%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU268+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 : n006.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 02:19:58 PM UTC 2026
% Result : Theorem 0.15s 0.48s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 14 unt; 0 def)
% Number of atoms : 172 ( 21 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 216 ( 87 ~; 88 |; 28 &)
% ( 8 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 90 ( 83 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_reflexive_in(A,B)
<=> ! [C] :
( in(C,B)
=> in(ordered_pair(C,C),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B] :
( relation(B)
=> ( B = inclusion_relation(A)
<=> ( ! [C,D] :
( ( in(D,A)
& in(C,A) )
=> ( in(ordered_pair(C,D),B)
<=> subset(C,D) ) )
& relation_field(B) = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A] :
( relation(A)
=> ( reflexive(A)
<=> is_reflexive_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A] : relation(inclusion_relation(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,conjecture,
! [A] : reflexive(inclusion_relation(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
~ ! [A] : reflexive(inclusion_relation(A)),
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f72,plain,
! [A] :
( ! [B] :
( is_reflexive_in(A,B)
<=> ! [C] :
( in(ordered_pair(C,C),A)
| ~ in(C,B) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f73,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ~ in(ordered_pair(C,C),A)
& in(C,B) )
| is_reflexive_in(A,B) )
& ( ! [C] :
( in(ordered_pair(C,C),A)
| ~ in(C,B) )
| ~ is_reflexive_in(A,B) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f72]) ).
fof(f74,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( ~ in(ordered_pair(C,C),A)
& in(C,B) )
| is_reflexive_in(A,B) )
& ! [B] :
( ! [C] :
( in(ordered_pair(C,C),A)
| ~ in(C,B) )
| ~ is_reflexive_in(A,B) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f73]) ).
fof(f75,plain,
! [A] :
( ( ! [B] :
( ( ~ in(ordered_pair(sK0_skl(B,A),sK0_skl(B,A)),A)
& in(sK0_skl(B,A),B) )
| is_reflexive_in(A,B) )
& ! [B] :
( ! [C] :
( in(ordered_pair(C,C),A)
| ~ in(C,B) )
| ~ is_reflexive_in(A,B) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f74]) ).
fof(f77,plain,
! [X0,X1] :
( in(sK0_skl(X1,X0),X1)
| is_reflexive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f78,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK0_skl(X1,X0),sK0_skl(X1,X0)),X0)
| is_reflexive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f79,plain,
! [A,B] :
( ( B = inclusion_relation(A)
<=> ( ! [C,D] :
( ( in(ordered_pair(C,D),B)
<=> subset(C,D) )
| ~ in(D,A)
| ~ in(C,A) )
& relation_field(B) = A ) )
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f80,plain,
! [A,B] :
( ( ( ? [C,D] :
( ( subset(C,D)
| in(ordered_pair(C,D),B) )
& ( ~ subset(C,D)
| ~ in(ordered_pair(C,D),B) )
& in(D,A)
& in(C,A) )
| relation_field(B) != A
| B = inclusion_relation(A) )
& ( ( ! [C,D] :
( ( ( ~ subset(C,D)
| in(ordered_pair(C,D),B) )
& ( subset(C,D)
| ~ in(ordered_pair(C,D),B) ) )
| ~ in(D,A)
| ~ in(C,A) )
& relation_field(B) = A )
| B != inclusion_relation(A) ) )
| ~ relation(B) ),
inference(NNF_transformation,[status(thm)],[f79]) ).
fof(f81,plain,
! [B] :
( ( ! [A] :
( ? [C,D] :
( ( subset(C,D)
| in(ordered_pair(C,D),B) )
& ( ~ subset(C,D)
| ~ in(ordered_pair(C,D),B) )
& in(D,A)
& in(C,A) )
| relation_field(B) != A
| B = inclusion_relation(A) )
& ! [A] :
( ( ! [C,D] :
( ( ( ~ subset(C,D)
| in(ordered_pair(C,D),B) )
& ( subset(C,D)
| ~ in(ordered_pair(C,D),B) ) )
| ~ in(D,A)
| ~ in(C,A) )
& relation_field(B) = A )
| B != inclusion_relation(A) ) )
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f80]) ).
fof(f82,plain,
! [B] :
( ( ! [A] :
( ( ( subset(sK1_skl(A,B),sK2_skl(A,B))
| in(ordered_pair(sK1_skl(A,B),sK2_skl(A,B)),B) )
& ( ~ subset(sK1_skl(A,B),sK2_skl(A,B))
| ~ in(ordered_pair(sK1_skl(A,B),sK2_skl(A,B)),B) )
& in(sK2_skl(A,B),A)
& in(sK1_skl(A,B),A) )
| relation_field(B) != A
| B = inclusion_relation(A) )
& ! [A] :
( ( ! [C,D] :
( ( ( ~ subset(C,D)
| in(ordered_pair(C,D),B) )
& ( subset(C,D)
| ~ in(ordered_pair(C,D),B) ) )
| ~ in(D,A)
| ~ in(C,A) )
& relation_field(B) = A )
| B != inclusion_relation(A) ) )
| ~ relation(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(C,sK1_skl(A,B)),skolemize(D,sK2_skl(A,B))],[f81]) ).
fof(f83,plain,
! [X0,X1] :
( relation_field(X0) = X1
| X0 != inclusion_relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f85,plain,
! [X0,X1,X2,X3] :
( ~ subset(X2,X3)
| in(ordered_pair(X2,X3),X0)
| ~ in(X3,X1)
| ~ in(X2,X1)
| X0 != inclusion_relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f93,plain,
! [A] :
( ( reflexive(A)
<=> is_reflexive_in(A,relation_field(A)) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f94,plain,
! [A] :
( ( ( ~ is_reflexive_in(A,relation_field(A))
| reflexive(A) )
& ( is_reflexive_in(A,relation_field(A))
| ~ reflexive(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f93]) ).
fof(f96,plain,
! [X0] :
( ~ is_reflexive_in(X0,relation_field(X0))
| reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f97,plain,
! [X0] : relation(inclusion_relation(X0)),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f154,plain,
! [A] : subset(A,A),
inference(miniscoping,[status(thm)],[f41]) ).
fof(f155,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f161,plain,
? [A] : ~ reflexive(inclusion_relation(A)),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f162,plain,
~ reflexive(inclusion_relation(sK13_skl)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl]),skolemize(A,sK13_skl)],[f161]) ).
fof(f163,plain,
~ reflexive(inclusion_relation(sK13_skl)),
inference(cnf_transformation,[status(thm)],[f162]) ).
fof(f182,plain,
! [X0] :
( relation_field(inclusion_relation(X0)) = X0
| ~ relation(inclusion_relation(X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f83]) ).
fof(f184,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| in(ordered_pair(X1,X2),inclusion_relation(X0))
| ~ in(X2,X0)
| ~ in(X1,X0)
| ~ relation(inclusion_relation(X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f85]) ).
fof(f241,plain,
! [X0] : relation_field(inclusion_relation(X0)) = X0,
inference(forward_subsumption_resolution,[status(thm)],[f182,f97]) ).
fof(f242,plain,
! [X0] :
( ~ is_reflexive_in(inclusion_relation(X0),X0)
| reflexive(inclusion_relation(X0))
| ~ relation(inclusion_relation(X0)) ),
inference(paramodulation,[status(thm)],[f241,f96]) ).
fof(f244,plain,
! [X0] :
( ~ is_reflexive_in(inclusion_relation(X0),X0)
| reflexive(inclusion_relation(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f242,f97]) ).
fof(f249,plain,
! [X0,X1,X2] :
( ~ subset(X0,X2)
| in(ordered_pair(X0,X2),inclusion_relation(X1))
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f184,f97]) ).
fof(f250,plain,
! [X0,X1] :
( is_reflexive_in(inclusion_relation(X1),X0)
| ~ relation(inclusion_relation(X1))
| ~ subset(sK0_skl(X0,inclusion_relation(X1)),sK0_skl(X0,inclusion_relation(X1)))
| ~ in(sK0_skl(X0,inclusion_relation(X1)),X1)
| ~ in(sK0_skl(X0,inclusion_relation(X1)),X1) ),
inference(resolution,[status(thm)],[f249,f78]) ).
fof(f253,plain,
! [X0,X1] :
( is_reflexive_in(inclusion_relation(X1),X0)
| ~ relation(inclusion_relation(X1))
| ~ subset(sK0_skl(X0,inclusion_relation(X1)),sK0_skl(X0,inclusion_relation(X1)))
| ~ in(sK0_skl(X0,inclusion_relation(X1)),X1) ),
inference(duplicate_literals_removal,[status(thm)],[f250]) ).
fof(f254,plain,
! [X0,X1] :
( is_reflexive_in(inclusion_relation(X1),X0)
| ~ relation(inclusion_relation(X1))
| ~ in(sK0_skl(X0,inclusion_relation(X1)),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f253,f155]) ).
fof(f256,plain,
! [X0,X1] :
( is_reflexive_in(inclusion_relation(X1),X0)
| ~ in(sK0_skl(X0,inclusion_relation(X1)),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f254,f97]) ).
fof(f257,plain,
! [X0] :
( is_reflexive_in(inclusion_relation(X0),X0)
| ~ relation(inclusion_relation(X0))
| is_reflexive_in(inclusion_relation(X0),X0) ),
inference(resolution,[status(thm)],[f256,f77]) ).
fof(f258,plain,
! [X0] :
( ~ relation(inclusion_relation(X0))
| is_reflexive_in(inclusion_relation(X0),X0) ),
inference(duplicate_literals_removal,[status(thm)],[f257]) ).
fof(f259,plain,
! [X0] : is_reflexive_in(inclusion_relation(X0),X0),
inference(forward_subsumption_resolution,[status(thm)],[f258,f97]) ).
fof(f260,plain,
! [X0] : reflexive(inclusion_relation(X0)),
inference(backward_subsumption_resolution,[status(thm)],[f244,f259]) ).
fof(f262,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f163,f260]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU268+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n006.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Mon Sep 21 06:05:12 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.44 % Drodi V4.1.1
% 0.15/0.48 % Refutation found
% 0.15/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/0.51 % Elapsed time: 0.076236 seconds
% 0.24/0.51 % CPU time: 0.199462 seconds
% 0.24/0.51 % Total memory used: 104.360 MB
% 0.24/0.51 % Net memory used: 104.306 MB
%------------------------------------------------------------------------------