%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM301+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 08:16:25 AM UTC 2026
% Result : Theorem 2.94s 0.83s
% Output : CNFRefutation 2.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 11 unt; 0 def)
% Number of atoms : 24 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 19 ( 10 ~; 6 |; 2 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 15 ( 2 sgn 4 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(less_entry_point_neg_neg,axiom,
! [X,Y,RDN_X,RDN_Y] :
( ( rdn_positive_less(RDN_Y,RDN_X)
& rdn_translate(Y,rdn_neg(RDN_Y))
& rdn_translate(X,rdn_neg(RDN_X)) )
=> less(X,Y) ),
file('theBenchmark.p',less_entry_point_neg_neg) ).
fof(something_less_nn2,conjecture,
? [X] : less(X,nn2),
file('theBenchmark.p',something_less_nn2) ).
fof(something_less_nn2_neg,negated_conjecture,
~ ? [X] : less(X,nn2),
inference(assume_negation,[status(cth)],[something_less_nn2]) ).
fof(rdnn3,axiom,
rdn_translate(nn3,rdn_neg(rdnn(n3))),
file('theBenchmark.p',rdnn3) ).
cnf(c_148,plain,
rdn_translate(nn3,rdn_neg(rdnn(n3))),
inference(clausify,[status(thm)],[rdnn3]) ).
fof(rdnn2,axiom,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
file('theBenchmark.p',rdnn2) ).
cnf(c_290,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(clausify,[status(thm)],[rdnn2]) ).
fof(rdn_positive_less23,axiom,
rdn_positive_less(rdnn(n2),rdnn(n3)),
file('theBenchmark.p',rdn_positive_less23) ).
cnf(c_302,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(clausify,[status(thm)],[rdn_positive_less23]) ).
cnf(c_317,plain,
( less(A,C)
| ~ rdn_positive_less(D,B)
| ~ rdn_translate(C,rdn_neg(D))
| ~ rdn_translate(A,rdn_neg(B)) ),
inference(clausify,[status(thm)],[less_entry_point_neg_neg]) ).
cnf(c_435,negated_conjecture,
~ less(A,nn2),
inference(clausify,[status(thm)],[something_less_nn2_neg]) ).
cnf(c_2094,plain,
( less(A,nn2)
| ~ rdn_positive_less(rdnn(n2),B)
| ~ rdn_translate(A,rdn_neg(B)) ),
inference(resolve,[status(thm)],[c_317,c_290]) ).
cnf(c_1830,negated_conjecture,
( ~ rdn_positive_less(rdnn(n2),B)
| ~ rdn_translate(A,rdn_neg(B)) ),
inference(resolve,[status(thm)],[c_435,c_2094]) ).
cnf(c_2095,plain,
~ rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(resolve,[status(thm)],[c_1830,c_148]) ).
cnf(c_2093,plain,
$false,
inference(resolve,[status(thm)],[c_302,c_2095]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM301+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n008.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 02:26:09 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 2604086 was started by sandbox2 on n008,
% 0.09/0.36 % Sat Sep 26 02:26:09 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.38
% 0.13/0.38 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SInE: 153 to sos, 248 to usable, of 401 axioms (tolerance 2.00, depth 0 fixpoint).
% 2.94/0.83
% 2.94/0.83 % SZS status Theorem for theBenchmark
% 2.94/0.83
% 2.94/0.83 % Proof 1 at 0.26 (+ 0.06) seconds.
% 2.94/0.83 % Length of proof is 9.
% 2.94/0.83 % Level of proof is 3.
% 2.94/0.83 % Maximum clause weight is 115.000.
% 2.94/0.83 % Given clauses 389.
% 2.94/0.83
% 2.94/0.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------