
| ? [B,C,D] :
( in(ordered_pair(B,C),A)
& in(ordered_pair(C,D),A)
& ~ in(ordered_pair(B,D),A) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f58]) ).
fof(f60,plain,
! [A] :
( ~ relation(A)
| ( ( ~ transitive(A)
| ! [B,D] :
( ! [C] :
( ~ in(ordered_pair(B,C),A)
| ~ in(ordered_pair(C,D),A) )
| in(ordered_pair(B,D),A) ) )
& ( transitive(A)
| ? [B,D] :
( ? [C] :
( in(ordered_pair(B,C),A)
& in(ordered_pair(C,D),A) )
& ~ in(ordered_pair(B,D),A) ) ) ) ),
inference(miniscoping,[status(esa)],[f59]) ).
fof(f61,plain,
! [A] :
( ~ relation(A)
| ( ( ~ transitive(A)
| ! [B,D] :
( ! [C] :
( ~ in(ordered_pair(B,C),A)
| ~ in(ordered_pair(C,D),A) )
| in(ordered_pair(B,D),A) ) )
& ( transitive(A)
| ( in(ordered_pair(sk0_1(A),sk0_3(A)),A)
& in(ordered_pair(sk0_3(A),sk0_2(A)),A)
& ~ in(ordered_pair(sk0_1(A),sk0_2(A)),A) ) ) ) ),
inference(skolemization,[status(esa)],[f60]) ).
fof(f62,plain,
! [X0,X1,X2,X3] :
( ~ relation(X0)
| ~ transitive(X0)
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(ordered_pair(X2,X3),X0)
| in(ordered_pair(X1,X3),X0) ),
inference(cnf_transformation,[status(esa)],[f61]) ).
fof(f63,plain,
! [X0] :
( ~ relation(X0)
| transitive(X0)
| in(ordered_pair(sk0_1(X0),sk0_3(X0)),X0) ),
inference(cnf_transformation,[status(esa)],[f61]) ).
fof(f64,plain,
! [X0] :
( ~ relation(X0)
| transitive(X0)
| in(ordered_pair(sk0_3(X0),sk0_2(X0)),X0) ),
inference(cnf_transformation,[status(esa)],[f61]) ).
fof(f65,plain,
! [X0] :
( ~ relation(X0)
| transitive(X0)
| ~ in(ordered_pair(sk0_1(X0),sk0_2(X0)),X0) ),
inference(cnf_transformation,[status(esa)],[f61]) ).
fof(f81,plain,
! [A,B,C,D] :
( ( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| ( in(A,C)
& in(B,D) ) )
& ( in(ordered_pair(A,B),cartesian_product2(C,D))
| ~ in(A,C)
| ~ in(B,D) ) ),
inference(NNF_transformation,[status(esa)],[f26]) ).
fof(f82,plain,
( ! [A,B,C,D] :
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| ( in(A,C)
& in(B,D) ) )
& ! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
| ~ in(A,C)
| ~ in(B,D) ) ),
inference(miniscoping,[status(esa)],[f81]) ).
fof(f83,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f82]) ).
fof(f84,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f82]) ).
fof(f85,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f82]) ).
fof(f86,plain,
! [A,B,C] :
( ~ relation(C)
| ( in(A,relation_restriction(C,B))
<=> ( in(A,C)
& in(A,cartesian_product2(B,B)) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f27]) ).
fof(f87,plain,
! [A,B,C] :
( ~ relation(C)
| ( ( ~ in(A,relation_restriction(C,B))
| ( in(A,C)
& in(A,cartesian_product2(B,B)) ) )
& ( in(A,relation_restriction(C,B))
| ~ in(A,C)
| ~ in(A,cartesian_product2(B,B)) ) ) ),
inference(NNF_transformation,[status(esa)],[f86]) ).
fof(f88,plain,
! [C] :
( ~ relation(C)
| ( ! [A,B] :
( ~ in(A,relation_restriction(C,B))
| ( in(A,C)
& in(A,cartesian_product2(B,B)) ) )
& ! [A,B] :
( in(A,relation_restriction(C,B))
| ~ in(A,C)
| ~ in(A,cartesian_product2(B,B)) ) ) ),
inference(miniscoping,[status(esa)],[f87]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| ~ in(X1,relation_restriction(X0,X2))
| in(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f88]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| ~ in(X1,relation_restriction(X0,X2))
| in(X1,cartesian_product2(X2,X2)) ),
inference(cnf_transformation,[status(esa)],[f88]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| in(X1,relation_restriction(X0,X2))
| ~ in(X1,X0)
| ~ in(X1,cartesian_product2(X2,X2)) ),
inference(cnf_transformation,[status(esa)],[f88]) ).
fof(f94,plain,
? [A,B] :
( relation(B)
& transitive(B)
& ~ transitive(relation_restriction(B,A)) ),
inference(pre_NNF_transformation,[status(esa)],[f30]) ).
fof(f95,plain,
? [B] :
( relation(B)
& transitive(B)
& ? [A] : ~ transitive(relation_restriction(B,A)) ),
inference(miniscoping,[status(esa)],[f94]) ).
fof(f96,plain,
( relation(sk0_9)
& transitive(sk0_9)
& ~ transitive(relation_restriction(sk0_9,sk0_10)) ),
inference(skolemization,[status(esa)],[f95]) ).
fof(f97,plain,
relation(sk0_9),
inference(cnf_transformation,[status(esa)],[f96]) ).
fof(f98,plain,
transitive(sk0_9),
inference(cnf_transformation,[status(esa)],[f96]) ).
fof(f99,plain,
~ transitive(relation_restriction(sk0_9,sk0_10)),
inference(cnf_transformation,[status(esa)],[f96]) ).
fof(f216,plain,
! [X0,X1] :
( ~ relation(relation_restriction(X0,X1))
| transitive(relation_restriction(X0,X1))
| ~ relation(X0)
| in(ordered_pair(sk0_1(relation_restriction(X0,X1)),sk0_3(relation_restriction(X0,X1))),cartesian_product2(X1,X1)) ),
inference(resolution,[status(thm)],[f63,f90]) ).
fof(f217,plain,
! [X0,X1] :
( transitive(relation_restriction(X0,X1))
| ~ relation(X0)
| in(ordered_pair(sk0_1(relation_restriction(X0,X1)),sk0_3(relation_restriction(X0,X1))),cartesian_product2(X1,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f216,f51]) ).
fof(f218,plain,
! [X0,X1] :
( ~ relation(relation_restriction(X0,X1))
| transitive(relation_restriction(X0,X1))
| ~ relation(X0)
| in(ordered_pair(sk0_1(relation_restriction(X0,X1)),sk0_3(relation_restriction(X0,X1))),X0) ),
inference(resolution,[status(thm)],[f63,f89]) ).
fof(f219,plain,
! [X0,X1] :
( transitive(relation_restriction(X0,X1))
| ~ relation(X0)
| in(ordered_pair(sk0_1(relation_restriction(X0,X1)),sk0_3(relation_restriction(X0,X1))),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f218,f51]) ).
fof(f277,plain,
( spl0_22
<=> relation(sk0_9) ),
introduced(split_symbol_definition) ).
fof(f279,plain,
( ~ relation(sk0_9)
| spl0_22 ),
inference(component_clause,[status(thm)],[f277]) ).
fof(f284,plain,
( $false
| spl0_22 ),
inference(forward_subsumption_resolution,[status(thm)],[f279,f97]) ).
fof(f285,plain,
spl0_22,
inference(contradiction_clause,[status(thm)],[f284]) ).
fof(f534,plain,
( spl0_47
<=> transitive(sk0_9) ),
introduced(split_symbol_definition) ).
fof(f536,plain,
( ~ transitive(sk0_9)
| spl0_47 ),
inference(component_clause,[status(thm)],[f534]) ).
fof(f557,plain,
! [X0,X1] :
( in(sk0_1(relation_restriction(X0,X1)),X1)
| transitive(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f83,f217]) ).
fof(f578,plain,
! [X0,X1] :
( ~ relation(relation_restriction(X0,X1))
| transitive(relation_restriction(X0,X1))
| ~ relation(X0)
| in(ordered_pair(sk0_3(relation_restriction(X0,X1)),sk0_2(relation_restriction(X0,X1))),cartesian_product2(X1,X1)) ),
inference(resolution,[status(thm)],[f64,f90]) ).
fof(f579,plain,
! [X0,X1] :
( transitive(relation_restriction(X0,X1))
| ~ relation(X0)
| in(ordered_pair(sk0_3(relation_restriction(X0,X1)),sk0_2(relation_restriction(X0,X1))),cartesian_product2(X1,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f578,f51]) ).
fof(f580,plain,
! [X0,X1] :
( ~ relation(relation_restriction(X0,X1))
| transitive(relation_restriction(X0,X1))
| ~ relation(X0)
| in(ordered_pair(sk0_3(relation_restriction(X0,X1)),sk0_2(relation_restriction(X0,X1))),X0) ),
inference(resolution,[status(thm)],[f64,f89]) ).
fof(f581,plain,
! [X0,X1] :
( transitive(relation_restriction(X0,X1))
| ~ relation(X0)
| in(ordered_pair(sk0_3(relation_restriction(X0,X1)),sk0_2(relation_restriction(X0,X1))),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f580,f51]) ).
fof(f602,plain,
! [X0,X1,X2,X3] :
( ~ in(X0,X1)
| ~ in(X2,X1)
| ~ relation(X3)
| in(ordered_pair(X0,X2),relation_restriction(X3,X1))
| ~ in(ordered_pair(X0,X2),X3) ),
inference(resolution,[status(thm)],[f85,f91]) ).
fof(f763,plain,
! [X0,X1,X2] :
( transitive(relation_restriction(X0,X1))
| ~ relation(X0)
| ~ relation(X0)
| ~ transitive(X0)
| ~ in(ordered_pair(X2,sk0_3(relation_restriction(X0,X1))),X0)
| in(ordered_pair(X2,sk0_2(relation_restriction(X0,X1))),X0) ),
inference(resolution,[status(thm)],[f581,f62]) ).
fof(f764,plain,
! [X0,X1,X2] :
( transitive(relation_restriction(X0,X1))
| ~ relation(X0)
| ~ transitive(X0)
| ~ in(ordered_pair(X2,sk0_3(relation_restriction(X0,X1))),X0)
| in(ordered_pair(X2,sk0_2(relation_restriction(X0,X1))),X0) ),
inference(duplicate_literals_removal,[status(esa)],[f763]) ).
fof(f1116,plain,
! [X0,X1] :
( in(sk0_2(relation_restriction(X0,X1)),X1)
| transitive(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f84,f579]) ).
fof(f1135,plain,
! [X0,X1] :
( ~ relation(relation_restriction(X0,X1))
| transitive(relation_restriction(X0,X1))
| ~ in(sk0_1(relation_restriction(X0,X1)),X1)
| ~ in(sk0_2(relation_restriction(X0,X1)),X1)
| ~ relation(X0)
| ~ in(ordered_pair(sk0_1(relation_restriction(X0,X1)),sk0_2(relation_restriction(X0,X1))),X0) ),
inference(resolution,[status(thm)],[f65,f602]) ).
fof(f1136,plain,
! [X0,X1] :
( transitive(relation_restriction(X0,X1))
| ~ in(sk0_1(relation_restriction(X0,X1)),X1)
| ~ in(sk0_2(relation_restriction(X0,X1)),X1)
| ~ relation(X0)
| ~ in(ordered_pair(sk0_1(relation_restriction(X0,X1)),sk0_2(relation_restriction(X0,X1))),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1135,f51]) ).
fof(f1597,plain,
! [X0,X1] :
( transitive(relation_restriction(X0,X1))
| ~ relation(X0)
| ~ transitive(X0)
| in(ordered_pair(sk0_1(relation_restriction(X0,X1)),sk0_2(relation_restriction(X0,X1))),X0)
| transitive(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f764,f219]) ).
fof(f1598,plain,
! [X0,X1] :
( transitive(relation_restriction(X0,X1))
| ~ relation(X0)
| ~ transitive(X0)
| in(ordered_pair(sk0_1(relation_restriction(X0,X1)),sk0_2(relation_restriction(X0,X1))),X0) ),
inference(duplicate_literals_removal,[status(esa)],[f1597]) ).
fof(f3289,plain,
! [X0,X1] :
( transitive(relation_restriction(X0,X1))
| ~ in(sk0_2(relation_restriction(X0,X1)),X1)
| ~ relation(X0)
| ~ in(ordered_pair(sk0_1(relation_restriction(X0,X1)),sk0_2(relation_restriction(X0,X1))),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1136,f557]) ).
fof(f3293,plain,
! [X0,X1] :
( transitive(relation_restriction(X0,X1))
| ~ in(sk0_2(relation_restriction(X0,X1)),X1)
| ~ relation(X0)
| transitive(relation_restriction(X0,X1))
| ~ relation(X0)
| ~ transitive(X0) ),
inference(resolution,[status(thm)],[f3289,f1598]) ).
fof(f3294,plain,
! [X0,X1] :
( transitive(relation_restriction(X0,X1))
| ~ in(sk0_2(relation_restriction(X0,X1)),X1)
| ~ relation(X0)
| ~ transitive(X0) ),
inference(duplicate_literals_removal,[status(esa)],[f3293]) ).
fof(f3295,plain,
! [X0,X1] :
( transitive(relation_restriction(X0,X1))
| ~ relation(X0)
| ~ transitive(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3294,f1116]) ).
fof(f3317,plain,
( ~ relation(sk0_9)
| ~ transitive(sk0_9) ),
inference(resolution,[status(thm)],[f3295,f99]) ).
fof(f3318,plain,
( ~ spl0_22
| ~ spl0_47 ),
inference(split_clause,[status(thm)],[f3317,f277,f534]) ).
fof(f3321,plain,
( $false
| spl0_47 ),
inference(forward_subsumption_resolution,[status(thm)],[f536,f98]) ).
fof(f3322,plain,
spl0_47,
inference(contradiction_clause,[status(thm)],[f3321]) ).
fof(f3323,plain,
$false,
inference(sat_refutation,[status(thm)],[f285,f3318,f3322]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU254+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue May 30 09:13:42 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.5.1
% 0.20/0.48 % Refutation found
% 0.20/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.50 % Elapsed time: 0.144058 seconds
% 0.20/0.50 % CPU time: 0.989390 seconds
% 0.20/0.50 % Memory used: 72.015 MB
%------------------------------------------------------------------------------