%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM853+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 : n026.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 08:18:13 AM UTC 2026
% Result : Theorem 0.15s 5.60s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 29 ( 12 unt; 0 def)
% Number of atoms : 48 ( 13 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 18 ~; 15 |; 0 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof('ass(cond(299, 0), 1)',axiom,
! [Vd456,Vd461,Vd462] :
( Vd461 = Vd462
=> vmul(Vd461,Vd456) = vmul(Vd462,Vd456) ),
file('theBenchmark.p','ass(cond(299, 0), 1)') ).
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('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), 2)',axiom,
! [Vd203,Vd204] :
( ~ less(Vd203,Vd204)
| ~ greater(Vd203,Vd204) ),
file('theBenchmark.p','ass(cond(goal(130), 0), 2)') ).
fof('ass(cond(goal(130), 0), 3)',axiom,
! [Vd203,Vd204] :
( ~ greater(Vd203,Vd204)
| Vd203 != Vd204 ),
file('theBenchmark.p','ass(cond(goal(130), 0), 3)') ).
fof('holds(conseq(307), 490, 0)',conjecture,
greater(vd486,vd488),
file('theBenchmark.p','holds(conseq(307), 490, 0)') ).
fof('holds(conseq(307), 490, 0)_neg',negated_conjecture,
~ greater(vd486,vd488),
inference(assume_negation,[status(cth)],['holds(conseq(307), 490, 0)']) ).
cnf(c_37,negated_conjecture,
~ greater(vd486,vd488),
inference(clausify,[status(thm)],['holds(conseq(307), 490, 0)_neg']) ).
cnf(c_58,plain,
( ~ greater(B,A)
| A != B ),
inference(clausify,[status(thm)],['ass(cond(goal(130), 0), 3)']) ).
cnf(c_59,plain,
( ~ less(A,B)
| ~ greater(A,B) ),
inference(clausify,[status(thm)],['ass(cond(goal(130), 0), 2)']) ).
cnf(c_61,plain,
( less(B,A)
| greater(B,A)
| A = B ),
inference(clausify,[status(thm)],['ass(cond(goal(130), 0), 0)']) ).
cnf(c_62,plain,
( less(B,A)
| ~ greater(A,B) ),
inference(clausify,[status(thm)],['ass(cond(140, 0), 0)']) ).
cnf(c_63,plain,
( greater(B,A)
| ~ less(A,B) ),
inference(clausify,[status(thm)],['ass(cond(147, 0), 0)']) ).
cnf(c_77,plain,
( greater(vmul(A,C),vmul(B,C))
| ~ greater(A,B) ),
inference(clausify,[status(thm)],['ass(cond(299, 0), 2)']) ).
cnf(c_78,plain,
( vmul(A,C) = vmul(B,C)
| A != B ),
inference(clausify,[status(thm)],['ass(cond(299, 0), 1)']) ).
fof('holds(antec(307), 489, 0)',axiom,
greater(vmul(vd486,vd487),vmul(vd488,vd487)),
file('theBenchmark.p','holds(antec(307), 489, 0)') ).
cnf(c_80,plain,
greater(vmul(vd486,vd487),vmul(vd488,vd487)),
inference(clausify,[status(thm)],['holds(antec(307), 489, 0)']) ).
cnf(c_284,negated_conjecture,
~ less(vd488,vd486),
inference(resolve,[status(thm)],[c_63,c_37]) ).
cnf(c_436,plain,
less(vmul(vd488,vd487),vmul(vd486,vd487)),
inference(resolve,[status(thm)],[c_80,c_62]) ).
cnf(c_437,plain,
vmul(vd488,vd487) != vmul(vd486,vd487),
inference(resolve,[status(thm)],[c_80,c_58]) ).
cnf(c_1486,plain,
( greater(vd488,vd486)
| vd486 = vd488 ),
inference(resolve,[status(thm)],[c_284,c_61]) ).
cnf(c_492,plain,
( greater(vd488,vd486)
| vd488 = vd486 ),
inference(copy,[status(thm)],[c_1486]) ).
cnf(c_507,plain,
( greater(vmul(vd488,A),vmul(vd486,A))
| vd488 = vd486 ),
inference(resolve,[status(thm)],[c_492,c_77]) ).
cnf(c_891,plain,
~ greater(vmul(vd488,vd487),vmul(vd486,vd487)),
inference(resolve,[status(thm)],[c_436,c_59]) ).
cnf(c_1477,plain,
vd488 != vd486,
inference(resolve,[status(thm)],[c_78,c_437]) ).
cnf(c_1484,plain,
greater(vmul(vd488,A),vmul(vd486,A)),
inference(resolve,[status(thm)],[c_1477,c_507]) ).
cnf(c_1485,plain,
$false,
inference(resolve,[status(thm)],[c_1484,c_891]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM853+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n026.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Sat Sep 26 04:16:02 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.39 % Process 48268 was started by sandbox2 on n026,
% 0.11/5.39 % Sat Sep 26 04:16:02 2026
% 0.11/5.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/5.40
% 0.15/5.40 % From the command line: assign(max_seconds, 300).
% 0.15/5.60
% 0.15/5.60 % SZS status Theorem for theBenchmark
% 0.15/5.60
% 0.15/5.60 % Proof 1 at 0.15 (+ 0.04) seconds.
% 0.15/5.60 % Length of proof is 26.
% 0.15/5.60 % Level of proof is 6.
% 0.15/5.60 % Maximum clause weight is 20.000.
% 0.15/5.60 % Given clauses 129.
% 0.15/5.60
% 0.15/5.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------