%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV133+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 : 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 09:06:52 AM UTC 2026
% Result : Theorem 31.49s 4.58s
% Output : CNFRefutation 31.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 7 unt; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 35 ( 8 ~; 4 |; 19 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 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_0003,conjecture,
( ( leq(a_select2(s_values7,pv1325),a_select2(s_values7,s_best7))
& 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(a_select2(s_values7,pv1325),a_select2(s_values7,s_worst7)) )
=> leq(n0,pv1325) ),
file('theBenchmark.p',gauss_array_0003) ).
fof(gauss_array_0003_neg,negated_conjecture,
~ ( ( leq(a_select2(s_values7,pv1325),a_select2(s_values7,s_best7))
& 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(a_select2(s_values7,pv1325),a_select2(s_values7,s_worst7)) )
=> leq(n0,pv1325) ),
inference(assume_negation,[status(cth)],[gauss_array_0003]) ).
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_332,plain,
gt(n2,n0),
inference(clausify,[status(thm)],[gt_2_0]) ).
cnf(c_362,negated_conjecture,
leq(n2,pv1325),
inference(clausify,[status(thm)],[gauss_array_0003_neg]) ).
cnf(c_368,negated_conjecture,
~ leq(n0,pv1325),
inference(clausify,[status(thm)],[gauss_array_0003_neg]) ).
cnf(c_1284,plain,
leq(n0,n2),
inference(resolve,[status(thm)],[c_332,c_66]) ).
cnf(c_2561,plain,
( leq(A,pv1325)
| ~ leq(A,n2) ),
inference(resolve,[status(thm)],[c_362,c_65]) ).
cnf(c_14508,plain,
leq(n0,pv1325),
inference(resolve,[status(thm)],[c_2561,c_1284]) ).
cnf(c_14507,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_368,c_14508]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV133+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n015.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sat Sep 26 13:18:30 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.44 % Process 4160293 was started by sandbox on n015,
% 0.16/0.44 % Sat Sep 26 13:18:30 2026
% 0.16/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.27/0.56
% 0.27/0.56 % From the command line: assign(max_seconds, 300).
% 31.49/4.58
% 31.49/4.58 % given #500 (I,wt=128): 574 leq(n0,f19(A,B,C,D,E,F,V6,V7)) | leq(n0,f22(A,B,C,D,E,F,V6,V7)) | leq(f23(A,B,C,D,E,F,V6,V7),V6) | -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(164,d,g),unit_del(e,64),unit_del(f,64)].
% 31.49/4.58
% 31.49/4.58 % SZS status Theorem for theBenchmark
% 31.49/4.58
% 31.49/4.58 % Proof 1 at 3.32 (+ 0.63) seconds.
% 31.49/4.58 % Length of proof is 11.
% 31.49/4.58 % Level of proof is 3.
% 31.49/4.58 % Maximum clause weight is 14.000.
% 31.49/4.58 % Given clauses 912.
% 31.49/4.58
% 31.49/4.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------