%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM849+2 : 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 : 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 0.15s 0.47s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 33 unt; 0 def)
% Number of atoms : 45 ( 44 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 9 ~; 0 |; 4 &)
% ( 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 : 40 ( 0 sgn 15 !; 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('ass(cond(261, 0), 0)',axiom,
! [Vd408,Vd409] : vmul(vsucc(Vd408),Vd409) = vplus(vmul(Vd408,Vd409),Vd409),
file('theBenchmark.p','ass(cond(261, 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('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('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_18,plain,
vplus(vmul(A,B),vmul(A,C)) = vmul(A,vplus(B,C)),
inference(clausify,[status(thm)],['ass(cond(281, 0), 0)']) ).
cnf(c_19,plain,
vmul(A,B) = vmul(B,A),
inference(clausify,[status(thm)],['ass(cond(270, 0), 0)']) ).
cnf(c_20,plain,
vplus(vmul(A,B),B) = vmul(vsucc(A),B),
inference(clausify,[status(thm)],['ass(cond(261, 0), 0)']) ).
cnf(c_21,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_23,plain,
vplus(A,B) = vplus(B,A),
inference(clausify,[status(thm)],['ass(cond(61, 0), 0)']) ).
cnf(c_26,plain,
vplus(A,v1) = vsucc(A),
inference(clausify,[status(thm)],['qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))']) ).
cnf(c_27,plain,
vsucc(A) = vplus(A,v1),
inference(copy,[status(thm)],[c_26]) ).
fof(nnf_11,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_11]) ).
cnf(c_28,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_60,negated_conjecture,
vmul(vmul(vd449,vd448),sK0) = vmul(vd448,vmul(vd449,sK0)),
inference(paramod,[status(thm)],[c_19,c_28]) ).
cnf(c_29,negated_conjecture,
vmul(sK0,vmul(vd449,vd448)) = vmul(vd448,vmul(vd449,sK0)),
inference(paramod,[status(thm)],[c_19,c_60]) ).
cnf(c_30,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_61,negated_conjecture,
vmul(vmul(vd449,vd448),vsucc(sK0)) != vmul(vd448,vmul(vd449,vsucc(sK0))),
inference(paramod,[status(thm)],[c_19,c_30]) ).
cnf(c_62,negated_conjecture,
vmul(vmul(vd449,vd448),vplus(sK0,v1)) != vmul(vd448,vmul(vd449,vsucc(sK0))),
inference(paramod,[status(thm)],[c_27,c_61]) ).
cnf(c_63,negated_conjecture,
vmul(vmul(vd449,vd448),vplus(v1,sK0)) != vmul(vd448,vmul(vd449,vsucc(sK0))),
inference(paramod,[status(thm)],[c_23,c_62]) ).
cnf(c_64,negated_conjecture,
vmul(vmul(vd449,vd448),vplus(v1,sK0)) != vmul(vd448,vmul(vd449,vplus(sK0,v1))),
inference(paramod,[status(thm)],[c_27,c_63]) ).
cnf(c_31,negated_conjecture,
vmul(vmul(vd449,vd448),vplus(v1,sK0)) != vmul(vd448,vmul(vd449,vplus(v1,sK0))),
inference(paramod,[status(thm)],[c_23,c_64]) ).
cnf(c_65,plain,
vplus(A,vmul(A,B)) = vmul(A,vsucc(B)),
inference(paramod,[status(thm)],[c_23,c_21]) ).
cnf(c_35,plain,
vplus(A,vmul(A,B)) = vmul(A,vplus(B,v1)),
inference(paramod,[status(thm)],[c_27,c_65]) ).
cnf(c_66,plain,
vplus(B,vmul(A,B)) = vmul(vsucc(A),B),
inference(paramod,[status(thm)],[c_23,c_20]) ).
cnf(c_36,plain,
vplus(A,vmul(B,A)) = vmul(vplus(B,v1),A),
inference(paramod,[status(thm)],[c_27,c_66]) ).
cnf(c_39,plain,
vplus(vmul(A,B),vmul(B,C)) = vmul(B,vplus(A,C)),
inference(paramod,[status(thm)],[c_19,c_18]) ).
cnf(c_67,plain,
vplus(vmul(vd449,vd448),vmul(vd448,vmul(vd449,sK0))) = vmul(vplus(sK0,v1),vmul(vd449,vd448)),
inference(paramod,[status(thm)],[c_29,c_36]) ).
cnf(c_68,plain,
vmul(vd448,vplus(vd449,vmul(vd449,sK0))) = vmul(vplus(sK0,v1),vmul(vd449,vd448)),
inference(paramod,[status(thm)],[c_39,c_67]) ).
cnf(c_69,plain,
vmul(vd448,vmul(vd449,vplus(sK0,v1))) = vmul(vplus(sK0,v1),vmul(vd449,vd448)),
inference(paramod,[status(thm)],[c_35,c_68]) ).
cnf(c_70,plain,
vmul(vd448,vmul(vd449,vplus(v1,sK0))) = vmul(vplus(sK0,v1),vmul(vd449,vd448)),
inference(paramod,[status(thm)],[c_23,c_69]) ).
cnf(c_71,plain,
vmul(vd448,vmul(vd449,vplus(v1,sK0))) = vmul(vplus(v1,sK0),vmul(vd449,vd448)),
inference(paramod,[status(thm)],[c_23,c_70]) ).
cnf(c_72,plain,
vmul(vd448,vmul(vd449,vplus(v1,sK0))) = vmul(vmul(vd449,vd448),vplus(v1,sK0)),
inference(paramod,[status(thm)],[c_19,c_71]) ).
cnf(c_73,plain,
vmul(vmul(vd449,vd448),vplus(v1,sK0)) = vmul(vd448,vmul(vd449,vplus(v1,sK0))),
inference(copy,[status(thm)],[c_72]) ).
cnf(c_59,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_31,c_73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM849+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.43 % Computer : n009.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Sat Sep 26 04:13:29 UTC 2026
% 0.15/0.44 % CPUTime :
% 0.15/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.44 % Process 3335587 was started by sandbox2 on n009,
% 0.15/0.44 % Sat Sep 26 04:13:29 2026
% 0.15/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.44
% 0.15/0.44 % From the command line: assign(max_seconds, 300).
% 0.15/0.47
% 0.15/0.47 % Assigning unary symbol vsucc kb_weight 0 and highest precedence (8).
% 0.15/0.47
% 0.15/0.47 % SZS status Theorem for theBenchmark
% 0.15/0.47
% 0.15/0.47 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.15/0.47 % Length of proof is 22.
% 0.15/0.47 % Level of proof is 4.
% 0.15/0.47 % Maximum clause weight is 45.000.
% 0.15/0.47 % Given clauses 9.
% 0.15/0.47
% 0.15/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------