%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM395+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 : 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 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 7 unt; 0 def)
% Number of atoms : 17 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 6 ~; 3 |; 2 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-1 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 2 ( 0 sgn 1 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_ordinal1,axiom,
! [A] :
( ordinal(A)
<=> ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',d4_ordinal1) ).
fof(l18_ordinal1,axiom,
( epsilon_connected(empty_set)
& epsilon_transitive(empty_set) ),
file('theBenchmark.p',l18_ordinal1) ).
fof(t27_ordinal1,conjecture,
ordinal(empty_set),
file('theBenchmark.p',t27_ordinal1) ).
fof(t27_ordinal1_neg,negated_conjecture,
~ ordinal(empty_set),
inference(assume_negation,[status(cth)],[t27_ordinal1]) ).
cnf(c_43,plain,
( ~ epsilon_connected(A)
| ~ epsilon_transitive(A)
| ordinal(A) ),
inference(clausify,[status(thm)],[d4_ordinal1]) ).
cnf(c_44,plain,
epsilon_transitive(empty_set),
inference(clausify,[status(thm)],[l18_ordinal1]) ).
cnf(c_45,plain,
( ~ epsilon_connected(empty_set)
| ordinal(empty_set) ),
inference(resolve,[status(thm)],[c_44,c_43]) ).
cnf(c_48,negated_conjecture,
~ ordinal(empty_set),
inference(clausify,[status(thm)],[t27_ordinal1_neg]) ).
cnf(c_49,plain,
epsilon_connected(empty_set),
inference(clausify,[status(thm)],[l18_ordinal1]) ).
cnf(c_64,negated_conjecture,
~ epsilon_connected(empty_set),
inference(resolve,[status(thm)],[c_48,c_45]) ).
cnf(c_63,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_49,c_64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM395+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 02:38:10 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 198655 was started by sandbox on n006,
% 0.09/0.37 % Sat Sep 26 02:38:10 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % 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 0.00 (+ 0.00) seconds.
% 0.13/0.39 % Length of proof is 9.
% 0.13/0.39 % Level of proof is 3.
% 0.13/0.39 % Maximum clause weight is 4.000.
% 0.13/0.39 % Given clauses 0.
% 0.13/0.39
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------