%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM394+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 01:40:26 PM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 9 unt; 0 def)
% Number of atoms : 133 ( 12 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 140 ( 49 ~; 58 |; 19 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 47 ( 43 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(B,A)
| ordinal_subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ in(B,A)
& A != B
& ~ in(A,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( in(B,A)
| ordinal_subset(A,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( in(B,A)
| ordinal_subset(A,B) ) ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f42,plain,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f43,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f53,plain,
! [A,B] :
( ordinal_subset(B,A)
| ordinal_subset(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f54,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f55,plain,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( subset(B,A)
| ~ in(B,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f56,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)],[f55]) ).
fof(f57,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)],[f56]) ).
fof(f58,plain,
( ! [A] :
( ( ~ subset(sK0_skl(A),A)
& in(sK0_skl(A),A) )
| epsilon_transitive(A) )
& ! [A] :
( ! [B] :
( subset(B,A)
| ~ in(B,A) )
| ~ epsilon_transitive(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(B,sK0_skl(A))],[f57]) ).
fof(f59,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ in(X1,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f106,plain,
! [A,B] :
( ( ordinal_subset(A,B)
<=> subset(A,B) )
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f107,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)],[f106]) ).
fof(f109,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f117,plain,
! [A] :
( ! [B] :
( in(B,A)
| A = B
| in(A,B)
| ~ ordinal(B) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f118,plain,
! [X0,X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f119,plain,
? [A] :
( ? [B] :
( ~ in(B,A)
& ~ ordinal_subset(A,B)
& ordinal(B) )
& ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f120,plain,
( ~ in(sK14_skl,sK13_skl)
& ~ ordinal_subset(sK13_skl,sK14_skl)
& ordinal(sK14_skl)
& ordinal(sK13_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl]),skolemize(A,sK13_skl),skolemize(B,sK14_skl)],[f119]) ).
fof(f121,plain,
ordinal(sK13_skl),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f122,plain,
ordinal(sK14_skl),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f123,plain,
~ ordinal_subset(sK13_skl,sK14_skl),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f124,plain,
~ in(sK14_skl,sK13_skl),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f146,plain,
! [X0] :
( ordinal_subset(X0,sK13_skl)
| ordinal_subset(sK13_skl,X0)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f54,f121]) ).
fof(f148,plain,
epsilon_transitive(sK14_skl),
inference(resolution,[status(thm)],[f43,f122]) ).
fof(f159,plain,
( ordinal_subset(sK13_skl,sK13_skl)
| ordinal_subset(sK13_skl,sK13_skl) ),
inference(resolution,[status(thm)],[f146,f121]) ).
fof(f161,plain,
ordinal_subset(sK13_skl,sK13_skl),
inference(duplicate_literals_removal,[status(thm)],[f159]) ).
fof(f165,plain,
! [X0] :
( in(X0,sK14_skl)
| sK14_skl = X0
| in(sK14_skl,X0)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f118,f122]) ).
fof(f178,plain,
( in(sK13_skl,sK14_skl)
| sK14_skl = sK13_skl
| in(sK14_skl,sK13_skl) ),
inference(resolution,[status(thm)],[f165,f121]) ).
fof(f179,plain,
( in(sK13_skl,sK14_skl)
| sK14_skl = sK13_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f178,f124]) ).
fof(f211,plain,
( subset(sK13_skl,sK14_skl)
| ~ epsilon_transitive(sK14_skl)
| sK14_skl = sK13_skl ),
inference(resolution,[status(thm)],[f179,f59]) ).
fof(f214,plain,
( subset(sK13_skl,sK14_skl)
| sK14_skl = sK13_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f211,f148]) ).
fof(f252,plain,
( ordinal_subset(sK13_skl,sK14_skl)
| ~ ordinal(sK14_skl)
| ~ ordinal(sK13_skl)
| sK14_skl = sK13_skl ),
inference(resolution,[status(thm)],[f214,f109]) ).
fof(f253,plain,
( ordinal_subset(sK13_skl,sK14_skl)
| ~ ordinal(sK14_skl)
| sK14_skl = sK13_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f252,f121]) ).
fof(f298,plain,
( ordinal_subset(sK13_skl,sK14_skl)
| sK14_skl = sK13_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f253,f122]) ).
fof(f299,plain,
sK14_skl = sK13_skl,
inference(resolution,[status(thm)],[f298,f123]) ).
fof(f323,plain,
~ ordinal_subset(sK13_skl,sK13_skl),
inference(backward_demodulation,[status(thm)],[f299,f123]) ).
fof(f338,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f323,f161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM394+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 02:30:06 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.43 % Elapsed time: 0.050380 seconds
% 0.09/0.43 % CPU time: 0.114417 seconds
% 0.09/0.43 % Total memory used: 41.144 MB
% 0.09/0.43 % Net memory used: 41.104 MB
%------------------------------------------------------------------------------