%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM848+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 : n005.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 0.17s 0.46s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 22 unt; 0 def)
% Number of atoms : 26 ( 25 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 8 ~; 0 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 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 : 17 ( 0 sgn 6 !; 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('qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))',axiom,
! [Vd42,Vd43] :
( vplus(Vd42,v1) = vsucc(Vd42)
& vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43)) ),
file('theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 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)']) ).
cnf(c_10,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_11,negated_conjecture,
vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))) != vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(copy,[status(thm)],[c_10]) ).
cnf(c_14,plain,
vsucc(A) = vplus(A,v1),
inference(clausify,[status(thm)],['qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))']) ).
cnf(c_22,plain,
vplus(A,B) = vplus(B,A),
inference(clausify,[status(thm)],['ass(cond(61, 0), 0)']) ).
cnf(c_24,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_37,plain,
vplus(A,vmul(A,B)) = vmul(A,vsucc(B)),
inference(paramod,[status(thm)],[c_22,c_24]) ).
cnf(c_38,plain,
vplus(A,vmul(A,B)) = vmul(A,vplus(B,v1)),
inference(paramod,[status(thm)],[c_14,c_37]) ).
cnf(c_25,plain,
vmul(A,vplus(B,v1)) = vplus(A,vmul(A,B)),
inference(copy,[status(thm)],[c_38]) ).
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_33,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)']) ).
cnf(c_39,plain,
vplus(vd436,vplus(vmul(vd436,vd437),vmul(vd436,vd439))) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(paramod,[status(thm)],[c_22,c_33]) ).
cnf(c_40,plain,
vplus(vd436,vplus(vmul(vd436,vd437),vmul(vd436,vd439))) = vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))),
inference(paramod,[status(thm)],[c_22,c_39]) ).
cnf(c_34,plain,
vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))) = vplus(vd436,vplus(vmul(vd436,vd437),vmul(vd436,vd439))),
inference(copy,[status(thm)],[c_40]) ).
cnf(c_41,negated_conjecture,
vplus(vmul(vd436,vd437),vmul(vd436,vplus(vd439,v1))) != vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(paramod,[status(thm)],[c_14,c_11]) ).
cnf(c_42,negated_conjecture,
vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))) != vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(paramod,[status(thm)],[c_25,c_41]) ).
cnf(c_43,negated_conjecture,
vplus(vd436,vplus(vmul(vd436,vd437),vmul(vd436,vd439))) != vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(paramod,[status(thm)],[c_34,c_42]) ).
cnf(c_44,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_22,c_43]) ).
cnf(c_45,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_34,c_44]) ).
cnf(c_36,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM848+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n005.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 04:12:47 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.45 % Process 1171006 was started by sandbox on n005,
% 0.17/0.45 % Sat Sep 26 04:12:47 2026
% 0.17/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 0.17/0.46
% 0.17/0.46 % SZS status Theorem for theBenchmark
% 0.17/0.46
% 0.17/0.46 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.17/0.46 % Length of proof is 13.
% 0.17/0.46 % Level of proof is 3.
% 0.17/0.46 % Maximum clause weight is 19.000.
% 0.17/0.46 % Given clauses 0.
% 0.17/0.46
% 0.17/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------