%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM854+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 08:18:14 AM UTC 2026
% Result : Theorem 0.17s 0.46s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 9 ( 7 unt; 0 def)
% Number of atoms : 11 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 5 ( 3 ~; 1 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 7 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof('ass(cond(299, 0), 2)',axiom,
! [Vd456,Vd457,Vd458] :
( greater(Vd457,Vd458)
=> greater(vmul(Vd457,Vd456),vmul(Vd458,Vd456)) ),
file('theBenchmark.p','ass(cond(299, 0), 2)') ).
fof('holds(conjunct1(315), 514, 0)',conjecture,
greater(vmul(vd508,vd511),vmul(vd509,vd511)),
file('theBenchmark.p','holds(conjunct1(315), 514, 0)') ).
fof('holds(conjunct1(315), 514, 0)_neg',negated_conjecture,
~ greater(vmul(vd508,vd511),vmul(vd509,vd511)),
inference(assume_negation,[status(cth)],['holds(conjunct1(315), 514, 0)']) ).
fof('holds(conjunct1(314), 510, 0)',axiom,
greater(vd508,vd509),
file('theBenchmark.p','holds(conjunct1(314), 510, 0)') ).
cnf(c_27,plain,
greater(vd508,vd509),
inference(clausify,[status(thm)],['holds(conjunct1(314), 510, 0)']) ).
cnf(c_33,plain,
( greater(vmul(A,C),vmul(B,C))
| ~ greater(A,B) ),
inference(clausify,[status(thm)],['ass(cond(299, 0), 2)']) ).
cnf(c_55,negated_conjecture,
~ greater(vmul(vd508,vd511),vmul(vd509,vd511)),
inference(clausify,[status(thm)],['holds(conjunct1(315), 514, 0)_neg']) ).
cnf(c_57,plain,
greater(vmul(vd508,A),vmul(vd509,A)),
inference(resolve,[status(thm)],[c_33,c_27]) ).
cnf(c_58,plain,
$false,
inference(resolve,[status(thm)],[c_57,c_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM854+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n014.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sat Sep 26 04:13:31 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 2115358 was started by sandbox2 on n014,
% 0.17/0.43 % Sat Sep 26 04:13:31 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 0.17/0.46
% 0.17/0.46 % SZS status Theorem for theBenchmark
% 0.17/0.46
% 0.17/0.46 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.17/0.46 % Length of proof is 7.
% 0.17/0.46 % Level of proof is 3.
% 0.17/0.46 % Maximum clause weight is 10.000.
% 0.17/0.46 % Given clauses 8.
% 0.17/0.46
% 0.17/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------