%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV202+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 : n004.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 208.56s 28.17s
% Output : CNFRefutation 208.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 51 ( 14 unt; 0 def)
% Number of atoms : 312 ( 211 equ)
% Maximal formula atoms : 51 ( 6 avg)
% Number of connectives : 348 ( 87 ~; 78 |; 170 &)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 44 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 18 con; 0-3 aty)
% Number of variables : 43 ( 0 sgn 26 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(leq_gt2,axiom,
! [X,Y] :
( ( X != Y
& leq(X,Y) )
=> gt(Y,X) ),
file('theBenchmark.p',leq_gt2) ).
fof(leq_gt_pred,axiom,
! [X,Y] :
( leq(X,pred(Y))
<=> gt(Y,X) ),
file('theBenchmark.p',leq_gt_pred) ).
fof(pred_minus_1,axiom,
! [X] : minus(X,n1) = pred(X),
file('theBenchmark.p',pred_minus_1) ).
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_0013,conjecture,
( ( ! [C,D] :
( ( leq(D,pred(pv5))
& leq(C,n2)
& leq(n0,D)
& leq(n0,C) )
=> a_select3(z_defuse,C,D) = use )
& ! [A,B] :
( ( leq(B,pred(pv5))
& leq(A,n2)
& leq(n0,B)
& leq(n0,A) )
=> a_select3(u_defuse,A,B) = use )
& gt(pv5,n0)
& leq(pv5,n998)
& leq(n0,pv5)
& 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,pv5)
& leq(E,n2)
& leq(n0,F)
& leq(n0,E) )
=> ( ( ~ ( pv5 = F
& n2 = E )
& ~ ( pv5 = F
& n1 = E )
& ~ ( pv5 = F
& n0 = E ) )
=> a_select3(u_defuse,E,F) = use ) ) ),
file('theBenchmark.p',quaternion_ds1_inuse_0013) ).
fof(quaternion_ds1_inuse_0013_neg,negated_conjecture,
~ ( ( ! [C,D] :
( ( leq(D,pred(pv5))
& leq(C,n2)
& leq(n0,D)
& leq(n0,C) )
=> a_select3(z_defuse,C,D) = use )
& ! [A,B] :
( ( leq(B,pred(pv5))
& leq(A,n2)
& leq(n0,B)
& leq(n0,A) )
=> a_select3(u_defuse,A,B) = use )
& gt(pv5,n0)
& leq(pv5,n998)
& leq(n0,pv5)
& 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,pv5)
& leq(E,n2)
& leq(n0,F)
& leq(n0,E) )
=> ( ( ~ ( pv5 = F
& n2 = E )
& ~ ( pv5 = F
& n1 = E )
& ~ ( pv5 = F
& n0 = E ) )
=> a_select3(u_defuse,E,F) = use ) ) ),
inference(assume_negation,[status(cth)],[quaternion_ds1_inuse_0013]) ).
cnf(c_67,plain,
( gt(B,A)
| B = A
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[leq_gt2]) ).
cnf(c_69,plain,
( ~ gt(B,A)
| leq(A,pred(B)) ),
inference(clausify,[status(thm)],[leq_gt_pred]) ).
cnf(c_302,plain,
minus(A,n1) = pred(A),
inference(clausify,[status(thm)],[pred_minus_1]) ).
cnf(c_303,plain,
pred(A) = minus(A,n1),
inference(copy,[status(thm)],[c_302]) ).
cnf(c_361,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,F] :
( a_select3(u_defuse,E,F) != use
& ( pv5 != F
| n2 != E )
& ( pv5 != F
| n1 != E )
& ( pv5 != F
| E != n0 )
& leq(F,pv5)
& leq(E,n2)
& leq(n0,F)
& leq(n0,E) )
& ! [C,D] :
( a_select3(z_defuse,C,D) = use
| ~ leq(D,pred(pv5))
| ~ leq(C,n2)
| ~ leq(n0,D)
| ~ leq(n0,C) )
& ! [A,B] :
( a_select3(u_defuse,A,B) = use
| ~ leq(B,pred(pv5))
| ~ leq(A,n2)
| ~ leq(n0,B)
| ~ leq(n0,A) )
& gt(pv5,n0)
& leq(pv5,n998)
& leq(n0,pv5)
& 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_0013_neg]) ).
fof(sk_quaternion_ds1_inuse_0013_neg,plain,
( a_select3(u_defuse,sK0,sK1) != use
& ( pv5 != sK1
| n2 != sK0 )
& ( pv5 != sK1
| n1 != sK0 )
& ( pv5 != sK1
| sK0 != n0 )
& leq(sK1,pv5)
& leq(sK0,n2)
& leq(n0,sK1)
& leq(n0,sK0)
& ! [C,D] :
( a_select3(z_defuse,C,D) = use
| ~ leq(D,pred(pv5))
| ~ leq(C,n2)
| ~ leq(n0,D)
| ~ leq(n0,C) )
& ! [A,B] :
( a_select3(u_defuse,A,B) = use
| ~ leq(B,pred(pv5))
| ~ leq(A,n2)
| ~ leq(n0,B)
| ~ leq(n0,A) )
& gt(pv5,n0)
& leq(pv5,n998)
& leq(n0,pv5)
& 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_403,negated_conjecture,
( a_select3(u_defuse,A,B) = use
| ~ leq(B,pred(pv5))
| ~ leq(A,n2)
| ~ leq(n0,B)
| ~ leq(n0,A) ),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0013_neg]) ).
cnf(c_404,negated_conjecture,
( a_select3(u_defuse,A,B) = use
| ~ leq(B,minus(pv5,n1))
| ~ leq(A,n2)
| ~ leq(n0,B)
| ~ leq(n0,A) ),
inference(paramod,[status(thm)],[c_303,c_403]) ).
cnf(c_407,negated_conjecture,
leq(n0,sK0),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0013_neg]) ).
cnf(c_408,negated_conjecture,
leq(n0,sK1),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0013_neg]) ).
cnf(c_409,negated_conjecture,
leq(sK0,n2),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0013_neg]) ).
cnf(c_410,negated_conjecture,
leq(sK1,pv5),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0013_neg]) ).
cnf(c_411,negated_conjecture,
( pv5 != sK1
| sK0 != n0 ),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0013_neg]) ).
cnf(c_412,negated_conjecture,
( sK1 != pv5
| sK0 != n0 ),
inference(copy,[status(thm)],[c_411]) ).
cnf(c_413,negated_conjecture,
( pv5 != sK1
| n1 != sK0 ),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0013_neg]) ).
cnf(c_3582,negated_conjecture,
( pv5 != sK1
| sK0 != n1 ),
inference(copy,[status(thm)],[c_413]) ).
cnf(c_414,negated_conjecture,
( sK1 != pv5
| sK0 != n1 ),
inference(copy,[status(thm)],[c_3582]) ).
cnf(c_415,negated_conjecture,
( pv5 != sK1
| n2 != sK0 ),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0013_neg]) ).
cnf(c_3583,negated_conjecture,
( pv5 != sK1
| sK0 != n2 ),
inference(copy,[status(thm)],[c_415]) ).
cnf(c_416,negated_conjecture,
( sK1 != pv5
| sK0 != n2 ),
inference(copy,[status(thm)],[c_3583]) ).
cnf(c_417,negated_conjecture,
a_select3(u_defuse,sK0,sK1) != use,
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0013_neg]) ).
cnf(c_855,plain,
( ~ gt(B,A)
| leq(A,minus(B,n1)) ),
inference(paramod,[status(thm)],[c_303,c_69]) ).
cnf(c_3584,negated_conjecture,
( a_select3(u_defuse,sK0,A) = use
| ~ leq(A,minus(pv5,n1))
| ~ leq(sK0,n2)
| ~ leq(n0,A) ),
inference(resolve,[status(thm)],[c_407,c_404]) ).
cnf(c_1111,negated_conjecture,
( a_select3(u_defuse,sK0,A) = use
| ~ leq(A,minus(pv5,n1))
| ~ leq(n0,A) ),
inference(resolve,[status(thm)],[c_409,c_3584]) ).
cnf(c_3585,negated_conjecture,
( n2 = sK0
| n1 = sK0
| n0 = sK0
| ~ leq(sK0,n2) ),
inference(resolve,[status(thm)],[c_407,c_361]) ).
cnf(c_3586,negated_conjecture,
( n2 = sK0
| n1 = sK0
| sK0 = n0
| ~ leq(sK0,n2) ),
inference(copy,[status(thm)],[c_3585]) ).
cnf(c_3587,negated_conjecture,
( n2 = sK0
| sK0 = n1
| sK0 = n0
| ~ leq(sK0,n2) ),
inference(copy,[status(thm)],[c_3586]) ).
cnf(c_3588,negated_conjecture,
( sK0 = n2
| sK0 = n1
| sK0 = n0
| ~ leq(sK0,n2) ),
inference(copy,[status(thm)],[c_3587]) ).
cnf(c_1113,negated_conjecture,
( sK0 = n2
| sK0 = n1
| sK0 = n0 ),
inference(resolve,[status(thm)],[c_409,c_3588]) ).
cnf(c_3589,negated_conjecture,
( gt(pv5,sK1)
| pv5 = sK1 ),
inference(resolve,[status(thm)],[c_410,c_67]) ).
cnf(c_1151,negated_conjecture,
( gt(pv5,sK1)
| sK1 = pv5 ),
inference(copy,[status(thm)],[c_3589]) ).
cnf(c_1668,plain,
( leq(sK1,minus(pv5,n1))
| sK1 = pv5 ),
inference(resolve,[status(thm)],[c_1151,c_855]) ).
cnf(c_1711,plain,
( sK1 != pv5
| sK0 = n2
| sK0 = n0 ),
inference(resolve,[status(thm)],[c_1113,c_414]) ).
cnf(c_3590,negated_conjecture,
( a_select3(u_defuse,sK0,sK1) = use
| ~ leq(sK1,minus(pv5,n1)) ),
inference(resolve,[status(thm)],[c_1111,c_408]) ).
cnf(c_3569,negated_conjecture,
~ leq(sK1,minus(pv5,n1)),
inference(resolve,[status(thm)],[c_417,c_3590]) ).
cnf(c_3573,plain,
sK1 = pv5,
inference(resolve,[status(thm)],[c_3569,c_1668]) ).
cnf(c_3591,plain,
( pv5 != pv5
| sK0 = n2
| sK0 = n0 ),
inference(paramod,[status(thm)],[c_3573,c_1711]) ).
cnf(c_3575,plain,
( sK0 = n2
| sK0 = n0 ),
inference(copy,[status(thm)],[c_3591]) ).
cnf(c_3592,negated_conjecture,
( pv5 != pv5
| sK0 != n2 ),
inference(paramod,[status(thm)],[c_3573,c_416]) ).
cnf(c_3578,negated_conjecture,
sK0 != n2,
inference(copy,[status(thm)],[c_3592]) ).
cnf(c_3593,negated_conjecture,
( pv5 != pv5
| sK0 != n0 ),
inference(paramod,[status(thm)],[c_3573,c_412]) ).
cnf(c_3580,negated_conjecture,
sK0 != n0,
inference(copy,[status(thm)],[c_3593]) ).
cnf(c_3594,negated_conjecture,
sK0 = n2,
inference(resolve,[status(thm)],[c_3580,c_3575]) ).
cnf(c_3581,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_3578,c_3594]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV202+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n004.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 13:18:51 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 1804347 was started by sandbox2 on n004,
% 0.17/0.43 % Sat Sep 26 13:18:51 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.25/0.55
% 0.25/0.55 % From the command line: assign(max_seconds, 300).
% 208.56/28.17
% 208.56/28.17 % given #500 (I,wt=61): 594 leq(n0,f18(A,B,n0,C)) | -leq(n0,D) | -leq(D,n0) | a_select3(tptp_mmul(A,tptp_mmul(B,trans(A))),n0,D) = a_select3(tptp_mmul(A,tptp_mmul(B,trans(A))),D,n0). [factor(150,b,c),flip(e),unit_del(b,64)].
% 208.56/28.17
% 208.56/28.17 % given #1000 (A,wt=26): 1054 n1 = A | a_select2(tptp_update2(rho_defuse,A,B),n1) = use. [resolve(374,a,323,b)].
% 208.56/28.17
% 208.56/28.17 % SZS status Theorem for theBenchmark
% 208.56/28.17
% 208.56/28.17 % Proof 1 at 2.57 (+ 0.74) seconds.
% 208.56/28.17 % Length of proof is 35.
% 208.56/28.17 % Level of proof is 8.
% 208.56/28.17 % Maximum clause weight is 30.000.
% 208.56/28.17 % Given clauses 1322.
% 208.56/28.17
% 208.56/28.17 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------