%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM845+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 : n012.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 0.02s 0.33s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 36 unt; 0 def)
% Number of atoms : 50 ( 49 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 27 ( 20 ~; 1 |; 3 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 41 ( 0 sgn 13 !; 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(goal(193), 0), 1)',axiom,
! [Vd301,Vd302,Vd303] :
( Vd301 = Vd302
=> vplus(Vd301,Vd303) = vplus(Vd302,Vd303) ),
file('theBenchmark.p','ass(cond(goal(193), 0), 1)') ).
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_78,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_79,plain,
vmul(A,vsucc(B)) = vplus(vmul(A,B),A),
inference(copy,[status(thm)],[c_78]) ).
cnf(c_92,plain,
( vplus(A,C) = vplus(B,C)
| A != B ),
inference(clausify,[status(thm)],['ass(cond(goal(193), 0), 1)']) ).
cnf(c_123,plain,
vplus(A,B) = vplus(B,A),
inference(clausify,[status(thm)],['ass(cond(61, 0), 0)']) ).
cnf(c_126,plain,
vplus(v1,A) = vsucc(A),
inference(clausify,[status(thm)],['ass(cond(43, 0), 0)']) ).
cnf(c_127,plain,
vsucc(A) = vplus(v1,A),
inference(copy,[status(thm)],[c_126]) ).
cnf(c_128,plain,
vplus(vplus(A,B),C) = vplus(A,vplus(B,C)),
inference(clausify,[status(thm)],['ass(cond(33, 0), 0)']) ).
fof(nnf_55,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_55]) ).
cnf(c_139,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_229,negated_conjecture,
vplus(sK0,vmul(vd411,sK0)) = vmul(vsucc(vd411),sK0),
inference(paramod,[status(thm)],[c_123,c_139]) ).
cnf(c_230,negated_conjecture,
vplus(sK0,vmul(vd411,sK0)) = vmul(vplus(v1,vd411),sK0),
inference(paramod,[status(thm)],[c_127,c_229]) ).
cnf(c_231,negated_conjecture,
vplus(sK0,vmul(vd411,sK0)) = vmul(vplus(vd411,v1),sK0),
inference(paramod,[status(thm)],[c_123,c_230]) ).
cnf(c_140,negated_conjecture,
vmul(vplus(vd411,v1),sK0) = vplus(sK0,vmul(vd411,sK0)),
inference(copy,[status(thm)],[c_231]) ).
cnf(c_141,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_232,negated_conjecture,
vplus(vmul(vd411,vplus(v1,sK0)),vsucc(sK0)) != vmul(vsucc(vd411),vsucc(sK0)),
inference(paramod,[status(thm)],[c_127,c_141]) ).
cnf(c_233,negated_conjecture,
vplus(vmul(vd411,vplus(v1,sK0)),vplus(v1,sK0)) != vmul(vsucc(vd411),vsucc(sK0)),
inference(paramod,[status(thm)],[c_127,c_232]) ).
cnf(c_234,negated_conjecture,
vplus(vplus(v1,sK0),vmul(vd411,vplus(v1,sK0))) != vmul(vsucc(vd411),vsucc(sK0)),
inference(paramod,[status(thm)],[c_123,c_233]) ).
cnf(c_235,negated_conjecture,
vplus(v1,vplus(sK0,vmul(vd411,vplus(v1,sK0)))) != vmul(vsucc(vd411),vsucc(sK0)),
inference(paramod,[status(thm)],[c_128,c_234]) ).
cnf(c_236,negated_conjecture,
vplus(v1,vplus(sK0,vmul(vd411,vplus(v1,sK0)))) != vmul(vplus(v1,vd411),vsucc(sK0)),
inference(paramod,[status(thm)],[c_127,c_235]) ).
cnf(c_237,negated_conjecture,
vplus(v1,vplus(sK0,vmul(vd411,vplus(v1,sK0)))) != vmul(vplus(vd411,v1),vsucc(sK0)),
inference(paramod,[status(thm)],[c_123,c_236]) ).
cnf(c_238,negated_conjecture,
vplus(v1,vplus(sK0,vmul(vd411,vplus(v1,sK0)))) != vmul(vplus(vd411,v1),vplus(v1,sK0)),
inference(paramod,[status(thm)],[c_127,c_237]) ).
cnf(c_142,negated_conjecture,
vmul(vplus(vd411,v1),vplus(v1,sK0)) != vplus(v1,vplus(sK0,vmul(vd411,vplus(v1,sK0)))),
inference(copy,[status(thm)],[c_238]) ).
cnf(c_239,plain,
vmul(A,vplus(v1,B)) = vplus(vmul(A,B),A),
inference(paramod,[status(thm)],[c_127,c_79]) ).
cnf(c_151,plain,
vmul(A,vplus(v1,B)) = vplus(A,vmul(A,B)),
inference(paramod,[status(thm)],[c_123,c_239]) ).
cnf(c_240,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_151,c_142]) ).
cnf(c_241,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_140,c_240]) ).
cnf(c_242,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_128,c_241]) ).
cnf(c_243,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_151,c_242]) ).
cnf(c_152,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_243]) ).
cnf(c_244,plain,
vplus(vplus(A,B),C) = vplus(vplus(B,A),C),
inference(resolve,[status(thm)],[c_123,c_92]) ).
cnf(c_245,plain,
vplus(A,vplus(B,C)) = vplus(vplus(B,A),C),
inference(paramod,[status(thm)],[c_128,c_244]) ).
cnf(c_212,plain,
vplus(A,vplus(B,C)) = vplus(B,vplus(A,C)),
inference(paramod,[status(thm)],[c_128,c_245]) ).
cnf(c_246,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_212,c_152]) ).
cnf(c_247,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_212,c_246]) ).
cnf(c_228,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_247]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM845+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Sat Sep 26 04:12:20 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.30 % Process 3885732 was started by sandbox2 on n012,
% 0.02/0.30 % Sat Sep 26 04:12:20 2026
% 0.02/0.30 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.02/0.30
% 0.02/0.30 % From the command line: assign(max_seconds, 300).
% 0.02/0.33
% 0.02/0.33 % SZS status Theorem for theBenchmark
% 0.02/0.33
% 0.02/0.33 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.02/0.33 % Length of proof is 21.
% 0.02/0.33 % Level of proof is 5.
% 0.02/0.33 % Maximum clause weight is 19.000.
% 0.02/0.33 % Given clauses 45.
% 0.02/0.33
% 0.02/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------