%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV174+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 09:06:57 AM UTC 2026
% Result : Theorem 225.96s 35.23s
% Output : CNFRefutation 225.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 11 unt; 0 def)
% Number of atoms : 116 ( 25 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 131 ( 39 ~; 34 |; 45 &)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-3 aty)
% Number of variables : 36 ( 0 sgn 22 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(leq_gt_pred,axiom,
! [X,Y] :
( leq(X,pred(Y))
<=> gt(Y,X) ),
file('theBenchmark.p',leq_gt_pred) ).
fof(pred_minus_1,axiom,
! [X] : minus(X,n1) = pred(X),
file('theBenchmark.p',pred_minus_1) ).
fof(cl5_nebula_init_0046,conjecture,
( ( ! [C] :
( ( leq(C,n4)
& leq(n0,C) )
=> a_select3(center_init,C,n0) = init )
& ! [A] :
( ( leq(A,pred(pv10))
& leq(n0,A) )
=> ! [B] :
( ( leq(B,n4)
& leq(n0,B) )
=> a_select3(q_init,A,B) = init ) )
& leq(pv10,n135299)
& leq(n0,pv10) )
=> ! [D,E] :
( ( leq(E,n4)
& leq(D,n135299)
& leq(n0,E)
& leq(n0,D) )
=> ( gt(pv10,D)
=> a_select3(q_init,D,E) = init ) ) ),
file('theBenchmark.p',cl5_nebula_init_0046) ).
fof(cl5_nebula_init_0046_neg,negated_conjecture,
~ ( ( ! [C] :
( ( leq(C,n4)
& leq(n0,C) )
=> a_select3(center_init,C,n0) = init )
& ! [A] :
( ( leq(A,pred(pv10))
& leq(n0,A) )
=> ! [B] :
( ( leq(B,n4)
& leq(n0,B) )
=> a_select3(q_init,A,B) = init ) )
& leq(pv10,n135299)
& leq(n0,pv10) )
=> ! [D,E] :
( ( leq(E,n4)
& leq(D,n135299)
& leq(n0,E)
& leq(n0,D) )
=> ( gt(pv10,D)
=> a_select3(q_init,D,E) = init ) ) ),
inference(assume_negation,[status(cth)],[cl5_nebula_init_0046]) ).
cnf(c_69,plain,
( ~ gt(B,A)
| leq(A,pred(B)) ),
inference(clausify,[status(thm)],[leq_gt_pred]) ).
cnf(c_302,plain,
minus(A,n1) = pred(A),
inference(clausify,[status(thm)],[pred_minus_1]) ).
cnf(c_303,plain,
pred(A) = minus(A,n1),
inference(copy,[status(thm)],[c_302]) ).
fof(nnf_56,plain,
( ? [D,E] :
( a_select3(q_init,D,E) != init
& gt(pv10,D)
& leq(E,n4)
& leq(D,n135299)
& leq(n0,E)
& leq(n0,D) )
& ! [C] :
( a_select3(center_init,C,n0) = init
| ~ leq(C,n4)
| ~ leq(n0,C) )
& ! [A] :
( ! [B] :
( a_select3(q_init,A,B) = init
| ~ leq(B,n4)
| ~ leq(n0,B) )
| ~ leq(A,pred(pv10))
| ~ leq(n0,A) )
& leq(pv10,n135299)
& leq(n0,pv10) ),
inference(fof_nnf,[status(thm)],[cl5_nebula_init_0046_neg]) ).
fof(sk_cl5_nebula_init_0046_neg_sk,plain,
( a_select3(q_init,sK0,sK1) != init
& gt(pv10,sK0)
& leq(sK1,n4)
& leq(sK0,n135299)
& leq(n0,sK1)
& leq(n0,sK0)
& ! [C] :
( a_select3(center_init,C,n0) = init
| ~ leq(C,n4)
| ~ leq(n0,C) )
& ! [A] :
( ! [B] :
( a_select3(q_init,A,B) = init
| ~ leq(B,n4)
| ~ leq(n0,B) )
| ~ leq(A,pred(pv10))
| ~ leq(n0,A) )
& leq(pv10,n135299)
& leq(n0,pv10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(D,sK0),skolemize(E,sK1)],[nnf_56]) ).
fof(sk_cl5_nebula_init_0046_neg,plain,
( a_select3(q_init,sK0,sK1) != init
& gt(pv10,sK0)
& leq(sK1,n4)
& leq(sK0,n135299)
& leq(n0,sK1)
& leq(n0,sK0)
& ! [VAR_0] :
( a_select3(center_init,VAR_0,n0) = init
| ~ leq(VAR_0,n4)
| ~ leq(n0,VAR_0) )
& ! [VAR_0,VAR_1] :
( a_select3(q_init,VAR_0,VAR_1) = init
| ~ leq(VAR_1,n4)
| ~ leq(n0,VAR_1)
| ~ leq(VAR_0,pred(pv10))
| ~ leq(n0,VAR_0) )
& leq(pv10,n135299)
& leq(n0,pv10) ),
inference(cnf_transformation,[status(thm)],[sk_cl5_nebula_init_0046_neg_sk]) ).
cnf(c_376,negated_conjecture,
( a_select3(q_init,A,B) = init
| ~ leq(B,n4)
| ~ leq(n0,B)
| ~ leq(A,pred(pv10))
| ~ leq(n0,A) ),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0046_neg]) ).
cnf(c_377,negated_conjecture,
( a_select3(q_init,A,B) = init
| ~ leq(B,n4)
| ~ leq(n0,B)
| ~ leq(A,minus(pv10,n1))
| ~ leq(n0,A) ),
inference(paramod,[status(thm)],[c_303,c_376]) ).
cnf(c_379,negated_conjecture,
leq(n0,sK0),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0046_neg]) ).
cnf(c_380,negated_conjecture,
leq(n0,sK1),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0046_neg]) ).
cnf(c_382,negated_conjecture,
leq(sK1,n4),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0046_neg]) ).
cnf(c_383,negated_conjecture,
gt(pv10,sK0),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0046_neg]) ).
cnf(c_384,negated_conjecture,
a_select3(q_init,sK0,sK1) != init,
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0046_neg]) ).
cnf(c_822,plain,
( ~ gt(B,A)
| leq(A,minus(B,n1)) ),
inference(paramod,[status(thm)],[c_303,c_69]) ).
cnf(c_3356,negated_conjecture,
( a_select3(q_init,A,sK1) = init
| ~ leq(sK1,n4)
| ~ leq(A,minus(pv10,n1))
| ~ leq(n0,A) ),
inference(resolve,[status(thm)],[c_380,c_377]) ).
cnf(c_1064,negated_conjecture,
( a_select3(q_init,A,sK1) = init
| ~ leq(A,minus(pv10,n1))
| ~ leq(n0,A) ),
inference(resolve,[status(thm)],[c_382,c_3356]) ).
cnf(c_1112,plain,
leq(sK0,minus(pv10,n1)),
inference(resolve,[status(thm)],[c_822,c_383]) ).
cnf(c_3357,negated_conjecture,
( a_select3(q_init,sK0,sK1) = init
| ~ leq(sK0,minus(pv10,n1)) ),
inference(resolve,[status(thm)],[c_1064,c_379]) ).
cnf(c_3358,negated_conjecture,
a_select3(q_init,sK0,sK1) = init,
inference(resolve,[status(thm)],[c_1112,c_3357]) ).
cnf(c_3355,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_384,c_3358]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV174+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.37 % Computer : n015.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Sat Sep 26 13:21:20 UTC 2026
% 0.11/5.37 % CPUTime :
% 0.11/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.38 % Process 4169862 was started by sandbox on n015,
% 0.11/5.38 % Sat Sep 26 13:21:20 2026
% 0.11/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/5.44
% 0.14/5.44 % From the command line: assign(max_seconds, 300).
% 225.96/35.23
% 225.96/35.23 % given #500 (I,wt=140): 592 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)].
% 225.96/35.23
% 225.96/35.23 % given #1000 (T,wt=11): 1365 -leq(n135299,A) | leq(n2,A). [resolve(998,a,65,a)].
% 225.96/35.23
% 225.96/35.23 % SZS status Theorem for theBenchmark
% 225.96/35.23
% 225.96/35.23 % Proof 1 at 4.15 (+ 1.24) seconds.
% 225.96/35.23 % Length of proof is 17.
% 225.96/35.23 % Level of proof is 5.
% 225.96/35.23 % Maximum clause weight is 30.000.
% 225.96/35.23 % Given clauses 1264.
% 225.96/35.23
% 225.96/35.23 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------