%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM390+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 : n005.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 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 45 ( 12 unt; 0 def)
% Number of atoms : 134 ( 11 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 138 ( 49 ~; 45 |; 27 &)
% ( 3 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 63 ( 58 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
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(f9,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( A != B
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [A] :
( epsilon_transitive(A)
=> ! [B] :
( ordinal(B)
=> ( proper_subset(A,B)
=> in(A,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,conjecture,
! [A] :
( epsilon_transitive(A)
=> ! [B] :
( ordinal(B)
=> ! [C] :
( ordinal(C)
=> ( ( in(B,C)
& subset(A,B) )
=> in(A,C) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
~ ! [A] :
( epsilon_transitive(A)
=> ! [B] :
( ordinal(B)
=> ! [C] :
( ordinal(C)
=> ( ( in(B,C)
& subset(A,B) )
=> in(A,C) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f38,axiom,
! [A,B] :
~ ( subset(B,A)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,plain,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f47,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f57,plain,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( subset(B,A)
| ~ in(B,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f58,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)],[f57]) ).
fof(f59,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)],[f58]) ).
fof(f60,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))],[f59]) ).
fof(f61,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ in(X1,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f64,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)],[f9]) ).
fof(f65,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)],[f64]) ).
fof(f68,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f119,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f120,plain,
! [A,C] :
( subset(A,C)
| ! [B] :
( ~ subset(B,C)
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f119]) ).
fof(f121,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f122,plain,
! [A] :
( ! [B] :
( in(A,B)
| ~ proper_subset(A,B)
| ~ ordinal(B) )
| ~ epsilon_transitive(A) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f123,plain,
! [X0,X1] :
( in(X0,X1)
| ~ proper_subset(X0,X1)
| ~ ordinal(X1)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f124,plain,
? [A] :
( ? [B] :
( ? [C] :
( ~ in(A,C)
& in(B,C)
& subset(A,B)
& ordinal(C) )
& ordinal(B) )
& epsilon_transitive(A) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f125,plain,
( ~ in(sK13_skl,sK15_skl)
& in(sK14_skl,sK15_skl)
& subset(sK13_skl,sK14_skl)
& ordinal(sK15_skl)
& ordinal(sK14_skl)
& epsilon_transitive(sK13_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl,sK15_skl]),skolemize(A,sK13_skl),skolemize(B,sK14_skl),skolemize(C,sK15_skl)],[f124]) ).
fof(f126,plain,
epsilon_transitive(sK13_skl),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f128,plain,
ordinal(sK15_skl),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f129,plain,
subset(sK13_skl,sK14_skl),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f130,plain,
in(sK14_skl,sK15_skl),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f131,plain,
~ in(sK13_skl,sK15_skl),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f149,plain,
! [A,B] :
( ~ subset(B,A)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f150,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f155,plain,
epsilon_transitive(sK15_skl),
inference(resolution,[status(thm)],[f47,f128]) ).
fof(f164,plain,
( subset(sK14_skl,sK15_skl)
| ~ epsilon_transitive(sK15_skl) ),
inference(resolution,[status(thm)],[f130,f61]) ).
fof(f166,plain,
subset(sK14_skl,sK15_skl),
inference(forward_subsumption_resolution,[status(thm)],[f164,f155]) ).
fof(f169,plain,
~ in(sK14_skl,sK13_skl),
inference(resolution,[status(thm)],[f150,f129]) ).
fof(f180,plain,
! [X0] :
( subset(X0,sK15_skl)
| ~ subset(X0,sK14_skl) ),
inference(resolution,[status(thm)],[f166,f121]) ).
fof(f200,plain,
subset(sK13_skl,sK15_skl),
inference(resolution,[status(thm)],[f180,f129]) ).
fof(f212,plain,
( sK13_skl = sK15_skl
| proper_subset(sK13_skl,sK15_skl) ),
inference(resolution,[status(thm)],[f200,f68]) ).
fof(f217,plain,
( in(sK13_skl,sK15_skl)
| ~ ordinal(sK15_skl)
| ~ epsilon_transitive(sK13_skl)
| sK13_skl = sK15_skl ),
inference(resolution,[status(thm)],[f212,f123]) ).
fof(f218,plain,
( in(sK13_skl,sK15_skl)
| ~ ordinal(sK15_skl)
| sK13_skl = sK15_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f217,f126]) ).
fof(f220,plain,
( in(sK13_skl,sK15_skl)
| sK13_skl = sK15_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f218,f128]) ).
fof(f221,plain,
sK13_skl = sK15_skl,
inference(resolution,[status(thm)],[f220,f131]) ).
fof(f239,plain,
in(sK14_skl,sK13_skl),
inference(backward_demodulation,[status(thm)],[f221,f130]) ).
fof(f246,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f239,f169]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM390+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n005.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 02:26:32 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.14/0.38 % Refutation found
% 0.14/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41 % Elapsed time: 0.048741 seconds
% 0.14/0.41 % CPU time: 0.137535 seconds
% 0.14/0.41 % Total memory used: 68.854 MB
% 0.14/0.41 % Net memory used: 68.821 MB
%------------------------------------------------------------------------------