%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU236+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 02:19:50 PM UTC 2026
% Result : Theorem 0.13s 0.50s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of formulae : 68 ( 9 unt; 0 def)
% Number of atoms : 234 ( 26 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 274 ( 108 ~; 105 |; 40 &)
% ( 10 <=>; 10 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 117 ( 107 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] : succ(A) = set_union2(A,singleton(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A] :
( ordinal(A)
=> ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [A] : in(A,succ(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,conjecture,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( in(A,B)
<=> ordinal_subset(succ(A),B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( in(A,B)
<=> ordinal_subset(succ(A),B) ) ) ),
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f53,axiom,
! [A,B,C] :
( ( subset(C,B)
& subset(A,B) )
=> subset(set_union2(A,C),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,plain,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f59,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f76,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f77,plain,
! [A,B] :
( ( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ( ! [C] :
( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(NNF_transformation,[status(thm)],[f11]) ).
fof(f78,plain,
( ! [A,B] :
( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(miniscoping,[status(thm)],[f77]) ).
fof(f79,plain,
( ! [A,B] :
( ( ( sK0_skl(B,A) = A
| in(sK0_skl(B,A),B) )
& ( sK0_skl(B,A) != A
| ~ in(sK0_skl(B,A),B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f78]) ).
fof(f80,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f84,plain,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( subset(B,A)
| ~ in(B,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f85,plain,
! [A] :
( ( ? [B] :
( ~ subset(B,A)
& in(B,A) )
| epsilon_transitive(A) )
& ( ! [B] :
( subset(B,A)
| ~ in(B,A) )
| ~ epsilon_transitive(A) ) ),
inference(NNF_transformation,[status(thm)],[f84]) ).
fof(f86,plain,
( ! [A] :
( ? [B] :
( ~ subset(B,A)
& in(B,A) )
| epsilon_transitive(A) )
& ! [A] :
( ! [B] :
( subset(B,A)
| ~ in(B,A) )
| ~ epsilon_transitive(A) ) ),
inference(miniscoping,[status(thm)],[f85]) ).
fof(f87,plain,
( ! [A] :
( ( ~ subset(sK1_skl(A),A)
& in(sK1_skl(A),A) )
| epsilon_transitive(A) )
& ! [A] :
( ! [B] :
( subset(B,A)
| ~ in(B,A) )
| ~ epsilon_transitive(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(B,sK1_skl(A))],[f86]) ).
fof(f88,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ in(X1,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f91,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f92,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f91]) ).
fof(f93,plain,
( ! [A,B] :
( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f92]) ).
fof(f94,plain,
( ! [A,B] :
( ( ~ in(sK2_skl(B,A),B)
& in(sK2_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(C,sK2_skl(B,A))],[f93]) ).
fof(f95,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f96,plain,
! [X0,X1] :
( in(sK2_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f97,plain,
! [X0,X1] :
( ~ in(sK2_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f118,plain,
! [A] :
( ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f122,plain,
! [X0] :
( ordinal(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f179,plain,
! [A,B] :
( ( ordinal_subset(A,B)
<=> subset(A,B) )
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f180,plain,
! [A,B] :
( ( ( ~ subset(A,B)
| ordinal_subset(A,B) )
& ( subset(A,B)
| ~ ordinal_subset(A,B) ) )
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(NNF_transformation,[status(thm)],[f179]) ).
fof(f181,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f180]) ).
fof(f182,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f180]) ).
fof(f188,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f194,plain,
? [A] :
( ? [B] :
( ( in(A,B)
<~> ordinal_subset(succ(A),B) )
& ordinal(B) )
& ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f195,plain,
? [A] :
( ? [B] :
( ( ~ ordinal_subset(succ(A),B)
| ~ in(A,B) )
& ( ordinal_subset(succ(A),B)
| in(A,B) )
& ordinal(B) )
& ordinal(A) ),
inference(NNF_transformation,[status(thm)],[f194]) ).
fof(f196,plain,
( ( ~ ordinal_subset(succ(sK17_skl),sK18_skl)
| ~ in(sK17_skl,sK18_skl) )
& ( ordinal_subset(succ(sK17_skl),sK18_skl)
| in(sK17_skl,sK18_skl) )
& ordinal(sK18_skl)
& ordinal(sK17_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl]),skolemize(A,sK17_skl),skolemize(B,sK18_skl)],[f195]) ).
fof(f197,plain,
ordinal(sK17_skl),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f198,plain,
ordinal(sK18_skl),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f199,plain,
( ordinal_subset(succ(sK17_skl),sK18_skl)
| in(sK17_skl,sK18_skl) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f200,plain,
( ~ ordinal_subset(succ(sK17_skl),sK18_skl)
| ~ in(sK17_skl,sK18_skl) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f219,plain,
! [A,B,C] :
( subset(set_union2(A,C),B)
| ~ subset(C,B)
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f53]) ).
fof(f220,plain,
! [X0,X1,X2] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f219]) ).
fof(f221,plain,
! [X0,X1] :
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f80]) ).
fof(f229,plain,
( in(sK17_skl,sK18_skl)
| subset(succ(sK17_skl),sK18_skl)
| ~ ordinal(sK18_skl)
| ~ ordinal(succ(sK17_skl)) ),
inference(resolution,[status(thm)],[f181,f199]) ).
fof(f233,plain,
( in(sK17_skl,sK18_skl)
| subset(succ(sK17_skl),sK18_skl)
| ~ ordinal(succ(sK17_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f229,f198]) ).
fof(f237,plain,
( ~ in(sK17_skl,sK18_skl)
| ~ subset(succ(sK17_skl),sK18_skl)
| ~ ordinal(sK18_skl)
| ~ ordinal(succ(sK17_skl)) ),
inference(resolution,[status(thm)],[f182,f200]) ).
fof(f239,plain,
( ~ in(sK17_skl,sK18_skl)
| ~ subset(succ(sK17_skl),sK18_skl)
| ~ ordinal(succ(sK17_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f237,f198]) ).
fof(f284,plain,
! [X0] :
( in(sK17_skl,sK18_skl)
| ~ ordinal(succ(sK17_skl))
| in(X0,sK18_skl)
| ~ in(X0,succ(sK17_skl)) ),
inference(resolution,[status(thm)],[f95,f233]) ).
fof(f329,plain,
( in(sK17_skl,sK18_skl)
| ~ ordinal(succ(sK17_skl))
| in(sK17_skl,sK18_skl) ),
inference(resolution,[status(thm)],[f284,f188]) ).
fof(f331,plain,
( ~ ordinal(succ(sK17_skl))
| in(sK17_skl,sK18_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f329]) ).
fof(f363,plain,
! [X0,X1] :
( sK2_skl(X1,singleton(X0)) = X0
| subset(singleton(X0),X1) ),
inference(resolution,[status(thm)],[f96,f221]) ).
fof(f378,plain,
( ~ subset(succ(sK17_skl),sK18_skl)
| ~ ordinal(succ(sK17_skl)) ),
inference(backward_subsumption_resolution,[status(thm)],[f239,f331]) ).
fof(f567,plain,
! [X0,X1] :
( subset(succ(X0),X1)
| ~ subset(singleton(X0),X1)
| ~ subset(X0,X1) ),
inference(paramodulation,[status(thm)],[f76,f220]) ).
fof(f723,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(paramodulation,[status(thm)],[f363,f97]) ).
fof(f727,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(duplicate_literals_removal,[status(thm)],[f723]) ).
fof(f1076,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(succ(X0),X1)
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[f567,f727]) ).
fof(f1733,plain,
( ~ ordinal(succ(sK17_skl))
| ~ in(sK17_skl,sK18_skl)
| ~ subset(sK17_skl,sK18_skl) ),
inference(resolution,[status(thm)],[f1076,f378]) ).
fof(f1739,plain,
( ~ ordinal(succ(sK17_skl))
| ~ subset(sK17_skl,sK18_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f1733,f331]) ).
fof(f1744,plain,
( ~ in(sK17_skl,sK18_skl)
| ~ epsilon_transitive(sK18_skl)
| ~ ordinal(succ(sK17_skl)) ),
inference(resolution,[status(thm)],[f1739,f88]) ).
fof(f1749,plain,
( ~ epsilon_transitive(sK18_skl)
| ~ ordinal(succ(sK17_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1744,f331]) ).
fof(f1755,plain,
( ~ ordinal(sK17_skl)
| ~ epsilon_transitive(sK18_skl) ),
inference(resolution,[status(thm)],[f1749,f122]) ).
fof(f1757,plain,
~ epsilon_transitive(sK18_skl),
inference(forward_subsumption_resolution,[status(thm)],[f1755,f197]) ).
fof(f1789,plain,
~ ordinal(sK18_skl),
inference(resolution,[status(thm)],[f1757,f59]) ).
fof(f1790,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1789,f198]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU236+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n026.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 06:04:52 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 0.13/0.50 % Refutation found
% 0.13/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.53 % Elapsed time: 0.179027 seconds
% 0.13/0.53 % CPU time: 1.043258 seconds
% 0.13/0.53 % Total memory used: 120.101 MB
% 0.13/0.53 % Net memory used: 118.333 MB
%------------------------------------------------------------------------------