%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV067+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 : n019.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 09:06:44 AM UTC 2026
% Result : Theorem 19.31s 2.95s
% Output : CNFRefutation 19.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 10 unt; 0 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 56 ( 17 ~; 10 |; 21 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-3 aty)
% Number of variables : 11 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(transitivity_leq,axiom,
! [X,Y,Z] :
( ( leq(Y,Z)
& leq(X,Y) )
=> leq(X,Z) ),
file('theBenchmark.p',transitivity_leq) ).
fof(leq_gt1,axiom,
! [X,Y] :
( gt(Y,X)
=> leq(X,Y) ),
file('theBenchmark.p',leq_gt1) ).
fof(cl5_nebula_array_0008,conjecture,
( ( leq(pv63,minus(n5,n1))
& leq(pv10,minus(n135300,n1))
& leq(n1,pv63)
& leq(n0,pv10) )
=> ( ( gt(a_select3(q,pv10,pv63),pv78)
=> ( leq(pv10,minus(n135300,n1))
& leq(n0,pv10) ) )
& ( ~ gt(a_select3(q,pv10,pv63),pv78)
=> ( leq(pv10,minus(n135300,n1))
& leq(n0,pv10) ) )
& leq(pv63,minus(n5,n1))
& leq(pv10,minus(n135300,n1))
& leq(n0,pv63)
& leq(n0,pv10) ) ),
file('theBenchmark.p',cl5_nebula_array_0008) ).
fof(cl5_nebula_array_0008_neg,negated_conjecture,
~ ( ( leq(pv63,minus(n5,n1))
& leq(pv10,minus(n135300,n1))
& leq(n1,pv63)
& leq(n0,pv10) )
=> ( ( gt(a_select3(q,pv10,pv63),pv78)
=> ( leq(pv10,minus(n135300,n1))
& leq(n0,pv10) ) )
& ( ~ gt(a_select3(q,pv10,pv63),pv78)
=> ( leq(pv10,minus(n135300,n1))
& leq(n0,pv10) ) )
& leq(pv63,minus(n5,n1))
& leq(pv10,minus(n135300,n1))
& leq(n0,pv63)
& leq(n0,pv10) ) ),
inference(assume_negation,[status(cth)],[cl5_nebula_array_0008]) ).
cnf(c_65,plain,
( leq(A,C)
| ~ leq(B,C)
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[transitivity_leq]) ).
cnf(c_66,plain,
( leq(B,A)
| ~ gt(A,B) ),
inference(clausify,[status(thm)],[leq_gt1]) ).
fof(gt_1_0,axiom,
gt(n1,n0),
file('theBenchmark.p',gt_1_0) ).
cnf(c_337,plain,
gt(n1,n0),
inference(clausify,[status(thm)],[gt_1_0]) ).
cnf(c_363,negated_conjecture,
leq(n0,pv10),
inference(clausify,[status(thm)],[cl5_nebula_array_0008_neg]) ).
cnf(c_364,negated_conjecture,
leq(n1,pv63),
inference(clausify,[status(thm)],[cl5_nebula_array_0008_neg]) ).
cnf(c_365,negated_conjecture,
leq(pv10,minus(n135300,n1)),
inference(clausify,[status(thm)],[cl5_nebula_array_0008_neg]) ).
cnf(c_366,negated_conjecture,
leq(pv63,minus(n5,n1)),
inference(clausify,[status(thm)],[cl5_nebula_array_0008_neg]) ).
cnf(c_367,negated_conjecture,
( ~ leq(pv63,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv63)
| ~ leq(n0,pv10) ),
inference(clausify,[status(thm)],[cl5_nebula_array_0008_neg]) ).
cnf(c_15795,negated_conjecture,
( ~ leq(pv63,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv63) ),
inference(resolve,[status(thm)],[c_363,c_367]) ).
cnf(c_15796,negated_conjecture,
( ~ leq(pv63,minus(n5,n1))
| ~ leq(n0,pv63) ),
inference(resolve,[status(thm)],[c_365,c_15795]) ).
cnf(c_368,negated_conjecture,
~ leq(n0,pv63),
inference(resolve,[status(thm)],[c_366,c_15796]) ).
cnf(c_1600,plain,
leq(n0,n1),
inference(resolve,[status(thm)],[c_337,c_66]) ).
cnf(c_2318,plain,
( leq(A,pv63)
| ~ leq(A,n1) ),
inference(resolve,[status(thm)],[c_364,c_65]) ).
cnf(c_15797,plain,
leq(n0,pv63),
inference(resolve,[status(thm)],[c_2318,c_1600]) ).
cnf(c_15794,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_368,c_15797]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV067+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n019.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 13:10:33 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 1395381 was started by sandbox2 on n019,
% 0.09/0.35 % Sat Sep 26 13:10:33 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.41
% 0.13/0.41 % From the command line: assign(max_seconds, 300).
% 19.31/2.95
% 19.31/2.95 % given #500 (I,wt=131): 573 leq(n0,f19(A,B,C,D,E,F,n0,V6)) | leq(n0,f22(A,B,C,D,E,F,n0,V6)) | leq(f23(A,B,C,D,E,F,n0,V6),n0) | -leq(n0,V7) | -leq(V7,n0) | a_select3(tptp_madd(A,tptp_mmul(B,tptp_mmul(tptp_madd(tptp_mmul(C,tptp_mmul(D,trans(C))),tptp_mmul(E,tptp_mmul(F,trans(E)))),trans(B)))),n0,V7) = a_select3(tptp_madd(A,tptp_mmul(B,tptp_mmul(tptp_madd(tptp_mmul(C,tptp_mmul(D,trans(C))),tptp_mmul(E,tptp_mmul(F,trans(E)))),trans(B)))),V7,n0). [factor(164,d,e),flip(g),unit_del(d,64)].
% 19.31/2.95
% 19.31/2.95 % SZS status Theorem for theBenchmark
% 19.31/2.95
% 19.31/2.95 % Proof 1 at 2.07 (+ 0.42) seconds.
% 19.31/2.95 % Length of proof is 15.
% 19.31/2.95 % Level of proof is 3.
% 19.31/2.95 % Maximum clause weight is 15.000.
% 19.31/2.95 % Given clauses 931.
% 19.31/2.95
% 19.31/2.95 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------