%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV210+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 : n009.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 09:07:02 AM UTC 2026
% Result : Theorem 14.71s 2.35s
% Output : CNFRefutation 14.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 15 ( 7 unt; 0 def)
% Number of atoms : 189 ( 126 equ)
% Maximal formula atoms : 42 ( 12 avg)
% Number of connectives : 204 ( 30 ~; 26 |; 140 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 12 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 17 con; 0-3 aty)
% Number of variables : 25 ( 0 sgn 20 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(quaternion_ds1_inuse_0021,conjecture,
( ( ! [C,D] :
( ( leq(D,n998)
& leq(C,n2)
& leq(n0,D)
& leq(n0,C) )
=> a_select3(z_defuse,C,D) = use )
& ! [A,B] :
( ( leq(B,n998)
& leq(A,n2)
& leq(n0,B)
& leq(n0,A) )
=> a_select3(u_defuse,A,B) = use )
& 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 )
=> ! [E,F] :
( ( leq(F,n998)
& leq(E,n2)
& leq(n0,F)
& leq(n0,E) )
=> a_select3(z_defuse,E,F) = use ) ),
file('theBenchmark.p',quaternion_ds1_inuse_0021) ).
fof(quaternion_ds1_inuse_0021_neg,negated_conjecture,
~ ( ( ! [C,D] :
( ( leq(D,n998)
& leq(C,n2)
& leq(n0,D)
& leq(n0,C) )
=> a_select3(z_defuse,C,D) = use )
& ! [A,B] :
( ( leq(B,n998)
& leq(A,n2)
& leq(n0,B)
& leq(n0,A) )
=> a_select3(u_defuse,A,B) = use )
& 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 )
=> ! [E,F] :
( ( leq(F,n998)
& leq(E,n2)
& leq(n0,F)
& leq(n0,E) )
=> a_select3(z_defuse,E,F) = use ) ),
inference(assume_negation,[status(cth)],[quaternion_ds1_inuse_0021]) ).
fof(nnf_56,plain,
( ? [E,F] :
( a_select3(z_defuse,E,F) != use
& leq(F,n998)
& leq(E,n2)
& leq(n0,F)
& leq(n0,E) )
& ! [C,D] :
( a_select3(z_defuse,C,D) = use
| ~ leq(D,n998)
| ~ leq(C,n2)
| ~ leq(n0,D)
| ~ leq(n0,C) )
& ! [A,B] :
( a_select3(u_defuse,A,B) = use
| ~ leq(B,n998)
| ~ 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_0021_neg]) ).
fof(sk_quaternion_ds1_inuse_0021_neg,plain,
( a_select3(z_defuse,sK0,sK1) != use
& leq(sK1,n998)
& leq(sK0,n2)
& leq(n0,sK1)
& leq(n0,sK0)
& ! [C,D] :
( a_select3(z_defuse,C,D) = use
| ~ leq(D,n998)
| ~ leq(C,n2)
| ~ leq(n0,D)
| ~ leq(n0,C) )
& ! [A,B] :
( a_select3(u_defuse,A,B) = use
| ~ leq(B,n998)
| ~ 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(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(E,sK0),skolemize(F,sK1)],[nnf_56]) ).
cnf(c_392,negated_conjecture,
( a_select3(z_defuse,A,B) = use
| ~ leq(B,n998)
| ~ leq(A,n2)
| ~ leq(n0,B)
| ~ leq(n0,A) ),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0021_neg]) ).
cnf(c_393,negated_conjecture,
leq(n0,sK0),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0021_neg]) ).
cnf(c_394,negated_conjecture,
leq(n0,sK1),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0021_neg]) ).
cnf(c_395,negated_conjecture,
leq(sK0,n2),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0021_neg]) ).
cnf(c_396,negated_conjecture,
leq(sK1,n998),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0021_neg]) ).
cnf(c_397,negated_conjecture,
a_select3(z_defuse,sK0,sK1) != use,
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0021_neg]) ).
cnf(c_2870,negated_conjecture,
( a_select3(z_defuse,sK0,A) = use
| ~ leq(A,n998)
| ~ leq(sK0,n2)
| ~ leq(n0,A) ),
inference(resolve,[status(thm)],[c_392,c_393]) ).
cnf(c_2871,negated_conjecture,
( a_select3(z_defuse,sK0,sK1) = use
| ~ leq(sK1,n998)
| ~ leq(sK0,n2) ),
inference(resolve,[status(thm)],[c_2870,c_394]) ).
cnf(c_2872,negated_conjecture,
( a_select3(z_defuse,sK0,sK1) = use
| ~ leq(sK1,n998) ),
inference(resolve,[status(thm)],[c_2871,c_395]) ).
cnf(c_2873,negated_conjecture,
a_select3(z_defuse,sK0,sK1) = use,
inference(resolve,[status(thm)],[c_2872,c_396]) ).
cnf(c_2869,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_397,c_2873]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV210+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.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 13:19:59 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 241413 was started by sandbox on n009,
% 0.09/0.37 % Sat Sep 26 13:19:59 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.42
% 0.09/0.42 % From the command line: assign(max_seconds, 300).
% 14.71/2.35
% 14.71/2.35 % SZS status Theorem for theBenchmark
% 14.71/2.35
% 14.71/2.35 % Proof 1 at 1.72 (+ 0.17) seconds.
% 14.71/2.35 % Length of proof is 8.
% 14.71/2.35 % Level of proof is 2.
% 14.71/2.35 % Maximum clause weight is 28.000.
% 14.71/2.35 % Given clauses 323.
% 14.71/2.35
% 14.71/2.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------