%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV204+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 : n012.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 09:07:01 AM UTC 2026
% Result : Theorem 22.04s 3.53s
% Output : CNFRefutation 22.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 23 ( 9 unt; 0 def)
% Number of atoms : 205 ( 154 equ)
% Maximal formula atoms : 40 ( 8 avg)
% Number of connectives : 211 ( 29 ~; 40 |; 133 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 16 con; 0-3 aty)
% Number of variables : 21 ( 0 sgn 19 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(finite_domain_2,axiom,
! [X] :
( ( leq(X,n2)
& leq(n0,X) )
=> ( X = n2
| X = n1
| X = n0 ) ),
file('theBenchmark.p',finite_domain_2) ).
fof(quaternion_ds1_inuse_0015,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] :
( ( leq(E,n2)
& leq(n0,E) )
=> a_select2(rho_defuse,E) = use ) ),
file('theBenchmark.p',quaternion_ds1_inuse_0015) ).
fof(quaternion_ds1_inuse_0015_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] :
( ( leq(E,n2)
& leq(n0,E) )
=> a_select2(rho_defuse,E) = use ) ),
inference(assume_negation,[status(cth)],[quaternion_ds1_inuse_0015]) ).
cnf(c_355,plain,
( n2 = A
| n1 = A
| n0 = A
| ~ leq(A,n2)
| ~ leq(n0,A) ),
inference(clausify,[status(thm)],[finite_domain_2]) ).
fof(nnf_56,plain,
( ? [E] :
( a_select2(rho_defuse,E) != use
& leq(E,n2)
& 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_0015_neg]) ).
fof(sk_quaternion_ds1_inuse_0015_neg,plain,
( a_select2(rho_defuse,sK0) != use
& leq(sK0,n2)
& 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]),skolemize(E,sK0)],[nnf_56]) ).
cnf(c_362,negated_conjecture,
a_select2(rho_defuse,n0) = use,
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0015_neg]) ).
cnf(c_363,negated_conjecture,
a_select2(rho_defuse,n1) = use,
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0015_neg]) ).
cnf(c_364,negated_conjecture,
a_select2(rho_defuse,n2) = use,
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0015_neg]) ).
cnf(c_391,negated_conjecture,
leq(n0,sK0),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0015_neg]) ).
cnf(c_392,negated_conjecture,
leq(sK0,n2),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0015_neg]) ).
cnf(c_393,negated_conjecture,
a_select2(rho_defuse,sK0) != use,
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0015_neg]) ).
cnf(c_18598,negated_conjecture,
( n2 = sK0
| n1 = sK0
| n0 = sK0
| ~ leq(sK0,n2) ),
inference(resolve,[status(thm)],[c_391,c_355]) ).
cnf(c_18599,negated_conjecture,
( n2 = sK0
| n1 = sK0
| sK0 = n0
| ~ leq(sK0,n2) ),
inference(copy,[status(thm)],[c_18598]) ).
cnf(c_18600,negated_conjecture,
( n2 = sK0
| sK0 = n1
| sK0 = n0
| ~ leq(sK0,n2) ),
inference(copy,[status(thm)],[c_18599]) ).
cnf(c_18601,negated_conjecture,
( sK0 = n2
| sK0 = n1
| sK0 = n0
| ~ leq(sK0,n2) ),
inference(copy,[status(thm)],[c_18600]) ).
cnf(c_2063,negated_conjecture,
( sK0 = n2
| sK0 = n1
| sK0 = n0 ),
inference(resolve,[status(thm)],[c_392,c_18601]) ).
cnf(c_18602,plain,
( a_select2(rho_defuse,n1) != use
| sK0 = n2
| sK0 = n0 ),
inference(paramod,[status(thm)],[c_2063,c_393]) ).
cnf(c_18591,negated_conjecture,
( sK0 = n2
| sK0 = n0 ),
inference(resolve,[status(thm)],[c_363,c_18602]) ).
cnf(c_18603,plain,
( a_select2(rho_defuse,n2) != use
| sK0 = n0 ),
inference(paramod,[status(thm)],[c_18591,c_393]) ).
cnf(c_18594,negated_conjecture,
sK0 = n0,
inference(resolve,[status(thm)],[c_364,c_18603]) ).
cnf(c_18604,plain,
a_select2(rho_defuse,n0) != use,
inference(paramod,[status(thm)],[c_18594,c_393]) ).
cnf(c_18597,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_362,c_18604]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWV204+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Sat Sep 26 13:19:19 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.30 % Process 698424 was started by sandbox2 on n012,
% 0.03/0.30 % Sat Sep 26 13:19:19 2026
% 0.03/0.30 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.33
% 0.09/0.33 % From the command line: assign(max_seconds, 300).
% 22.04/3.53
% 22.04/3.53 % given #500 (I,wt=58): 571 leq(n0,f18(A,B,C,D)) | -leq(n0,C) | a_select3(tptp_mmul(A,tptp_mmul(B,trans(A))),n0,C) = a_select3(tptp_mmul(A,tptp_mmul(B,trans(A))),C,n0). [factor(150,b,e),unit_del(c,64),unit_del(d,64)].
% 22.04/3.53
% 22.04/3.53 % given #1000 (A,wt=40): 959 leq(f4(A,B),B) | -leq(n0,C) | -leq(C,B) | -leq(n0,B) | a_select3(inv(A),B,C) = a_select3(inv(A),C,B). [resolve(86,e,64,a)].
% 22.04/3.53
% 22.04/3.53 % SZS status Theorem for theBenchmark
% 22.04/3.53
% 22.04/3.53 % Proof 1 at 2.55 (+ 0.53) seconds.
% 22.04/3.53 % Length of proof is 13.
% 22.04/3.53 % Level of proof is 5.
% 22.04/3.53 % Maximum clause weight is 20.000.
% 22.04/3.53 % Given clauses 1179.
% 22.04/3.53
% 22.04/3.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------