%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM849+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 : n009.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 0.13s 0.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 26 unt; 0 def)
% Number of atoms : 36 ( 35 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 12 ~; 0 |; 3 &)
% ( 0 <=>; 2 =>; 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 : 31 ( 0 sgn 12 !; 1 ?)
% 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('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('qu(ind(296), imp(296))',conjecture,
! [Vd454] :
( vmul(vmul(vd448,vd449),Vd454) = vmul(vd448,vmul(vd449,Vd454))
=> vmul(vmul(vd448,vd449),vsucc(Vd454)) = vmul(vd448,vmul(vd449,vsucc(Vd454))) ),
file('theBenchmark.p','qu(ind(296), imp(296))') ).
fof('qu(ind(296), imp(296))_neg',negated_conjecture,
~ ! [Vd454] :
( vmul(vmul(vd448,vd449),Vd454) = vmul(vd448,vmul(vd449,Vd454))
=> vmul(vmul(vd448,vd449),vsucc(Vd454)) = vmul(vd448,vmul(vd449,vsucc(Vd454))) ),
inference(assume_negation,[status(cth)],['qu(ind(296), imp(296))']) ).
cnf(c_62,plain,
vplus(vmul(A,B),vmul(A,C)) = vmul(A,vplus(B,C)),
inference(clausify,[status(thm)],['ass(cond(281, 0), 0)']) ).
cnf(c_63,plain,
vmul(A,B) = vmul(B,A),
inference(clausify,[status(thm)],['ass(cond(270, 0), 0)']) ).
cnf(c_66,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_110,plain,
vplus(A,B) = vplus(B,A),
inference(clausify,[status(thm)],['ass(cond(61, 0), 0)']) ).
cnf(c_113,plain,
vplus(v1,A) = vsucc(A),
inference(clausify,[status(thm)],['ass(cond(43, 0), 0)']) ).
cnf(c_114,plain,
vsucc(A) = vplus(v1,A),
inference(copy,[status(thm)],[c_113]) ).
fof(nnf_54,plain,
? [Vd454] :
( vmul(vmul(vd448,vd449),vsucc(Vd454)) != vmul(vd448,vmul(vd449,vsucc(Vd454)))
& vmul(vmul(vd448,vd449),Vd454) = vmul(vd448,vmul(vd449,Vd454)) ),
inference(fof_nnf,[status(thm)],['qu(ind(296), imp(296))_neg']) ).
fof('sk_qu(ind(296), imp(296))_neg',plain,
( vmul(vmul(vd448,vd449),vsucc(sK0)) != vmul(vd448,vmul(vd449,vsucc(sK0)))
& vmul(vmul(vd448,vd449),sK0) = vmul(vd448,vmul(vd449,sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Vd454,sK0)],[nnf_54]) ).
cnf(c_126,negated_conjecture,
vmul(vmul(vd448,vd449),sK0) = vmul(vd448,vmul(vd449,sK0)),
inference(split_conjunct,[status(thm)],['sk_qu(ind(296), imp(296))_neg']) ).
cnf(c_288,negated_conjecture,
vmul(vmul(vd449,vd448),sK0) = vmul(vd448,vmul(vd449,sK0)),
inference(paramod,[status(thm)],[c_63,c_126]) ).
cnf(c_127,negated_conjecture,
vmul(sK0,vmul(vd449,vd448)) = vmul(vd448,vmul(vd449,sK0)),
inference(paramod,[status(thm)],[c_63,c_288]) ).
cnf(c_128,negated_conjecture,
vmul(vmul(vd448,vd449),vsucc(sK0)) != vmul(vd448,vmul(vd449,vsucc(sK0))),
inference(split_conjunct,[status(thm)],['sk_qu(ind(296), imp(296))_neg']) ).
cnf(c_289,negated_conjecture,
vmul(vmul(vd449,vd448),vsucc(sK0)) != vmul(vd448,vmul(vd449,vsucc(sK0))),
inference(paramod,[status(thm)],[c_63,c_128]) ).
cnf(c_290,negated_conjecture,
vmul(vmul(vd449,vd448),vplus(v1,sK0)) != vmul(vd448,vmul(vd449,vsucc(sK0))),
inference(paramod,[status(thm)],[c_114,c_289]) ).
cnf(c_129,negated_conjecture,
vmul(vmul(vd449,vd448),vplus(v1,sK0)) != vmul(vd448,vmul(vd449,vplus(v1,sK0))),
inference(paramod,[status(thm)],[c_114,c_290]) ).
cnf(c_291,plain,
vplus(A,vmul(A,B)) = vmul(A,vsucc(B)),
inference(paramod,[status(thm)],[c_110,c_66]) ).
cnf(c_136,plain,
vplus(A,vmul(A,B)) = vmul(A,vplus(v1,B)),
inference(paramod,[status(thm)],[c_114,c_291]) ).
cnf(c_139,plain,
vplus(vmul(A,B),vmul(B,C)) = vmul(B,vplus(A,C)),
inference(paramod,[status(thm)],[c_63,c_62]) ).
cnf(c_292,plain,
vplus(vmul(vd449,vd448),vmul(vmul(vd449,vd448),sK0)) != vmul(vd448,vmul(vd449,vplus(v1,sK0))),
inference(paramod,[status(thm)],[c_136,c_129]) ).
cnf(c_293,plain,
vplus(vmul(vd449,vd448),vmul(sK0,vmul(vd449,vd448))) != vmul(vd448,vmul(vd449,vplus(v1,sK0))),
inference(paramod,[status(thm)],[c_63,c_292]) ).
cnf(c_294,plain,
vplus(vmul(vd449,vd448),vmul(vd448,vmul(vd449,sK0))) != vmul(vd448,vmul(vd449,vplus(v1,sK0))),
inference(paramod,[status(thm)],[c_127,c_293]) ).
cnf(c_295,plain,
vmul(vd448,vplus(vd449,vmul(vd449,sK0))) != vmul(vd448,vmul(vd449,vplus(v1,sK0))),
inference(paramod,[status(thm)],[c_139,c_294]) ).
cnf(c_296,plain,
vmul(vd448,vmul(vd449,vplus(v1,sK0))) != vmul(vd448,vmul(vd449,vplus(v1,sK0))),
inference(paramod,[status(thm)],[c_136,c_295]) ).
cnf(c_287,plain,
$false,
inference(copy,[status(thm)],[c_296]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM849+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 04:12:59 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 3333606 was started by sandbox on n009,
% 0.08/0.36 % Sat Sep 26 04:12:59 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.42
% 0.13/0.42 % SZS status Theorem for theBenchmark
% 0.13/0.42
% 0.13/0.42 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.13/0.42 % Length of proof is 19.
% 0.13/0.42 % Level of proof is 4.
% 0.13/0.42 % Maximum clause weight is 39.000.
% 0.13/0.42 % Given clauses 56.
% 0.13/0.42
% 0.13/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------