%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM410+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 : n003.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 0.09s 0.43s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 10 unt; 0 def)
% Number of atoms : 78 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 83 ( 34 ~; 27 |; 13 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 29 ( 8 sgn 9 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d7_ordinal1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( transfinite_sequence(A)
<=> ordinal(relation_dom(A)) ) ),
file('theBenchmark.p',d7_ordinal1) ).
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(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t46_ordinal1,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ( ordinal(relation_dom(A))
=> transfinite_sequence_of(A,relation_rng(A)) ) ),
file('theBenchmark.p',t46_ordinal1) ).
fof(t46_ordinal1_neg,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ( ordinal(relation_dom(A))
=> transfinite_sequence_of(A,relation_rng(A)) ) ),
inference(assume_negation,[status(cth)],[t46_ordinal1]) ).
cnf(c_48,plain,
( ~ ordinal(relation_dom(A))
| transfinite_sequence(A)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d7_ordinal1]) ).
cnf(c_50,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_51,plain,
( function(A)
| ~ transfinite_sequence_of(A,B) ),
inference(clausify,[status(thm)],[dt_m1_ordinal1]) ).
fof(nnf_44,plain,
? [A] :
( ~ transfinite_sequence_of(A,relation_rng(A))
& ordinal(relation_dom(A))
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[t46_ordinal1_neg]) ).
fof(sk_t46_ordinal1_neg,plain,
( ~ transfinite_sequence_of(sK0,relation_rng(sK0))
& ordinal(relation_dom(sK0))
& function(sK0)
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_44]) ).
cnf(c_61,negated_conjecture,
function(sK0),
inference(split_conjunct,[status(thm)],[sk_t46_ordinal1_neg]) ).
cnf(c_117,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
cnf(c_127,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t46_ordinal1_neg]) ).
cnf(c_128,negated_conjecture,
ordinal(relation_dom(sK0)),
inference(split_conjunct,[status(thm)],[sk_t46_ordinal1_neg]) ).
cnf(c_129,negated_conjecture,
~ transfinite_sequence_of(sK0,relation_rng(sK0)),
inference(split_conjunct,[status(thm)],[sk_t46_ordinal1_neg]) ).
cnf(c_134,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_51,c_50]) ).
cnf(c_183,negated_conjecture,
( ~ subset(relation_rng(sK0),A)
| transfinite_sequence_of(sK0,A)
| ~ transfinite_sequence(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_61,c_50]) ).
cnf(c_184,negated_conjecture,
( ~ subset(relation_rng(sK0),A)
| transfinite_sequence_of(sK0,A)
| ~ transfinite_sequence(sK0) ),
inference(resolve,[status(thm)],[c_127,c_183]) ).
cnf(c_185,negated_conjecture,
( ~ ordinal(relation_dom(sK0))
| transfinite_sequence(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_61,c_48]) ).
cnf(c_263,negated_conjecture,
( ~ ordinal(relation_dom(sK0))
| transfinite_sequence(sK0) ),
inference(resolve,[status(thm)],[c_127,c_185]) ).
cnf(c_186,negated_conjecture,
transfinite_sequence(sK0),
inference(resolve,[status(thm)],[c_128,c_263]) ).
cnf(c_189,negated_conjecture,
( ~ subset(relation_rng(sK0),A)
| transfinite_sequence_of(sK0,A) ),
inference(resolve,[status(thm)],[c_186,c_184]) ).
cnf(c_264,negated_conjecture,
( ~ subset(relation_rng(sK0),B)
| transfinite_sequence_of(sK0,B)
| ~ transfinite_sequence(sK0)
| ~ transfinite_sequence_of(sK0,A) ),
inference(resolve,[status(thm)],[c_134,c_127]) ).
cnf(c_265,negated_conjecture,
( ~ subset(relation_rng(sK0),B)
| transfinite_sequence_of(sK0,B)
| ~ transfinite_sequence_of(sK0,A) ),
inference(resolve,[status(thm)],[c_264,c_186]) ).
cnf(c_266,negated_conjecture,
( ~ subset(relation_rng(sK0),relation_rng(sK0))
| ~ transfinite_sequence_of(sK0,A) ),
inference(resolve,[status(thm)],[c_265,c_129]) ).
cnf(c_259,negated_conjecture,
~ transfinite_sequence_of(sK0,A),
inference(resolve,[status(thm)],[c_266,c_117]) ).
cnf(c_261,negated_conjecture,
~ subset(relation_rng(sK0),A),
inference(resolve,[status(thm)],[c_259,c_189]) ).
cnf(c_262,plain,
$false,
inference(resolve,[status(thm)],[c_261,c_117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM410+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n003.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 02:41:08 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1845401 was started by sandbox on n003,
% 0.09/0.37 % Sat Sep 26 02:41:08 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.39
% 0.09/0.39 % From the command line: assign(max_seconds, 300).
% 0.09/0.43
% 0.09/0.43 % SZS status Theorem for theBenchmark
% 0.09/0.43
% 0.09/0.43 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.09/0.43 % Length of proof is 22.
% 0.09/0.43 % Level of proof is 6.
% 0.09/0.43 % Maximum clause weight is 24.000.
% 0.09/0.43 % Given clauses 85.
% 0.09/0.43
% 0.09/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------