%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV050+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 09:06:42 AM UTC 2026
% Result : Theorem 2.61s 0.90s
% Output : CNFRefutation 2.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 17 unt; 0 def)
% Number of atoms : 47 ( 46 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 45 ( 24 ~; 13 |; 6 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 15 con; 0-3 aty)
% Number of variables : 6 ( 1 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sum_plus_base,axiom,
! [Body] : sum(n0,tptp_minus_1,Body) = n0,
file('theBenchmark.p',sum_plus_base) ).
fof(pred_minus_1,axiom,
! [X] : minus(X,n1) = pred(X),
file('theBenchmark.p',pred_minus_1) ).
fof(pred_succ,axiom,
! [X] : pred(succ(X)) = X,
file('theBenchmark.p',pred_succ) ).
fof(cl5_nebula_norm_0022,conjecture,
( ( pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89)))))
& pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))) )
=> ( pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89)))))
& pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
& n0 = sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) ) ),
file('theBenchmark.p',cl5_nebula_norm_0022) ).
fof(cl5_nebula_norm_0022_neg,negated_conjecture,
~ ( ( pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89)))))
& pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))) )
=> ( pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89)))))
& pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
& n0 = sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) ) ),
inference(assume_negation,[status(cth)],[cl5_nebula_norm_0022]) ).
cnf(c_278,plain,
sum(n0,tptp_minus_1,A) = n0,
inference(clausify,[status(thm)],[sum_plus_base]) ).
fof(succ_tptp_minus_1,axiom,
succ(tptp_minus_1) = n0,
file('theBenchmark.p',succ_tptp_minus_1) ).
cnf(c_281,plain,
succ(tptp_minus_1) = n0,
inference(clausify,[status(thm)],[succ_tptp_minus_1]) ).
cnf(c_300,plain,
minus(A,n1) = pred(A),
inference(clausify,[status(thm)],[pred_minus_1]) ).
cnf(c_301,plain,
pred(succ(A)) = A,
inference(clausify,[status(thm)],[pred_succ]) ).
cnf(c_358,negated_conjecture,
sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))) = pv86,
inference(clausify,[status(thm)],[cl5_nebula_norm_0022_neg]) ).
cnf(c_359,negated_conjecture,
sum(n0,pred(n5),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))) = pv86,
inference(paramod,[status(thm)],[c_300,c_358]) ).
cnf(c_360,negated_conjecture,
sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) = pv88,
inference(clausify,[status(thm)],[cl5_nebula_norm_0022_neg]) ).
cnf(c_361,negated_conjecture,
sum(n0,pred(n5),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) = pv88,
inference(paramod,[status(thm)],[c_300,c_360]) ).
cnf(c_362,negated_conjecture,
( sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) != pv88
| sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))) != pv86
| sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) != n0 ),
inference(clausify,[status(thm)],[cl5_nebula_norm_0022_neg]) ).
cnf(c_1189,negated_conjecture,
( sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) != pv88
| sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))) != pv86
| sum(n0,pred(n0),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) != n0 ),
inference(paramod,[status(thm)],[c_300,c_362]) ).
cnf(c_1190,negated_conjecture,
( sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) != pv88
| sum(n0,pred(n5),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))) != pv86
| sum(n0,pred(n0),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) != n0 ),
inference(paramod,[status(thm)],[c_300,c_1189]) ).
cnf(c_1191,negated_conjecture,
( sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) != pv88
| pv86 != pv86
| sum(n0,pred(n0),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) != n0 ),
inference(paramod,[status(thm)],[c_359,c_1190]) ).
cnf(c_1192,negated_conjecture,
( sum(n0,pred(n5),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) != pv88
| pv86 != pv86
| sum(n0,pred(n0),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) != n0 ),
inference(paramod,[status(thm)],[c_300,c_1191]) ).
cnf(c_1193,negated_conjecture,
( pv88 != pv88
| pv86 != pv86
| sum(n0,pred(n0),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) != n0 ),
inference(paramod,[status(thm)],[c_361,c_1192]) ).
cnf(c_1194,negated_conjecture,
( pv88 != pv88
| sum(n0,pred(n0),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) != n0 ),
inference(copy,[status(thm)],[c_1193]) ).
cnf(c_363,negated_conjecture,
sum(n0,pred(n0),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) != n0,
inference(copy,[status(thm)],[c_1194]) ).
cnf(c_1183,plain,
pred(n0) = tptp_minus_1,
inference(paramod,[status(thm)],[c_281,c_301]) ).
cnf(c_1195,negated_conjecture,
sum(n0,tptp_minus_1,divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) != n0,
inference(paramod,[status(thm)],[c_1183,c_363]) ).
cnf(c_1196,negated_conjecture,
n0 != n0,
inference(paramod,[status(thm)],[c_278,c_1195]) ).
cnf(c_1188,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_1196]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV050+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 13:14:00 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 948172 was started by sandbox on n016,
% 0.10/0.38 % Sat Sep 26 13:14:00 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.44
% 0.10/0.44 % From the command line: assign(max_seconds, 300).
% 2.61/0.90
% 2.61/0.90 % SZS status Theorem for theBenchmark
% 2.61/0.90
% 2.61/0.90 % Proof 1 at 0.23 (+ 0.02) seconds.
% 2.61/0.90 % Length of proof is 16.
% 2.61/0.90 % Level of proof is 4.
% 2.61/0.90 % Maximum clause weight is 54.000.
% 2.61/0.90 % Given clauses 232.
% 2.61/0.90
% 2.61/0.90 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------