%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM394+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 : n018.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 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 10 unt; 0 def)
% Number of atoms : 90 ( 7 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 89 ( 33 ~; 33 |; 11 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 30 ( 0 sgn 13 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc1_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',cc1_ordinal1) ).
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(d2_ordinal1,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('theBenchmark.p',d2_ordinal1) ).
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(t24_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ in(B,A)
& A != B
& ~ in(A,B) ) ) ),
file('theBenchmark.p',t24_ordinal1) ).
fof(t26_ordinal1,conjecture,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( in(B,A)
| ordinal_subset(A,B) ) ) ),
file('theBenchmark.p',t26_ordinal1) ).
fof(t26_ordinal1_neg,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( in(B,A)
| ordinal_subset(A,B) ) ) ),
inference(assume_negation,[status(cth)],[t26_ordinal1]) ).
cnf(c_43,plain,
( subset(B,A)
| ~ in(B,A)
| ~ epsilon_transitive(A) ),
inference(clausify,[status(thm)],[d2_ordinal1]) ).
cnf(c_48,plain,
( epsilon_transitive(A)
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[cc1_ordinal1]) ).
cnf(c_61,plain,
( subset(B,A)
| ~ in(B,A)
| ~ ordinal(A) ),
inference(resolve,[status(thm)],[c_48,c_43]) ).
cnf(c_70,plain,
( ordinal_subset(B,A)
| ordinal_subset(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[connectedness_r1_ordinal1]) ).
cnf(c_81,plain,
( ~ subset(A,B)
| ordinal_subset(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[redefinition_r1_ordinal1]) ).
cnf(c_85,plain,
( in(B,A)
| B = A
| in(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[t24_ordinal1]) ).
fof(nnf_35,plain,
? [A] :
( ? [B] :
( ~ in(B,A)
& ~ ordinal_subset(A,B)
& ordinal(B) )
& ordinal(A) ),
inference(fof_nnf,[status(thm)],[t26_ordinal1_neg]) ).
fof(sk_t26_ordinal1_neg,plain,
( ~ in(sK1,sK0)
& ~ ordinal_subset(sK0,sK1)
& ordinal(sK1)
& ordinal(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_35]) ).
cnf(c_94,negated_conjecture,
ordinal(sK0),
inference(split_conjunct,[status(thm)],[sk_t26_ordinal1_neg]) ).
cnf(c_95,negated_conjecture,
ordinal(sK1),
inference(split_conjunct,[status(thm)],[sk_t26_ordinal1_neg]) ).
cnf(c_96,negated_conjecture,
~ ordinal_subset(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t26_ordinal1_neg]) ).
cnf(c_97,negated_conjecture,
~ in(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_t26_ordinal1_neg]) ).
cnf(c_122,plain,
( in(sK0,A)
| sK0 = A
| in(A,sK0)
| ~ ordinal(A) ),
inference(resolve,[status(thm)],[c_94,c_85]) ).
cnf(c_123,plain,
( ordinal_subset(sK0,A)
| ordinal_subset(A,sK0)
| ~ ordinal(A) ),
inference(resolve,[status(thm)],[c_94,c_70]) ).
cnf(c_167,plain,
( ordinal_subset(sK0,sK0)
| ~ ordinal(sK0) ),
inference(factor,[status(thm)],[c_123]) ).
cnf(c_125,negated_conjecture,
ordinal_subset(sK0,sK0),
inference(resolve,[status(thm)],[c_94,c_167]) ).
cnf(c_168,negated_conjecture,
( ~ subset(sK0,A)
| ordinal_subset(sK0,A)
| ~ ordinal(A) ),
inference(resolve,[status(thm)],[c_81,c_94]) ).
cnf(c_169,negated_conjecture,
( ~ subset(sK0,sK1)
| ordinal_subset(sK0,sK1) ),
inference(resolve,[status(thm)],[c_168,c_95]) ).
cnf(c_130,negated_conjecture,
~ subset(sK0,sK1),
inference(resolve,[status(thm)],[c_169,c_96]) ).
cnf(c_170,negated_conjecture,
( subset(A,sK1)
| ~ in(A,sK1) ),
inference(resolve,[status(thm)],[c_61,c_95]) ).
cnf(c_144,negated_conjecture,
~ in(sK0,sK1),
inference(resolve,[status(thm)],[c_170,c_130]) ).
cnf(c_171,negated_conjecture,
( in(sK0,sK1)
| sK0 = sK1
| in(sK1,sK0) ),
inference(resolve,[status(thm)],[c_122,c_95]) ).
cnf(c_172,negated_conjecture,
( in(sK0,sK1)
| sK1 = sK0
| in(sK1,sK0) ),
inference(copy,[status(thm)],[c_171]) ).
cnf(c_173,negated_conjecture,
( in(sK0,sK1)
| sK1 = sK0 ),
inference(resolve,[status(thm)],[c_97,c_172]) ).
cnf(c_164,negated_conjecture,
sK1 = sK0,
inference(resolve,[status(thm)],[c_144,c_173]) ).
cnf(c_174,plain,
~ ordinal_subset(sK0,sK0),
inference(paramod,[status(thm)],[c_164,c_96]) ).
cnf(c_166,plain,
$false,
inference(resolve,[status(thm)],[c_125,c_174]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM394+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n018.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 02:40:36 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 3517852 was started by sandbox on n018,
% 0.13/0.36 % Sat Sep 26 02:40:36 2026
% 0.13/0.36 % 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).
% 0.13/0.38
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 23.
% 0.13/0.38 % Level of proof is 5.
% 0.13/0.38 % Maximum clause weight is 18.000.
% 0.13/0.38 % Given clauses 83.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------