%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM856+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 38.38s 10.92s
% Output : CNFRefutation 38.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 66 ( 24 unt; 0 def)
% Number of atoms : 122 ( 10 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 92 ( 36 ~; 44 |; 4 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 84 ( 0 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof('dis(antec(scope(318)))',axiom,
( ( greater(vd517,vd518)
& geq(vd519,vd520) )
| ( geq(vd517,vd518)
& greater(vd519,vd520) ) ),
file('theBenchmark.p','dis(antec(scope(318)))') ).
fof('ass(cond(conjunct2(conjunct2(307)), 0), 0)',axiom,
! [Vd496,Vd497,Vd498] :
( less(vmul(Vd496,Vd497),vmul(Vd498,Vd497))
=> less(Vd496,Vd498) ),
file('theBenchmark.p','ass(cond(conjunct2(conjunct2(307)), 0), 0)') ).
fof('ass(cond(299, 0), 0)',axiom,
! [Vd456,Vd465,Vd466] :
( less(Vd465,Vd466)
=> less(vmul(Vd465,Vd456),vmul(Vd466,Vd456)) ),
file('theBenchmark.p','ass(cond(299, 0), 0)') ).
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(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)), 17), 1)',axiom,
! [Vd249,Vd250] :
( leq(Vd250,Vd249)
<=> ( Vd250 = Vd249
| less(Vd250,Vd249) ) ),
file('theBenchmark.p','def(cond(conseq(axiom(3)), 17), 1)') ).
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(goal(130), 0), 0)',axiom,
! [Vd203,Vd204] :
( less(Vd203,Vd204)
| greater(Vd203,Vd204)
| Vd203 = Vd204 ),
file('theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
fof('ass(cond(goal(130), 0), 1)',axiom,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| Vd203 != Vd204 ),
file('theBenchmark.p','ass(cond(goal(130), 0), 1)') ).
fof('holds(conseq(scope(318)), 525, 0)',conjecture,
greater(vmul(vd517,vd519),vmul(vd518,vd520)),
file('theBenchmark.p','holds(conseq(scope(318)), 525, 0)') ).
fof('holds(conseq(scope(318)), 525, 0)_neg',negated_conjecture,
~ greater(vmul(vd517,vd519),vmul(vd518,vd520)),
inference(assume_negation,[status(cth)],['holds(conseq(scope(318)), 525, 0)']) ).
cnf(c_60,plain,
( geq(vd519,vd520)
| greater(vd519,vd520) ),
inference(clausify,[status(thm)],['dis(antec(scope(318)))']) ).
cnf(c_61,plain,
( greater(vd517,vd518)
| greater(vd519,vd520) ),
inference(clausify,[status(thm)],['dis(antec(scope(318)))']) ).
cnf(c_63,plain,
( greater(vd517,vd518)
| geq(vd517,vd518) ),
inference(clausify,[status(thm)],['dis(antec(scope(318)))']) ).
cnf(c_65,plain,
( less(A,C)
| ~ less(vmul(A,B),vmul(C,B)) ),
inference(clausify,[status(thm)],['ass(cond(conjunct2(conjunct2(307)), 0), 0)']) ).
cnf(c_68,plain,
( less(vmul(A,C),vmul(B,C))
| ~ less(A,B) ),
inference(clausify,[status(thm)],['ass(cond(299, 0), 0)']) ).
cnf(c_74,plain,
vmul(A,B) = vmul(B,A),
inference(clausify,[status(thm)],['ass(cond(270, 0), 0)']) ).
cnf(c_96,plain,
( less(C,B)
| ~ leq(C,A)
| ~ less(A,B) ),
inference(clausify,[status(thm)],['ass(cond(goal(177), 0), 0)']) ).
cnf(c_97,plain,
( less(C,B)
| ~ less(C,A)
| ~ leq(A,B) ),
inference(clausify,[status(thm)],['ass(cond(goal(177), 0), 0)']) ).
cnf(c_100,plain,
( leq(B,A)
| ~ geq(A,B) ),
inference(clausify,[status(thm)],['ass(cond(158, 0), 0)']) ).
cnf(c_103,plain,
( B != A
| leq(A,B) ),
inference(clausify,[status(thm)],['def(cond(conseq(axiom(3)), 17), 1)']) ).
cnf(c_105,plain,
( ~ greater(A,B)
| geq(A,B) ),
inference(clausify,[status(thm)],['def(cond(conseq(axiom(3)), 16), 1)']) ).
cnf(c_106,plain,
( B != A
| geq(A,B) ),
inference(clausify,[status(thm)],['def(cond(conseq(axiom(3)), 16), 1)']) ).
cnf(c_107,plain,
( greater(B,A)
| ~ less(A,B) ),
inference(clausify,[status(thm)],['ass(cond(147, 0), 0)']) ).
cnf(c_108,plain,
( less(B,A)
| ~ greater(A,B) ),
inference(clausify,[status(thm)],['ass(cond(140, 0), 0)']) ).
cnf(c_109,plain,
( less(B,A)
| greater(B,A)
| A = B ),
inference(clausify,[status(thm)],['ass(cond(goal(130), 0), 0)']) ).
cnf(c_110,plain,
( ~ less(B,A)
| A != B ),
inference(clausify,[status(thm)],['ass(cond(goal(130), 0), 1)']) ).
cnf(c_134,negated_conjecture,
~ greater(vmul(vd517,vd519),vmul(vd518,vd520)),
inference(clausify,[status(thm)],['holds(conseq(scope(318)), 525, 0)_neg']) ).
cnf(c_267,plain,
leq(vmul(A,B),vmul(B,A)),
inference(resolve,[status(thm)],[c_103,c_74]) ).
cnf(c_36647,plain,
( geq(vd517,vd518)
| geq(vd517,vd518) ),
inference(resolve,[status(thm)],[c_105,c_63]) ).
cnf(c_282,plain,
geq(vd517,vd518),
inference(copy,[status(thm)],[c_36647]) ).
cnf(c_36648,plain,
( geq(vd519,vd520)
| geq(vd519,vd520) ),
inference(resolve,[status(thm)],[c_105,c_60]) ).
cnf(c_284,plain,
geq(vd519,vd520),
inference(copy,[status(thm)],[c_36648]) ).
cnf(c_300,plain,
( greater(vd519,vd520)
| less(vd518,vd517) ),
inference(resolve,[status(thm)],[c_108,c_61]) ).
cnf(c_302,plain,
( geq(A,B)
| less(A,B)
| greater(A,B) ),
inference(resolve,[status(thm)],[c_109,c_106]) ).
cnf(c_347,plain,
~ less(A,A),
inference(xxres,[status(thm)],[c_110]) ).
cnf(c_648,plain,
~ greater(vmul(vd519,vd517),vmul(vd518,vd520)),
inference(paramod,[status(thm)],[c_74,c_134]) ).
cnf(c_649,plain,
~ greater(vmul(vd517,vd519),vmul(vd520,vd518)),
inference(paramod,[status(thm)],[c_74,c_134]) ).
cnf(c_686,plain,
leq(vd518,vd517),
inference(resolve,[status(thm)],[c_282,c_100]) ).
cnf(c_692,plain,
leq(vd520,vd519),
inference(resolve,[status(thm)],[c_284,c_100]) ).
cnf(c_36649,plain,
( less(A,vd517)
| ~ less(A,vd518) ),
inference(resolve,[status(thm)],[c_97,c_686]) ).
cnf(c_781,plain,
~ less(vd517,vd518),
inference(resolve,[status(thm)],[c_36649,c_347]) ).
cnf(c_36650,plain,
( less(A,vd519)
| ~ less(A,vd520) ),
inference(resolve,[status(thm)],[c_97,c_692]) ).
cnf(c_790,plain,
~ less(vd519,vd520),
inference(resolve,[status(thm)],[c_36650,c_347]) ).
cnf(c_828,plain,
~ less(vmul(vd517,A),vmul(vd518,A)),
inference(resolve,[status(thm)],[c_65,c_781]) ).
cnf(c_832,plain,
~ less(vmul(vd519,A),vmul(vd520,A)),
inference(resolve,[status(thm)],[c_65,c_790]) ).
cnf(c_1049,plain,
( less(vd520,vd519)
| less(vd518,vd517) ),
inference(resolve,[status(thm)],[c_300,c_108]) ).
cnf(c_2544,plain,
( less(vmul(vd518,A),vmul(vd517,A))
| less(vd520,vd519) ),
inference(resolve,[status(thm)],[c_1049,c_68]) ).
cnf(c_36651,plain,
( geq(A,B)
| geq(A,B)
| less(A,B) ),
inference(resolve,[status(thm)],[c_302,c_105]) ).
cnf(c_9133,plain,
( geq(A,B)
| less(A,B) ),
inference(copy,[status(thm)],[c_36651]) ).
cnf(c_9181,plain,
( greater(B,A)
| geq(A,B) ),
inference(resolve,[status(thm)],[c_9133,c_107]) ).
cnf(c_9521,plain,
( leq(A,B)
| greater(A,B) ),
inference(resolve,[status(thm)],[c_9181,c_100]) ).
cnf(c_10918,plain,
( less(C,B)
| ~ less(C,A)
| greater(A,B) ),
inference(resolve,[status(thm)],[c_9521,c_97]) ).
cnf(c_11379,plain,
~ less(vmul(A,vd517),vmul(vd518,A)),
inference(paramod,[status(thm)],[c_74,c_828]) ).
cnf(c_36652,plain,
( less(vmul(B,A),C)
| ~ less(vmul(A,B),C) ),
inference(resolve,[status(thm)],[c_96,c_267]) ).
cnf(c_11756,plain,
~ less(vmul(A,vd519),vmul(vd520,A)),
inference(resolve,[status(thm)],[c_36652,c_832]) ).
cnf(c_36653,plain,
( less(A,vmul(vd518,vd520))
| ~ less(A,vmul(vd519,vd517)) ),
inference(resolve,[status(thm)],[c_10918,c_648]) ).
cnf(c_24825,plain,
~ less(vmul(vd520,vd517),vmul(vd519,vd517)),
inference(resolve,[status(thm)],[c_36653,c_11379]) ).
cnf(c_36654,plain,
( less(A,vmul(vd520,vd518))
| ~ less(A,vmul(vd517,vd519)) ),
inference(resolve,[status(thm)],[c_10918,c_649]) ).
cnf(c_25196,plain,
~ less(vmul(vd518,vd519),vmul(vd517,vd519)),
inference(resolve,[status(thm)],[c_36654,c_11756]) ).
cnf(c_36587,plain,
~ less(vd520,vd519),
inference(resolve,[status(thm)],[c_68,c_24825]) ).
cnf(c_36645,plain,
less(vmul(vd518,A),vmul(vd517,A)),
inference(resolve,[status(thm)],[c_36587,c_2544]) ).
cnf(c_36646,plain,
$false,
inference(resolve,[status(thm)],[c_36645,c_25196]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM856+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n017.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sat Sep 26 04:09:23 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.38 % Process 3965802 was started by sandbox on n017,
% 0.10/5.38 % Sat Sep 26 04:09:23 2026
% 0.10/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.40
% 0.10/5.40 % From the command line: assign(max_seconds, 300).
% 38.38/10.92
% 38.38/10.92 % given #500 (T,wt=14): 591 less(A,vsucc(A)). [resolve(128,a,114,b(flip))].
% 38.38/10.92
% 38.38/10.92 % given #1000 (A,wt=32): 442 vplus(vmul(vsucc(A),B),C) != vplus(vmul(A,B),B). [ur(118,a,76,a(flip))].
% 38.38/10.92
% 38.38/10.92 % SZS status Theorem for theBenchmark
% 38.38/10.92
% 38.38/10.92 % Proof 1 at 4.35 (+ 1.14) seconds.
% 38.38/10.92 % Length of proof is 57.
% 38.38/10.92 % Level of proof is 10.
% 38.38/10.92 % Maximum clause weight is 20.000.
% 38.38/10.92 % Given clauses 1291.
% 38.38/10.92
% 38.38/10.92 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------