%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU261+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 02:19:56 PM UTC 2026
% Result : Theorem 0.14s 0.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 74 ( 19 unt; 0 def)
% Number of atoms : 291 ( 0 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 384 ( 167 ~; 159 |; 38 &)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 39 ( 36 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A] :
( relation(A)
=> ( well_ordering(A)
<=> ( well_founded_relation(A)
& connected(A)
& antisymmetric(A)
& transitive(A)
& reflexive(A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( relation_isomorphism(A,B,C)
=> ( ( well_founded_relation(A)
=> well_founded_relation(B) )
& ( antisymmetric(A)
=> antisymmetric(B) )
& ( connected(A)
=> connected(B) )
& ( transitive(A)
=> transitive(B) )
& ( reflexive(A)
=> reflexive(B) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,conjecture,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( ( relation_isomorphism(A,B,C)
& well_ordering(A) )
=> well_ordering(B) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
~ ! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( ( relation_isomorphism(A,B,C)
& well_ordering(A) )
=> well_ordering(B) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,plain,
! [A] :
( ( well_ordering(A)
<=> ( well_founded_relation(A)
& connected(A)
& antisymmetric(A)
& transitive(A)
& reflexive(A) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f7,plain,
! [A] :
( ( ( ~ well_founded_relation(A)
| ~ connected(A)
| ~ antisymmetric(A)
| ~ transitive(A)
| ~ reflexive(A)
| well_ordering(A) )
& ( ( well_founded_relation(A)
& connected(A)
& antisymmetric(A)
& transitive(A)
& reflexive(A) )
| ~ well_ordering(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f8,plain,
! [X0] :
( reflexive(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f9,plain,
! [X0] :
( transitive(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f10,plain,
! [X0] :
( antisymmetric(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f11,plain,
! [X0] :
( connected(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f12,plain,
! [X0] :
( well_founded_relation(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f13,plain,
! [X0] :
( ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0)
| well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f17,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( well_founded_relation(B)
| ~ well_founded_relation(A) )
& ( antisymmetric(B)
| ~ antisymmetric(A) )
& ( connected(B)
| ~ connected(A) )
& ( transitive(B)
| ~ transitive(A) )
& ( reflexive(B)
| ~ reflexive(A) ) )
| ~ relation_isomorphism(A,B,C)
| ~ function(C)
| ~ relation(C) )
| ~ relation(B) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f18,plain,
! [X0,X1,X2] :
( reflexive(X1)
| ~ reflexive(X0)
| ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( transitive(X1)
| ~ transitive(X0)
| ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f20,plain,
! [X0,X1,X2] :
( connected(X1)
| ~ connected(X0)
| ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f21,plain,
! [X0,X1,X2] :
( antisymmetric(X1)
| ~ antisymmetric(X0)
| ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f22,plain,
! [X0,X1,X2] :
( well_founded_relation(X1)
| ~ well_founded_relation(X0)
| ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f23,plain,
? [A] :
( ? [B] :
( ? [C] :
( ~ well_ordering(B)
& relation_isomorphism(A,B,C)
& well_ordering(A)
& function(C)
& relation(C) )
& relation(B) )
& relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f24,plain,
( ~ well_ordering(sK2_skl)
& relation_isomorphism(sK1_skl,sK2_skl,sK3_skl)
& well_ordering(sK1_skl)
& function(sK3_skl)
& relation(sK3_skl)
& relation(sK2_skl)
& relation(sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl]),skolemize(A,sK1_skl),skolemize(B,sK2_skl),skolemize(C,sK3_skl)],[f23]) ).
fof(f25,plain,
relation(sK1_skl),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
relation(sK2_skl),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f27,plain,
relation(sK3_skl),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f28,plain,
function(sK3_skl),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f29,plain,
well_ordering(sK1_skl),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f30,plain,
relation_isomorphism(sK1_skl,sK2_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f31,plain,
~ well_ordering(sK2_skl),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f32,plain,
( reflexive(sK1_skl)
| ~ relation(sK1_skl) ),
inference(resolution,[status(thm)],[f8,f29]) ).
fof(f33,plain,
reflexive(sK1_skl),
inference(forward_subsumption_resolution,[status(thm)],[f32,f25]) ).
fof(f34,plain,
( transitive(sK1_skl)
| ~ relation(sK1_skl) ),
inference(resolution,[status(thm)],[f9,f29]) ).
fof(f35,plain,
transitive(sK1_skl),
inference(forward_subsumption_resolution,[status(thm)],[f34,f25]) ).
fof(f36,plain,
( antisymmetric(sK1_skl)
| ~ relation(sK1_skl) ),
inference(resolution,[status(thm)],[f10,f29]) ).
fof(f37,plain,
antisymmetric(sK1_skl),
inference(forward_subsumption_resolution,[status(thm)],[f36,f25]) ).
fof(f38,plain,
( connected(sK1_skl)
| ~ relation(sK1_skl) ),
inference(resolution,[status(thm)],[f11,f29]) ).
fof(f39,plain,
connected(sK1_skl),
inference(forward_subsumption_resolution,[status(thm)],[f38,f25]) ).
fof(f40,plain,
( well_founded_relation(sK1_skl)
| ~ relation(sK1_skl) ),
inference(resolution,[status(thm)],[f12,f29]) ).
fof(f41,plain,
well_founded_relation(sK1_skl),
inference(forward_subsumption_resolution,[status(thm)],[f40,f25]) ).
fof(f47,plain,
( reflexive(sK2_skl)
| ~ reflexive(sK1_skl)
| ~ function(sK3_skl)
| ~ relation(sK3_skl)
| ~ relation(sK2_skl)
| ~ relation(sK1_skl) ),
inference(resolution,[status(thm)],[f18,f30]) ).
fof(f48,plain,
( reflexive(sK2_skl)
| ~ reflexive(sK1_skl)
| ~ function(sK3_skl)
| ~ relation(sK3_skl)
| ~ relation(sK2_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f47,f25]) ).
fof(f49,plain,
( reflexive(sK2_skl)
| ~ reflexive(sK1_skl)
| ~ function(sK3_skl)
| ~ relation(sK3_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f48,f26]) ).
fof(f50,plain,
( reflexive(sK2_skl)
| ~ reflexive(sK1_skl)
| ~ relation(sK3_skl) ),
inference(resolution,[status(thm)],[f49,f28]) ).
fof(f52,plain,
( reflexive(sK2_skl)
| ~ reflexive(sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f50,f27]) ).
fof(f54,plain,
reflexive(sK2_skl),
inference(forward_subsumption_resolution,[status(thm)],[f52,f33]) ).
fof(f55,plain,
( ~ well_founded_relation(sK2_skl)
| ~ connected(sK2_skl)
| ~ antisymmetric(sK2_skl)
| ~ transitive(sK2_skl)
| well_ordering(sK2_skl)
| ~ relation(sK2_skl) ),
inference(resolution,[status(thm)],[f54,f13]) ).
fof(f56,plain,
( ~ well_founded_relation(sK2_skl)
| ~ connected(sK2_skl)
| ~ antisymmetric(sK2_skl)
| ~ transitive(sK2_skl)
| well_ordering(sK2_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f55,f26]) ).
fof(f57,plain,
( ~ well_founded_relation(sK2_skl)
| ~ connected(sK2_skl)
| ~ antisymmetric(sK2_skl)
| ~ transitive(sK2_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f56,f31]) ).
fof(f58,plain,
( transitive(sK2_skl)
| ~ transitive(sK1_skl)
| ~ function(sK3_skl)
| ~ relation(sK3_skl)
| ~ relation(sK2_skl)
| ~ relation(sK1_skl) ),
inference(resolution,[status(thm)],[f19,f30]) ).
fof(f59,plain,
( transitive(sK2_skl)
| ~ transitive(sK1_skl)
| ~ function(sK3_skl)
| ~ relation(sK3_skl)
| ~ relation(sK2_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f58,f25]) ).
fof(f60,plain,
( transitive(sK2_skl)
| ~ transitive(sK1_skl)
| ~ function(sK3_skl)
| ~ relation(sK3_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f59,f26]) ).
fof(f61,plain,
( transitive(sK2_skl)
| ~ transitive(sK1_skl)
| ~ relation(sK3_skl) ),
inference(resolution,[status(thm)],[f60,f28]) ).
fof(f63,plain,
( transitive(sK2_skl)
| ~ transitive(sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f61,f27]) ).
fof(f65,plain,
( ~ well_founded_relation(sK2_skl)
| ~ connected(sK2_skl)
| ~ antisymmetric(sK2_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f57,f66]) ).
fof(f66,plain,
transitive(sK2_skl),
inference(forward_subsumption_resolution,[status(thm)],[f63,f35]) ).
fof(f69,plain,
( connected(sK2_skl)
| ~ connected(sK1_skl)
| ~ function(sK3_skl)
| ~ relation(sK3_skl)
| ~ relation(sK2_skl)
| ~ relation(sK1_skl) ),
inference(resolution,[status(thm)],[f20,f30]) ).
fof(f70,plain,
( connected(sK2_skl)
| ~ connected(sK1_skl)
| ~ function(sK3_skl)
| ~ relation(sK3_skl)
| ~ relation(sK2_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f69,f25]) ).
fof(f71,plain,
( connected(sK2_skl)
| ~ connected(sK1_skl)
| ~ function(sK3_skl)
| ~ relation(sK3_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f70,f26]) ).
fof(f72,plain,
( connected(sK2_skl)
| ~ connected(sK1_skl)
| ~ relation(sK3_skl) ),
inference(resolution,[status(thm)],[f71,f28]) ).
fof(f74,plain,
( connected(sK2_skl)
| ~ connected(sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f72,f27]) ).
fof(f76,plain,
( antisymmetric(sK2_skl)
| ~ antisymmetric(sK1_skl)
| ~ function(sK3_skl)
| ~ relation(sK3_skl)
| ~ relation(sK2_skl)
| ~ relation(sK1_skl) ),
inference(resolution,[status(thm)],[f21,f30]) ).
fof(f77,plain,
( antisymmetric(sK2_skl)
| ~ antisymmetric(sK1_skl)
| ~ function(sK3_skl)
| ~ relation(sK3_skl)
| ~ relation(sK2_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f76,f25]) ).
fof(f78,plain,
( well_founded_relation(sK2_skl)
| ~ well_founded_relation(sK1_skl)
| ~ function(sK3_skl)
| ~ relation(sK3_skl)
| ~ relation(sK2_skl)
| ~ relation(sK1_skl) ),
inference(resolution,[status(thm)],[f22,f30]) ).
fof(f79,plain,
( well_founded_relation(sK2_skl)
| ~ well_founded_relation(sK1_skl)
| ~ function(sK3_skl)
| ~ relation(sK3_skl)
| ~ relation(sK2_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f78,f25]) ).
fof(f80,plain,
( antisymmetric(sK2_skl)
| ~ antisymmetric(sK1_skl)
| ~ function(sK3_skl)
| ~ relation(sK3_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f77,f26]) ).
fof(f81,plain,
( antisymmetric(sK2_skl)
| ~ antisymmetric(sK1_skl)
| ~ relation(sK3_skl) ),
inference(resolution,[status(thm)],[f80,f28]) ).
fof(f83,plain,
( antisymmetric(sK2_skl)
| ~ antisymmetric(sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f81,f27]) ).
fof(f85,plain,
( ~ well_founded_relation(sK2_skl)
| ~ antisymmetric(sK2_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f65,f86]) ).
fof(f86,plain,
connected(sK2_skl),
inference(forward_subsumption_resolution,[status(thm)],[f74,f39]) ).
fof(f89,plain,
antisymmetric(sK2_skl),
inference(forward_subsumption_resolution,[status(thm)],[f83,f37]) ).
fof(f92,plain,
~ well_founded_relation(sK2_skl),
inference(forward_subsumption_resolution,[status(thm)],[f85,f89]) ).
fof(f93,plain,
( well_founded_relation(sK2_skl)
| ~ well_founded_relation(sK1_skl)
| ~ function(sK3_skl)
| ~ relation(sK3_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f79,f26]) ).
fof(f94,plain,
( well_founded_relation(sK2_skl)
| ~ well_founded_relation(sK1_skl)
| ~ relation(sK3_skl) ),
inference(resolution,[status(thm)],[f93,f28]) ).
fof(f96,plain,
( well_founded_relation(sK2_skl)
| ~ well_founded_relation(sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f94,f27]) ).
fof(f99,plain,
well_founded_relation(sK2_skl),
inference(forward_subsumption_resolution,[status(thm)],[f96,f41]) ).
fof(f100,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f92,f99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU261+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 06:03:55 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.14/0.41 % Refutation found
% 0.14/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.45 % Elapsed time: 0.074648 seconds
% 0.14/0.45 % CPU time: 0.188639 seconds
% 0.14/0.45 % Total memory used: 56.123 MB
% 0.14/0.45 % Net memory used: 55.783 MB
%------------------------------------------------------------------------------