%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU238+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 02:19:51 PM UTC 2026
% Result : Theorem 2.85s 0.81s
% Output : CNFRefutation 2.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 10
% Syntax : Number of formulae : 74 ( 6 unt; 1 def)
% Number of atoms : 308 ( 34 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 393 ( 159 ~; 163 |; 48 &)
% ( 8 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 109 ( 100 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( A != B
& subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A] :
( ordinal(A)
=> ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [A] : in(A,succ(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [A] :
( epsilon_transitive(A)
=> ! [B] :
( ordinal(B)
=> ( proper_subset(A,B)
=> in(A,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( in(A,B)
<=> ordinal_subset(succ(A),B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [A] :
( ordinal(A)
=> ( being_limit_ordinal(A)
<=> ! [B] :
( ordinal(B)
=> ( in(B,A)
=> in(succ(B),A) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,conjecture,
! [A] :
( ordinal(A)
=> ( ~ ( being_limit_ordinal(A)
& ? [B] :
( A = succ(B)
& ordinal(B) ) )
& ~ ( ! [B] :
( ordinal(B)
=> A != succ(B) )
& ~ being_limit_ordinal(A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> ( ~ ( being_limit_ordinal(A)
& ? [B] :
( A = succ(B)
& ordinal(B) ) )
& ~ ( ! [B] :
( ordinal(B)
=> A != succ(B) )
& ~ being_limit_ordinal(A) ) ) ),
inference(negated_conjecture,[status(cth)],[f49]) ).
fof(f56,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f57,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f81,plain,
! [A,B] :
( ( A = B
| ~ subset(A,B)
| proper_subset(A,B) )
& ( ( A != B
& subset(A,B) )
| ~ proper_subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f82,plain,
( ! [A,B] :
( A = B
| ~ subset(A,B)
| proper_subset(A,B) )
& ! [A,B] :
( ( A != B
& subset(A,B) )
| ~ proper_subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f81]) ).
fof(f85,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f106,plain,
! [A] :
( ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f108,plain,
! [X0] :
( epsilon_transitive(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f110,plain,
! [X0] :
( ordinal(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f169,plain,
! [A,B] :
( ( ordinal_subset(A,B)
<=> subset(A,B) )
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f170,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)],[f169]) ).
fof(f171,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f170]) ).
fof(f178,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f182,plain,
! [A] :
( ! [B] :
( in(A,B)
| ~ proper_subset(A,B)
| ~ ordinal(B) )
| ~ epsilon_transitive(A) ),
inference(pre_NNF_transformation,[status(thm)],[f44]) ).
fof(f183,plain,
! [X0,X1] :
( in(X0,X1)
| ~ proper_subset(X0,X1)
| ~ ordinal(X1)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[status(thm)],[f182]) ).
fof(f186,plain,
! [A] :
( ! [B] :
( ( in(A,B)
<=> ordinal_subset(succ(A),B) )
| ~ ordinal(B) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f187,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)],[f186]) ).
fof(f188,plain,
! [X0,X1] :
( ordinal_subset(succ(X0),X1)
| ~ in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f194,plain,
! [A] :
( ( being_limit_ordinal(A)
<=> ! [B] :
( in(succ(B),A)
| ~ in(B,A)
| ~ ordinal(B) ) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f48]) ).
fof(f195,plain,
! [A] :
( ( ( ? [B] :
( ~ in(succ(B),A)
& in(B,A)
& ordinal(B) )
| being_limit_ordinal(A) )
& ( ! [B] :
( in(succ(B),A)
| ~ in(B,A)
| ~ ordinal(B) )
| ~ being_limit_ordinal(A) ) )
| ~ ordinal(A) ),
inference(NNF_transformation,[status(thm)],[f194]) ).
fof(f196,plain,
! [A] :
( ( ( ( ~ in(succ(sK14_skl(A)),A)
& in(sK14_skl(A),A)
& ordinal(sK14_skl(A)) )
| being_limit_ordinal(A) )
& ( ! [B] :
( in(succ(B),A)
| ~ in(B,A)
| ~ ordinal(B) )
| ~ being_limit_ordinal(A) ) )
| ~ ordinal(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl]),skolemize(B,sK14_skl(A))],[f195]) ).
fof(f197,plain,
! [X0,X1] :
( in(succ(X1),X0)
| ~ in(X1,X0)
| ~ ordinal(X1)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f198,plain,
! [X0] :
( ordinal(sK14_skl(X0))
| being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f199,plain,
! [X0] :
( in(sK14_skl(X0),X0)
| being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f200,plain,
! [X0] :
( ~ in(succ(sK14_skl(X0)),X0)
| being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f201,plain,
? [A] :
( ( ( being_limit_ordinal(A)
& ? [B] :
( A = succ(B)
& ordinal(B) ) )
| ( ! [B] :
( A != succ(B)
| ~ ordinal(B) )
& ~ being_limit_ordinal(A) ) )
& ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f202,definition,
! [A] :
( sP0_prd(A)
<=> ( ! [B] :
( A != succ(B)
| ~ ordinal(B) )
& ~ being_limit_ordinal(A) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f203,plain,
? [A] :
( ( ( being_limit_ordinal(A)
& ? [B] :
( A = succ(B)
& ordinal(B) ) )
| sP0_prd(A) )
& ordinal(A) ),
inference(formula_renaming,[status(thm)],[f201,f202]) ).
fof(f204,plain,
( ( ( being_limit_ordinal(sK15_skl)
& sK15_skl = succ(sK16_skl)
& ordinal(sK16_skl) )
| sP0_prd(sK15_skl) )
& ordinal(sK15_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl,sK16_skl]),skolemize(A,sK15_skl),skolemize(B,sK16_skl)],[f203]) ).
fof(f205,plain,
ordinal(sK15_skl),
inference(cnf_transformation,[status(thm)],[f204]) ).
fof(f206,plain,
( ordinal(sK16_skl)
| sP0_prd(sK15_skl) ),
inference(cnf_transformation,[status(thm)],[f204]) ).
fof(f207,plain,
( sK15_skl = succ(sK16_skl)
| sP0_prd(sK15_skl) ),
inference(cnf_transformation,[status(thm)],[f204]) ).
fof(f208,plain,
( being_limit_ordinal(sK15_skl)
| sP0_prd(sK15_skl) ),
inference(cnf_transformation,[status(thm)],[f204]) ).
fof(f223,plain,
! [A] :
( ( ? [B] :
( A = succ(B)
& ordinal(B) )
| being_limit_ordinal(A)
| sP0_prd(A) )
& ( ( ! [B] :
( A != succ(B)
| ~ ordinal(B) )
& ~ being_limit_ordinal(A) )
| ~ sP0_prd(A) ) ),
inference(NNF_transformation,[status(thm)],[f202]) ).
fof(f224,plain,
( ! [A] :
( ? [B] :
( A = succ(B)
& ordinal(B) )
| being_limit_ordinal(A)
| sP0_prd(A) )
& ! [A] :
( ( ! [B] :
( A != succ(B)
| ~ ordinal(B) )
& ~ being_limit_ordinal(A) )
| ~ sP0_prd(A) ) ),
inference(miniscoping,[status(thm)],[f223]) ).
fof(f225,plain,
( ! [A] :
( ( A = succ(sK17_skl(A))
& ordinal(sK17_skl(A)) )
| being_limit_ordinal(A)
| sP0_prd(A) )
& ! [A] :
( ( ! [B] :
( A != succ(B)
| ~ ordinal(B) )
& ~ being_limit_ordinal(A) )
| ~ sP0_prd(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl]),skolemize(B,sK17_skl(A))],[f224]) ).
fof(f226,plain,
! [X0] :
( ~ being_limit_ordinal(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f225]) ).
fof(f227,plain,
! [X0,X1] :
( X0 != succ(X1)
| ~ ordinal(X1)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f225]) ).
fof(f236,plain,
( sP0_prd(sK15_skl)
| in(sK16_skl,sK15_skl) ),
inference(paramodulation,[status(thm)],[f207,f178]) ).
fof(f252,plain,
! [X0] :
( sP0_prd(sK15_skl)
| in(sK15_skl,X0)
| ~ in(sK16_skl,X0)
| ~ ordinal(sK16_skl)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(paramodulation,[status(thm)],[f207,f197]) ).
fof(f254,plain,
! [X0] :
( sP0_prd(sK15_skl)
| in(sK15_skl,X0)
| ~ in(sK16_skl,X0)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f252,f206]) ).
fof(f275,plain,
( sP0_prd(sK15_skl)
| sP0_prd(sK15_skl)
| in(sK15_skl,sK15_skl)
| ~ being_limit_ordinal(sK15_skl)
| ~ ordinal(sK15_skl) ),
inference(resolution,[status(thm)],[f254,f236]) ).
fof(f277,plain,
( sP0_prd(sK15_skl)
| in(sK15_skl,sK15_skl)
| ~ being_limit_ordinal(sK15_skl)
| ~ ordinal(sK15_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f275]) ).
fof(f278,plain,
( sP0_prd(sK15_skl)
| in(sK15_skl,sK15_skl)
| ~ being_limit_ordinal(sK15_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f277,f205]) ).
fof(f284,plain,
( sP0_prd(sK15_skl)
| in(sK15_skl,sK15_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f278,f208]) ).
fof(f286,plain,
( ~ in(sK15_skl,sK15_skl)
| sP0_prd(sK15_skl) ),
inference(resolution,[status(thm)],[f284,f57]) ).
fof(f289,plain,
sP0_prd(sK15_skl),
inference(forward_subsumption_resolution,[status(thm)],[f286,f284]) ).
fof(f333,plain,
! [X0,X1] :
( X0 = X1
| proper_subset(X0,X1)
| ~ ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f171,f85]) ).
fof(f731,plain,
! [X0,X1] :
( succ(X0) = X1
| proper_subset(succ(X0),X1)
| ~ ordinal(X1)
| ~ ordinal(succ(X0))
| ~ in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f188,f333]) ).
fof(f733,plain,
! [X0,X1] :
( succ(X0) = X1
| proper_subset(succ(X0),X1)
| ~ ordinal(succ(X0))
| ~ in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f731]) ).
fof(f734,plain,
! [X0,X1] :
( succ(X0) = X1
| proper_subset(succ(X0),X1)
| ~ in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f733,f110]) ).
fof(f756,plain,
! [X0,X1] :
( in(succ(X0),X1)
| ~ ordinal(X1)
| ~ epsilon_transitive(succ(X0))
| succ(X0) = X1
| ~ in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f734,f183]) ).
fof(f760,plain,
! [X0,X1] :
( in(succ(X0),X1)
| ~ epsilon_transitive(succ(X0))
| succ(X0) = X1
| ~ in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f756]) ).
fof(f761,plain,
! [X0,X1] :
( in(succ(X0),X1)
| succ(X0) = X1
| ~ in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f760,f108]) ).
fof(f943,plain,
! [X0] :
( succ(sK14_skl(X0)) = X0
| ~ in(sK14_skl(X0),X0)
| ~ ordinal(X0)
| ~ ordinal(sK14_skl(X0))
| being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f200,f761]) ).
fof(f945,plain,
! [X0] :
( succ(sK14_skl(X0)) = X0
| ~ in(sK14_skl(X0),X0)
| ~ ordinal(sK14_skl(X0))
| being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f943]) ).
fof(f946,plain,
! [X0] :
( succ(sK14_skl(X0)) = X0
| ~ in(sK14_skl(X0),X0)
| being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f945,f198]) ).
fof(f1112,plain,
! [X0] :
( succ(sK14_skl(X0)) = X0
| being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f946,f199]) ).
fof(f1114,plain,
! [X0] :
( ~ ordinal(sK14_skl(X0))
| ~ sP0_prd(X0)
| being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f1112,f227]) ).
fof(f1116,plain,
! [X0] :
( ~ ordinal(sK14_skl(X0))
| ~ sP0_prd(X0)
| ~ ordinal(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1114,f226]) ).
fof(f1117,plain,
! [X0] :
( being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ sP0_prd(X0)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f1116,f198]) ).
fof(f1119,plain,
! [X0] :
( being_limit_ordinal(X0)
| ~ sP0_prd(X0)
| ~ ordinal(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1117]) ).
fof(f1120,plain,
! [X0] :
( ~ sP0_prd(X0)
| ~ ordinal(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1119,f226]) ).
fof(f1128,plain,
~ sP0_prd(sK15_skl),
inference(resolution,[status(thm)],[f1120,f205]) ).
fof(f1130,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1128,f289]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU238+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 06:04:00 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 2.85/0.81 % Refutation found
% 2.85/0.81 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.85/0.81 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.60/0.83 % Elapsed time: 0.467449 seconds
% 0.60/0.83 % CPU time: 3.446212 seconds
% 0.60/0.83 % Total memory used: 156.163 MB
% 0.60/0.83 % Net memory used: 151.790 MB
%------------------------------------------------------------------------------