%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM851+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 : n007.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 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 19 unt; 0 def)
% Number of atoms : 19 ( 18 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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('holds(conseq_conjunct2(conseq(302)), 475, 1)',conjecture,
vmul(vplus(vd471,vd473),vd469) = vplus(vmul(vd471,vd469),vmul(vd473,vd469)),
file('theBenchmark.p','holds(conseq_conjunct2(conseq(302)), 475, 1)') ).
fof('holds(conseq_conjunct2(conseq(302)), 475, 1)_neg',negated_conjecture,
vmul(vplus(vd471,vd473),vd469) != vplus(vmul(vd471,vd469),vmul(vd473,vd469)),
inference(assume_negation,[status(cth)],['holds(conseq_conjunct2(conseq(302)), 475, 1)']) ).
cnf(c_31,negated_conjecture,
vmul(vplus(vd471,vd473),vd469) != vplus(vmul(vd471,vd469),vmul(vd473,vd469)),
inference(clausify,[status(thm)],['holds(conseq_conjunct2(conseq(302)), 475, 1)_neg']) ).
cnf(c_32,negated_conjecture,
vplus(vmul(vd471,vd469),vmul(vd473,vd469)) != vmul(vplus(vd471,vd473),vd469),
inference(copy,[status(thm)],[c_31]) ).
cnf(c_58,plain,
vmul(A,B) = vmul(B,A),
inference(clausify,[status(thm)],['ass(cond(270, 0), 0)']) ).
cnf(c_59,plain,
vmul(A,vplus(B,C)) = vplus(vmul(A,B),vmul(A,C)),
inference(clausify,[status(thm)],['ass(cond(281, 0), 0)']) ).
cnf(c_60,plain,
vplus(vmul(A,B),vmul(A,C)) = vmul(A,vplus(B,C)),
inference(copy,[status(thm)],[c_59]) ).
fof('holds(conseq_conjunct1(conseq(302)), 474, 0)',axiom,
vd470 = vplus(vd471,vd473),
file('theBenchmark.p','holds(conseq_conjunct1(conseq(302)), 474, 0)') ).
cnf(c_62,plain,
vd470 = vplus(vd471,vd473),
inference(clausify,[status(thm)],['holds(conseq_conjunct1(conseq(302)), 474, 0)']) ).
cnf(c_63,plain,
vplus(vd471,vd473) = vd470,
inference(copy,[status(thm)],[c_62]) ).
cnf(c_154,negated_conjecture,
vplus(vmul(vd471,vd469),vmul(vd469,vd473)) != vmul(vplus(vd471,vd473),vd469),
inference(paramod,[status(thm)],[c_58,c_32]) ).
cnf(c_69,negated_conjecture,
vplus(vmul(vd471,vd469),vmul(vd469,vd473)) != vmul(vd470,vd469),
inference(paramod,[status(thm)],[c_63,c_154]) ).
cnf(c_151,plain,
vplus(vmul(A,B),vmul(B,C)) = vmul(B,vplus(A,C)),
inference(paramod,[status(thm)],[c_58,c_60]) ).
cnf(c_155,negated_conjecture,
vmul(vd469,vplus(vd471,vd473)) != vmul(vd470,vd469),
inference(paramod,[status(thm)],[c_151,c_69]) ).
cnf(c_156,negated_conjecture,
vmul(vd469,vd470) != vmul(vd470,vd469),
inference(paramod,[status(thm)],[c_63,c_155]) ).
cnf(c_157,negated_conjecture,
vmul(vd470,vd469) != vmul(vd470,vd469),
inference(paramod,[status(thm)],[c_58,c_156]) ).
cnf(c_153,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM851+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 04:11:25 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 2750578 was started by sandbox on n007,
% 0.09/0.36 % Sat Sep 26 04:11:25 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.40
% 0.09/0.40 % SZS status Theorem for theBenchmark
% 0.09/0.40
% 0.09/0.40 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.09/0.40 % Length of proof is 13.
% 0.09/0.40 % Level of proof is 4.
% 0.09/0.40 % Maximum clause weight is 28.000.
% 0.09/0.40 % Given clauses 18.
% 0.09/0.40
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------