%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU254+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:19:55 PM UTC 2026
% Result : Theorem 0.28s 0.90s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 65 ( 6 unt; 2 def)
% Number of atoms : 231 ( 0 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 278 ( 112 ~; 124 |; 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 : 144 ( 134 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [A,B] :
( relation(A)
=> relation(relation_restriction(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A] :
( relation(A)
=> ( transitive(A)
<=> ! [B,C,D] :
( ( in(ordered_pair(C,D),A)
& in(ordered_pair(B,C),A) )
=> in(ordered_pair(B,D),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_restriction(C,B))
<=> ( in(A,cartesian_product2(B,B))
& in(A,C) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
! [A,B] :
( relation(B)
=> ( transitive(B)
=> transitive(relation_restriction(B,A)) ) ),
file('/export/starexec/sandbox/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(relation_restriction(A,B))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f50,plain,
! [A] :
( ! [B] : relation(relation_restriction(A,B))
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f49]) ).
fof(f51,plain,
! [X0,X1] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f58,plain,
! [A] :
( ( transitive(A)
<=> ! [B,C,D] :
( in(ordered_pair(B,D),A)
| ~ in(ordered_pair(C,D),A)
| ~ in(ordered_pair(B,C),A) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f59,plain,
! [A] :
( ( ( ? [B,C,D] :
( ~ in(ordered_pair(B,D),A)
& in(ordered_pair(C,D),A)
& in(ordered_pair(B,C),A) )
| transitive(A) )
& ( ! [B,C,D] :
( in(ordered_pair(B,D),A)
| ~ in(ordered_pair(C,D),A)
| ~ in(ordered_pair(B,C),A) )
| ~ transitive(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f58]) ).
fof(f60,plain,
! [A] :
( ( ( ? [B,D] :
( ~ in(ordered_pair(B,D),A)
& ? [C] :
( in(ordered_pair(C,D),A)
& in(ordered_pair(B,C),A) ) )
| transitive(A) )
& ( ! [B,D] :
( in(ordered_pair(B,D),A)
| ! [C] :
( ~ in(ordered_pair(C,D),A)
| ~ in(ordered_pair(B,C),A) ) )
| ~ transitive(A) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f59]) ).
fof(f61,plain,
! [A] :
( ( ( ( ~ in(ordered_pair(sK1_skl(A),sK2_skl(A)),A)
& in(ordered_pair(sK3_skl(A),sK2_skl(A)),A)
& in(ordered_pair(sK1_skl(A),sK3_skl(A)),A) )
| transitive(A) )
& ( ! [B,D] :
( in(ordered_pair(B,D),A)
| ! [C] :
( ~ in(ordered_pair(C,D),A)
| ~ in(ordered_pair(B,C),A) ) )
| ~ transitive(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl]),skolemize(B,sK1_skl(A)),skolemize(D,sK2_skl(A)),skolemize(C,sK3_skl(A))],[f60]) ).
fof(f62,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X1,X2),X0)
| ~ transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
! [X0] :
( in(ordered_pair(sK1_skl(X0),sK3_skl(X0)),X0)
| transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f64,plain,
! [X0] :
( in(ordered_pair(sK3_skl(X0),sK2_skl(X0)),X0)
| transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f65,plain,
! [X0] :
( ~ in(ordered_pair(sK1_skl(X0),sK2_skl(X0)),X0)
| transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f81,plain,
! [A,B,C,D] :
( ( ~ in(B,D)
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,D)) )
& ( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(NNF_transformation,[status(thm)],[f26]) ).
fof(f82,plain,
( ! [A,B,C,D] :
( ~ in(B,D)
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,D)) )
& ! [A,B,C,D] :
( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(miniscoping,[status(thm)],[f81]) ).
fof(f83,plain,
! [X0,X1,X2,X3] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f84,plain,
! [X0,X1,X2,X3] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f85,plain,
! [X0,X1,X2,X3] :
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f86,plain,
! [A,B,C] :
( ( in(A,relation_restriction(C,B))
<=> ( in(A,cartesian_product2(B,B))
& in(A,C) ) )
| ~ relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f87,plain,
! [A,B,C] :
( ( ( ~ in(A,cartesian_product2(B,B))
| ~ in(A,C)
| in(A,relation_restriction(C,B)) )
& ( ( in(A,cartesian_product2(B,B))
& in(A,C) )
| ~ in(A,relation_restriction(C,B)) ) )
| ~ relation(C) ),
inference(NNF_transformation,[status(thm)],[f86]) ).
fof(f88,plain,
! [C] :
( ( ! [A,B] :
( ~ in(A,cartesian_product2(B,B))
| ~ in(A,C)
| in(A,relation_restriction(C,B)) )
& ! [A,B] :
( ( in(A,cartesian_product2(B,B))
& in(A,C) )
| ~ in(A,relation_restriction(C,B)) ) )
| ~ relation(C) ),
inference(miniscoping,[status(thm)],[f87]) ).
fof(f89,plain,
! [X0,X1,X2] :
( in(X1,X0)
| ~ in(X1,relation_restriction(X0,X2))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f88]) ).
fof(f90,plain,
! [X0,X1,X2] :
( in(X1,cartesian_product2(X2,X2))
| ~ in(X1,relation_restriction(X0,X2))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f88]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ~ in(X1,cartesian_product2(X2,X2))
| ~ in(X1,X0)
| in(X1,relation_restriction(X0,X2))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f88]) ).
fof(f94,plain,
? [A,B] :
( ~ transitive(relation_restriction(B,A))
& transitive(B)
& relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f95,plain,
? [B] :
( ? [A] : ~ transitive(relation_restriction(B,A))
& transitive(B)
& relation(B) ),
inference(miniscoping,[status(thm)],[f94]) ).
fof(f96,plain,
( ~ transitive(relation_restriction(sK9_skl,sK10_skl))
& transitive(sK9_skl)
& relation(sK9_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl]),skolemize(B,sK9_skl),skolemize(A,sK10_skl)],[f95]) ).
fof(f97,plain,
relation(sK9_skl),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f98,plain,
transitive(sK9_skl),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f99,plain,
~ transitive(relation_restriction(sK9_skl,sK10_skl)),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f177,plain,
! [X0,X1] :
( in(ordered_pair(sK1_skl(relation_restriction(X0,X1)),sK3_skl(relation_restriction(X0,X1))),cartesian_product2(X1,X1))
| ~ relation(X0)
| transitive(relation_restriction(X0,X1))
| ~ relation(relation_restriction(X0,X1)) ),
inference(resolution,[status(thm)],[f63,f90]) ).
fof(f178,plain,
! [X0,X1] :
( in(ordered_pair(sK1_skl(relation_restriction(X0,X1)),sK3_skl(relation_restriction(X0,X1))),X0)
| ~ relation(X0)
| transitive(relation_restriction(X0,X1))
| ~ relation(relation_restriction(X0,X1)) ),
inference(resolution,[status(thm)],[f63,f89]) ).
fof(f182,plain,
! [X0,X1] :
( in(ordered_pair(sK1_skl(relation_restriction(X0,X1)),sK3_skl(relation_restriction(X0,X1))),cartesian_product2(X1,X1))
| ~ relation(X0)
| transitive(relation_restriction(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f177,f51]) ).
fof(f183,plain,
! [X0,X1] :
( in(ordered_pair(sK1_skl(relation_restriction(X0,X1)),sK3_skl(relation_restriction(X0,X1))),X0)
| ~ relation(X0)
| transitive(relation_restriction(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f178,f51]) ).
fof(f195,definition,
( sQ3_spl
<=> relation(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f197,plain,
( sQ3_spl
| ~ relation(sK9_skl) ),
inference(component_clause,[status(thm)],[f195]) ).
fof(f202,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f197,f97]) ).
fof(f203,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f202]) ).
fof(f528,plain,
! [X0,X1] :
( ~ relation(X0)
| transitive(relation_restriction(X0,X1))
| in(sK1_skl(relation_restriction(X0,X1)),X1) ),
inference(resolution,[status(thm)],[f83,f182]) ).
fof(f586,plain,
! [X0,X1] :
( in(ordered_pair(sK3_skl(relation_restriction(X0,X1)),sK2_skl(relation_restriction(X0,X1))),cartesian_product2(X1,X1))
| ~ relation(X0)
| transitive(relation_restriction(X0,X1))
| ~ relation(relation_restriction(X0,X1)) ),
inference(resolution,[status(thm)],[f64,f90]) ).
fof(f587,plain,
! [X0,X1] :
( in(ordered_pair(sK3_skl(relation_restriction(X0,X1)),sK2_skl(relation_restriction(X0,X1))),X0)
| ~ relation(X0)
| transitive(relation_restriction(X0,X1))
| ~ relation(relation_restriction(X0,X1)) ),
inference(resolution,[status(thm)],[f64,f89]) ).
fof(f596,plain,
! [X0,X1] :
( in(ordered_pair(sK3_skl(relation_restriction(X0,X1)),sK2_skl(relation_restriction(X0,X1))),cartesian_product2(X1,X1))
| ~ relation(X0)
| transitive(relation_restriction(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f586,f51]) ).
fof(f597,plain,
! [X0,X1] :
( in(ordered_pair(sK3_skl(relation_restriction(X0,X1)),sK2_skl(relation_restriction(X0,X1))),X0)
| ~ relation(X0)
| transitive(relation_restriction(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f587,f51]) ).
fof(f606,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X0,X2),X3)
| in(ordered_pair(X0,X2),relation_restriction(X3,X1))
| ~ relation(X3)
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f85,f91]) ).
fof(f792,plain,
! [X0,X1] :
( transitive(relation_restriction(X0,X1))
| ~ relation(relation_restriction(X0,X1))
| ~ in(ordered_pair(sK1_skl(relation_restriction(X0,X1)),sK2_skl(relation_restriction(X0,X1))),X0)
| ~ relation(X0)
| ~ in(sK2_skl(relation_restriction(X0,X1)),X1)
| ~ in(sK1_skl(relation_restriction(X0,X1)),X1) ),
inference(resolution,[status(thm)],[f606,f65]) ).
fof(f800,plain,
! [X0,X1] :
( transitive(relation_restriction(X0,X1))
| ~ relation(relation_restriction(X0,X1))
| ~ in(ordered_pair(sK1_skl(relation_restriction(X0,X1)),sK2_skl(relation_restriction(X0,X1))),X0)
| ~ relation(X0)
| ~ in(sK2_skl(relation_restriction(X0,X1)),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f792,f528]) ).
fof(f1013,plain,
! [X0,X1] :
( in(sK2_skl(relation_restriction(X0,X1)),X1)
| ~ relation(X0)
| transitive(relation_restriction(X0,X1)) ),
inference(resolution,[status(thm)],[f596,f84]) ).
fof(f1022,plain,
! [X0,X1] :
( transitive(relation_restriction(X0,X1))
| ~ relation(relation_restriction(X0,X1))
| ~ in(ordered_pair(sK1_skl(relation_restriction(X0,X1)),sK2_skl(relation_restriction(X0,X1))),X0)
| ~ relation(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f800,f1013]) ).
fof(f1033,plain,
! [X0,X1] :
( transitive(relation_restriction(X0,X1))
| ~ in(ordered_pair(sK1_skl(relation_restriction(X0,X1)),sK2_skl(relation_restriction(X0,X1))),X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1022,f51]) ).
fof(f1095,plain,
! [X0,X1,X2] :
( in(ordered_pair(X2,sK2_skl(relation_restriction(X0,X1))),X0)
| ~ in(ordered_pair(X2,sK3_skl(relation_restriction(X0,X1))),X0)
| ~ transitive(X0)
| ~ relation(X0)
| ~ relation(X0)
| transitive(relation_restriction(X0,X1)) ),
inference(resolution,[status(thm)],[f597,f62]) ).
fof(f1107,plain,
! [X0,X1,X2] :
( in(ordered_pair(X2,sK2_skl(relation_restriction(X0,X1))),X0)
| ~ in(ordered_pair(X2,sK3_skl(relation_restriction(X0,X1))),X0)
| ~ transitive(X0)
| ~ relation(X0)
| transitive(relation_restriction(X0,X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f1095]) ).
fof(f2826,plain,
! [X0,X1] :
( ~ relation(X0)
| transitive(relation_restriction(X0,X1))
| in(ordered_pair(sK1_skl(relation_restriction(X0,X1)),sK2_skl(relation_restriction(X0,X1))),X0)
| ~ transitive(X0)
| ~ relation(X0)
| transitive(relation_restriction(X0,X1)) ),
inference(resolution,[status(thm)],[f1107,f183]) ).
fof(f2835,plain,
! [X0,X1] :
( in(ordered_pair(sK1_skl(relation_restriction(X0,X1)),sK2_skl(relation_restriction(X0,X1))),X0)
| ~ transitive(X0)
| ~ relation(X0)
| transitive(relation_restriction(X0,X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f2826]) ).
fof(f2836,plain,
! [X0,X1] :
( ~ transitive(X0)
| ~ relation(X0)
| transitive(relation_restriction(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f2835,f1033]) ).
fof(f2879,plain,
( ~ transitive(sK9_skl)
| ~ relation(sK9_skl) ),
inference(resolution,[status(thm)],[f2836,f99]) ).
fof(f2881,definition,
( sQ145_spl
<=> transitive(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f2883,plain,
( sQ145_spl
| ~ transitive(sK9_skl) ),
inference(component_clause,[status(thm)],[f2881]) ).
fof(f2884,plain,
( ~ sQ145_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2879,f195,f2881]) ).
fof(f2886,plain,
( sQ145_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2883,f98]) ).
fof(f2887,plain,
sQ145_spl,
inference(contradiction_clause,[status(thm)],[f2886]) ).
fof(f2888,plain,
$false,
inference(sat_refutation,[status(thm)],[f203,f2884,f2887]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU254+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n013.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 06:03:20 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.46 % Drodi V4.1.1
% 0.28/0.90 % Refutation found
% 0.28/0.90 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.28/0.90 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.28/0.95 % Elapsed time: 0.489247 seconds
% 0.28/0.95 % CPU time: 3.453982 seconds
% 0.28/0.95 % Total memory used: 139.574 MB
% 0.28/0.95 % Net memory used: 136.393 MB
%------------------------------------------------------------------------------