%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU238+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 : 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 02:19:50 PM UTC 2026
% Result : Theorem 6.61s 1.69s
% Output : CNFRefutation 6.61s
% 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/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( A != B
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,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(f43,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [A] : in(A,succ(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,axiom,
! [A] :
( epsilon_transitive(A)
=> ! [B] :
( ordinal(B)
=> ( proper_subset(A,B)
=> in(A,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( in(A,B)
<=> ordinal_subset(succ(A),B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,axiom,
! [A] :
( ordinal(A)
=> ( being_limit_ordinal(A)
<=> ! [B] :
( ordinal(B)
=> ( in(B,A)
=> in(succ(B),A) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,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/sandbox/benchmark/theBenchmark.p') ).
fof(f55,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)],[f54]) ).
fof(f61,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f62,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f86,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(f87,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)],[f86]) ).
fof(f90,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f111,plain,
! [A] :
( ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f113,plain,
! [X0] :
( epsilon_transitive(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f115,plain,
! [X0] :
( ordinal(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f170,plain,
! [A,B] :
( ( ordinal_subset(A,B)
<=> subset(A,B) )
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f171,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)],[f170]) ).
fof(f172,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f179,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f183,plain,
! [A] :
( ! [B] :
( in(A,B)
| ~ proper_subset(A,B)
| ~ ordinal(B) )
| ~ epsilon_transitive(A) ),
inference(pre_NNF_transformation,[status(thm)],[f49]) ).
fof(f184,plain,
! [X0,X1] :
( in(X0,X1)
| ~ proper_subset(X0,X1)
| ~ ordinal(X1)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[status(thm)],[f183]) ).
fof(f187,plain,
! [A] :
( ! [B] :
( ( in(A,B)
<=> ordinal_subset(succ(A),B) )
| ~ ordinal(B) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f51]) ).
fof(f188,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)],[f187]) ).
fof(f189,plain,
! [X0,X1] :
( ordinal_subset(succ(X0),X1)
| ~ in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f195,plain,
! [A] :
( ( being_limit_ordinal(A)
<=> ! [B] :
( in(succ(B),A)
| ~ in(B,A)
| ~ ordinal(B) ) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f53]) ).
fof(f196,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)],[f195]) ).
fof(f197,plain,
! [A] :
( ( ( ( ~ in(succ(sK13_skl(A)),A)
& in(sK13_skl(A),A)
& ordinal(sK13_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,[sK13_skl]),skolemize(B,sK13_skl(A))],[f196]) ).
fof(f198,plain,
! [X0,X1] :
( in(succ(X1),X0)
| ~ in(X1,X0)
| ~ ordinal(X1)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f199,plain,
! [X0] :
( ordinal(sK13_skl(X0))
| being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f200,plain,
! [X0] :
( in(sK13_skl(X0),X0)
| being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f201,plain,
! [X0] :
( ~ in(succ(sK13_skl(X0)),X0)
| being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f202,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)],[f55]) ).
fof(f203,definition,
! [A] :
( sP0_prd(A)
<=> ( ! [B] :
( A != succ(B)
| ~ ordinal(B) )
& ~ being_limit_ordinal(A) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f204,plain,
? [A] :
( ( ( being_limit_ordinal(A)
& ? [B] :
( A = succ(B)
& ordinal(B) ) )
| sP0_prd(A) )
& ordinal(A) ),
inference(formula_renaming,[status(thm)],[f202,f203]) ).
fof(f205,plain,
( ( ( being_limit_ordinal(sK14_skl)
& sK14_skl = succ(sK15_skl)
& ordinal(sK15_skl) )
| sP0_prd(sK14_skl) )
& ordinal(sK14_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl]),skolemize(A,sK14_skl),skolemize(B,sK15_skl)],[f204]) ).
fof(f206,plain,
ordinal(sK14_skl),
inference(cnf_transformation,[status(thm)],[f205]) ).
fof(f207,plain,
( ordinal(sK15_skl)
| sP0_prd(sK14_skl) ),
inference(cnf_transformation,[status(thm)],[f205]) ).
fof(f208,plain,
( sK14_skl = succ(sK15_skl)
| sP0_prd(sK14_skl) ),
inference(cnf_transformation,[status(thm)],[f205]) ).
fof(f209,plain,
( being_limit_ordinal(sK14_skl)
| sP0_prd(sK14_skl) ),
inference(cnf_transformation,[status(thm)],[f205]) ).
fof(f224,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)],[f203]) ).
fof(f225,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)],[f224]) ).
fof(f226,plain,
( ! [A] :
( ( A = succ(sK16_skl(A))
& ordinal(sK16_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,[sK16_skl]),skolemize(B,sK16_skl(A))],[f225]) ).
fof(f227,plain,
! [X0] :
( ~ being_limit_ordinal(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f226]) ).
fof(f228,plain,
! [X0,X1] :
( X0 != succ(X1)
| ~ ordinal(X1)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f226]) ).
fof(f237,plain,
( sP0_prd(sK14_skl)
| in(sK15_skl,sK14_skl) ),
inference(paramodulation,[status(thm)],[f208,f179]) ).
fof(f253,plain,
! [X0] :
( sP0_prd(sK14_skl)
| in(sK14_skl,X0)
| ~ in(sK15_skl,X0)
| ~ ordinal(sK15_skl)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(paramodulation,[status(thm)],[f208,f198]) ).
fof(f255,plain,
! [X0] :
( sP0_prd(sK14_skl)
| in(sK14_skl,X0)
| ~ in(sK15_skl,X0)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f253,f207]) ).
fof(f276,plain,
( sP0_prd(sK14_skl)
| sP0_prd(sK14_skl)
| in(sK14_skl,sK14_skl)
| ~ being_limit_ordinal(sK14_skl)
| ~ ordinal(sK14_skl) ),
inference(resolution,[status(thm)],[f255,f237]) ).
fof(f278,plain,
( sP0_prd(sK14_skl)
| in(sK14_skl,sK14_skl)
| ~ being_limit_ordinal(sK14_skl)
| ~ ordinal(sK14_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f276]) ).
fof(f279,plain,
( sP0_prd(sK14_skl)
| in(sK14_skl,sK14_skl)
| ~ being_limit_ordinal(sK14_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f278,f206]) ).
fof(f285,plain,
( sP0_prd(sK14_skl)
| in(sK14_skl,sK14_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f279,f209]) ).
fof(f287,plain,
( ~ in(sK14_skl,sK14_skl)
| sP0_prd(sK14_skl) ),
inference(resolution,[status(thm)],[f285,f62]) ).
fof(f290,plain,
sP0_prd(sK14_skl),
inference(forward_subsumption_resolution,[status(thm)],[f287,f285]) ).
fof(f334,plain,
! [X0,X1] :
( X0 = X1
| proper_subset(X0,X1)
| ~ ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f172,f90]) ).
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)],[f189,f334]) ).
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,f115]) ).
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,f184]) ).
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,f113]) ).
fof(f951,plain,
! [X0] :
( succ(sK13_skl(X0)) = X0
| ~ in(sK13_skl(X0),X0)
| ~ ordinal(X0)
| ~ ordinal(sK13_skl(X0))
| being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f201,f761]) ).
fof(f953,plain,
! [X0] :
( succ(sK13_skl(X0)) = X0
| ~ in(sK13_skl(X0),X0)
| ~ ordinal(sK13_skl(X0))
| being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f951]) ).
fof(f954,plain,
! [X0] :
( succ(sK13_skl(X0)) = X0
| ~ in(sK13_skl(X0),X0)
| being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f953,f199]) ).
fof(f1123,plain,
! [X0] :
( succ(sK13_skl(X0)) = X0
| being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f954,f200]) ).
fof(f1125,plain,
! [X0] :
( ~ ordinal(sK13_skl(X0))
| ~ sP0_prd(X0)
| being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f1123,f228]) ).
fof(f1127,plain,
! [X0] :
( ~ ordinal(sK13_skl(X0))
| ~ sP0_prd(X0)
| ~ ordinal(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1125,f227]) ).
fof(f1128,plain,
! [X0] :
( being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ sP0_prd(X0)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f1127,f199]) ).
fof(f1130,plain,
! [X0] :
( being_limit_ordinal(X0)
| ~ sP0_prd(X0)
| ~ ordinal(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1128]) ).
fof(f1131,plain,
! [X0] :
( ~ sP0_prd(X0)
| ~ ordinal(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1130,f227]) ).
fof(f1139,plain,
~ sP0_prd(sK14_skl),
inference(resolution,[status(thm)],[f1131,f206]) ).
fof(f1141,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1139,f290]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU238+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 : n003.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 06:03:45 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.46 % Drodi V4.1.1
% 6.61/1.69 % Refutation found
% 6.61/1.69 % SZS status Theorem for theBenchmark: Theorem is valid
% 6.61/1.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.64/1.75 % Elapsed time: 1.287713 seconds
% 0.64/1.75 % CPU time: 9.672399 seconds
% 0.64/1.75 % Total memory used: 175.229 MB
% 0.64/1.75 % Net memory used: 169.327 MB
%------------------------------------------------------------------------------