%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM845+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 : n007.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 08:18:11 AM UTC 2026
% Result : Theorem 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 35 unt; 0 def)
% Number of atoms : 45 ( 44 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 24 ( 19 ~; 0 |; 3 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 10 !; 1 ?)
% 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('ass(cond(33, 0), 0)',axiom,
! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)),
file('theBenchmark.p','ass(cond(33, 0), 0)') ).
fof('qu(ind(267), imp(267))',conjecture,
! [Vd416] :
( vmul(vsucc(vd411),Vd416) = vplus(vmul(vd411,Vd416),Vd416)
=> vmul(vsucc(vd411),vsucc(Vd416)) = vplus(vmul(vd411,vsucc(Vd416)),vsucc(Vd416)) ),
file('theBenchmark.p','qu(ind(267), imp(267))') ).
fof('qu(ind(267), imp(267))_neg',negated_conjecture,
~ ! [Vd416] :
( vmul(vsucc(vd411),Vd416) = vplus(vmul(vd411,Vd416),Vd416)
=> vmul(vsucc(vd411),vsucc(Vd416)) = vplus(vmul(vd411,vsucc(Vd416)),vsucc(Vd416)) ),
inference(assume_negation,[status(cth)],['qu(ind(267), imp(267))']) ).
cnf(c_32,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_33,plain,
vmul(A,vsucc(B)) = vplus(vmul(A,B),A),
inference(copy,[status(thm)],[c_32]) ).
cnf(c_35,plain,
vplus(A,B) = vplus(B,A),
inference(clausify,[status(thm)],['ass(cond(61, 0), 0)']) ).
cnf(c_36,plain,
vplus(v1,A) = vsucc(A),
inference(clausify,[status(thm)],['ass(cond(43, 0), 0)']) ).
cnf(c_37,plain,
vsucc(A) = vplus(v1,A),
inference(copy,[status(thm)],[c_36]) ).
cnf(c_38,plain,
vplus(vplus(A,B),C) = vplus(A,vplus(B,C)),
inference(clausify,[status(thm)],['ass(cond(33, 0), 0)']) ).
fof(nnf_14,plain,
? [Vd416] :
( vplus(vmul(vd411,vsucc(Vd416)),vsucc(Vd416)) != vmul(vsucc(vd411),vsucc(Vd416))
& vplus(vmul(vd411,Vd416),Vd416) = vmul(vsucc(vd411),Vd416) ),
inference(fof_nnf,[status(thm)],['qu(ind(267), imp(267))_neg']) ).
fof('sk_qu(ind(267), imp(267))_neg',plain,
( vplus(vmul(vd411,vsucc(sK0)),vsucc(sK0)) != vmul(vsucc(vd411),vsucc(sK0))
& vplus(vmul(vd411,sK0),sK0) = vmul(vsucc(vd411),sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Vd416,sK0)],[nnf_14]) ).
cnf(c_42,negated_conjecture,
vplus(vmul(vd411,sK0),sK0) = vmul(vsucc(vd411),sK0),
inference(split_conjunct,[status(thm)],['sk_qu(ind(267), imp(267))_neg']) ).
cnf(c_55,negated_conjecture,
vplus(sK0,vmul(vd411,sK0)) = vmul(vsucc(vd411),sK0),
inference(paramod,[status(thm)],[c_35,c_42]) ).
cnf(c_56,negated_conjecture,
vplus(sK0,vmul(vd411,sK0)) = vmul(vplus(v1,vd411),sK0),
inference(paramod,[status(thm)],[c_37,c_55]) ).
cnf(c_57,negated_conjecture,
vplus(sK0,vmul(vd411,sK0)) = vmul(vplus(vd411,v1),sK0),
inference(paramod,[status(thm)],[c_35,c_56]) ).
cnf(c_43,negated_conjecture,
vmul(vplus(vd411,v1),sK0) = vplus(sK0,vmul(vd411,sK0)),
inference(copy,[status(thm)],[c_57]) ).
cnf(c_44,negated_conjecture,
vplus(vmul(vd411,vsucc(sK0)),vsucc(sK0)) != vmul(vsucc(vd411),vsucc(sK0)),
inference(split_conjunct,[status(thm)],['sk_qu(ind(267), imp(267))_neg']) ).
cnf(c_58,negated_conjecture,
vplus(vmul(vd411,vplus(v1,sK0)),vsucc(sK0)) != vmul(vsucc(vd411),vsucc(sK0)),
inference(paramod,[status(thm)],[c_37,c_44]) ).
cnf(c_59,negated_conjecture,
vplus(vmul(vd411,vplus(v1,sK0)),vplus(v1,sK0)) != vmul(vsucc(vd411),vsucc(sK0)),
inference(paramod,[status(thm)],[c_37,c_58]) ).
cnf(c_60,negated_conjecture,
vplus(vplus(v1,sK0),vmul(vd411,vplus(v1,sK0))) != vmul(vsucc(vd411),vsucc(sK0)),
inference(paramod,[status(thm)],[c_35,c_59]) ).
cnf(c_61,negated_conjecture,
vplus(v1,vplus(sK0,vmul(vd411,vplus(v1,sK0)))) != vmul(vsucc(vd411),vsucc(sK0)),
inference(paramod,[status(thm)],[c_38,c_60]) ).
cnf(c_62,negated_conjecture,
vplus(v1,vplus(sK0,vmul(vd411,vplus(v1,sK0)))) != vmul(vplus(v1,vd411),vsucc(sK0)),
inference(paramod,[status(thm)],[c_37,c_61]) ).
cnf(c_63,negated_conjecture,
vplus(v1,vplus(sK0,vmul(vd411,vplus(v1,sK0)))) != vmul(vplus(vd411,v1),vsucc(sK0)),
inference(paramod,[status(thm)],[c_35,c_62]) ).
cnf(c_64,negated_conjecture,
vplus(v1,vplus(sK0,vmul(vd411,vplus(v1,sK0)))) != vmul(vplus(vd411,v1),vplus(v1,sK0)),
inference(paramod,[status(thm)],[c_37,c_63]) ).
cnf(c_45,negated_conjecture,
vmul(vplus(vd411,v1),vplus(v1,sK0)) != vplus(v1,vplus(sK0,vmul(vd411,vplus(v1,sK0)))),
inference(copy,[status(thm)],[c_64]) ).
cnf(c_65,plain,
vmul(A,vplus(v1,B)) = vplus(vmul(A,B),A),
inference(paramod,[status(thm)],[c_37,c_33]) ).
cnf(c_47,plain,
vmul(A,vplus(v1,B)) = vplus(A,vmul(A,B)),
inference(paramod,[status(thm)],[c_35,c_65]) ).
cnf(c_66,negated_conjecture,
vplus(vplus(vd411,v1),vmul(vplus(vd411,v1),sK0)) != vplus(v1,vplus(sK0,vmul(vd411,vplus(v1,sK0)))),
inference(paramod,[status(thm)],[c_47,c_45]) ).
cnf(c_67,negated_conjecture,
vplus(vplus(vd411,v1),vplus(sK0,vmul(vd411,sK0))) != vplus(v1,vplus(sK0,vmul(vd411,vplus(v1,sK0)))),
inference(paramod,[status(thm)],[c_43,c_66]) ).
cnf(c_68,negated_conjecture,
vplus(vd411,vplus(v1,vplus(sK0,vmul(vd411,sK0)))) != vplus(v1,vplus(sK0,vmul(vd411,vplus(v1,sK0)))),
inference(paramod,[status(thm)],[c_38,c_67]) ).
cnf(c_69,negated_conjecture,
vplus(vd411,vplus(v1,vplus(sK0,vmul(vd411,sK0)))) != vplus(v1,vplus(sK0,vplus(vd411,vmul(vd411,sK0)))),
inference(paramod,[status(thm)],[c_47,c_68]) ).
cnf(c_51,negated_conjecture,
vplus(v1,vplus(sK0,vplus(vd411,vmul(vd411,sK0)))) != vplus(vd411,vplus(v1,vplus(sK0,vmul(vd411,sK0)))),
inference(copy,[status(thm)],[c_69]) ).
cnf(c_70,plain,
vplus(vplus(A,B),C) = vplus(B,vplus(A,C)),
inference(paramod,[status(thm)],[c_35,c_38]) ).
cnf(c_53,plain,
vplus(A,vplus(B,C)) = vplus(B,vplus(A,C)),
inference(paramod,[status(thm)],[c_38,c_70]) ).
cnf(c_71,negated_conjecture,
vplus(v1,vplus(vd411,vplus(sK0,vmul(vd411,sK0)))) != vplus(vd411,vplus(v1,vplus(sK0,vmul(vd411,sK0)))),
inference(paramod,[status(thm)],[c_53,c_51]) ).
cnf(c_72,negated_conjecture,
vplus(vd411,vplus(v1,vplus(sK0,vmul(vd411,sK0)))) != vplus(vd411,vplus(v1,vplus(sK0,vmul(vd411,sK0)))),
inference(paramod,[status(thm)],[c_53,c_71]) ).
cnf(c_54,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM845+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n007.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 26 04:10:38 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 2748989 was started by sandbox on n007,
% 0.07/0.35 % Sat Sep 26 04:10:38 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.37
% 0.12/0.37 % SZS status Theorem for theBenchmark
% 0.12/0.37
% 0.12/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/0.37 % Length of proof is 19.
% 0.12/0.37 % Level of proof is 5.
% 0.12/0.37 % Maximum clause weight is 19.000.
% 0.12/0.37 % Given clauses 4.
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------