%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV188+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 : n010.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 0.14s 10.82s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 13 unt; 0 def)
% Number of atoms : 161 ( 42 equ)
% Maximal formula atoms : 26 ( 6 avg)
% Number of connectives : 198 ( 63 ~; 57 |; 51 &)
% ( 1 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 15 con; 0-3 aty)
% Number of variables : 50 ( 0 sgn 43 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(irreflexivity_gt,axiom,
! [X] : ~ gt(X,X),
file('theBenchmark.p',irreflexivity_gt) ).
fof(leq_succ,axiom,
! [X,Y] :
( leq(X,Y)
=> leq(X,succ(Y)) ),
file('theBenchmark.p',leq_succ) ).
fof(leq_succ_gt_equiv,axiom,
! [X,Y] :
( leq(X,Y)
<=> gt(succ(Y),X) ),
file('theBenchmark.p',leq_succ_gt_equiv) ).
fof(finite_domain_0,axiom,
! [X] :
( ( leq(X,n0)
& leq(n0,X) )
=> X = n0 ),
file('theBenchmark.p',finite_domain_0) ).
fof(cl5_nebula_init_0116,conjecture,
( ( ( gt(loopcounter,n1)
=> ! [G] :
( ( leq(G,n4)
& leq(n0,G) )
=> a_select2(sigmaold_init,G) = init ) )
& ( gt(loopcounter,n1)
=> ! [F] :
( ( leq(F,n4)
& leq(n0,F) )
=> a_select2(rhoold_init,F) = init ) )
& ( gt(loopcounter,n1)
=> ! [E] :
( ( leq(E,n4)
& leq(n0,E) )
=> a_select2(muold_init,E) = init ) )
& ! [D] :
( ( leq(D,n4)
& leq(n0,D) )
=> a_select3(center_init,D,n0) = init )
& ! [C] :
( ( leq(C,n4)
& leq(n0,C) )
=> a_select2(rho_init,C) = init )
& ! [A] :
( ( leq(A,n135299)
& leq(n0,A) )
=> ! [B] :
( ( leq(B,n4)
& leq(n0,B) )
=> a_select3(q_init,A,B) = init ) ) )
=> ! [H] :
( ( leq(H,tptp_minus_1)
& leq(n0,H) )
=> a_select2(mu_init,H) = init ) ),
file('theBenchmark.p',cl5_nebula_init_0116) ).
fof(cl5_nebula_init_0116_neg,negated_conjecture,
~ ( ( ( gt(loopcounter,n1)
=> ! [G] :
( ( leq(G,n4)
& leq(n0,G) )
=> a_select2(sigmaold_init,G) = init ) )
& ( gt(loopcounter,n1)
=> ! [F] :
( ( leq(F,n4)
& leq(n0,F) )
=> a_select2(rhoold_init,F) = init ) )
& ( gt(loopcounter,n1)
=> ! [E] :
( ( leq(E,n4)
& leq(n0,E) )
=> a_select2(muold_init,E) = init ) )
& ! [D] :
( ( leq(D,n4)
& leq(n0,D) )
=> a_select3(center_init,D,n0) = init )
& ! [C] :
( ( leq(C,n4)
& leq(n0,C) )
=> a_select2(rho_init,C) = init )
& ! [A] :
( ( leq(A,n135299)
& leq(n0,A) )
=> ! [B] :
( ( leq(B,n4)
& leq(n0,B) )
=> a_select3(q_init,A,B) = init ) ) )
=> ! [H] :
( ( leq(H,tptp_minus_1)
& leq(n0,H) )
=> a_select2(mu_init,H) = init ) ),
inference(assume_negation,[status(cth)],[cl5_nebula_init_0116]) ).
cnf(c_63,plain,
~ gt(A,A),
inference(clausify,[status(thm)],[irreflexivity_gt]) ).
cnf(c_71,plain,
( leq(A,succ(B))
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[leq_succ]) ).
cnf(c_72,plain,
( gt(succ(B),A)
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[leq_succ_gt_equiv]) ).
fof(succ_tptp_minus_1,axiom,
succ(tptp_minus_1) = n0,
file('theBenchmark.p',succ_tptp_minus_1) ).
cnf(c_281,plain,
succ(tptp_minus_1) = n0,
inference(clausify,[status(thm)],[succ_tptp_minus_1]) ).
cnf(c_352,plain,
( n0 = A
| ~ leq(A,n0)
| ~ leq(n0,A) ),
inference(clausify,[status(thm)],[finite_domain_0]) ).
fof(nnf_56,plain,
( ? [H] :
( a_select2(mu_init,H) != init
& leq(H,tptp_minus_1)
& leq(n0,H) )
& ( ! [G] :
( a_select2(sigmaold_init,G) = init
| ~ leq(G,n4)
| ~ leq(n0,G) )
| ~ gt(loopcounter,n1) )
& ( ! [F] :
( a_select2(rhoold_init,F) = init
| ~ leq(F,n4)
| ~ leq(n0,F) )
| ~ gt(loopcounter,n1) )
& ( ! [E] :
( a_select2(muold_init,E) = init
| ~ leq(E,n4)
| ~ leq(n0,E) )
| ~ gt(loopcounter,n1) )
& ! [D] :
( a_select3(center_init,D,n0) = init
| ~ leq(D,n4)
| ~ leq(n0,D) )
& ! [C] :
( a_select2(rho_init,C) = 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) ) ),
inference(fof_nnf,[status(thm)],[cl5_nebula_init_0116_neg]) ).
fof(sk_cl5_nebula_init_0116_neg_sk,plain,
( a_select2(mu_init,sK0) != init
& leq(sK0,tptp_minus_1)
& leq(n0,sK0)
& ( ! [G] :
( a_select2(sigmaold_init,G) = init
| ~ leq(G,n4)
| ~ leq(n0,G) )
| ~ gt(loopcounter,n1) )
& ( ! [F] :
( a_select2(rhoold_init,F) = init
| ~ leq(F,n4)
| ~ leq(n0,F) )
| ~ gt(loopcounter,n1) )
& ( ! [E] :
( a_select2(muold_init,E) = init
| ~ leq(E,n4)
| ~ leq(n0,E) )
| ~ gt(loopcounter,n1) )
& ! [D] :
( a_select3(center_init,D,n0) = init
| ~ leq(D,n4)
| ~ leq(n0,D) )
& ! [C] :
( a_select2(rho_init,C) = 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) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(H,sK0)],[nnf_56]) ).
fof(sk_cl5_nebula_init_0116_neg,plain,
( a_select2(mu_init,sK0) != init
& leq(sK0,tptp_minus_1)
& 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] :
( a_select2(rho_init,VAR_0) = 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) ) ),
inference(cnf_transformation,[status(thm)],[sk_cl5_nebula_init_0116_neg_sk]) ).
cnf(c_371,negated_conjecture,
leq(n0,sK0),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0116_neg]) ).
cnf(c_372,negated_conjecture,
leq(sK0,tptp_minus_1),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0116_neg]) ).
cnf(c_2054,negated_conjecture,
( n0 = sK0
| ~ leq(sK0,n0) ),
inference(resolve,[status(thm)],[c_371,c_352]) ).
cnf(c_1397,negated_conjecture,
( sK0 = n0
| ~ leq(sK0,n0) ),
inference(copy,[status(thm)],[c_2054]) ).
cnf(c_2055,negated_conjecture,
gt(succ(tptp_minus_1),sK0),
inference(resolve,[status(thm)],[c_372,c_72]) ).
cnf(c_1871,negated_conjecture,
gt(n0,sK0),
inference(paramod,[status(thm)],[c_281,c_2055]) ).
cnf(c_2056,negated_conjecture,
leq(sK0,succ(tptp_minus_1)),
inference(resolve,[status(thm)],[c_372,c_71]) ).
cnf(c_1872,negated_conjecture,
leq(sK0,n0),
inference(paramod,[status(thm)],[c_281,c_2056]) ).
cnf(c_2013,negated_conjecture,
sK0 = n0,
inference(resolve,[status(thm)],[c_1872,c_1397]) ).
cnf(c_2057,negated_conjecture,
gt(n0,n0),
inference(paramod,[status(thm)],[c_2013,c_1871]) ).
cnf(c_2053,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_63,c_2057]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV188+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/10.37 % Computer : n010.cluster.edu
% 0.12/10.37 % Model : x86_64 x86_64
% 0.12/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.37 % Memory : 8046.5625MB
% 0.12/10.37 % OS : Linux 6.8.0-71-generic
% 0.12/10.37 % CPULimit : 300
% 0.12/10.37 % WCLimit : 300
% 0.12/10.37 % DateTime : Sat Sep 26 13:19:16 UTC 2026
% 0.12/10.38 % CPUTime :
% 0.12/10.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/10.38 % Process 3419878 was started by sandbox on n010,
% 0.12/10.38 % Sat Sep 26 13:19:16 2026
% 0.12/10.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/10.41
% 0.14/10.41 % From the command line: assign(max_seconds, 300).
% 0.14/10.82
% 0.14/10.82 % SZS status Theorem for theBenchmark
% 0.14/10.82
% 0.14/10.82 % Proof 1 at 0.33 (+ 0.04) seconds.
% 0.14/10.82 % Length of proof is 17.
% 0.14/10.82 % Level of proof is 4.
% 0.14/10.82 % Maximum clause weight is 17.000.
% 0.14/10.82 % Given clauses 298.
% 0.14/10.82
% 0.14/10.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------