%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV135+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 : n011.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 09:06:52 AM UTC 2026
% Result : Theorem 20.43s 7.00s
% Output : CNFRefutation 20.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 7 unt; 0 def)
% Number of atoms : 37 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 29 ( 6 ~; 4 |; 15 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 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(gauss_array_0005,conjecture,
( ( leq(pv1325,n3)
& leq(s_worst7,n3)
& leq(s_sworst7,n3)
& leq(s_best7,n3)
& leq(n2,pv1325)
& leq(n0,s_worst7)
& leq(n0,s_sworst7)
& leq(n0,s_best7) )
=> leq(n0,pv1325) ),
file('theBenchmark.p',gauss_array_0005) ).
fof(gauss_array_0005_neg,negated_conjecture,
~ ( ( leq(pv1325,n3)
& leq(s_worst7,n3)
& leq(s_sworst7,n3)
& leq(s_best7,n3)
& leq(n2,pv1325)
& leq(n0,s_worst7)
& leq(n0,s_sworst7)
& leq(n0,s_best7) )
=> leq(n0,pv1325) ),
inference(assume_negation,[status(cth)],[gauss_array_0005]) ).
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_2_0,axiom,
gt(n2,n0),
file('theBenchmark.p',gt_2_0) ).
cnf(c_334,plain,
gt(n2,n0),
inference(clausify,[status(thm)],[gt_2_0]) ).
cnf(c_359,negated_conjecture,
leq(n2,pv1325),
inference(clausify,[status(thm)],[gauss_array_0005_neg]) ).
cnf(c_364,negated_conjecture,
~ leq(n0,pv1325),
inference(clausify,[status(thm)],[gauss_array_0005_neg]) ).
cnf(c_1631,plain,
leq(n0,n2),
inference(resolve,[status(thm)],[c_334,c_66]) ).
cnf(c_3101,plain,
( leq(A,pv1325)
| ~ leq(A,n2) ),
inference(resolve,[status(thm)],[c_359,c_65]) ).
cnf(c_13838,plain,
leq(n0,pv1325),
inference(resolve,[status(thm)],[c_3101,c_1631]) ).
cnf(c_13837,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_364,c_13838]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV135+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.38 % Computer : n011.cluster.edu
% 0.06/0.38 % Model : x86_64 x86_64
% 0.06/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.38 % Memory : 8046.5625MB
% 0.06/0.38 % OS : Linux 6.8.0-71-generic
% 0.06/0.38 % CPULimit : 300
% 0.06/0.38 % WCLimit : 300
% 0.06/0.38 % DateTime : Sat Sep 26 13:15:00 UTC 2026
% 0.06/0.38 % CPUTime :
% 0.06/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.06/0.39 % Process 635648 was started by sandbox on n011,
% 0.06/0.39 % Sat Sep 26 13:15:00 2026
% 0.06/0.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.47
% 0.11/0.47 % From the command line: assign(max_seconds, 300).
% 20.43/7.00
% 20.43/7.00 % given #500 (I,wt=140): 572 leq(n0,f19(A,B,C,D,E,F,V6,V7)) | leq(n0,f22(A,B,C,D,E,F,V6,V7)) | leq(n0,f24(A,B,C,D,E,F,V6,V7)) | -leq(n0,V6) | 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,V6) = 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)))),V6,n0). [factor(165,d,g),unit_del(e,64),unit_del(f,64)].
% 20.43/7.00
% 20.43/7.00 % SZS status Theorem for theBenchmark
% 20.43/7.00
% 20.43/7.00 % Proof 1 at 2.40 (+ 0.50) seconds.
% 20.43/7.00 % Length of proof is 11.
% 20.43/7.00 % Level of proof is 3.
% 20.43/7.00 % Maximum clause weight is 14.000.
% 20.43/7.00 % Given clauses 920.
% 20.43/7.00
% 20.43/7.00 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------