%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV161+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 09:06:56 AM UTC 2026
% Result : Theorem 24.97s 8.08s
% Output : CNFRefutation 24.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 8 unt; 0 def)
% Number of atoms : 65 ( 23 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 60 ( 16 ~; 13 |; 23 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 16 ( 0 sgn 10 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(leq_gt2,axiom,
! [X,Y] :
( ( X != Y
& leq(X,Y) )
=> gt(Y,X) ),
file('theBenchmark.p',leq_gt2) ).
fof(leq_gt_pred,axiom,
! [X,Y] :
( leq(X,pred(Y))
<=> gt(Y,X) ),
file('theBenchmark.p',leq_gt_pred) ).
fof(cl5_nebula_norm_0011,conjecture,
( ( ! [A] :
( ( leq(A,pred(pv10))
& leq(n0,A) )
=> sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1 )
& leq(pv10,n135299)
& leq(n0,pv10)
& sum(n0,n4,a_select3(q,pv10,tptp_sum_index)) = n1 )
=> ! [B] :
( ( leq(B,pv10)
& leq(n0,B) )
=> sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 ) ),
file('theBenchmark.p',cl5_nebula_norm_0011) ).
fof(cl5_nebula_norm_0011_neg,negated_conjecture,
~ ( ( ! [A] :
( ( leq(A,pred(pv10))
& leq(n0,A) )
=> sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1 )
& leq(pv10,n135299)
& leq(n0,pv10)
& sum(n0,n4,a_select3(q,pv10,tptp_sum_index)) = n1 )
=> ! [B] :
( ( leq(B,pv10)
& leq(n0,B) )
=> sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 ) ),
inference(assume_negation,[status(cth)],[cl5_nebula_norm_0011]) ).
cnf(c_67,plain,
( gt(B,A)
| B = A
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[leq_gt2]) ).
cnf(c_69,plain,
( ~ gt(B,A)
| leq(A,pred(B)) ),
inference(clausify,[status(thm)],[leq_gt_pred]) ).
fof(nnf_56,plain,
( ? [B] :
( sum(n0,n4,a_select3(q,B,tptp_sum_index)) != n1
& leq(B,pv10)
& leq(n0,B) )
& ! [A] :
( sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1
| ~ leq(A,pred(pv10))
| ~ leq(n0,A) )
& leq(pv10,n135299)
& leq(n0,pv10)
& sum(n0,n4,a_select3(q,pv10,tptp_sum_index)) = n1 ),
inference(fof_nnf,[status(thm)],[cl5_nebula_norm_0011_neg]) ).
fof(sk_cl5_nebula_norm_0011_neg,plain,
( sum(n0,n4,a_select3(q,sK0,tptp_sum_index)) != n1
& leq(sK0,pv10)
& leq(n0,sK0)
& ! [A] :
( sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1
| ~ leq(A,pred(pv10))
| ~ leq(n0,A) )
& leq(pv10,n135299)
& leq(n0,pv10)
& sum(n0,n4,a_select3(q,pv10,tptp_sum_index)) = n1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(B,sK0)],[nnf_56]) ).
cnf(c_363,negated_conjecture,
sum(n0,n4,a_select3(q,pv10,tptp_sum_index)) = n1,
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_norm_0011_neg]) ).
cnf(c_366,negated_conjecture,
( sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1
| ~ leq(A,pred(pv10))
| ~ leq(n0,A) ),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_norm_0011_neg]) ).
cnf(c_367,negated_conjecture,
leq(n0,sK0),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_norm_0011_neg]) ).
cnf(c_368,negated_conjecture,
leq(sK0,pv10),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_norm_0011_neg]) ).
cnf(c_369,negated_conjecture,
sum(n0,n4,a_select3(q,sK0,tptp_sum_index)) != n1,
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_norm_0011_neg]) ).
cnf(c_14756,negated_conjecture,
( sum(n0,n4,a_select3(q,sK0,tptp_sum_index)) = n1
| ~ leq(sK0,pred(pv10)) ),
inference(resolve,[status(thm)],[c_367,c_366]) ).
cnf(c_2439,negated_conjecture,
~ leq(sK0,pred(pv10)),
inference(resolve,[status(thm)],[c_369,c_14756]) ).
cnf(c_14757,negated_conjecture,
( gt(pv10,sK0)
| pv10 = sK0 ),
inference(resolve,[status(thm)],[c_368,c_67]) ).
cnf(c_2919,negated_conjecture,
( gt(pv10,sK0)
| sK0 = pv10 ),
inference(copy,[status(thm)],[c_14757]) ).
cnf(c_14758,plain,
( leq(sK0,pred(pv10))
| sK0 = pv10 ),
inference(resolve,[status(thm)],[c_2919,c_69]) ).
cnf(c_14752,plain,
sK0 = pv10,
inference(resolve,[status(thm)],[c_2439,c_14758]) ).
cnf(c_14759,plain,
sum(n0,n4,a_select3(q,pv10,tptp_sum_index)) != n1,
inference(paramod,[status(thm)],[c_14752,c_369]) ).
cnf(c_14755,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_363,c_14759]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV161+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n020.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 13:18:04 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1669259 was started by sandbox on n020,
% 0.09/0.37 % Sat Sep 26 13:18:04 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.40
% 0.15/0.40 % From the command line: assign(max_seconds, 300).
% 24.97/8.08
% 24.97/8.08 % given #500 (I,wt=143): 572 leq(n0,f19(A,B,C,D,E,F,n0,V6)) | leq(n0,f22(A,B,C,D,E,F,n0,V6)) | leq(n0,f23(A,B,C,D,E,F,n0,V6)) | -leq(n0,V7) | -leq(V7,n0) | 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,V7) = 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)))),V7,n0). [factor(163,d,e),flip(g),unit_del(d,64)].
% 24.97/8.08
% 24.97/8.08 % SZS status Theorem for theBenchmark
% 24.97/8.08
% 24.97/8.08 % Proof 1 at 2.96 (+ 0.53) seconds.
% 24.97/8.08 % Length of proof is 14.
% 24.97/8.08 % Level of proof is 4.
% 24.97/8.08 % Maximum clause weight is 31.000.
% 24.97/8.08 % Given clauses 955.
% 24.97/8.08
% 24.97/8.08 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------