%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM393+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 08:16:54 AM UTC 2026
% Result : Theorem 0.14s 5.45s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 9 unt; 0 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 57 ( 24 ~; 19 |; 6 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 23 ( 0 sgn 10 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(connectedness_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(B,A)
| ordinal_subset(A,B) ) ),
file('theBenchmark.p',connectedness_r1_ordinal1) ).
fof(d9_xboole_0,axiom,
! [A,B] :
( inclusion_comparable(A,B)
<=> ( subset(B,A)
| subset(A,B) ) ),
file('theBenchmark.p',d9_xboole_0) ).
fof(redefinition_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
file('theBenchmark.p',redefinition_r1_ordinal1) ).
fof(t25_ordinal1,conjecture,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> inclusion_comparable(A,B) ) ),
file('theBenchmark.p',t25_ordinal1) ).
fof(t25_ordinal1_neg,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> inclusion_comparable(A,B) ) ),
inference(assume_negation,[status(cth)],[t25_ordinal1]) ).
cnf(c_62,plain,
( ordinal_subset(B,A)
| ordinal_subset(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[connectedness_r1_ordinal1]) ).
cnf(c_64,plain,
( ~ subset(A,B)
| inclusion_comparable(A,B) ),
inference(clausify,[status(thm)],[d9_xboole_0]) ).
cnf(c_65,plain,
( ~ subset(B,A)
| inclusion_comparable(A,B) ),
inference(clausify,[status(thm)],[d9_xboole_0]) ).
cnf(c_75,plain,
( subset(A,B)
| ~ ordinal_subset(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[redefinition_r1_ordinal1]) ).
fof(nnf_36,plain,
? [A] :
( ? [B] :
( ~ inclusion_comparable(A,B)
& ordinal(B) )
& ordinal(A) ),
inference(fof_nnf,[status(thm)],[t25_ordinal1_neg]) ).
fof(sk_t25_ordinal1_neg,plain,
( ~ inclusion_comparable(sK0,sK1)
& ordinal(sK1)
& ordinal(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_36]) ).
cnf(c_90,negated_conjecture,
ordinal(sK0),
inference(split_conjunct,[status(thm)],[sk_t25_ordinal1_neg]) ).
cnf(c_91,negated_conjecture,
ordinal(sK1),
inference(split_conjunct,[status(thm)],[sk_t25_ordinal1_neg]) ).
cnf(c_92,negated_conjecture,
~ inclusion_comparable(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t25_ordinal1_neg]) ).
cnf(c_115,negated_conjecture,
~ subset(sK1,sK0),
inference(resolve,[status(thm)],[c_65,c_92]) ).
cnf(c_116,negated_conjecture,
~ subset(sK0,sK1),
inference(resolve,[status(thm)],[c_64,c_92]) ).
cnf(c_131,negated_conjecture,
( subset(sK1,A)
| ~ ordinal_subset(sK1,A)
| ~ ordinal(A) ),
inference(resolve,[status(thm)],[c_75,c_91]) ).
cnf(c_132,negated_conjecture,
( subset(sK1,sK0)
| ~ ordinal_subset(sK1,sK0) ),
inference(resolve,[status(thm)],[c_131,c_90]) ).
cnf(c_122,negated_conjecture,
~ ordinal_subset(sK1,sK0),
inference(resolve,[status(thm)],[c_132,c_115]) ).
cnf(c_133,negated_conjecture,
( subset(sK0,A)
| ~ ordinal_subset(sK0,A)
| ~ ordinal(A) ),
inference(resolve,[status(thm)],[c_75,c_90]) ).
cnf(c_134,negated_conjecture,
( subset(sK0,sK1)
| ~ ordinal_subset(sK0,sK1) ),
inference(resolve,[status(thm)],[c_133,c_91]) ).
cnf(c_124,negated_conjecture,
~ ordinal_subset(sK0,sK1),
inference(resolve,[status(thm)],[c_134,c_116]) ).
cnf(c_135,negated_conjecture,
( ordinal_subset(sK0,A)
| ordinal_subset(A,sK0)
| ~ ordinal(A) ),
inference(resolve,[status(thm)],[c_62,c_90]) ).
cnf(c_136,negated_conjecture,
( ordinal_subset(sK0,sK1)
| ~ ordinal(sK1) ),
inference(resolve,[status(thm)],[c_135,c_122]) ).
cnf(c_137,negated_conjecture,
~ ordinal(sK1),
inference(resolve,[status(thm)],[c_136,c_124]) ).
cnf(c_130,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_91,c_137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM393+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/5.42 % Computer : n006.cluster.edu
% 0.14/5.42 % Model : x86_64 x86_64
% 0.14/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.42 % Memory : 8046.5625MB
% 0.14/5.42 % OS : Linux 6.8.0-71-generic
% 0.14/5.42 % CPULimit : 300
% 0.14/5.42 % WCLimit : 300
% 0.14/5.42 % DateTime : Sat Sep 26 02:38:01 UTC 2026
% 0.14/5.42 % CPUTime :
% 0.14/5.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/5.42 % Process 198041 was started by sandbox2 on n006,
% 0.14/5.42 % Sat Sep 26 02:38:01 2026
% 0.14/5.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/5.44
% 0.14/5.44 % From the command line: assign(max_seconds, 300).
% 0.14/5.45
% 0.14/5.45 % SZS status Theorem for theBenchmark
% 0.14/5.45
% 0.14/5.45 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/5.45 % Length of proof is 16.
% 0.14/5.45 % Level of proof is 4.
% 0.14/5.45 % Maximum clause weight is 10.000.
% 0.14/5.45 % Given clauses 48.
% 0.14/5.45
% 0.14/5.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------