%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV141+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 : 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 09:06:53 AM UTC 2026
% Result : Theorem 21.05s 3.10s
% Output : CNFRefutation 21.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 7 unt; 0 def)
% Number of atoms : 69 ( 2 equ)
% Maximal formula atoms : 27 ( 5 avg)
% Number of connectives : 74 ( 18 ~; 3 |; 26 &)
% ( 0 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 9 con; 0-1 aty)
% Number of variables : 5 ( 0 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(leq_succ_gt,axiom,
! [X,Y] :
( leq(succ(X),Y)
=> gt(Y,X) ),
file('theBenchmark.p',leq_succ_gt) ).
fof(gauss_array_0011,conjecture,
( ( ( gt(loopcounter,n0)
=> leq(s_worst7,n3) )
& ( gt(loopcounter,n0)
=> leq(s_sworst7,n3) )
& ( gt(loopcounter,n0)
=> leq(s_best7,n3) )
& ( gt(loopcounter,n0)
=> leq(n0,s_worst7) )
& ( gt(loopcounter,n0)
=> leq(n0,s_sworst7) )
& ( gt(loopcounter,n0)
=> leq(n0,s_best7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_worst7,n3) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_sworst7,n3) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_best7,n3) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_worst7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_sworst7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_best7) )
& leq(n1,loopcounter)
& leq(tptp_float_0_001,pv1341) )
=> leq(n0,s_worst7) ),
file('theBenchmark.p',gauss_array_0011) ).
fof(gauss_array_0011_neg,negated_conjecture,
~ ( ( ( gt(loopcounter,n0)
=> leq(s_worst7,n3) )
& ( gt(loopcounter,n0)
=> leq(s_sworst7,n3) )
& ( gt(loopcounter,n0)
=> leq(s_best7,n3) )
& ( gt(loopcounter,n0)
=> leq(n0,s_worst7) )
& ( gt(loopcounter,n0)
=> leq(n0,s_sworst7) )
& ( gt(loopcounter,n0)
=> leq(n0,s_best7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_worst7,n3) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_sworst7,n3) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_best7,n3) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_worst7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_sworst7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_best7) )
& leq(n1,loopcounter)
& leq(tptp_float_0_001,pv1341) )
=> leq(n0,s_worst7) ),
inference(assume_negation,[status(cth)],[gauss_array_0011]) ).
cnf(c_307,plain,
( gt(B,A)
| ~ leq(succ(A),B) ),
inference(clausify,[status(thm)],[leq_succ_gt]) ).
fof(successor_1,axiom,
succ(n0) = n1,
file('theBenchmark.p',successor_1) ).
cnf(c_353,plain,
succ(n0) = n1,
inference(clausify,[status(thm)],[successor_1]) ).
cnf(c_357,negated_conjecture,
leq(n1,loopcounter),
inference(clausify,[status(thm)],[gauss_array_0011_neg]) ).
cnf(c_360,negated_conjecture,
( leq(n0,s_worst7)
| ~ gt(loopcounter,n0) ),
inference(clausify,[status(thm)],[gauss_array_0011_neg]) ).
cnf(c_364,negated_conjecture,
~ leq(n0,s_worst7),
inference(clausify,[status(thm)],[gauss_array_0011_neg]) ).
cnf(c_827,negated_conjecture,
~ gt(loopcounter,n0),
inference(resolve,[status(thm)],[c_364,c_360]) ).
cnf(c_1798,plain,
( gt(A,n0)
| ~ leq(n1,A) ),
inference(paramod,[status(thm)],[c_353,c_307]) ).
cnf(c_11088,negated_conjecture,
gt(loopcounter,n0),
inference(resolve,[status(thm)],[c_1798,c_357]) ).
cnf(c_11087,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_827,c_11088]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV141+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n019.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 13:15:50 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 1403370 was started by sandbox on n019,
% 0.08/0.35 % Sat Sep 26 13:15:50 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.41
% 0.13/0.41 % From the command line: assign(max_seconds, 300).
% 21.05/3.10
% 21.05/3.10 % given #500 (I,wt=140): 578 leq(n0,f19(A,B,C,D,E,F,V6,V7)) | leq(f22(A,B,C,D,E,F,V6,V7),V6) | leq(n0,f23(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(168,d,g),unit_del(e,64),unit_del(f,64)].
% 21.05/3.10
% 21.05/3.10 % SZS status Theorem for theBenchmark
% 21.05/3.10
% 21.05/3.10 % Proof 1 at 2.22 (+ 0.43) seconds.
% 21.05/3.10 % Length of proof is 10.
% 21.05/3.10 % Level of proof is 3.
% 21.05/3.10 % Maximum clause weight is 17.000.
% 21.05/3.10 % Given clauses 886.
% 21.05/3.10
% 21.05/3.10 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------