%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV181+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 : n019.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 27.45s 3.97s
% Output : CNFRefutation 27.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 12 unt; 0 def)
% Number of atoms : 90 ( 19 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 76 ( 12 ~; 9 |; 29 &)
% ( 1 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 14 con; 0-3 aty)
% Number of variables : 32 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(irreflexivity_gt,axiom,
! [X] : ~ gt(X,X),
file('theBenchmark.p',irreflexivity_gt) ).
fof(leq_gt1,axiom,
! [X,Y] :
( gt(Y,X)
=> leq(X,Y) ),
file('theBenchmark.p',leq_gt1) ).
fof(leq_succ_gt_equiv,axiom,
! [X,Y] :
( leq(X,Y)
<=> gt(succ(Y),X) ),
file('theBenchmark.p',leq_succ_gt_equiv) ).
fof(leq_succ_gt,axiom,
! [X,Y] :
( leq(succ(X),Y)
=> gt(Y,X) ),
file('theBenchmark.p',leq_succ_gt) ).
fof(finite_domain_0,axiom,
! [X] :
( ( leq(X,n0)
& leq(n0,X) )
=> X = n0 ),
file('theBenchmark.p',finite_domain_0) ).
fof(cl5_nebula_init_0081,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 ) )
& gt(n1,loopcounter)
& leq(n1,loopcounter)
& leq(tptp_float_0_001,pv76) )
=> ! [G] :
( ( leq(G,n4)
& leq(n0,G) )
=> a_select2(muold_init,G) = init ) ),
file('theBenchmark.p',cl5_nebula_init_0081) ).
fof(cl5_nebula_init_0081_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 ) )
& gt(n1,loopcounter)
& leq(n1,loopcounter)
& leq(tptp_float_0_001,pv76) )
=> ! [G] :
( ( leq(G,n4)
& leq(n0,G) )
=> a_select2(muold_init,G) = init ) ),
inference(assume_negation,[status(cth)],[cl5_nebula_init_0081]) ).
cnf(c_63,plain,
~ gt(A,A),
inference(clausify,[status(thm)],[irreflexivity_gt]) ).
cnf(c_66,plain,
( leq(B,A)
| ~ gt(A,B) ),
inference(clausify,[status(thm)],[leq_gt1]) ).
cnf(c_73,plain,
( ~ gt(succ(B),A)
| leq(A,B) ),
inference(clausify,[status(thm)],[leq_succ_gt_equiv]) ).
cnf(c_307,plain,
( gt(B,A)
| ~ leq(succ(A),B) ),
inference(clausify,[status(thm)],[leq_succ_gt]) ).
cnf(c_354,plain,
( n0 = A
| ~ leq(A,n0)
| ~ leq(n0,A) ),
inference(clausify,[status(thm)],[finite_domain_0]) ).
fof(successor_1,axiom,
succ(n0) = n1,
file('theBenchmark.p',successor_1) ).
cnf(c_360,plain,
succ(n0) = n1,
inference(clausify,[status(thm)],[successor_1]) ).
cnf(c_364,negated_conjecture,
leq(n1,loopcounter),
inference(clausify,[status(thm)],[cl5_nebula_init_0081_neg]) ).
cnf(c_365,negated_conjecture,
gt(n1,loopcounter),
inference(clausify,[status(thm)],[cl5_nebula_init_0081_neg]) ).
cnf(c_1830,plain,
( ~ gt(n1,A)
| leq(A,n0) ),
inference(paramod,[status(thm)],[c_360,c_73]) ).
cnf(c_1844,plain,
( gt(A,n0)
| ~ leq(n1,A) ),
inference(paramod,[status(thm)],[c_360,c_307]) ).
cnf(c_16753,plain,
leq(loopcounter,n0),
inference(resolve,[status(thm)],[c_1830,c_365]) ).
cnf(c_17938,plain,
( n0 = loopcounter
| ~ leq(n0,loopcounter) ),
inference(resolve,[status(thm)],[c_16753,c_354]) ).
cnf(c_17025,plain,
( loopcounter = n0
| ~ leq(n0,loopcounter) ),
inference(copy,[status(thm)],[c_17938]) ).
cnf(c_17060,plain,
gt(loopcounter,n0),
inference(resolve,[status(thm)],[c_1844,c_364]) ).
cnf(c_17069,plain,
leq(n0,loopcounter),
inference(resolve,[status(thm)],[c_17060,c_66]) ).
cnf(c_17091,plain,
loopcounter = n0,
inference(resolve,[status(thm)],[c_17069,c_17025]) ).
cnf(c_17939,plain,
gt(n0,n0),
inference(paramod,[status(thm)],[c_17091,c_17060]) ).
cnf(c_17937,plain,
$false,
inference(resolve,[status(thm)],[c_63,c_17939]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV181+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 : n019.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 13:18:48 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1408165 was started by sandbox2 on n019,
% 0.09/0.36 % Sat Sep 26 13:18:48 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.42
% 0.13/0.42 % From the command line: assign(max_seconds, 300).
% 27.45/3.97
% 27.45/3.97 % given #500 (I,wt=131): 572 leq(n0,f19(A,B,C,D,E,F,n0,V6)) | leq(f21(A,B,C,D,E,F,n0,V6),n0) | leq(f24(A,B,C,D,E,F,n0,V6),n0) | -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(161,d,e),flip(g),unit_del(d,64)].
% 27.45/3.97
% 27.45/3.97 % SZS status Theorem for theBenchmark
% 27.45/3.97
% 27.45/3.97 % Proof 1 at 2.86 (+ 0.56) seconds.
% 27.45/3.97 % Length of proof is 22.
% 27.45/3.97 % Level of proof is 6.
% 27.45/3.97 % Maximum clause weight is 17.000.
% 27.45/3.97 % Given clauses 941.
% 27.45/3.97
% 27.45/3.97 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------