%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM852+1 : 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 : 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 08:18:13 AM UTC 2026
% Result : Theorem 0.09s 0.62s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 22 ( 16 unt; 0 def)
% Number of atoms : 28 ( 14 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 9 ~; 4 |; 0 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 28 ( 2 sgn 9 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof('ass(cond(302, 0), 2)',axiom,
! [Vd470,Vd471] :
( greater(Vd470,Vd471)
=> vmul(Vd470,vd469) = vmul(vplus(Vd471,vskolem9(Vd470,Vd471)),vd469) ),
file('theBenchmark.p','ass(cond(302, 0), 2)') ).
fof('ass(cond(281, 0), 0)',axiom,
! [Vd432,Vd433,Vd434] : vmul(Vd432,vplus(Vd433,Vd434)) = vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)),
file('theBenchmark.p','ass(cond(281, 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('def(cond(conseq(axiom(3)), 11), 1)',axiom,
! [Vd193,Vd194] :
( greater(Vd194,Vd193)
<=> ? [Vd196] : Vd194 = vplus(Vd193,Vd196) ),
file('theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
fof('holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)',conjecture,
greater(vmul(vd481,vd469),vmul(vd480,vd469)),
file('theBenchmark.p','holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)') ).
fof('holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)_neg',negated_conjecture,
~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
inference(assume_negation,[status(cth)],['holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)']) ).
fof('holds(conseq_conjunct1(conseq(304)), 483, 0)',axiom,
greater(vd481,vd480),
file('theBenchmark.p','holds(conseq_conjunct1(conseq(304)), 483, 0)') ).
cnf(c_57,plain,
greater(vd481,vd480),
inference(clausify,[status(thm)],['holds(conseq_conjunct1(conseq(304)), 483, 0)']) ).
cnf(c_63,plain,
( vmul(vplus(B,vskolem9(A,B)),vd469) = vmul(A,vd469)
| ~ greater(A,B) ),
inference(clausify,[status(thm)],['ass(cond(302, 0), 2)']) ).
cnf(c_66,plain,
vplus(vmul(A,B),vmul(A,C)) = vmul(A,vplus(B,C)),
inference(clausify,[status(thm)],['ass(cond(281, 0), 0)']) ).
cnf(c_67,plain,
vmul(A,vplus(B,C)) = vplus(vmul(A,B),vmul(A,C)),
inference(copy,[status(thm)],[c_66]) ).
cnf(c_68,plain,
vmul(A,B) = vmul(B,A),
inference(clausify,[status(thm)],['ass(cond(270, 0), 0)']) ).
cnf(c_110,plain,
( vplus(B,C) != A
| greater(A,B) ),
inference(clausify,[status(thm)],['def(cond(conseq(axiom(3)), 11), 1)']) ).
cnf(c_131,negated_conjecture,
~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
inference(clausify,[status(thm)],['holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)_neg']) ).
cnf(c_311,negated_conjecture,
~ greater(vmul(vd469,vd481),vmul(vd480,vd469)),
inference(paramod,[status(thm)],[c_68,c_131]) ).
cnf(c_132,negated_conjecture,
~ greater(vmul(vd469,vd481),vmul(vd469,vd480)),
inference(paramod,[status(thm)],[c_68,c_311]) ).
cnf(c_312,plain,
( vmul(vd469,vplus(B,vskolem9(A,B))) = vmul(A,vd469)
| ~ greater(A,B) ),
inference(paramod,[status(thm)],[c_68,c_63]) ).
cnf(c_133,plain,
( vplus(vmul(vd469,B),vmul(vd469,vskolem9(A,B))) = vmul(A,vd469)
| ~ greater(A,B) ),
inference(paramod,[status(thm)],[c_67,c_312]) ).
cnf(c_306,negated_conjecture,
vplus(vmul(vd469,vd480),A) != vmul(vd469,vd481),
inference(resolve,[status(thm)],[c_110,c_132]) ).
cnf(c_313,plain,
vplus(vmul(vd469,vd480),vmul(vd469,vskolem9(vd481,vd480))) = vmul(vd481,vd469),
inference(resolve,[status(thm)],[c_133,c_57]) ).
cnf(c_314,plain,
vplus(vmul(vd469,vd480),vmul(vd469,vskolem9(vd481,vd480))) = vmul(vd469,vd481),
inference(paramod,[status(thm)],[c_68,c_313]) ).
cnf(c_310,plain,
$false,
inference(resolve,[status(thm)],[c_306,c_314]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM852+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.57 % Computer : n013.cluster.edu
% 0.09/0.57 % Model : x86_64 x86_64
% 0.09/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.57 % Memory : 8046.5625MB
% 0.09/0.57 % OS : Linux 6.8.0-71-generic
% 0.09/0.57 % CPULimit : 300
% 0.09/0.57 % WCLimit : 300
% 0.09/0.57 % DateTime : Sat Sep 26 04:12:51 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.09/0.57 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.57 % Process 1908867 was started by sandbox on n013,
% 0.09/0.57 % Sat Sep 26 04:12:51 2026
% 0.09/0.57 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.59
% 0.09/0.59 % From the command line: assign(max_seconds, 300).
% 0.09/0.62
% 0.09/0.62 % SZS status Theorem for theBenchmark
% 0.09/0.62
% 0.09/0.62 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.09/0.62 % Length of proof is 16.
% 0.09/0.62 % Level of proof is 4.
% 0.09/0.62 % Maximum clause weight is 36.000.
% 0.09/0.62 % Given clauses 57.
% 0.09/0.62
% 0.09/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------