%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV191+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 : n007.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 09:07:00 AM UTC 2026
% Result : Theorem 7.57s 1.47s
% Output : CNFRefutation 7.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 13 unt; 0 def)
% Number of atoms : 159 ( 119 equ)
% Maximal formula atoms : 32 ( 6 avg)
% Number of connectives : 145 ( 11 ~; 6 |; 121 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 17 con; 0-3 aty)
% Number of variables : 18 ( 0 sgn 10 !; 2 ?)
% 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(quaternion_ds1_inuse_0002,conjecture,
( ( a_select2(xinit_noise_defuse,n5) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n3) = use
& a_select3(u_defuse,n2,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n0,n0) = use
& a_select2(sigma_defuse,n5) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(rho_defuse,n2) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n0) = use )
=> ! [A,B] :
( ( leq(B,tptp_minus_1)
& leq(A,n2)
& leq(n0,B)
& leq(n0,A) )
=> a_select3(z_defuse,A,B) = use ) ),
file('theBenchmark.p',quaternion_ds1_inuse_0002) ).
fof(quaternion_ds1_inuse_0002_neg,negated_conjecture,
~ ( ( a_select2(xinit_noise_defuse,n5) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n3) = use
& a_select3(u_defuse,n2,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n0,n0) = use
& a_select2(sigma_defuse,n5) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(rho_defuse,n2) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n0) = use )
=> ! [A,B] :
( ( leq(B,tptp_minus_1)
& leq(A,n2)
& leq(n0,B)
& leq(n0,A) )
=> a_select3(z_defuse,A,B) = use ) ),
inference(assume_negation,[status(cth)],[quaternion_ds1_inuse_0002]) ).
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_344,plain,
( n0 = A
| ~ leq(A,n0)
| ~ leq(n0,A) ),
inference(clausify,[status(thm)],[finite_domain_0]) ).
fof(nnf_56,plain,
( ? [A,B] :
( a_select3(z_defuse,A,B) != use
& leq(B,tptp_minus_1)
& leq(A,n2)
& leq(n0,B)
& leq(n0,A) )
& a_select2(xinit_noise_defuse,n5) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n3) = use
& a_select3(u_defuse,n2,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n0,n0) = use
& a_select2(sigma_defuse,n5) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(rho_defuse,n2) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n0) = use ),
inference(fof_nnf,[status(thm)],[quaternion_ds1_inuse_0002_neg]) ).
fof(sk_quaternion_ds1_inuse_0002_neg,plain,
( a_select3(z_defuse,sK1,sK0) != use
& leq(sK0,tptp_minus_1)
& leq(sK1,n2)
& leq(n0,sK0)
& leq(n0,sK1)
& a_select2(xinit_noise_defuse,n5) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n3) = use
& a_select3(u_defuse,n2,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n0,n0) = use
& a_select2(sigma_defuse,n5) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(rho_defuse,n2) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n0) = use ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0]),skolemize(A,sK1),skolemize(B,sK0)],[nnf_56]) ).
cnf(c_385,negated_conjecture,
leq(n0,sK0),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0002_neg]) ).
cnf(c_387,negated_conjecture,
leq(sK0,tptp_minus_1),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0002_neg]) ).
cnf(c_2564,negated_conjecture,
( n0 = sK0
| ~ leq(sK0,n0) ),
inference(resolve,[status(thm)],[c_385,c_344]) ).
cnf(c_1756,negated_conjecture,
( sK0 = n0
| ~ leq(sK0,n0) ),
inference(copy,[status(thm)],[c_2564]) ).
cnf(c_2565,negated_conjecture,
gt(succ(tptp_minus_1),sK0),
inference(resolve,[status(thm)],[c_387,c_72]) ).
cnf(c_2381,negated_conjecture,
gt(n0,sK0),
inference(paramod,[status(thm)],[c_281,c_2565]) ).
cnf(c_2566,negated_conjecture,
leq(sK0,succ(tptp_minus_1)),
inference(resolve,[status(thm)],[c_387,c_71]) ).
cnf(c_2382,negated_conjecture,
leq(sK0,n0),
inference(paramod,[status(thm)],[c_281,c_2566]) ).
cnf(c_2523,negated_conjecture,
sK0 = n0,
inference(resolve,[status(thm)],[c_2382,c_1756]) ).
cnf(c_2567,negated_conjecture,
gt(n0,n0),
inference(paramod,[status(thm)],[c_2523,c_2381]) ).
cnf(c_2563,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_63,c_2567]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV191+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 : n007.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 13:16:39 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 3825514 was started by sandbox on n007,
% 0.09/0.37 % Sat Sep 26 13:16:39 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.43
% 0.09/0.43 % From the command line: assign(max_seconds, 300).
% 7.57/1.47
% 7.57/1.47 % SZS status Theorem for theBenchmark
% 7.57/1.47
% 7.57/1.47 % Proof 1 at 0.75 (+ 0.12) seconds.
% 7.57/1.47 % Length of proof is 17.
% 7.57/1.47 % Level of proof is 4.
% 7.57/1.47 % Maximum clause weight is 17.000.
% 7.57/1.47 % Given clauses 314.
% 7.57/1.47
% 7.57/1.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------