%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV199+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 09:07:01 AM UTC 2026
% Result : Theorem 7.60s 1.81s
% Output : CNFRefutation 7.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 46 ( 14 unt; 0 def)
% Number of atoms : 291 ( 207 equ)
% Maximal formula atoms : 51 ( 6 avg)
% Number of connectives : 325 ( 80 ~; 63 |; 170 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 44 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 18 con; 0-3 aty)
% Number of variables : 26 ( 0 sgn 22 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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_0010,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,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_0010) ).
fof(quaternion_ds1_inuse_0010_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,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_0010]) ).
cnf(c_359,plain,
( n0 = A
| ~ leq(A,n0)
| ~ leq(n0,A) ),
inference(clausify,[status(thm)],[finite_domain_0]) ).
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(z_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) )
& 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_0010_neg]) ).
fof(sk_quaternion_ds1_inuse_0010_neg,plain,
( a_select3(z_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) )
& 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_400,negated_conjecture,
leq(n0,pv5),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0010_neg]) ).
cnf(c_401,negated_conjecture,
leq(pv5,n0),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0010_neg]) ).
cnf(c_407,negated_conjecture,
leq(n0,sK0),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0010_neg]) ).
cnf(c_408,negated_conjecture,
leq(n0,sK1),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0010_neg]) ).
cnf(c_409,negated_conjecture,
leq(sK0,n2),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0010_neg]) ).
cnf(c_410,negated_conjecture,
leq(sK1,pv5),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0010_neg]) ).
cnf(c_411,negated_conjecture,
( pv5 != sK1
| sK0 != n0 ),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0010_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_0010_neg]) ).
cnf(c_1866,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_1866]) ).
cnf(c_415,negated_conjecture,
( pv5 != sK1
| n2 != sK0 ),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0010_neg]) ).
cnf(c_1867,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_1867]) ).
cnf(c_1868,negated_conjecture,
( n0 = pv5
| ~ leq(pv5,n0) ),
inference(resolve,[status(thm)],[c_400,c_359]) ).
cnf(c_1869,negated_conjecture,
( pv5 = n0
| ~ leq(pv5,n0) ),
inference(copy,[status(thm)],[c_1868]) ).
cnf(c_1468,negated_conjecture,
pv5 = n0,
inference(resolve,[status(thm)],[c_401,c_1869]) ).
cnf(c_1475,negated_conjecture,
( sK1 != n0
| sK0 != n2 ),
inference(paramod,[status(thm)],[c_1468,c_416]) ).
cnf(c_1476,negated_conjecture,
( sK1 != n0
| sK0 != n1 ),
inference(paramod,[status(thm)],[c_1468,c_414]) ).
cnf(c_1477,negated_conjecture,
( sK1 != n0
| sK0 != n0 ),
inference(paramod,[status(thm)],[c_1468,c_412]) ).
cnf(c_1478,negated_conjecture,
leq(sK1,n0),
inference(paramod,[status(thm)],[c_1468,c_410]) ).
cnf(c_1870,negated_conjecture,
( n2 = sK0
| n1 = sK0
| n0 = sK0
| ~ leq(sK0,n2) ),
inference(resolve,[status(thm)],[c_407,c_361]) ).
cnf(c_1871,negated_conjecture,
( n2 = sK0
| n1 = sK0
| sK0 = n0
| ~ leq(sK0,n2) ),
inference(copy,[status(thm)],[c_1870]) ).
cnf(c_1872,negated_conjecture,
( n2 = sK0
| sK0 = n1
| sK0 = n0
| ~ leq(sK0,n2) ),
inference(copy,[status(thm)],[c_1871]) ).
cnf(c_1873,negated_conjecture,
( sK0 = n2
| sK0 = n1
| sK0 = n0
| ~ leq(sK0,n2) ),
inference(copy,[status(thm)],[c_1872]) ).
cnf(c_1482,negated_conjecture,
( sK0 = n2
| sK0 = n1
| sK0 = n0 ),
inference(resolve,[status(thm)],[c_409,c_1873]) ).
cnf(c_1874,negated_conjecture,
( n0 = sK1
| ~ leq(sK1,n0) ),
inference(resolve,[status(thm)],[c_408,c_359]) ).
cnf(c_1875,negated_conjecture,
( sK1 = n0
| ~ leq(sK1,n0) ),
inference(copy,[status(thm)],[c_1874]) ).
cnf(c_1857,negated_conjecture,
sK1 = n0,
inference(resolve,[status(thm)],[c_1478,c_1875]) ).
cnf(c_1876,negated_conjecture,
( n0 != n0
| sK0 != n0 ),
inference(paramod,[status(thm)],[c_1857,c_1477]) ).
cnf(c_1858,negated_conjecture,
sK0 != n0,
inference(copy,[status(thm)],[c_1876]) ).
cnf(c_1877,negated_conjecture,
( n0 != n0
| sK0 != n1 ),
inference(paramod,[status(thm)],[c_1857,c_1476]) ).
cnf(c_1859,negated_conjecture,
sK0 != n1,
inference(copy,[status(thm)],[c_1877]) ).
cnf(c_1878,negated_conjecture,
( n0 != n0
| sK0 != n2 ),
inference(paramod,[status(thm)],[c_1857,c_1475]) ).
cnf(c_1860,negated_conjecture,
sK0 != n2,
inference(copy,[status(thm)],[c_1878]) ).
cnf(c_1879,negated_conjecture,
( sK0 = n2
| sK0 = n1 ),
inference(resolve,[status(thm)],[c_1858,c_1482]) ).
cnf(c_1880,negated_conjecture,
sK0 = n2,
inference(resolve,[status(thm)],[c_1859,c_1879]) ).
cnf(c_1865,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1860,c_1880]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV199+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n007.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 13:17:09 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 3826519 was started by sandbox on n007,
% 0.18/0.44 % Sat Sep 26 13:17:09 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.27/0.56
% 0.27/0.56 % From the command line: assign(max_seconds, 300).
% 7.60/1.81
% 7.60/1.81 % SZS status Theorem for theBenchmark
% 7.60/1.81
% 7.60/1.81 % Proof 1 at 1.03 (+ 0.18) seconds.
% 7.60/1.81 % Length of proof is 28.
% 7.60/1.81 % Level of proof is 6.
% 7.60/1.81 % Maximum clause weight is 20.000.
% 7.60/1.81 % Given clauses 313.
% 7.60/1.81
% 7.60/1.81 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------