%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM857+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 : n018.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 2.59s 0.82s
% Output : CNFRefutation 2.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 43 ( 24 unt; 0 def)
% Number of atoms : 69 ( 15 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 48 ( 22 ~; 18 |; 3 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 50 ( 2 sgn 16 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof('ass(cond(318, 0), 0)',axiom,
! [Vd517,Vd518,Vd519,Vd520] :
( ( ( greater(Vd517,Vd518)
& geq(Vd519,Vd520) )
| ( geq(Vd517,Vd518)
& greater(Vd519,Vd520) ) )
=> greater(vmul(Vd517,Vd519),vmul(Vd518,Vd520)) ),
file('theBenchmark.p','ass(cond(318, 0), 0)') ).
fof('qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))',axiom,
! [Vd396,Vd397] :
( vmul(Vd396,v1) = Vd396
& vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396) ),
file('theBenchmark.p','qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))') ).
fof('ass(cond(241, 0), 0)',axiom,
! [Vd386,Vd387] :
( less(Vd386,vplus(Vd387,v1))
=> leq(Vd386,Vd387) ),
file('theBenchmark.p','ass(cond(241, 0), 0)') ).
fof('ass(cond(163, 0), 0)',axiom,
! [Vd258,Vd259] :
( leq(Vd258,Vd259)
=> geq(Vd259,Vd258) ),
file('theBenchmark.p','ass(cond(163, 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('def(cond(conseq(axiom(3)), 12), 1)',axiom,
! [Vd198,Vd199] :
( less(Vd199,Vd198)
<=> ? [Vd201] : Vd198 = vplus(Vd199,Vd201) ),
file('theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
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(conseq(323), 532, 0)',conjecture,
geq(vmul(vd526,vd529),vmul(vd527,vd530)),
file('theBenchmark.p','holds(conseq(323), 532, 0)') ).
fof('holds(conseq(323), 532, 0)_neg',negated_conjecture,
~ geq(vmul(vd526,vd529),vmul(vd527,vd530)),
inference(assume_negation,[status(cth)],['holds(conseq(323), 532, 0)']) ).
fof('holds(conjunct2(antec(323)), 531, 0)',axiom,
geq(vd529,vd530),
file('theBenchmark.p','holds(conjunct2(antec(323)), 531, 0)') ).
cnf(c_60,plain,
geq(vd529,vd530),
inference(clausify,[status(thm)],['holds(conjunct2(antec(323)), 531, 0)']) ).
fof('holds(conjunct1(antec(323)), 528, 0)',axiom,
geq(vd526,vd527),
file('theBenchmark.p','holds(conjunct1(antec(323)), 528, 0)') ).
cnf(c_61,plain,
geq(vd526,vd527),
inference(clausify,[status(thm)],['holds(conjunct1(antec(323)), 528, 0)']) ).
cnf(c_62,plain,
( greater(vmul(C,A),vmul(D,B))
| ~ geq(C,D)
| ~ greater(A,B) ),
inference(clausify,[status(thm)],['ass(cond(318, 0), 0)']) ).
cnf(c_63,plain,
( greater(vmul(C,A),vmul(D,B))
| ~ greater(C,D)
| ~ geq(A,B) ),
inference(clausify,[status(thm)],['ass(cond(318, 0), 0)']) ).
cnf(c_80,plain,
vmul(A,v1) = A,
inference(clausify,[status(thm)],['qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))']) ).
cnf(c_81,plain,
( leq(A,B)
| ~ less(A,vplus(B,v1)) ),
inference(clausify,[status(thm)],['ass(cond(241, 0), 0)']) ).
cnf(c_99,plain,
( geq(B,A)
| ~ leq(A,B) ),
inference(clausify,[status(thm)],['ass(cond(163, 0), 0)']) ).
cnf(c_104,plain,
( B = A
| greater(A,B)
| ~ geq(A,B) ),
inference(clausify,[status(thm)],['def(cond(conseq(axiom(3)), 16), 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_114,plain,
( vplus(A,C) != B
| less(A,B) ),
inference(clausify,[status(thm)],['def(cond(conseq(axiom(3)), 12), 1)']) ).
cnf(c_123,plain,
vplus(A,B) = vplus(B,A),
inference(clausify,[status(thm)],['ass(cond(61, 0), 0)']) ).
cnf(c_137,negated_conjecture,
~ geq(vmul(vd526,vd529),vmul(vd527,vd530)),
inference(clausify,[status(thm)],['holds(conseq(323), 532, 0)_neg']) ).
cnf(c_146,plain,
( greater(vmul(A,vd529),vmul(B,vd530))
| ~ greater(A,B) ),
inference(resolve,[status(thm)],[c_63,c_60]) ).
cnf(c_200,plain,
( vd527 = vd526
| greater(vd526,vd527) ),
inference(resolve,[status(thm)],[c_104,c_61]) ).
cnf(c_201,plain,
( vd530 = vd529
| greater(vd529,vd530) ),
inference(resolve,[status(thm)],[c_104,c_60]) ).
cnf(c_1537,plain,
geq(A,vmul(A,v1)),
inference(resolve,[status(thm)],[c_106,c_80]) ).
cnf(c_203,plain,
geq(A,A),
inference(paramod,[status(thm)],[c_80,c_1537]) ).
cnf(c_266,plain,
less(A,vplus(B,A)),
inference(resolve,[status(thm)],[c_123,c_114]) ).
cnf(c_337,negated_conjecture,
~ greater(vmul(vd526,vd529),vmul(vd527,vd530)),
inference(resolve,[status(thm)],[c_105,c_137]) ).
cnf(c_338,negated_conjecture,
~ leq(vmul(vd527,vd530),vmul(vd526,vd529)),
inference(resolve,[status(thm)],[c_99,c_137]) ).
cnf(c_1538,plain,
( greater(vmul(vd526,vd529),vmul(vd527,vd530))
| vd527 = vd526 ),
inference(resolve,[status(thm)],[c_200,c_146]) ).
cnf(c_457,plain,
vd527 = vd526,
inference(resolve,[status(thm)],[c_337,c_1538]) ).
cnf(c_460,negated_conjecture,
~ leq(vmul(vd526,vd530),vmul(vd526,vd529)),
inference(paramod,[status(thm)],[c_457,c_338]) ).
cnf(c_461,negated_conjecture,
~ greater(vmul(vd526,vd529),vmul(vd526,vd530)),
inference(paramod,[status(thm)],[c_457,c_337]) ).
cnf(c_1539,plain,
~ less(vmul(vd526,vd530),vplus(vmul(vd526,vd529),v1)),
inference(resolve,[status(thm)],[c_81,c_460]) ).
cnf(c_1342,plain,
~ less(vmul(vd526,vd530),vplus(v1,vmul(vd526,vd529))),
inference(paramod,[status(thm)],[c_123,c_1539]) ).
cnf(c_1540,plain,
( greater(vmul(C,A),vmul(C,B))
| ~ greater(A,B) ),
inference(resolve,[status(thm)],[c_62,c_203]) ).
cnf(c_1514,plain,
~ greater(vd529,vd530),
inference(resolve,[status(thm)],[c_1540,c_461]) ).
cnf(c_1515,plain,
vd530 = vd529,
inference(resolve,[status(thm)],[c_1514,c_201]) ).
cnf(c_1541,plain,
~ less(vmul(vd526,vd529),vplus(v1,vmul(vd526,vd529))),
inference(paramod,[status(thm)],[c_1515,c_1342]) ).
cnf(c_1536,plain,
$false,
inference(resolve,[status(thm)],[c_266,c_1541]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM857+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n018.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 04:15:51 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.42 % Process 3686678 was started by sandbox2 on n018,
% 0.15/0.42 % Sat Sep 26 04:15:51 2026
% 0.15/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.44
% 0.15/0.44 % From the command line: assign(max_seconds, 300).
% 2.59/0.82
% 2.59/0.82 % SZS status Theorem for theBenchmark
% 2.59/0.82
% 2.59/0.82 % Proof 1 at 0.25 (+ 0.11) seconds.
% 2.59/0.82 % Length of proof is 35.
% 2.59/0.82 % Level of proof is 7.
% 2.59/0.82 % Maximum clause weight is 24.000.
% 2.59/0.82 % Given clauses 218.
% 2.59/0.82
% 2.59/0.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------