%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM411+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 : n026.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 01:40:27 PM UTC 2026
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 8 unt; 3 def)
% Number of atoms : 134 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 152 ( 66 ~; 59 |; 15 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 4 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 59 ( 56 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [A,B] :
( ( transfinite_sequence(B)
& function(B)
& relation(B) )
=> ( transfinite_sequence_of(B,A)
<=> subset(relation_rng(B),A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B] :
( transfinite_sequence_of(B,A)
=> ( transfinite_sequence(B)
& function(B)
& relation(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,conjecture,
! [A,B] :
( subset(A,B)
=> ! [C] :
( transfinite_sequence_of(C,A)
=> transfinite_sequence_of(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
~ ! [A,B] :
( subset(A,B)
=> ! [C] :
( transfinite_sequence_of(C,A)
=> transfinite_sequence_of(C,B) ) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
fof(f64,plain,
! [A,B] :
( ( transfinite_sequence_of(B,A)
<=> subset(relation_rng(B),A) )
| ~ transfinite_sequence(B)
| ~ function(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f65,plain,
! [A,B] :
( ( ( ~ subset(relation_rng(B),A)
| transfinite_sequence_of(B,A) )
& ( subset(relation_rng(B),A)
| ~ transfinite_sequence_of(B,A) ) )
| ~ transfinite_sequence(B)
| ~ function(B)
| ~ relation(B) ),
inference(NNF_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
! [B] :
( ( ! [A] :
( ~ subset(relation_rng(B),A)
| transfinite_sequence_of(B,A) )
& ! [A] :
( subset(relation_rng(B),A)
| ~ transfinite_sequence_of(B,A) ) )
| ~ transfinite_sequence(B)
| ~ function(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( subset(relation_rng(X0),X1)
| ~ transfinite_sequence_of(X0,X1)
| ~ transfinite_sequence(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( ~ subset(relation_rng(X0),X1)
| transfinite_sequence_of(X0,X1)
| ~ transfinite_sequence(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f69,plain,
! [A,B] :
( ( transfinite_sequence(B)
& function(B)
& relation(B) )
| ~ transfinite_sequence_of(B,A) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f70,plain,
! [B] :
( ( transfinite_sequence(B)
& function(B)
& relation(B) )
| ! [A] : ~ transfinite_sequence_of(B,A) ),
inference(miniscoping,[status(thm)],[f69]) ).
fof(f71,plain,
! [X0,X1] :
( relation(X0)
| ~ transfinite_sequence_of(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f72,plain,
! [X0,X1] :
( function(X0)
| ~ transfinite_sequence_of(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f73,plain,
! [X0,X1] :
( transfinite_sequence(X0)
| ~ transfinite_sequence_of(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f156,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f157,plain,
! [A,C] :
( subset(A,C)
| ! [B] :
( ~ subset(B,C)
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f156]) ).
fof(f158,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f157]) ).
fof(f165,plain,
? [A,B] :
( ? [C] :
( ~ transfinite_sequence_of(C,B)
& transfinite_sequence_of(C,A) )
& subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f166,plain,
( ~ transfinite_sequence_of(sK18_skl,sK17_skl)
& transfinite_sequence_of(sK18_skl,sK16_skl)
& subset(sK16_skl,sK17_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl,sK17_skl,sK18_skl]),skolemize(A,sK16_skl),skolemize(B,sK17_skl),skolemize(C,sK18_skl)],[f165]) ).
fof(f167,plain,
subset(sK16_skl,sK17_skl),
inference(cnf_transformation,[status(thm)],[f166]) ).
fof(f168,plain,
transfinite_sequence_of(sK18_skl,sK16_skl),
inference(cnf_transformation,[status(thm)],[f166]) ).
fof(f169,plain,
~ transfinite_sequence_of(sK18_skl,sK17_skl),
inference(cnf_transformation,[status(thm)],[f166]) ).
fof(f185,plain,
! [X0,X1] :
( subset(relation_rng(X0),X1)
| ~ transfinite_sequence_of(X0,X1)
| ~ transfinite_sequence(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f67,f71]) ).
fof(f186,plain,
! [X0,X1] :
( subset(relation_rng(X0),X1)
| ~ transfinite_sequence_of(X0,X1)
| ~ function(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f185,f73]) ).
fof(f187,plain,
transfinite_sequence(sK18_skl),
inference(resolution,[status(thm)],[f73,f168]) ).
fof(f188,plain,
! [X0,X1] :
( subset(relation_rng(X0),X1)
| ~ transfinite_sequence_of(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f186,f72]) ).
fof(f190,plain,
! [X0] :
( ~ subset(relation_rng(sK18_skl),X0)
| transfinite_sequence_of(sK18_skl,X0)
| ~ function(sK18_skl)
| ~ relation(sK18_skl) ),
inference(resolution,[status(thm)],[f187,f68]) ).
fof(f191,definition,
( sQ0_spl
<=> relation(sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f193,plain,
( sQ0_spl
| ~ relation(sK18_skl) ),
inference(component_clause,[status(thm)],[f191]) ).
fof(f194,definition,
( sQ1_spl
<=> function(sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f196,plain,
( sQ1_spl
| ~ function(sK18_skl) ),
inference(component_clause,[status(thm)],[f194]) ).
fof(f197,definition,
! [X0] :
( sQ2_spl
<=> ( ~ subset(relation_rng(sK18_skl),X0)
| transfinite_sequence_of(sK18_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f198,plain,
! [X0] :
( ~ sQ2_spl
| ~ subset(relation_rng(sK18_skl),X0)
| transfinite_sequence_of(sK18_skl,X0) ),
inference(component_clause,[status(thm)],[f197]) ).
fof(f200,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f190,f191,f194,f197]) ).
fof(f201,plain,
( ~ sQ2_spl
| ~ subset(relation_rng(sK18_skl),sK17_skl) ),
inference(resolution,[status(thm)],[f198,f169]) ).
fof(f211,plain,
! [X0] :
( sQ1_spl
| ~ transfinite_sequence_of(sK18_skl,X0) ),
inference(resolution,[status(thm)],[f196,f72]) ).
fof(f216,plain,
( sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f168,f211]) ).
fof(f217,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f216]) ).
fof(f219,plain,
! [X0] :
( sQ0_spl
| ~ transfinite_sequence_of(sK18_skl,X0) ),
inference(resolution,[status(thm)],[f193,f71]) ).
fof(f220,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f168,f219]) ).
fof(f221,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f220]) ).
fof(f251,plain,
! [X0] :
( ~ sQ2_spl
| ~ subset(X0,sK17_skl)
| ~ subset(relation_rng(sK18_skl),X0) ),
inference(resolution,[status(thm)],[f201,f158]) ).
fof(f255,plain,
! [X0] :
( ~ sQ2_spl
| ~ transfinite_sequence_of(sK18_skl,X0)
| ~ subset(X0,sK17_skl) ),
inference(resolution,[status(thm)],[f251,f188]) ).
fof(f258,plain,
( ~ sQ2_spl
| ~ subset(sK16_skl,sK17_skl) ),
inference(resolution,[status(thm)],[f255,f168]) ).
fof(f260,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f258,f167]) ).
fof(f261,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f260]) ).
fof(f262,plain,
$false,
inference(sat_refutation,[status(thm)],[f200,f217,f221,f261]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM411+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n026.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 02:30:06 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.41 % Elapsed time: 0.051084 seconds
% 0.12/0.41 % CPU time: 0.129970 seconds
% 0.12/0.41 % Total memory used: 64.322 MB
% 0.12/0.41 % Net memory used: 64.300 MB
%------------------------------------------------------------------------------