%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM855+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 : n019.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 4.83s 1.03s
% Output : CNFRefutation 4.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 20 unt; 0 def)
% Number of atoms : 36 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 10 ~; 5 |; 1 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof('ass(cond(270, 0), 0)',axiom,
! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418),
file('theBenchmark.p','ass(cond(270, 0), 0)') ).
fof('ass(cond(168, 0), 0)',axiom,
! [Vd262,Vd263,Vd265] :
( ( less(Vd262,Vd263)
& less(Vd263,Vd265) )
=> less(Vd262,Vd265) ),
file('theBenchmark.p','ass(cond(168, 0), 0)') ).
fof('ass(cond(147, 0), 0)',axiom,
! [Vd226,Vd227] :
( less(Vd226,Vd227)
=> greater(Vd227,Vd226) ),
file('theBenchmark.p','ass(cond(147, 0), 0)') ).
fof('ass(cond(140, 0), 0)',axiom,
! [Vd208,Vd209] :
( greater(Vd208,Vd209)
=> less(Vd209,Vd208) ),
file('theBenchmark.p','ass(cond(140, 0), 0)') ).
fof('holds(conseq_conjunct2(315), 516, 0)',conjecture,
greater(vmul(vd508,vd511),vmul(vd509,vd512)),
file('theBenchmark.p','holds(conseq_conjunct2(315), 516, 0)') ).
fof('holds(conseq_conjunct2(315), 516, 0)_neg',negated_conjecture,
~ greater(vmul(vd508,vd511),vmul(vd509,vd512)),
inference(assume_negation,[status(cth)],['holds(conseq_conjunct2(315), 516, 0)']) ).
fof('holds(conjunct2(315), 515, 2)',axiom,
vmul(vd512,vd509) = vmul(vd509,vd512),
file('theBenchmark.p','holds(conjunct2(315), 515, 2)') ).
cnf(c_58,plain,
vmul(vd512,vd509) = vmul(vd509,vd512),
inference(clausify,[status(thm)],['holds(conjunct2(315), 515, 2)']) ).
fof('holds(conjunct2(315), 515, 1)',axiom,
greater(vmul(vd511,vd509),vmul(vd512,vd509)),
file('theBenchmark.p','holds(conjunct2(315), 515, 1)') ).
cnf(c_59,plain,
greater(vmul(vd511,vd509),vmul(vd512,vd509)),
inference(clausify,[status(thm)],['holds(conjunct2(315), 515, 1)']) ).
cnf(c_60,plain,
greater(vmul(vd511,vd509),vmul(vd509,vd512)),
inference(paramod,[status(thm)],[c_58,c_59]) ).
fof('holds(conjunct1(315), 514, 0)',axiom,
greater(vmul(vd508,vd511),vmul(vd509,vd511)),
file('theBenchmark.p','holds(conjunct1(315), 514, 0)') ).
cnf(c_63,plain,
greater(vmul(vd508,vd511),vmul(vd509,vd511)),
inference(clausify,[status(thm)],['holds(conjunct1(315), 514, 0)']) ).
cnf(c_75,plain,
vmul(A,B) = vmul(B,A),
inference(clausify,[status(thm)],['ass(cond(270, 0), 0)']) ).
cnf(c_99,plain,
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ),
inference(clausify,[status(thm)],['ass(cond(168, 0), 0)']) ).
cnf(c_108,plain,
( greater(B,A)
| ~ less(A,B) ),
inference(clausify,[status(thm)],['ass(cond(147, 0), 0)']) ).
cnf(c_109,plain,
( less(B,A)
| ~ greater(A,B) ),
inference(clausify,[status(thm)],['ass(cond(140, 0), 0)']) ).
cnf(c_138,negated_conjecture,
~ greater(vmul(vd508,vd511),vmul(vd509,vd512)),
inference(clausify,[status(thm)],['holds(conseq_conjunct2(315), 516, 0)_neg']) ).
cnf(c_139,negated_conjecture,
~ greater(vmul(vd511,vd508),vmul(vd509,vd512)),
inference(paramod,[status(thm)],[c_75,c_138]) ).
cnf(c_140,plain,
greater(vmul(vd509,vd511),vmul(vd509,vd512)),
inference(paramod,[status(thm)],[c_75,c_60]) ).
cnf(c_141,plain,
greater(vmul(vd511,vd508),vmul(vd509,vd511)),
inference(paramod,[status(thm)],[c_75,c_63]) ).
cnf(c_322,negated_conjecture,
~ less(vmul(vd509,vd512),vmul(vd511,vd508)),
inference(resolve,[status(thm)],[c_108,c_139]) ).
cnf(c_327,plain,
less(vmul(vd509,vd512),vmul(vd509,vd511)),
inference(resolve,[status(thm)],[c_140,c_109]) ).
cnf(c_337,plain,
less(vmul(vd509,vd511),vmul(vd511,vd508)),
inference(resolve,[status(thm)],[c_141,c_109]) ).
cnf(c_2623,plain,
( less(vmul(vd509,vd512),A)
| ~ less(vmul(vd509,vd511),A) ),
inference(resolve,[status(thm)],[c_99,c_327]) ).
cnf(c_2624,plain,
~ less(vmul(vd509,vd511),vmul(vd511,vd508)),
inference(resolve,[status(thm)],[c_2623,c_322]) ).
cnf(c_2622,plain,
$false,
inference(resolve,[status(thm)],[c_337,c_2624]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM855+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 04:13:48 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 378587 was started by sandbox2 on n019,
% 0.10/0.36 % Sat Sep 26 04:13:48 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.39
% 0.15/0.39 % From the command line: assign(max_seconds, 300).
% 4.83/1.03
% 4.83/1.03 % SZS status Theorem for theBenchmark
% 4.83/1.03
% 4.83/1.03 % Proof 1 at 0.44 (+ 0.19) seconds.
% 4.83/1.03 % Length of proof is 21.
% 4.83/1.03 % Level of proof is 4.
% 4.83/1.03 % Maximum clause weight is 9.000.
% 4.83/1.03 % Given clauses 371.
% 4.83/1.03
% 4.83/1.03 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------