%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV197+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 : n010.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 13.75s 2.40s
% Output : CNFRefutation 13.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 49 ( 16 unt; 0 def)
% Number of atoms : 295 ( 201 equ)
% Maximal formula atoms : 51 ( 6 avg)
% Number of connectives : 322 ( 76 ~; 62 |; 170 &)
% ( 1 <=>; 13 =>; 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 : 21 ( 21 usr; 18 con; 0-3 aty)
% Number of variables : 34 ( 0 sgn 26 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(leq_gt1,axiom,
! [X,Y] :
( gt(Y,X)
=> leq(X,Y) ),
file('theBenchmark.p',leq_gt1) ).
fof(leq_gt_pred,axiom,
! [X,Y] :
( leq(X,pred(Y))
<=> gt(Y,X) ),
file('theBenchmark.p',leq_gt_pred) ).
fof(finite_domain_0,axiom,
! [X] :
( ( leq(X,n0)
& leq(n0,X) )
=> X = n0 ),
file('theBenchmark.p',finite_domain_0) ).
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_0008,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 )
& leq(pv5,n998)
& leq(pv5,n0)
& 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,pred(pv5))
& leq(E,n2)
& leq(n0,F)
& leq(n0,E) )
=> ( ( ~ ( pv5 = F
& n2 = E )
& ~ ( pv5 = F
& n1 = E )
& ~ ( pv5 = F
& n0 = E ) )
=> a_select3(z_defuse,E,F) = use ) ) ),
file('theBenchmark.p',quaternion_ds1_inuse_0008) ).
fof(quaternion_ds1_inuse_0008_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 )
& leq(pv5,n998)
& leq(pv5,n0)
& 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,pred(pv5))
& leq(E,n2)
& leq(n0,F)
& leq(n0,E) )
=> ( ( ~ ( pv5 = F
& n2 = E )
& ~ ( pv5 = F
& n1 = E )
& ~ ( pv5 = F
& n0 = E ) )
=> a_select3(z_defuse,E,F) = use ) ) ),
inference(assume_negation,[status(cth)],[quaternion_ds1_inuse_0008]) ).
cnf(c_66,plain,
( leq(B,A)
| ~ gt(A,B) ),
inference(clausify,[status(thm)],[leq_gt1]) ).
cnf(c_68,plain,
( gt(B,A)
| ~ leq(A,pred(B)) ),
inference(clausify,[status(thm)],[leq_gt_pred]) ).
cnf(c_353,plain,
( n0 = A
| ~ leq(A,n0)
| ~ leq(n0,A) ),
inference(clausify,[status(thm)],[finite_domain_0]) ).
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,F] :
( a_select3(z_defuse,E,F) != use
& ( pv5 != F
| n2 != E )
& ( pv5 != F
| n1 != E )
& ( pv5 != F
| E != n0 )
& leq(F,pred(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) )
& leq(pv5,n998)
& leq(pv5,n0)
& 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_0008_neg]) ).
fof(sk_quaternion_ds1_inuse_0008_neg,plain,
( a_select3(z_defuse,sK0,sK1) != use
& ( pv5 != sK1
| n2 != sK0 )
& ( pv5 != sK1
| n1 != sK0 )
& ( pv5 != sK1
| sK0 != n0 )
& leq(sK1,pred(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) )
& leq(pv5,n998)
& leq(pv5,n0)
& 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_389,negated_conjecture,
leq(n0,pv5),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0008_neg]) ).
cnf(c_390,negated_conjecture,
leq(pv5,n0),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0008_neg]) ).
cnf(c_394,negated_conjecture,
leq(n0,sK0),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0008_neg]) ).
cnf(c_395,negated_conjecture,
leq(n0,sK1),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0008_neg]) ).
cnf(c_396,negated_conjecture,
leq(sK0,n2),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0008_neg]) ).
cnf(c_397,negated_conjecture,
leq(sK1,pred(pv5)),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0008_neg]) ).
cnf(c_398,negated_conjecture,
( pv5 != sK1
| sK0 != n0 ),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0008_neg]) ).
cnf(c_399,negated_conjecture,
( sK1 != pv5
| sK0 != n0 ),
inference(copy,[status(thm)],[c_398]) ).
cnf(c_400,negated_conjecture,
( pv5 != sK1
| n1 != sK0 ),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0008_neg]) ).
cnf(c_13173,negated_conjecture,
( pv5 != sK1
| sK0 != n1 ),
inference(copy,[status(thm)],[c_400]) ).
cnf(c_401,negated_conjecture,
( sK1 != pv5
| sK0 != n1 ),
inference(copy,[status(thm)],[c_13173]) ).
cnf(c_402,negated_conjecture,
( pv5 != sK1
| n2 != sK0 ),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0008_neg]) ).
cnf(c_13174,negated_conjecture,
( pv5 != sK1
| sK0 != n2 ),
inference(copy,[status(thm)],[c_402]) ).
cnf(c_403,negated_conjecture,
( sK1 != pv5
| sK0 != n2 ),
inference(copy,[status(thm)],[c_13174]) ).
cnf(c_13175,negated_conjecture,
( n0 = pv5
| ~ leq(pv5,n0) ),
inference(resolve,[status(thm)],[c_389,c_353]) ).
cnf(c_13176,negated_conjecture,
( pv5 = n0
| ~ leq(pv5,n0) ),
inference(copy,[status(thm)],[c_13175]) ).
cnf(c_2060,negated_conjecture,
pv5 = n0,
inference(resolve,[status(thm)],[c_390,c_13176]) ).
cnf(c_13177,negated_conjecture,
( n2 = sK0
| n1 = sK0
| n0 = sK0
| ~ leq(sK0,n2) ),
inference(resolve,[status(thm)],[c_394,c_355]) ).
cnf(c_13178,negated_conjecture,
( n2 = sK0
| n1 = sK0
| sK0 = n0
| ~ leq(sK0,n2) ),
inference(copy,[status(thm)],[c_13177]) ).
cnf(c_13179,negated_conjecture,
( n2 = sK0
| sK0 = n1
| sK0 = n0
| ~ leq(sK0,n2) ),
inference(copy,[status(thm)],[c_13178]) ).
cnf(c_13180,negated_conjecture,
( sK0 = n2
| sK0 = n1
| sK0 = n0
| ~ leq(sK0,n2) ),
inference(copy,[status(thm)],[c_13179]) ).
cnf(c_2744,negated_conjecture,
( sK0 = n2
| sK0 = n1
| sK0 = n0 ),
inference(resolve,[status(thm)],[c_396,c_13180]) ).
cnf(c_13181,negated_conjecture,
( n0 = sK1
| ~ leq(sK1,n0) ),
inference(resolve,[status(thm)],[c_395,c_353]) ).
cnf(c_3125,negated_conjecture,
( sK1 = n0
| ~ leq(sK1,n0) ),
inference(copy,[status(thm)],[c_13181]) ).
cnf(c_3752,plain,
gt(pv5,sK1),
inference(resolve,[status(thm)],[c_397,c_68]) ).
cnf(c_12830,plain,
( sK1 != n0
| sK0 != n0 ),
inference(paramod,[status(thm)],[c_2060,c_399]) ).
cnf(c_12831,plain,
( sK1 != n0
| sK0 != n1 ),
inference(paramod,[status(thm)],[c_2060,c_401]) ).
cnf(c_12832,plain,
( sK1 != n0
| sK0 != n2 ),
inference(paramod,[status(thm)],[c_2060,c_403]) ).
cnf(c_12956,plain,
leq(sK1,pv5),
inference(resolve,[status(thm)],[c_3752,c_66]) ).
cnf(c_13098,plain,
leq(sK1,n0),
inference(paramod,[status(thm)],[c_2060,c_12956]) ).
cnf(c_13167,negated_conjecture,
sK1 = n0,
inference(resolve,[status(thm)],[c_13098,c_3125]) ).
cnf(c_13168,plain,
sK0 != n2,
inference(resolve,[status(thm)],[c_13167,c_12832]) ).
cnf(c_13169,plain,
sK0 != n1,
inference(resolve,[status(thm)],[c_13167,c_12831]) ).
cnf(c_13170,plain,
sK0 != n0,
inference(resolve,[status(thm)],[c_13167,c_12830]) ).
cnf(c_13182,negated_conjecture,
( sK0 = n2
| sK0 = n1 ),
inference(resolve,[status(thm)],[c_13170,c_2744]) ).
cnf(c_13183,negated_conjecture,
sK0 = n2,
inference(resolve,[status(thm)],[c_13169,c_13182]) ).
cnf(c_13172,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_13168,c_13183]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV197+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.35 % Computer : n010.cluster.edu
% 0.03/0.35 % Model : x86_64 x86_64
% 0.03/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.35 % Memory : 8046.5625MB
% 0.03/0.35 % OS : Linux 6.8.0-71-generic
% 0.03/0.35 % CPULimit : 300
% 0.03/0.35 % WCLimit : 300
% 0.03/0.35 % DateTime : Sat Sep 26 13:19:30 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.36 % Process 3420424 was started by sandbox on n010,
% 0.03/0.36 % Sat Sep 26 13:19:30 2026
% 0.03/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.03/0.42
% 0.03/0.42 % From the command line: assign(max_seconds, 300).
% 13.75/2.40
% 13.75/2.40 % given #500 (I,wt=57): 574 leq(f16(A,B,C),C) | -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(146,b,e),unit_del(c,64),unit_del(d,64)].
% 13.75/2.40
% 13.75/2.40 % SZS status Theorem for theBenchmark
% 13.75/2.40
% 13.75/2.40 % Proof 1 at 1.64 (+ 0.30) seconds.
% 13.75/2.40 % Length of proof is 35.
% 13.75/2.40 % Level of proof is 7.
% 13.75/2.40 % Maximum clause weight is 20.000.
% 13.75/2.40 % Given clauses 882.
% 13.75/2.40
% 13.75/2.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------