%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM844+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 : n015.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 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 22 unt; 0 def)
% Number of atoms : 22 ( 21 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 13 ( 13 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 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 : 13 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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('holds(266, 415, 3)',conjecture,
vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),
file('theBenchmark.p','holds(266, 415, 3)') ).
fof('holds(266, 415, 3)_neg',negated_conjecture,
vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) != vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),
inference(assume_negation,[status(cth)],['holds(266, 415, 3)']) ).
cnf(c_29,plain,
vplus(A,B) = vplus(B,A),
inference(clausify,[status(thm)],['ass(cond(61, 0), 0)']) ).
cnf(c_32,plain,
vplus(v1,A) = vsucc(A),
inference(clausify,[status(thm)],['ass(cond(43, 0), 0)']) ).
cnf(c_33,plain,
vsucc(A) = vplus(v1,A),
inference(copy,[status(thm)],[c_32]) ).
cnf(c_34,plain,
vplus(vplus(A,B),C) = vplus(A,vplus(B,C)),
inference(clausify,[status(thm)],['ass(cond(33, 0), 0)']) ).
cnf(c_44,negated_conjecture,
vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)) != vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),
inference(clausify,[status(thm)],['holds(266, 415, 3)_neg']) ).
cnf(c_46,negated_conjecture,
vplus(vmul(vd411,vd413),vplus(vplus(v1,vd411),vd413)) != vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),
inference(paramod,[status(thm)],[c_33,c_44]) ).
cnf(c_47,negated_conjecture,
vplus(vmul(vd411,vd413),vplus(vplus(vd411,v1),vd413)) != vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),
inference(paramod,[status(thm)],[c_29,c_46]) ).
cnf(c_48,negated_conjecture,
vplus(vmul(vd411,vd413),vplus(vd413,vplus(vd411,v1))) != vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),
inference(paramod,[status(thm)],[c_29,c_47]) ).
cnf(c_49,negated_conjecture,
vplus(vplus(vd413,vplus(vd411,v1)),vmul(vd411,vd413)) != vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),
inference(paramod,[status(thm)],[c_29,c_48]) ).
cnf(c_50,negated_conjecture,
vplus(vd413,vplus(vplus(vd411,v1),vmul(vd411,vd413))) != vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),
inference(paramod,[status(thm)],[c_34,c_49]) ).
cnf(c_51,negated_conjecture,
vplus(vd413,vplus(vd411,vplus(v1,vmul(vd411,vd413)))) != vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),
inference(paramod,[status(thm)],[c_34,c_50]) ).
cnf(c_52,negated_conjecture,
vplus(vd413,vplus(vd411,vplus(v1,vmul(vd411,vd413)))) != vplus(vmul(vd411,vd413),vplus(vd413,vplus(v1,vd411))),
inference(paramod,[status(thm)],[c_33,c_51]) ).
cnf(c_53,negated_conjecture,
vplus(vd413,vplus(vd411,vplus(v1,vmul(vd411,vd413)))) != vplus(vmul(vd411,vd413),vplus(vd413,vplus(vd411,v1))),
inference(paramod,[status(thm)],[c_29,c_52]) ).
cnf(c_54,negated_conjecture,
vplus(vd413,vplus(vd411,vplus(v1,vmul(vd411,vd413)))) != vplus(vplus(vd413,vplus(vd411,v1)),vmul(vd411,vd413)),
inference(paramod,[status(thm)],[c_29,c_53]) ).
cnf(c_55,negated_conjecture,
vplus(vd413,vplus(vd411,vplus(v1,vmul(vd411,vd413)))) != vplus(vd413,vplus(vplus(vd411,v1),vmul(vd411,vd413))),
inference(paramod,[status(thm)],[c_34,c_54]) ).
cnf(c_56,negated_conjecture,
vplus(vd413,vplus(vd411,vplus(v1,vmul(vd411,vd413)))) != vplus(vd413,vplus(vd411,vplus(v1,vmul(vd411,vd413)))),
inference(paramod,[status(thm)],[c_34,c_55]) ).
cnf(c_45,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM844+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 04:15:29 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3103044 was started by sandbox2 on n015,
% 0.09/0.37 % Sat Sep 26 04:15:29 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.39
% 0.09/0.39 % SZS status Theorem for theBenchmark
% 0.09/0.39
% 0.09/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.39 % Length of proof is 10.
% 0.09/0.39 % Level of proof is 3.
% 0.09/0.39 % Maximum clause weight is 11.000.
% 0.09/0.39 % Given clauses 0.
% 0.09/0.39
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------