%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM411+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 : Sun Sep 27 08:16:55 AM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 9 unt; 0 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 91 ( 40 ~; 34 |; 9 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 41 ( 5 sgn 13 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d8_ordinal1,axiom,
! [A,B] :
( ( transfinite_sequence(B)
& function(B)
& relation(B) )
=> ( transfinite_sequence_of(B,A)
<=> subset(relation_rng(B),A) ) ),
file('theBenchmark.p',d8_ordinal1) ).
fof(dt_m1_ordinal1,axiom,
! [A,B] :
( transfinite_sequence_of(B,A)
=> ( transfinite_sequence(B)
& function(B)
& relation(B) ) ),
file('theBenchmark.p',dt_m1_ordinal1) ).
fof(t1_xboole_1,axiom,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('theBenchmark.p',t1_xboole_1) ).
fof(t47_ordinal1,conjecture,
! [A,B] :
( subset(A,B)
=> ! [C] :
( transfinite_sequence_of(C,A)
=> transfinite_sequence_of(C,B) ) ),
file('theBenchmark.p',t47_ordinal1) ).
fof(t47_ordinal1_neg,negated_conjecture,
~ ! [A,B] :
( subset(A,B)
=> ! [C] :
( transfinite_sequence_of(C,A)
=> transfinite_sequence_of(C,B) ) ),
inference(assume_negation,[status(cth)],[t47_ordinal1]) ).
cnf(c_45,plain,
( subset(relation_rng(A),B)
| ~ transfinite_sequence_of(A,B)
| ~ transfinite_sequence(A)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d8_ordinal1]) ).
cnf(c_46,plain,
( ~ subset(relation_rng(A),B)
| transfinite_sequence_of(A,B)
| ~ transfinite_sequence(A)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d8_ordinal1]) ).
cnf(c_47,plain,
( function(A)
| ~ transfinite_sequence_of(A,B) ),
inference(clausify,[status(thm)],[dt_m1_ordinal1]) ).
cnf(c_67,plain,
( relation(A)
| ~ transfinite_sequence_of(A,B) ),
inference(clausify,[status(thm)],[dt_m1_ordinal1]) ).
cnf(c_68,plain,
( transfinite_sequence(A)
| ~ transfinite_sequence_of(A,B) ),
inference(clausify,[status(thm)],[dt_m1_ordinal1]) ).
cnf(c_96,plain,
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t1_xboole_1]) ).
fof(nnf_42,plain,
? [A,B] :
( ? [C] :
( ~ transfinite_sequence_of(C,B)
& transfinite_sequence_of(C,A) )
& subset(A,B) ),
inference(fof_nnf,[status(thm)],[t47_ordinal1_neg]) ).
fof(sk_t47_ordinal1_neg,plain,
( ~ transfinite_sequence_of(sK2,sK1)
& transfinite_sequence_of(sK2,sK0)
& subset(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_42]) ).
cnf(c_105,negated_conjecture,
subset(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t47_ordinal1_neg]) ).
cnf(c_106,negated_conjecture,
transfinite_sequence_of(sK2,sK0),
inference(split_conjunct,[status(thm)],[sk_t47_ordinal1_neg]) ).
cnf(c_107,negated_conjecture,
~ transfinite_sequence_of(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_t47_ordinal1_neg]) ).
cnf(c_110,plain,
( ~ subset(relation_rng(A),C)
| transfinite_sequence_of(A,C)
| ~ transfinite_sequence(A)
| ~ relation(A)
| ~ transfinite_sequence_of(A,B) ),
inference(resolve,[status(thm)],[c_47,c_46]) ).
cnf(c_111,plain,
( subset(relation_rng(A),C)
| ~ transfinite_sequence_of(A,C)
| ~ transfinite_sequence(A)
| ~ relation(A)
| ~ transfinite_sequence_of(A,B) ),
inference(resolve,[status(thm)],[c_47,c_45]) ).
cnf(c_129,plain,
( subset(relation_rng(A),B)
| ~ transfinite_sequence(A)
| ~ relation(A)
| ~ transfinite_sequence_of(A,B) ),
inference(factor,[status(thm)],[c_111]) ).
cnf(c_160,plain,
transfinite_sequence(sK2),
inference(resolve,[status(thm)],[c_106,c_68]) ).
cnf(c_161,plain,
relation(sK2),
inference(resolve,[status(thm)],[c_106,c_67]) ).
cnf(c_190,negated_conjecture,
( subset(relation_rng(sK2),sK0)
| ~ transfinite_sequence(sK2)
| ~ relation(sK2) ),
inference(resolve,[status(thm)],[c_129,c_106]) ).
cnf(c_191,negated_conjecture,
( subset(relation_rng(sK2),sK0)
| ~ transfinite_sequence(sK2) ),
inference(resolve,[status(thm)],[c_161,c_190]) ).
cnf(c_174,negated_conjecture,
subset(relation_rng(sK2),sK0),
inference(resolve,[status(thm)],[c_160,c_191]) ).
cnf(c_192,negated_conjecture,
( ~ subset(relation_rng(sK2),A)
| transfinite_sequence_of(sK2,A)
| ~ transfinite_sequence(sK2)
| ~ relation(sK2) ),
inference(resolve,[status(thm)],[c_110,c_106]) ).
cnf(c_193,negated_conjecture,
( ~ subset(relation_rng(sK2),A)
| transfinite_sequence_of(sK2,A)
| ~ transfinite_sequence(sK2) ),
inference(resolve,[status(thm)],[c_192,c_161]) ).
cnf(c_194,negated_conjecture,
( ~ subset(relation_rng(sK2),A)
| transfinite_sequence_of(sK2,A) ),
inference(resolve,[status(thm)],[c_193,c_160]) ).
cnf(c_179,negated_conjecture,
~ subset(relation_rng(sK2),sK1),
inference(resolve,[status(thm)],[c_194,c_107]) ).
cnf(c_195,negated_conjecture,
( subset(A,sK1)
| ~ subset(A,sK0) ),
inference(resolve,[status(thm)],[c_96,c_105]) ).
cnf(c_196,negated_conjecture,
~ subset(relation_rng(sK2),sK0),
inference(resolve,[status(thm)],[c_195,c_179]) ).
cnf(c_189,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_174,c_196]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM411+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 02:39:16 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 1955184 was started by sandbox on n014,
% 0.08/0.36 % Sat Sep 26 02:39:16 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.39
% 0.13/0.39 % SZS status Theorem for theBenchmark
% 0.13/0.39
% 0.13/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.13/0.39 % Length of proof is 21.
% 0.13/0.39 % Level of proof is 5.
% 0.13/0.39 % Maximum clause weight is 14.000.
% 0.13/0.39 % Given clauses 65.
% 0.13/0.39
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------