%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV142+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 : n020.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 18.34s 3.09s
% Output : CNFRefutation 18.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 8 unt; 0 def)
% Number of atoms : 82 ( 5 equ)
% Maximal formula atoms : 27 ( 4 avg)
% Number of connectives : 86 ( 22 ~; 8 |; 28 &)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 9 con; 0-0 aty)
% Number of variables : 11 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(transitivity_gt,axiom,
! [X,Y,Z] :
( ( gt(Y,Z)
& gt(X,Y) )
=> gt(X,Z) ),
file('theBenchmark.p',transitivity_gt) ).
fof(leq_gt2,axiom,
! [X,Y] :
( ( X != Y
& leq(X,Y) )
=> gt(Y,X) ),
file('theBenchmark.p',leq_gt2) ).
fof(gauss_array_0012,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(s_best7,n3) ),
file('theBenchmark.p',gauss_array_0012) ).
fof(gauss_array_0012_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(s_best7,n3) ),
inference(assume_negation,[status(cth)],[gauss_array_0012]) ).
cnf(c_62,plain,
( gt(A,C)
| ~ gt(B,C)
| ~ gt(A,B) ),
inference(clausify,[status(thm)],[transitivity_gt]) ).
cnf(c_67,plain,
( gt(B,A)
| B = A
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[leq_gt2]) ).
fof(gt_1_0,axiom,
gt(n1,n0),
file('theBenchmark.p',gt_1_0) ).
cnf(c_331,plain,
gt(n1,n0),
inference(clausify,[status(thm)],[gt_1_0]) ).
cnf(c_359,negated_conjecture,
leq(n1,loopcounter),
inference(clausify,[status(thm)],[gauss_array_0012_neg]) ).
cnf(c_363,negated_conjecture,
( leq(s_best7,n3)
| ~ gt(loopcounter,n0) ),
inference(clausify,[status(thm)],[gauss_array_0012_neg]) ).
cnf(c_366,negated_conjecture,
~ leq(s_best7,n3),
inference(clausify,[status(thm)],[gauss_array_0012_neg]) ).
cnf(c_829,negated_conjecture,
~ gt(loopcounter,n0),
inference(resolve,[status(thm)],[c_366,c_363]) ).
cnf(c_1276,plain,
( gt(A,n0)
| ~ gt(A,n1) ),
inference(resolve,[status(thm)],[c_331,c_62]) ).
cnf(c_1606,plain,
( gt(loopcounter,n1)
| loopcounter = n1 ),
inference(resolve,[status(thm)],[c_359,c_67]) ).
cnf(c_7879,plain,
( gt(loopcounter,n0)
| loopcounter = n1 ),
inference(resolve,[status(thm)],[c_1606,c_1276]) ).
cnf(c_7754,negated_conjecture,
loopcounter = n1,
inference(resolve,[status(thm)],[c_829,c_7879]) ).
cnf(c_7880,negated_conjecture,
~ gt(n1,n0),
inference(paramod,[status(thm)],[c_7754,c_829]) ).
cnf(c_7878,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_331,c_7880]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV142+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n020.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 26 13:16:21 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.34 % Process 1665543 was started by sandbox on n020,
% 0.08/0.34 % Sat Sep 26 13:16:21 2026
% 0.08/0.34 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.40
% 0.11/0.40 % From the command line: assign(max_seconds, 300).
% 18.34/3.09
% 18.34/3.09 % given #500 (I,wt=140): 580 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)].
% 18.34/3.09
% 18.34/3.09 % SZS status Theorem for theBenchmark
% 18.34/3.09
% 18.34/3.09 % Proof 1 at 2.24 (+ 0.40) seconds.
% 18.34/3.09 % Length of proof is 14.
% 18.34/3.09 % Level of proof is 4.
% 18.34/3.09 % Maximum clause weight is 14.000.
% 18.34/3.09 % Given clauses 861.
% 18.34/3.09
% 18.34/3.09 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------