%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM851+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 : n002.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 0.11s 5.57s
% Output : CNFRefutation 0.11s
% 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)']) ).
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_54,plain,
vd470 = vplus(vd471,vd473),
inference(clausify,[status(thm)],['holds(conseq_conjunct1(conseq(302)), 474, 0)']) ).
cnf(c_55,plain,
vplus(vd471,vd473) = vd470,
inference(copy,[status(thm)],[c_54]) ).
cnf(c_58,plain,
vmul(A,vplus(B,C)) = vplus(vmul(A,B),vmul(A,C)),
inference(clausify,[status(thm)],['ass(cond(281, 0), 0)']) ).
cnf(c_59,plain,
vplus(vmul(A,B),vmul(A,C)) = vmul(A,vplus(B,C)),
inference(copy,[status(thm)],[c_58]) ).
cnf(c_60,plain,
vmul(A,B) = vmul(B,A),
inference(clausify,[status(thm)],['ass(cond(270, 0), 0)']) ).
cnf(c_123,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_134,negated_conjecture,
vmul(vd470,vd469) != vplus(vmul(vd471,vd469),vmul(vd473,vd469)),
inference(paramod,[status(thm)],[c_55,c_123]) ).
cnf(c_135,negated_conjecture,
vmul(vd470,vd469) != vplus(vmul(vd471,vd469),vmul(vd469,vd473)),
inference(paramod,[status(thm)],[c_60,c_134]) ).
cnf(c_124,negated_conjecture,
vplus(vmul(vd471,vd469),vmul(vd469,vd473)) != vmul(vd470,vd469),
inference(copy,[status(thm)],[c_135]) ).
cnf(c_131,plain,
vplus(vmul(A,B),vmul(B,C)) = vmul(B,vplus(A,C)),
inference(paramod,[status(thm)],[c_60,c_59]) ).
cnf(c_136,negated_conjecture,
vmul(vd469,vplus(vd471,vd473)) != vmul(vd470,vd469),
inference(paramod,[status(thm)],[c_131,c_124]) ).
cnf(c_137,negated_conjecture,
vmul(vd469,vd470) != vmul(vd470,vd469),
inference(paramod,[status(thm)],[c_55,c_136]) ).
cnf(c_138,negated_conjecture,
vmul(vd470,vd469) != vmul(vd470,vd469),
inference(paramod,[status(thm)],[c_60,c_137]) ).
cnf(c_133,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_138]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM851+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.53 % Computer : n002.cluster.edu
% 0.11/5.53 % Model : x86_64 x86_64
% 0.11/5.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.53 % Memory : 8046.5625MB
% 0.11/5.53 % OS : Linux 6.8.0-71-generic
% 0.11/5.53 % CPULimit : 300
% 0.11/5.53 % WCLimit : 300
% 0.11/5.53 % DateTime : Sat Sep 26 04:16:12 UTC 2026
% 0.11/5.54 % CPUTime :
% 0.11/5.54 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.54 % Process 797064 was started by sandbox on n002,
% 0.11/5.54 % Sat Sep 26 04:16:12 2026
% 0.11/5.54 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/5.55
% 0.11/5.55 % From the command line: assign(max_seconds, 300).
% 0.11/5.57
% 0.11/5.57 % SZS status Theorem for theBenchmark
% 0.11/5.57
% 0.11/5.57 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.11/5.57 % Length of proof is 12.
% 0.11/5.57 % Level of proof is 4.
% 0.11/5.57 % Maximum clause weight is 28.000.
% 0.11/5.57 % Given clauses 5.
% 0.11/5.57
% 0.11/5.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------