%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM842+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 : 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 08:18:10 AM UTC 2026
% Result : Theorem 16.91s 2.53s
% Output : CNFRefutation 16.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of formulae : 66 ( 22 unt; 0 def)
% Number of atoms : 126 ( 20 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 100 ( 40 ~; 47 |; 4 &)
% ( 2 <=>; 7 =>; 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 : 92 ( 0 sgn 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof('dis(antec(218))',axiom,
( ( greater(vd353,vd354)
& geq(vd355,vd356) )
| ( geq(vd353,vd354)
& greater(vd355,vd356) ) ),
file('theBenchmark.p','dis(antec(218))') ).
fof('ass(cond(goal(202), 0), 0)',axiom,
! [Vd328,Vd329,Vd330] :
( less(vplus(Vd328,Vd330),vplus(Vd329,Vd330))
=> less(Vd328,Vd329) ),
file('theBenchmark.p','ass(cond(goal(202), 0), 0)') ).
fof('ass(cond(goal(202), 0), 2)',axiom,
! [Vd328,Vd329,Vd330] :
( greater(vplus(Vd328,Vd330),vplus(Vd329,Vd330))
=> greater(Vd328,Vd329) ),
file('theBenchmark.p','ass(cond(goal(202), 0), 2)') ).
fof('ass(cond(goal(193), 0), 2)',axiom,
! [Vd301,Vd302,Vd303] :
( greater(Vd301,Vd302)
=> greater(vplus(Vd301,Vd303),vplus(Vd302,Vd303)) ),
file('theBenchmark.p','ass(cond(goal(193), 0), 2)') ).
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(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('ass(cond(goal(130), 0), 3)',axiom,
! [Vd203,Vd204] :
( ~ greater(Vd203,Vd204)
| Vd203 != Vd204 ),
file('theBenchmark.p','ass(cond(goal(130), 0), 3)') ).
fof('ass(cond(81, 0), 0)',axiom,
! [Vd104,Vd105] :
( Vd104 != Vd105
=> ! [Vd107] : vplus(Vd107,Vd104) != vplus(Vd107,Vd105) ),
file('theBenchmark.p','ass(cond(81, 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(conseq(218), 361, 0)',conjecture,
greater(vplus(vd353,vd355),vplus(vd354,vd356)),
file('theBenchmark.p','holds(conseq(218), 361, 0)') ).
fof('holds(conseq(218), 361, 0)_neg',negated_conjecture,
~ greater(vplus(vd353,vd355),vplus(vd354,vd356)),
inference(assume_negation,[status(cth)],['holds(conseq(218), 361, 0)']) ).
cnf(c_42,plain,
( geq(vd355,vd356)
| greater(vd355,vd356) ),
inference(clausify,[status(thm)],['dis(antec(218))']) ).
cnf(c_43,plain,
( greater(vd353,vd354)
| greater(vd355,vd356) ),
inference(clausify,[status(thm)],['dis(antec(218))']) ).
cnf(c_45,plain,
( greater(vd353,vd354)
| geq(vd353,vd354) ),
inference(clausify,[status(thm)],['dis(antec(218))']) ).
cnf(c_47,plain,
( less(A,C)
| ~ less(vplus(A,B),vplus(C,B)) ),
inference(clausify,[status(thm)],['ass(cond(goal(202), 0), 0)']) ).
cnf(c_49,plain,
( greater(A,C)
| ~ greater(vplus(A,B),vplus(C,B)) ),
inference(clausify,[status(thm)],['ass(cond(goal(202), 0), 2)']) ).
cnf(c_52,plain,
( greater(vplus(A,C),vplus(B,C))
| ~ greater(A,B) ),
inference(clausify,[status(thm)],['ass(cond(goal(193), 0), 2)']) ).
cnf(c_55,plain,
( less(C,B)
| ~ leq(C,A)
| ~ less(A,B) ),
inference(clausify,[status(thm)],['ass(cond(goal(177), 0), 0)']) ).
cnf(c_56,plain,
( less(C,B)
| ~ less(C,A)
| ~ leq(A,B) ),
inference(clausify,[status(thm)],['ass(cond(goal(177), 0), 0)']) ).
cnf(c_59,plain,
( leq(B,A)
| ~ geq(A,B) ),
inference(clausify,[status(thm)],['ass(cond(158, 0), 0)']) ).
cnf(c_61,plain,
( ~ less(A,B)
| leq(A,B) ),
inference(clausify,[status(thm)],['def(cond(conseq(axiom(3)), 17), 1)']) ).
cnf(c_62,plain,
( B != A
| leq(A,B) ),
inference(clausify,[status(thm)],['def(cond(conseq(axiom(3)), 17), 1)']) ).
cnf(c_64,plain,
( ~ greater(A,B)
| geq(A,B) ),
inference(clausify,[status(thm)],['def(cond(conseq(axiom(3)), 16), 1)']) ).
cnf(c_67,plain,
( less(B,A)
| ~ greater(A,B) ),
inference(clausify,[status(thm)],['ass(cond(140, 0), 0)']) ).
cnf(c_68,plain,
( less(B,A)
| greater(B,A)
| A = B ),
inference(clausify,[status(thm)],['ass(cond(goal(130), 0), 0)']) ).
cnf(c_69,plain,
( ~ less(B,A)
| A != B ),
inference(clausify,[status(thm)],['ass(cond(goal(130), 0), 1)']) ).
cnf(c_71,plain,
( ~ greater(B,A)
| A != B ),
inference(clausify,[status(thm)],['ass(cond(goal(130), 0), 3)']) ).
cnf(c_80,plain,
( vplus(C,A) != vplus(C,B)
| A = B ),
inference(clausify,[status(thm)],['ass(cond(81, 0), 0)']) ).
cnf(c_82,plain,
vplus(A,B) = vplus(B,A),
inference(clausify,[status(thm)],['ass(cond(61, 0), 0)']) ).
cnf(c_93,negated_conjecture,
~ greater(vplus(vd353,vd355),vplus(vd354,vd356)),
inference(clausify,[status(thm)],['holds(conseq(218), 361, 0)_neg']) ).
cnf(c_105,plain,
( greater(vd355,vd356)
| greater(vplus(vd353,A),vplus(vd354,A)) ),
inference(resolve,[status(thm)],[c_52,c_43]) ).
cnf(c_9797,plain,
( geq(vd353,vd354)
| geq(vd353,vd354) ),
inference(resolve,[status(thm)],[c_64,c_45]) ).
cnf(c_120,plain,
geq(vd353,vd354),
inference(copy,[status(thm)],[c_9797]) ).
cnf(c_9798,plain,
( geq(vd355,vd356)
| geq(vd355,vd356) ),
inference(resolve,[status(thm)],[c_64,c_42]) ).
cnf(c_122,plain,
geq(vd355,vd356),
inference(copy,[status(thm)],[c_9798]) ).
cnf(c_128,plain,
( leq(A,B)
| less(A,B)
| greater(A,B) ),
inference(resolve,[status(thm)],[c_68,c_62]) ).
cnf(c_147,plain,
~ less(A,A),
inference(xxres,[status(thm)],[c_69]) ).
cnf(c_9799,plain,
( less(B,A)
| greater(B,A)
| B = A ),
inference(copy,[status(thm)],[c_68]) ).
cnf(c_217,plain,
( less(vplus(C,A),vplus(C,B))
| greater(vplus(C,A),vplus(C,B))
| A = B ),
inference(resolve,[status(thm)],[c_80,c_9799]) ).
cnf(c_402,plain,
leq(vd354,vd353),
inference(resolve,[status(thm)],[c_120,c_59]) ).
cnf(c_403,plain,
leq(vd356,vd355),
inference(resolve,[status(thm)],[c_122,c_59]) ).
cnf(c_9800,plain,
( less(A,vd353)
| ~ less(A,vd354) ),
inference(resolve,[status(thm)],[c_56,c_402]) ).
cnf(c_410,plain,
~ less(vd353,vd354),
inference(resolve,[status(thm)],[c_9800,c_147]) ).
cnf(c_9801,plain,
( less(A,vd355)
| ~ less(A,vd356) ),
inference(resolve,[status(thm)],[c_56,c_403]) ).
cnf(c_417,plain,
~ less(vd355,vd356),
inference(resolve,[status(thm)],[c_9801,c_147]) ).
cnf(c_432,plain,
( vd356 != vd355
| greater(vplus(vd353,A),vplus(vd354,A)) ),
inference(resolve,[status(thm)],[c_105,c_71]) ).
cnf(c_455,plain,
~ less(vplus(vd353,A),vplus(vd354,A)),
inference(resolve,[status(thm)],[c_47,c_410]) ).
cnf(c_457,plain,
~ greater(vd356,vd355),
inference(resolve,[status(thm)],[c_67,c_417]) ).
cnf(c_460,plain,
~ greater(vplus(vd356,A),vplus(vd355,A)),
inference(resolve,[status(thm)],[c_49,c_457]) ).
cnf(c_9802,plain,
( leq(A,B)
| leq(A,B)
| greater(A,B) ),
inference(resolve,[status(thm)],[c_128,c_61]) ).
cnf(c_659,plain,
( leq(A,B)
| greater(A,B) ),
inference(copy,[status(thm)],[c_9802]) ).
cnf(c_923,plain,
( less(A,C)
| ~ less(B,C)
| greater(A,B) ),
inference(resolve,[status(thm)],[c_659,c_55]) ).
cnf(c_9803,negated_conjecture,
( less(vplus(vd353,vd355),A)
| ~ less(vplus(vd354,vd356),A) ),
inference(resolve,[status(thm)],[c_923,c_93]) ).
cnf(c_4193,negated_conjecture,
~ less(vplus(vd354,vd356),vplus(vd354,vd355)),
inference(resolve,[status(thm)],[c_9803,c_455]) ).
cnf(c_8661,plain,
~ greater(vplus(A,vd356),vplus(vd355,A)),
inference(paramod,[status(thm)],[c_82,c_460]) ).
cnf(c_9271,plain,
( greater(vplus(vd354,vd356),vplus(vd354,vd355))
| vd356 = vd355 ),
inference(resolve,[status(thm)],[c_4193,c_217]) ).
cnf(c_9771,plain,
~ greater(vplus(A,vd356),vplus(A,vd355)),
inference(paramod,[status(thm)],[c_82,c_8661]) ).
cnf(c_9778,plain,
vd356 = vd355,
inference(resolve,[status(thm)],[c_9771,c_9271]) ).
cnf(c_9784,plain,
greater(vplus(vd353,A),vplus(vd354,A)),
inference(resolve,[status(thm)],[c_9778,c_432]) ).
cnf(c_9804,plain,
~ greater(vplus(vd353,vd355),vplus(vd354,vd355)),
inference(paramod,[status(thm)],[c_9778,c_93]) ).
cnf(c_9796,plain,
$false,
inference(resolve,[status(thm)],[c_9784,c_9804]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM842+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/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 04:12:34 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 377057 was started by sandbox on n019,
% 0.10/0.37 % Sat Sep 26 04:12:34 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 16.91/2.53
% 16.91/2.53 % given #500 (F,wt=17): 4191 -less(vplus(vd356,vd354),vplus(vd354,vd355)). [ur(923,a,378,a,c,455,a)].
% 16.91/2.53
% 16.91/2.53 % SZS status Theorem for theBenchmark
% 16.91/2.53
% 16.91/2.53 % Proof 1 at 1.73 (+ 0.41) seconds.
% 16.91/2.53 % Length of proof is 57.
% 16.91/2.53 % Level of proof is 11.
% 16.91/2.53 % Maximum clause weight is 27.000.
% 16.91/2.53 % Given clauses 529.
% 16.91/2.53
% 16.91/2.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------