%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM412+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 : n012.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 0.03s 0.31s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 47 ( 13 unt; 0 def)
% Number of atoms : 140 ( 7 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 159 ( 66 ~; 61 |; 20 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 62 ( 59 !; 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] :
( ( ordinal(B)
& transfinite_sequence(A)
& function(A)
& relation(A) )
=> transfinite_sequence_of(tseq_dom_restriction(A,B),relation_rng(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B] :
( transfinite_sequence_of(B,A)
=> ( transfinite_sequence(B)
& function(B)
& relation(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [A,B] :
( ( ordinal(B)
& transfinite_sequence(A)
& function(A)
& relation(A) )
=> tseq_dom_restriction(A,B) = relation_dom_restriction(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [A,B] :
( subset(A,B)
=> ! [C] :
( transfinite_sequence_of(C,A)
=> transfinite_sequence_of(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,conjecture,
! [A,B] :
( transfinite_sequence_of(B,A)
=> ! [C] :
( ordinal(C)
=> transfinite_sequence_of(tseq_dom_restriction(B,C),A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
~ ! [A,B] :
( transfinite_sequence_of(B,A)
=> ! [C] :
( ordinal(C)
=> transfinite_sequence_of(tseq_dom_restriction(B,C),A) ) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f69,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(f70,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)],[f69]) ).
fof(f71,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)],[f70]) ).
fof(f72,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)],[f71]) ).
fof(f74,plain,
! [A,B] :
( transfinite_sequence_of(tseq_dom_restriction(A,B),relation_rng(A))
| ~ ordinal(B)
| ~ transfinite_sequence(A)
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f75,plain,
! [X0,X1] :
( transfinite_sequence_of(tseq_dom_restriction(X0,X1),relation_rng(X0))
| ~ ordinal(X1)
| ~ transfinite_sequence(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f79,plain,
! [A,B] :
( ( transfinite_sequence(B)
& function(B)
& relation(B) )
| ~ transfinite_sequence_of(B,A) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f80,plain,
! [B] :
( ( transfinite_sequence(B)
& function(B)
& relation(B) )
| ! [A] : ~ transfinite_sequence_of(B,A) ),
inference(miniscoping,[status(thm)],[f79]) ).
fof(f81,plain,
! [X0,X1] :
( relation(X0)
| ~ transfinite_sequence_of(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f82,plain,
! [X0,X1] :
( function(X0)
| ~ transfinite_sequence_of(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f83,plain,
! [X0,X1] :
( transfinite_sequence(X0)
| ~ transfinite_sequence_of(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f170,plain,
! [A,B] :
( tseq_dom_restriction(A,B) = relation_dom_restriction(A,B)
| ~ ordinal(B)
| ~ transfinite_sequence(A)
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f171,plain,
! [X0,X1] :
( tseq_dom_restriction(X0,X1) = relation_dom_restriction(X0,X1)
| ~ ordinal(X1)
| ~ transfinite_sequence(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f170]) ).
fof(f182,plain,
! [A,B] :
( ! [C] :
( transfinite_sequence_of(C,B)
| ~ transfinite_sequence_of(C,A) )
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f183,plain,
! [X0,X1,X2] :
( transfinite_sequence_of(X2,X1)
| ~ transfinite_sequence_of(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f182]) ).
fof(f184,plain,
? [A,B] :
( ? [C] :
( ~ transfinite_sequence_of(tseq_dom_restriction(B,C),A)
& ordinal(C) )
& transfinite_sequence_of(B,A) ),
inference(pre_NNF_transformation,[status(thm)],[f44]) ).
fof(f185,plain,
( ~ transfinite_sequence_of(tseq_dom_restriction(sK17_skl,sK18_skl),sK16_skl)
& ordinal(sK18_skl)
& transfinite_sequence_of(sK17_skl,sK16_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)],[f184]) ).
fof(f186,plain,
transfinite_sequence_of(sK17_skl,sK16_skl),
inference(cnf_transformation,[status(thm)],[f185]) ).
fof(f187,plain,
ordinal(sK18_skl),
inference(cnf_transformation,[status(thm)],[f185]) ).
fof(f188,plain,
~ transfinite_sequence_of(tseq_dom_restriction(sK17_skl,sK18_skl),sK16_skl),
inference(cnf_transformation,[status(thm)],[f185]) ).
fof(f203,plain,
relation(sK17_skl),
inference(resolution,[status(thm)],[f81,f186]) ).
fof(f204,plain,
function(sK17_skl),
inference(resolution,[status(thm)],[f82,f186]) ).
fof(f218,plain,
! [X0,X1] :
( subset(relation_rng(X0),X1)
| ~ transfinite_sequence_of(X0,X1)
| ~ transfinite_sequence(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f72,f81]) ).
fof(f219,plain,
( subset(relation_rng(sK17_skl),sK16_skl)
| ~ transfinite_sequence(sK17_skl)
| ~ function(sK17_skl) ),
inference(resolution,[status(thm)],[f218,f186]) ).
fof(f220,plain,
( subset(relation_rng(sK17_skl),sK16_skl)
| ~ transfinite_sequence(sK17_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f219,f204]) ).
fof(f224,plain,
transfinite_sequence(sK17_skl),
inference(resolution,[status(thm)],[f83,f186]) ).
fof(f229,plain,
! [X0] :
( tseq_dom_restriction(sK17_skl,X0) = relation_dom_restriction(sK17_skl,X0)
| ~ ordinal(X0)
| ~ function(sK17_skl)
| ~ relation(sK17_skl) ),
inference(resolution,[status(thm)],[f224,f171]) ).
fof(f230,plain,
! [X0] :
( transfinite_sequence_of(tseq_dom_restriction(sK17_skl,X0),relation_rng(sK17_skl))
| ~ ordinal(X0)
| ~ function(sK17_skl)
| ~ relation(sK17_skl) ),
inference(resolution,[status(thm)],[f224,f75]) ).
fof(f231,plain,
! [X0] :
( tseq_dom_restriction(sK17_skl,X0) = relation_dom_restriction(sK17_skl,X0)
| ~ ordinal(X0)
| ~ function(sK17_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f229,f203]) ).
fof(f232,plain,
! [X0] :
( transfinite_sequence_of(tseq_dom_restriction(sK17_skl,X0),relation_rng(sK17_skl))
| ~ ordinal(X0)
| ~ function(sK17_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f230,f203]) ).
fof(f233,plain,
subset(relation_rng(sK17_skl),sK16_skl),
inference(forward_subsumption_resolution,[status(thm)],[f220,f224]) ).
fof(f241,plain,
! [X0] :
( tseq_dom_restriction(sK17_skl,X0) = relation_dom_restriction(sK17_skl,X0)
| ~ ordinal(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f231,f204]) ).
fof(f243,plain,
tseq_dom_restriction(sK17_skl,sK18_skl) = relation_dom_restriction(sK17_skl,sK18_skl),
inference(resolution,[status(thm)],[f241,f187]) ).
fof(f244,plain,
! [X0] :
( transfinite_sequence_of(tseq_dom_restriction(sK17_skl,X0),relation_rng(sK17_skl))
| ~ ordinal(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f232,f204]) ).
fof(f246,plain,
transfinite_sequence_of(tseq_dom_restriction(sK17_skl,sK18_skl),relation_rng(sK17_skl)),
inference(resolution,[status(thm)],[f244,f187]) ).
fof(f252,plain,
~ transfinite_sequence_of(relation_dom_restriction(sK17_skl,sK18_skl),sK16_skl),
inference(backward_demodulation,[status(thm)],[f243,f188]) ).
fof(f259,plain,
transfinite_sequence_of(relation_dom_restriction(sK17_skl,sK18_skl),relation_rng(sK17_skl)),
inference(forward_demodulation,[status(thm)],[f243,f246]) ).
fof(f473,plain,
! [X0] :
( transfinite_sequence_of(X0,sK16_skl)
| ~ transfinite_sequence_of(X0,relation_rng(sK17_skl)) ),
inference(resolution,[status(thm)],[f183,f233]) ).
fof(f511,plain,
transfinite_sequence_of(relation_dom_restriction(sK17_skl,sK18_skl),sK16_skl),
inference(resolution,[status(thm)],[f473,f259]) ).
fof(f514,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f511,f252]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM412+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Mon Sep 21 02:27:06 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.30 % Drodi V4.1.1
% 0.03/0.31 % Refutation found
% 0.03/0.31 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.03/0.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.07/0.33 % Elapsed time: 0.038640 seconds
% 0.07/0.33 % CPU time: 0.097718 seconds
% 0.07/0.33 % Total memory used: 83.660 MB
% 0.07/0.33 % Net memory used: 83.590 MB
%------------------------------------------------------------------------------