%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV182+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 09:06:58 AM UTC 2026
% Result : Theorem 22.89s 3.82s
% Output : CNFRefutation 22.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 10 unt; 0 def)
% Number of atoms : 162 ( 39 equ)
% Maximal formula atoms : 25 ( 6 avg)
% Number of connectives : 200 ( 63 ~; 58 |; 55 &)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 14 con; 0-3 aty)
% Number of variables : 45 ( 0 sgn 37 !; 1 ?)
% 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(cl5_nebula_init_0086,conjecture,
( ( ( gt(loopcounter,n0)
=> ! [F] :
( ( leq(F,n4)
& leq(n0,F) )
=> a_select2(sigma_init,F) = init ) )
& ( gt(loopcounter,n0)
=> ! [E] :
( ( leq(E,n4)
& leq(n0,E) )
=> a_select2(rho_init,E) = init ) )
& ( gt(loopcounter,n0)
=> ! [D] :
( ( leq(D,n4)
& leq(n0,D) )
=> a_select2(mu_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 ) )
& leq(n1,loopcounter)
& leq(tptp_float_0_001,pv76) )
=> ! [G] :
( ( leq(G,n4)
& leq(n0,G) )
=> a_select2(rho_init,G) = init ) ),
file('theBenchmark.p',cl5_nebula_init_0086) ).
fof(cl5_nebula_init_0086_neg,negated_conjecture,
~ ( ( ( gt(loopcounter,n0)
=> ! [F] :
( ( leq(F,n4)
& leq(n0,F) )
=> a_select2(sigma_init,F) = init ) )
& ( gt(loopcounter,n0)
=> ! [E] :
( ( leq(E,n4)
& leq(n0,E) )
=> a_select2(rho_init,E) = init ) )
& ( gt(loopcounter,n0)
=> ! [D] :
( ( leq(D,n4)
& leq(n0,D) )
=> a_select2(mu_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 ) )
& leq(n1,loopcounter)
& leq(tptp_float_0_001,pv76) )
=> ! [G] :
( ( leq(G,n4)
& leq(n0,G) )
=> a_select2(rho_init,G) = init ) ),
inference(assume_negation,[status(cth)],[cl5_nebula_init_0086]) ).
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_335,plain,
gt(n1,n0),
inference(clausify,[status(thm)],[gt_1_0]) ).
fof(nnf_56,plain,
( ? [G] :
( a_select2(rho_init,G) != init
& leq(G,n4)
& leq(n0,G) )
& ( ! [F] :
( a_select2(sigma_init,F) = init
| ~ leq(F,n4)
| ~ leq(n0,F) )
| ~ gt(loopcounter,n0) )
& ( ! [E] :
( a_select2(rho_init,E) = init
| ~ leq(E,n4)
| ~ leq(n0,E) )
| ~ gt(loopcounter,n0) )
& ( ! [D] :
( a_select2(mu_init,D) = init
| ~ leq(D,n4)
| ~ leq(n0,D) )
| ~ gt(loopcounter,n0) )
& ! [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) )
& leq(n1,loopcounter)
& leq(tptp_float_0_001,pv76) ),
inference(fof_nnf,[status(thm)],[cl5_nebula_init_0086_neg]) ).
fof(sk_cl5_nebula_init_0086_neg_sk,plain,
( a_select2(rho_init,sK0) != init
& leq(sK0,n4)
& leq(n0,sK0)
& ( ! [F] :
( a_select2(sigma_init,F) = init
| ~ leq(F,n4)
| ~ leq(n0,F) )
| ~ gt(loopcounter,n0) )
& ( ! [E] :
( a_select2(rho_init,E) = init
| ~ leq(E,n4)
| ~ leq(n0,E) )
| ~ gt(loopcounter,n0) )
& ( ! [D] :
( a_select2(mu_init,D) = init
| ~ leq(D,n4)
| ~ leq(n0,D) )
| ~ gt(loopcounter,n0) )
& ! [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) )
& leq(n1,loopcounter)
& leq(tptp_float_0_001,pv76) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(G,sK0)],[nnf_56]) ).
fof(sk_cl5_nebula_init_0086_neg,plain,
( a_select2(rho_init,sK0) != init
& leq(sK0,n4)
& leq(n0,sK0)
& ! [VAR_0] :
( a_select2(sigma_init,VAR_0) = init
| ~ leq(VAR_0,n4)
| ~ leq(n0,VAR_0)
| ~ gt(loopcounter,n0) )
& ! [VAR_0] :
( a_select2(rho_init,VAR_0) = init
| ~ leq(VAR_0,n4)
| ~ leq(n0,VAR_0)
| ~ gt(loopcounter,n0) )
& ! [VAR_0] :
( a_select2(mu_init,VAR_0) = init
| ~ leq(VAR_0,n4)
| ~ leq(n0,VAR_0)
| ~ gt(loopcounter,n0) )
& ! [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) )
& leq(n1,loopcounter)
& leq(tptp_float_0_001,pv76) ),
inference(cnf_transformation,[status(thm)],[sk_cl5_nebula_init_0086_neg_sk]) ).
cnf(c_366,negated_conjecture,
leq(n1,loopcounter),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0086_neg]) ).
cnf(c_370,negated_conjecture,
( a_select2(rho_init,A) = init
| ~ leq(A,n4)
| ~ leq(n0,A)
| ~ gt(loopcounter,n0) ),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0086_neg]) ).
cnf(c_372,negated_conjecture,
leq(n0,sK0),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0086_neg]) ).
cnf(c_373,negated_conjecture,
leq(sK0,n4),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0086_neg]) ).
cnf(c_374,negated_conjecture,
a_select2(rho_init,sK0) != init,
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0086_neg]) ).
cnf(c_1307,plain,
( gt(A,n0)
| ~ gt(A,n1) ),
inference(resolve,[status(thm)],[c_335,c_62]) ).
cnf(c_1649,plain,
( gt(loopcounter,n1)
| loopcounter = n1 ),
inference(resolve,[status(thm)],[c_366,c_67]) ).
cnf(c_10904,negated_conjecture,
( a_select2(rho_init,sK0) = init
| ~ leq(sK0,n4)
| ~ gt(loopcounter,n0) ),
inference(resolve,[status(thm)],[c_372,c_370]) ).
cnf(c_10905,negated_conjecture,
( a_select2(rho_init,sK0) = init
| ~ gt(loopcounter,n0) ),
inference(resolve,[status(thm)],[c_373,c_10904]) ).
cnf(c_1714,negated_conjecture,
~ gt(loopcounter,n0),
inference(resolve,[status(thm)],[c_374,c_10905]) ).
cnf(c_10906,plain,
( gt(loopcounter,n0)
| loopcounter = n1 ),
inference(resolve,[status(thm)],[c_1649,c_1307]) ).
cnf(c_10874,plain,
loopcounter = n1,
inference(resolve,[status(thm)],[c_1714,c_10906]) ).
cnf(c_10907,negated_conjecture,
~ gt(n1,n0),
inference(paramod,[status(thm)],[c_10874,c_1714]) ).
cnf(c_10903,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_335,c_10907]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV182+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 13:18:45 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 3418929 was started by sandbox2 on n010,
% 0.09/0.37 % Sat Sep 26 13:18:45 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.48
% 0.15/0.48 % From the command line: assign(max_seconds, 300).
% 22.89/3.82
% 22.89/3.82 % given #500 (I,wt=140): 574 leq(n0,f19(A,B,C,D,E,F,V6,V7)) | leq(f21(A,B,C,D,E,F,V6,V7),V6) | leq(f24(A,B,C,D,E,F,V6,V7),V6) | -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(161,d,g),unit_del(e,64),unit_del(f,64)].
% 22.89/3.82
% 22.89/3.82 % SZS status Theorem for theBenchmark
% 22.89/3.82
% 22.89/3.82 % Proof 1 at 2.75 (+ 0.47) seconds.
% 22.89/3.82 % Length of proof is 16.
% 22.89/3.82 % Level of proof is 4.
% 22.89/3.82 % Maximum clause weight is 24.000.
% 22.89/3.82 % Given clauses 905.
% 22.89/3.82
% 22.89/3.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------