%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV046+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 5.78s 1.30s
% Output : CNFRefutation 5.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 23 unt; 0 def)
% Number of atoms : 91 ( 57 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 98 ( 43 ~; 35 |; 14 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 15 con; 0-3 aty)
% Number of variables : 12 ( 2 sgn 6 !; 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(sel2_update_1,axiom,
! [X,U,VAL] : a_select2(tptp_update2(X,U,VAL),U) = VAL,
file('theBenchmark.p',sel2_update_1) ).
fof(cl5_nebula_norm_0010,conjecture,
( ( leq(pv35,minus(n5,n1))
& leq(n0,pv35)
& pv80 = sum(n0,minus(n135300,n1),times(a_select3(q,pv81,pv35),a_select2(x,pv81)))
& pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35)) )
=> ( ( n0 = pv44
=> true )
& ( n0 != pv44
=> ( leq(pv35,minus(n5,n1))
& leq(n0,pv35)
& pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35))
& n0 = sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) ) ) ) ),
file('theBenchmark.p',cl5_nebula_norm_0010) ).
fof(cl5_nebula_norm_0010_neg,negated_conjecture,
~ ( ( leq(pv35,minus(n5,n1))
& leq(n0,pv35)
& pv80 = sum(n0,minus(n135300,n1),times(a_select3(q,pv81,pv35),a_select2(x,pv81)))
& pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35)) )
=> ( ( n0 = pv44
=> true )
& ( n0 != pv44
=> ( leq(pv35,minus(n5,n1))
& leq(n0,pv35)
& pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35))
& n0 = sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) ) ) ) ),
inference(assume_negation,[status(cth)],[cl5_nebula_norm_0010]) ).
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_314,plain,
a_select2(tptp_update2(A,B,C),B) = C,
inference(clausify,[status(thm)],[sel2_update_1]) ).
fof(ttrue,axiom,
true,
file('theBenchmark.p',ttrue) ).
cnf(c_319,plain,
true,
inference(clausify,[status(thm)],[ttrue]) ).
cnf(c_365,negated_conjecture,
sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35)) = pv78,
inference(clausify,[status(thm)],[cl5_nebula_norm_0010_neg]) ).
cnf(c_366,negated_conjecture,
sum(n0,pred(n135300),a_select3(q,pv79,pv35)) = pv78,
inference(paramod,[status(thm)],[c_300,c_365]) ).
cnf(c_369,negated_conjecture,
leq(n0,pv35),
inference(clausify,[status(thm)],[cl5_nebula_norm_0010_neg]) ).
cnf(c_370,negated_conjecture,
leq(pv35,minus(n5,n1)),
inference(clausify,[status(thm)],[cl5_nebula_norm_0010_neg]) ).
cnf(c_371,negated_conjecture,
leq(pv35,pred(n5)),
inference(paramod,[status(thm)],[c_300,c_370]) ).
cnf(c_372,negated_conjecture,
( ~ true
| pv44 != n0 ),
inference(clausify,[status(thm)],[cl5_nebula_norm_0010_neg]) ).
cnf(c_373,negated_conjecture,
pv44 != n0,
inference(resolve,[status(thm)],[c_319,c_372]) ).
cnf(c_374,negated_conjecture,
( pv44 = n0
| ~ leq(pv35,minus(n5,n1))
| ~ leq(n0,pv35)
| sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35)) != pv78
| sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) != n0 ),
inference(clausify,[status(thm)],[cl5_nebula_norm_0010_neg]) ).
cnf(c_1189,negated_conjecture,
( pv44 = n0
| ~ leq(pv35,minus(n5,n1))
| ~ leq(n0,pv35)
| sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35)) != pv78
| sum(n0,pred(n0),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) != n0 ),
inference(paramod,[status(thm)],[c_300,c_374]) ).
cnf(c_1190,negated_conjecture,
( pv44 = n0
| ~ leq(pv35,minus(n5,n1))
| ~ leq(n0,pv35)
| sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35)) != pv78
| sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) != n0 ),
inference(paramod,[status(thm)],[c_314,c_1189]) ).
cnf(c_1191,negated_conjecture,
( pv44 = n0
| ~ leq(pv35,minus(n5,n1))
| ~ leq(n0,pv35)
| sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35)) != pv78
| sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) != n0 ),
inference(paramod,[status(thm)],[c_314,c_1190]) ).
cnf(c_1192,negated_conjecture,
( pv44 = n0
| ~ leq(pv35,minus(n5,n1))
| ~ leq(n0,pv35)
| sum(n0,pred(n135300),a_select3(q,pv79,pv35)) != pv78
| sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) != n0 ),
inference(paramod,[status(thm)],[c_300,c_1191]) ).
cnf(c_1193,negated_conjecture,
( pv44 = n0
| ~ leq(pv35,minus(n5,n1))
| ~ leq(n0,pv35)
| pv78 != pv78
| sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) != n0 ),
inference(paramod,[status(thm)],[c_366,c_1192]) ).
cnf(c_1194,negated_conjecture,
( pv44 = n0
| ~ leq(pv35,pred(n5))
| ~ leq(n0,pv35)
| pv78 != pv78
| sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) != n0 ),
inference(paramod,[status(thm)],[c_300,c_1193]) ).
cnf(c_1195,negated_conjecture,
( pv44 = n0
| ~ leq(pv35,pred(n5))
| ~ leq(n0,pv35)
| sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) != n0 ),
inference(copy,[status(thm)],[c_1194]) ).
cnf(c_1196,negated_conjecture,
( pv44 = n0
| ~ leq(pv35,pred(n5))
| sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) != n0 ),
inference(resolve,[status(thm)],[c_369,c_1195]) ).
cnf(c_1197,negated_conjecture,
( pv44 = n0
| sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) != n0 ),
inference(resolve,[status(thm)],[c_371,c_1196]) ).
cnf(c_375,negated_conjecture,
sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) != n0,
inference(resolve,[status(thm)],[c_373,c_1197]) ).
cnf(c_1183,plain,
pred(n0) = tptp_minus_1,
inference(paramod,[status(thm)],[c_281,c_301]) ).
cnf(c_1198,negated_conjecture,
sum(n0,tptp_minus_1,times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) != n0,
inference(paramod,[status(thm)],[c_1183,c_375]) ).
cnf(c_1199,negated_conjecture,
n0 != n0,
inference(paramod,[status(thm)],[c_278,c_1198]) ).
cnf(c_1188,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_1199]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV046+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n026.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 13:12:11 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 1066089 was started by sandbox2 on n026,
% 0.10/0.38 % Sat Sep 26 13:12:11 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.47
% 0.14/0.47 % From the command line: assign(max_seconds, 300).
% 5.78/1.30
% 5.78/1.30 % SZS status Theorem for theBenchmark
% 5.78/1.30
% 5.78/1.30 % Proof 1 at 0.66 (+ 0.11) seconds.
% 5.78/1.30 % Length of proof is 22.
% 5.78/1.30 % Level of proof is 4.
% 5.78/1.30 % Maximum clause weight is 58.000.
% 5.78/1.30 % Given clauses 232.
% 5.78/1.30
% 5.78/1.30 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------