%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM388+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 01:40:25 PM UTC 2026
% Result : Theorem 0.11s 0.41s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 11 unt; 0 def)
% Number of atoms : 117 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 116 ( 41 ~; 36 |; 24 &)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 65 ( 60 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,conjecture,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ! [C] :
( epsilon_transitive(C)
=> ( ( in(A,B)
& in(C,A) )
=> in(C,B) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ! [C] :
( epsilon_transitive(C)
=> ( ( in(A,B)
& in(C,A) )
=> in(C,B) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f27,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,plain,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f39,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f49,plain,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( subset(B,A)
| ~ in(B,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f50,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)],[f49]) ).
fof(f51,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)],[f50]) ).
fof(f52,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))],[f51]) ).
fof(f53,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ in(X1,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f102,plain,
? [A] :
( ? [B] :
( ? [C] :
( ~ in(C,B)
& in(A,B)
& in(C,A)
& epsilon_transitive(C) )
& ordinal(B) )
& ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f103,plain,
( ~ in(sK15_skl,sK14_skl)
& in(sK13_skl,sK14_skl)
& in(sK15_skl,sK13_skl)
& epsilon_transitive(sK15_skl)
& ordinal(sK14_skl)
& ordinal(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)],[f102]) ).
fof(f105,plain,
ordinal(sK14_skl),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f107,plain,
in(sK15_skl,sK13_skl),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f108,plain,
in(sK13_skl,sK14_skl),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f109,plain,
~ in(sK15_skl,sK14_skl),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f112,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f113,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f114,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(NNF_transformation,[status(thm)],[f28]) ).
fof(f115,plain,
( ! [A,B] :
( ~ subset(A,B)
| element(A,powerset(B)) )
& ! [A,B] :
( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(miniscoping,[status(thm)],[f114]) ).
fof(f117,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f118,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f119,plain,
! [A,C] :
( element(A,C)
| ! [B] :
( ~ element(B,powerset(C))
| ~ in(A,B) ) ),
inference(miniscoping,[status(thm)],[f118]) ).
fof(f120,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f126,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f127,plain,
! [B] :
( ~ empty(B)
| ! [A] : ~ in(A,B) ),
inference(miniscoping,[status(thm)],[f126]) ).
fof(f128,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f132,plain,
epsilon_transitive(sK14_skl),
inference(resolution,[status(thm)],[f39,f105]) ).
fof(f141,plain,
( subset(sK13_skl,sK14_skl)
| ~ epsilon_transitive(sK14_skl) ),
inference(resolution,[status(thm)],[f53,f108]) ).
fof(f143,plain,
subset(sK13_skl,sK14_skl),
inference(forward_subsumption_resolution,[status(thm)],[f141,f132]) ).
fof(f146,plain,
~ empty(sK14_skl),
inference(resolution,[status(thm)],[f128,f108]) ).
fof(f178,plain,
element(sK13_skl,powerset(sK14_skl)),
inference(resolution,[status(thm)],[f117,f143]) ).
fof(f189,plain,
! [X0] :
( element(X0,sK14_skl)
| ~ in(X0,sK13_skl) ),
inference(resolution,[status(thm)],[f178,f120]) ).
fof(f198,plain,
element(sK15_skl,sK14_skl),
inference(resolution,[status(thm)],[f189,f107]) ).
fof(f217,plain,
( in(sK15_skl,sK14_skl)
| empty(sK14_skl) ),
inference(resolution,[status(thm)],[f198,f113]) ).
fof(f218,plain,
in(sK15_skl,sK14_skl),
inference(forward_subsumption_resolution,[status(thm)],[f217,f146]) ).
fof(f219,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f218,f109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM388+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 02:29:36 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.41 % Refutation found
% 0.11/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.44 % Elapsed time: 0.063375 seconds
% 0.11/0.44 % CPU time: 0.160699 seconds
% 0.11/0.44 % Total memory used: 81.480 MB
% 0.11/0.44 % Net memory used: 81.432 MB
%------------------------------------------------------------------------------