%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV187+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 : n012.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 09:06:59 AM UTC 2026
% Result : Theorem 2.10s 0.64s
% Output : CNFRefutation 2.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 6 unt; 0 def)
% Number of atoms : 135 ( 35 equ)
% Maximal formula atoms : 24 ( 9 avg)
% Number of connectives : 177 ( 56 ~; 51 |; 48 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-3 aty)
% Number of variables : 35 ( 0 sgn 32 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cl5_nebula_init_0111,conjecture,
( ( ( gt(loopcounter,n1)
=> ! [F] :
( ( leq(F,n4)
& leq(n0,F) )
=> a_select2(sigmaold_init,F) = init ) )
& ( gt(loopcounter,n1)
=> ! [E] :
( ( leq(E,n4)
& leq(n0,E) )
=> a_select2(rhoold_init,E) = init ) )
& ( gt(loopcounter,n1)
=> ! [D] :
( ( leq(D,n4)
& leq(n0,D) )
=> a_select2(muold_init,D) = init ) )
& ! [C] :
( ( leq(C,n4)
& leq(n0,C) )
=> a_select3(center_init,C,n0) = init )
& ! [A] :
( ( leq(A,n135299)
& leq(n0,A) )
=> ! [B] :
( ( leq(B,n4)
& leq(n0,B) )
=> a_select3(q_init,A,B) = init ) )
& gt(loopcounter,n1) )
=> ! [G] :
( ( leq(G,n4)
& leq(n0,G) )
=> a_select2(sigmaold_init,G) = init ) ),
file('theBenchmark.p',cl5_nebula_init_0111) ).
fof(cl5_nebula_init_0111_neg,negated_conjecture,
~ ( ( ( gt(loopcounter,n1)
=> ! [F] :
( ( leq(F,n4)
& leq(n0,F) )
=> a_select2(sigmaold_init,F) = init ) )
& ( gt(loopcounter,n1)
=> ! [E] :
( ( leq(E,n4)
& leq(n0,E) )
=> a_select2(rhoold_init,E) = init ) )
& ( gt(loopcounter,n1)
=> ! [D] :
( ( leq(D,n4)
& leq(n0,D) )
=> a_select2(muold_init,D) = init ) )
& ! [C] :
( ( leq(C,n4)
& leq(n0,C) )
=> a_select3(center_init,C,n0) = init )
& ! [A] :
( ( leq(A,n135299)
& leq(n0,A) )
=> ! [B] :
( ( leq(B,n4)
& leq(n0,B) )
=> a_select3(q_init,A,B) = init ) )
& gt(loopcounter,n1) )
=> ! [G] :
( ( leq(G,n4)
& leq(n0,G) )
=> a_select2(sigmaold_init,G) = init ) ),
inference(assume_negation,[status(cth)],[cl5_nebula_init_0111]) ).
fof(nnf_56,plain,
( ? [G] :
( a_select2(sigmaold_init,G) != init
& leq(G,n4)
& leq(n0,G) )
& ( ! [F] :
( a_select2(sigmaold_init,F) = init
| ~ leq(F,n4)
| ~ leq(n0,F) )
| ~ gt(loopcounter,n1) )
& ( ! [E] :
( a_select2(rhoold_init,E) = init
| ~ leq(E,n4)
| ~ leq(n0,E) )
| ~ gt(loopcounter,n1) )
& ( ! [D] :
( a_select2(muold_init,D) = init
| ~ leq(D,n4)
| ~ leq(n0,D) )
| ~ gt(loopcounter,n1) )
& ! [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,n135299)
| ~ leq(n0,A) )
& gt(loopcounter,n1) ),
inference(fof_nnf,[status(thm)],[cl5_nebula_init_0111_neg]) ).
fof(sk_cl5_nebula_init_0111_neg_sk,plain,
( a_select2(sigmaold_init,sK0) != init
& leq(sK0,n4)
& leq(n0,sK0)
& ( ! [F] :
( a_select2(sigmaold_init,F) = init
| ~ leq(F,n4)
| ~ leq(n0,F) )
| ~ gt(loopcounter,n1) )
& ( ! [E] :
( a_select2(rhoold_init,E) = init
| ~ leq(E,n4)
| ~ leq(n0,E) )
| ~ gt(loopcounter,n1) )
& ( ! [D] :
( a_select2(muold_init,D) = init
| ~ leq(D,n4)
| ~ leq(n0,D) )
| ~ gt(loopcounter,n1) )
& ! [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,n135299)
| ~ leq(n0,A) )
& gt(loopcounter,n1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(G,sK0)],[nnf_56]) ).
fof(sk_cl5_nebula_init_0111_neg,plain,
( a_select2(sigmaold_init,sK0) != init
& leq(sK0,n4)
& leq(n0,sK0)
& ! [VAR_0] :
( a_select2(sigmaold_init,VAR_0) = init
| ~ leq(VAR_0,n4)
| ~ leq(n0,VAR_0)
| ~ gt(loopcounter,n1) )
& ! [VAR_0] :
( a_select2(rhoold_init,VAR_0) = init
| ~ leq(VAR_0,n4)
| ~ leq(n0,VAR_0)
| ~ gt(loopcounter,n1) )
& ! [VAR_0] :
( a_select2(muold_init,VAR_0) = init
| ~ leq(VAR_0,n4)
| ~ leq(n0,VAR_0)
| ~ gt(loopcounter,n1) )
& ! [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,n135299)
| ~ leq(n0,VAR_0) )
& gt(loopcounter,n1) ),
inference(cnf_transformation,[status(thm)],[sk_cl5_nebula_init_0111_neg_sk]) ).
cnf(c_363,negated_conjecture,
gt(loopcounter,n1),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0111_neg]) ).
cnf(c_370,negated_conjecture,
( a_select2(sigmaold_init,A) = init
| ~ leq(A,n4)
| ~ leq(n0,A)
| ~ gt(loopcounter,n1) ),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0111_neg]) ).
cnf(c_371,negated_conjecture,
( a_select2(sigmaold_init,A) = init
| ~ leq(A,n4)
| ~ leq(n0,A) ),
inference(resolve,[status(thm)],[c_363,c_370]) ).
cnf(c_372,negated_conjecture,
leq(n0,sK0),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0111_neg]) ).
cnf(c_373,negated_conjecture,
leq(sK0,n4),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0111_neg]) ).
cnf(c_374,negated_conjecture,
a_select2(sigmaold_init,sK0) != init,
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0111_neg]) ).
cnf(c_1867,negated_conjecture,
( a_select2(sigmaold_init,sK0) = init
| ~ leq(sK0,n4) ),
inference(resolve,[status(thm)],[c_372,c_371]) ).
cnf(c_1868,negated_conjecture,
a_select2(sigmaold_init,sK0) = init,
inference(resolve,[status(thm)],[c_373,c_1867]) ).
cnf(c_1866,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_374,c_1868]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWV187+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/0.29 % Computer : n012.cluster.edu
% 0.05/0.29 % Model : x86_64 x86_64
% 0.05/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.29 % Memory : 8046.5625MB
% 0.05/0.29 % OS : Linux 6.8.0-71-generic
% 0.05/0.29 % CPULimit : 300
% 0.05/0.29 % WCLimit : 300
% 0.05/0.29 % DateTime : Sat Sep 26 13:18:04 UTC 2026
% 0.05/0.30 % CPUTime :
% 0.05/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.05/0.30 % Process 696173 was started by sandbox on n012,
% 0.05/0.30 % Sat Sep 26 13:18:04 2026
% 0.05/0.30 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.32
% 0.09/0.32 % From the command line: assign(max_seconds, 300).
% 2.10/0.64
% 2.10/0.64 % SZS status Theorem for theBenchmark
% 2.10/0.64
% 2.10/0.64 % Proof 1 at 0.26 (+ 0.04) seconds.
% 2.10/0.64 % Length of proof is 8.
% 2.10/0.64 % Level of proof is 3.
% 2.10/0.64 % Maximum clause weight is 21.000.
% 2.10/0.64 % Given clauses 297.
% 2.10/0.64
% 2.10/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------