%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM841+1 : 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 : n013.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 08:18:10 AM UTC 2026
% Result : Theorem 0.80s 0.57s
% Output : CNFRefutation 0.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 30 ( 18 unt; 0 def)
% Number of atoms : 47 ( 3 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 30 ( 13 ~; 10 |; 2 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof('ass(cond(goal(177), 0), 0)',axiom,
! [Vd281,Vd282,Vd283] :
( ( ( less(Vd281,Vd282)
& leq(Vd282,Vd283) )
| ( leq(Vd281,Vd282)
& less(Vd282,Vd283) ) )
=> less(Vd281,Vd283) ),
file('theBenchmark.p','ass(cond(goal(177), 0), 0)') ).
fof('ass(cond(158, 0), 0)',axiom,
! [Vd254,Vd255] :
( geq(Vd254,Vd255)
=> leq(Vd255,Vd254) ),
file('theBenchmark.p','ass(cond(158, 0), 0)') ).
fof('def(cond(conseq(axiom(3)), 16), 1)',axiom,
! [Vd244,Vd245] :
( geq(Vd245,Vd244)
<=> ( Vd245 = Vd244
| greater(Vd245,Vd244) ) ),
file('theBenchmark.p','def(cond(conseq(axiom(3)), 16), 1)') ).
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('ass(cond(61, 0), 0)',axiom,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
file('theBenchmark.p','ass(cond(61, 0), 0)') ).
fof('holds(214, 352, 0)',conjecture,
greater(vplus(vd344,vd347),vplus(vd345,vd348)),
file('theBenchmark.p','holds(214, 352, 0)') ).
fof('holds(214, 352, 0)_neg',negated_conjecture,
~ greater(vplus(vd344,vd347),vplus(vd345,vd348)),
inference(assume_negation,[status(cth)],['holds(214, 352, 0)']) ).
cnf(c_40,plain,
( leq(B,A)
| ~ geq(A,B) ),
inference(clausify,[status(thm)],['ass(cond(158, 0), 0)']) ).
cnf(c_43,plain,
( ~ greater(A,B)
| geq(A,B) ),
inference(clausify,[status(thm)],['def(cond(conseq(axiom(3)), 16), 1)']) ).
cnf(c_46,plain,
( leq(B,A)
| ~ greater(A,B) ),
inference(resolve,[status(thm)],[c_43,c_40]) ).
cnf(c_48,negated_conjecture,
~ greater(vplus(vd344,vd347),vplus(vd345,vd348)),
inference(clausify,[status(thm)],['holds(214, 352, 0)_neg']) ).
cnf(c_62,plain,
vplus(A,B) = vplus(B,A),
inference(clausify,[status(thm)],['ass(cond(61, 0), 0)']) ).
cnf(c_77,plain,
( less(B,A)
| ~ greater(A,B) ),
inference(clausify,[status(thm)],['ass(cond(140, 0), 0)']) ).
cnf(c_78,plain,
( greater(B,A)
| ~ less(A,B) ),
inference(clausify,[status(thm)],['ass(cond(147, 0), 0)']) ).
cnf(c_84,plain,
( less(C,B)
| ~ leq(C,A)
| ~ less(A,B) ),
inference(clausify,[status(thm)],['ass(cond(goal(177), 0), 0)']) ).
fof('holds(212, 350, 0)',axiom,
greater(vplus(vd344,vd347),vplus(vd345,vd347)),
file('theBenchmark.p','holds(212, 350, 0)') ).
cnf(c_95,plain,
greater(vplus(vd344,vd347),vplus(vd345,vd347)),
inference(clausify,[status(thm)],['holds(212, 350, 0)']) ).
cnf(c_96,plain,
greater(vplus(vd347,vd344),vplus(vd345,vd347)),
inference(paramod,[status(thm)],[c_62,c_95]) ).
fof('holds(213, 351, 1)',axiom,
greater(vplus(vd347,vd345),vplus(vd348,vd345)),
file('theBenchmark.p','holds(213, 351, 1)') ).
cnf(c_98,plain,
greater(vplus(vd347,vd345),vplus(vd348,vd345)),
inference(clausify,[status(thm)],['holds(213, 351, 1)']) ).
cnf(c_1098,plain,
greater(vplus(vd345,vd347),vplus(vd348,vd345)),
inference(paramod,[status(thm)],[c_62,c_98]) ).
cnf(c_99,plain,
greater(vplus(vd345,vd347),vplus(vd345,vd348)),
inference(paramod,[status(thm)],[c_62,c_1098]) ).
cnf(c_103,negated_conjecture,
~ greater(vplus(vd347,vd344),vplus(vd345,vd348)),
inference(paramod,[status(thm)],[c_62,c_48]) ).
cnf(c_205,plain,
less(vplus(vd345,vd347),vplus(vd347,vd344)),
inference(resolve,[status(thm)],[c_96,c_77]) ).
cnf(c_215,plain,
leq(vplus(vd345,vd348),vplus(vd345,vd347)),
inference(resolve,[status(thm)],[c_99,c_46]) ).
cnf(c_241,negated_conjecture,
~ less(vplus(vd345,vd348),vplus(vd347,vd344)),
inference(resolve,[status(thm)],[c_78,c_103]) ).
cnf(c_1099,plain,
( less(A,vplus(vd347,vd344))
| ~ leq(A,vplus(vd345,vd347)) ),
inference(resolve,[status(thm)],[c_84,c_205]) ).
cnf(c_1100,plain,
~ leq(vplus(vd345,vd348),vplus(vd345,vd347)),
inference(resolve,[status(thm)],[c_1099,c_241]) ).
cnf(c_1097,plain,
$false,
inference(resolve,[status(thm)],[c_215,c_1100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM841+1 : 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 : n013.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 04:12:06 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 1907465 was started by sandbox2 on n013,
% 0.13/0.36 % Sat Sep 26 04:12:06 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.80/0.57
% 0.80/0.57 % SZS status Theorem for theBenchmark
% 0.80/0.57
% 0.80/0.57 % Proof 1 at 0.14 (+ 0.05) seconds.
% 0.80/0.57 % Length of proof is 24.
% 0.80/0.57 % Level of proof is 4.
% 0.80/0.57 % Maximum clause weight is 9.000.
% 0.80/0.57 % Given clauses 214.
% 0.80/0.57
% 0.80/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------