%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM343+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 08:16:28 AM UTC 2026
% Result : Theorem 0.17s 0.51s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 2
% Syntax : Number of formulae : 7 ( 3 unt; 0 def)
% Number of atoms : 14 ( 1 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 13 ( 6 ~; 1 |; 3 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 8 ( 1 sgn 2 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(less_property,axiom,
! [X,Y] :
( less(X,Y)
<=> ( Y != X
& ~ less(Y,X) ) ),
file('theBenchmark.p',less_property) ).
fof(sum_something_n0_samething,conjecture,
? [X] :
( ( less(X,n1)
& less(nn1,X) )
=> sum(n21,X,n21) ),
file('theBenchmark.p',sum_something_n0_samething) ).
fof(sum_something_n0_samething_neg,negated_conjecture,
~ ? [X] :
( ( less(X,n1)
& less(nn1,X) )
=> sum(n21,X,n21) ),
inference(assume_negation,[status(cth)],[sum_something_n0_samething]) ).
cnf(c_318,plain,
( ~ less(B,A)
| ~ less(A,B) ),
inference(clausify,[status(thm)],[less_property]) ).
cnf(c_436,negated_conjecture,
less(A,n1),
inference(clausify,[status(thm)],[sum_something_n0_samething_neg]) ).
cnf(c_440,plain,
~ less(A,A),
inference(factor,[status(thm)],[c_318]) ).
cnf(c_441,plain,
$false,
inference(resolve,[status(thm)],[c_440,c_436]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM343+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.45 % Computer : n008.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Sat Sep 26 02:29:24 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.46 % Process 2606638 was started by sandbox on n008,
% 0.17/0.46 % Sat Sep 26 02:29:24 2026
% 0.17/0.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.48
% 0.17/0.48 % From the command line: assign(max_seconds, 300).
% 0.17/0.48
% 0.17/0.48 % SInE: 154 to sos, 247 to usable, of 401 axioms (tolerance 2.00, depth 0 fixpoint).
% 0.17/0.51
% 0.17/0.51 % SZS status Theorem for theBenchmark
% 0.17/0.51
% 0.17/0.51 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.17/0.51 % Length of proof is 6.
% 0.17/0.51 % Level of proof is 3.
% 0.17/0.51 % Maximum clause weight is 11.000.
% 0.17/0.51 % Given clauses 0.
% 0.17/0.51
% 0.17/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------