%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM848+1 : 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 : n020.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 08:18:12 AM UTC 2026
% Result : Theorem 0.19s 0.48s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 29 unt; 0 def)
% Number of atoms : 31 ( 30 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 8 ~; 0 |; 1 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof('qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))',axiom,
! [Vd396,Vd397] :
( vmul(Vd396,v1) = Vd396
& vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396) ),
file('theBenchmark.p','qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 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('ass(cond(43, 0), 0)',axiom,
! [Vd59] : vplus(v1,Vd59) = vsucc(Vd59),
file('theBenchmark.p','ass(cond(43, 0), 0)') ).
fof('holds(286, 441, 4)',conjecture,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) = vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
file('theBenchmark.p','holds(286, 441, 4)') ).
fof('holds(286, 441, 4)_neg',negated_conjecture,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(assume_negation,[status(cth)],['holds(286, 441, 4)']) ).
fof('holds(286, 441, 3)',axiom,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
file('theBenchmark.p','holds(286, 441, 3)') ).
cnf(c_50,plain,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(clausify,[status(thm)],['holds(286, 441, 3)']) ).
fof('holds(286, 441, 2)',axiom,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) = vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),
file('theBenchmark.p','holds(286, 441, 2)') ).
cnf(c_51,plain,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) = vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),
inference(clausify,[status(thm)],['holds(286, 441, 2)']) ).
cnf(c_52,plain,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(paramod,[status(thm)],[c_50,c_51]) ).
fof('holds(285, 440, 0)',axiom,
vmul(vd436,vplus(vd437,vd439)) = vplus(vmul(vd436,vd437),vmul(vd436,vd439)),
file('theBenchmark.p','holds(285, 440, 0)') ).
cnf(c_57,plain,
vmul(vd436,vplus(vd437,vd439)) = vplus(vmul(vd436,vd437),vmul(vd436,vd439)),
inference(clausify,[status(thm)],['holds(285, 440, 0)']) ).
cnf(c_67,plain,
vplus(vmul(A,B),A) = vmul(A,vsucc(B)),
inference(clausify,[status(thm)],['qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))']) ).
cnf(c_68,plain,
vmul(A,vsucc(B)) = vplus(vmul(A,B),A),
inference(copy,[status(thm)],[c_67]) ).
cnf(c_112,plain,
vplus(A,B) = vplus(B,A),
inference(clausify,[status(thm)],['ass(cond(61, 0), 0)']) ).
cnf(c_114,plain,
vsucc(A) = vplus(v1,A),
inference(clausify,[status(thm)],['ass(cond(43, 0), 0)']) ).
cnf(c_126,negated_conjecture,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(clausify,[status(thm)],['holds(286, 441, 4)_neg']) ).
cnf(c_137,negated_conjecture,
vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(paramod,[status(thm)],[c_112,c_126]) ).
cnf(c_138,negated_conjecture,
vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))) != vplus(vmul(vd436,vd437),vmul(vd436,vplus(v1,vd439))),
inference(paramod,[status(thm)],[c_114,c_137]) ).
cnf(c_127,negated_conjecture,
vplus(vmul(vd436,vd437),vmul(vd436,vplus(v1,vd439))) != vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))),
inference(copy,[status(thm)],[c_138]) ).
cnf(c_139,plain,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(paramod,[status(thm)],[c_57,c_52]) ).
cnf(c_140,plain,
vplus(vd436,vplus(vmul(vd436,vd437),vmul(vd436,vd439))) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(paramod,[status(thm)],[c_112,c_139]) ).
cnf(c_141,plain,
vplus(vd436,vplus(vmul(vd436,vd437),vmul(vd436,vd439))) = vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))),
inference(paramod,[status(thm)],[c_112,c_140]) ).
cnf(c_128,plain,
vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))) = vplus(vd436,vplus(vmul(vd436,vd437),vmul(vd436,vd439))),
inference(copy,[status(thm)],[c_141]) ).
cnf(c_142,plain,
vmul(A,vplus(v1,B)) = vplus(vmul(A,B),A),
inference(paramod,[status(thm)],[c_114,c_68]) ).
cnf(c_133,plain,
vmul(A,vplus(v1,B)) = vplus(A,vmul(A,B)),
inference(paramod,[status(thm)],[c_112,c_142]) ).
cnf(c_143,negated_conjecture,
vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))) != vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))),
inference(paramod,[status(thm)],[c_133,c_127]) ).
cnf(c_144,negated_conjecture,
vplus(vd436,vplus(vmul(vd436,vd437),vmul(vd436,vd439))) != vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))),
inference(paramod,[status(thm)],[c_128,c_143]) ).
cnf(c_145,negated_conjecture,
vplus(vd436,vplus(vmul(vd436,vd437),vmul(vd436,vd439))) != vplus(vd436,vplus(vmul(vd436,vd437),vmul(vd436,vd439))),
inference(paramod,[status(thm)],[c_128,c_144]) ).
cnf(c_136,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM848+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.43 % Computer : n020.cluster.edu
% 0.19/0.43 % Model : x86_64 x86_64
% 0.19/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.43 % Memory : 8046.5625MB
% 0.19/0.43 % OS : Linux 6.8.0-71-generic
% 0.19/0.43 % CPULimit : 300
% 0.19/0.43 % WCLimit : 300
% 0.19/0.43 % DateTime : Sat Sep 26 04:13:49 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.44 % Process 576728 was started by sandbox2 on n020,
% 0.19/0.44 % Sat Sep 26 04:13:49 2026
% 0.19/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 0.19/0.48
% 0.19/0.48 % SZS status Theorem for theBenchmark
% 0.19/0.48
% 0.19/0.48 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.19/0.48 % Length of proof is 17.
% 0.19/0.48 % Level of proof is 4.
% 0.19/0.48 % Maximum clause weight is 19.000.
% 0.19/0.48 % Given clauses 0.
% 0.19/0.48
% 0.19/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------