%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV228+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 : 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 09:07:04 AM UTC 2026
% Result : Theorem 1.26s 0.60s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 19 ( 7 unt; 0 def)
% Number of atoms : 279 ( 230 equ)
% Maximal formula atoms : 64 ( 14 avg)
% Number of connectives : 434 ( 174 ~; 70 |; 180 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-3 aty)
% Number of variables : 22 ( 0 sgn 20 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(quaternion_ds1_symm_0681,conjecture,
( ( ! [C,D] :
( ( leq(D,n2)
& leq(C,n2)
& leq(n0,D)
& leq(n0,C) )
=> a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C) )
& ! [A,B] :
( ( leq(B,n5)
& leq(A,n5)
& leq(n0,B)
& leq(n0,A) )
=> a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A) ) )
=> ! [E,F] :
( ( leq(F,n5)
& leq(E,n5)
& leq(n0,F)
& leq(n0,E) )
=> ( ( n3 = F
& n3 = E
& n0 = F
& ~ ( n5 = F
& n5 = E )
& ~ ( n5 = E
& n4 = F )
& ~ ( n5 = F
& n4 = E )
& ~ ( n4 = F
& n4 = E )
& ~ ( n5 = E
& n3 = F )
& ~ ( n4 = E
& n3 = F )
& ~ ( n5 = F
& n3 = E )
& ~ ( n4 = F
& n3 = E )
& ~ ( n3 = F
& n3 = E )
& ~ ( n5 = E
& n2 = F )
& ~ ( n4 = E
& n2 = F )
& ~ ( n3 = E
& n2 = F )
& ~ ( n5 = F
& n2 = E )
& ~ ( n4 = F
& n2 = E )
& ~ ( n5 = E
& n1 = F )
& ~ ( n4 = E
& n1 = F )
& ~ ( n3 = E
& n1 = F )
& ~ ( n5 = F
& n1 = E )
& ~ ( n4 = F
& n1 = E )
& ~ ( n5 = E
& n0 = F )
& ~ ( n4 = E
& n0 = F )
& ~ ( n5 = F
& n0 = E )
& ~ ( n4 = F
& n0 = E ) )
=> n0 = a_select2(xinit_noise,n3) ) ) ),
file('theBenchmark.p',quaternion_ds1_symm_0681) ).
fof(quaternion_ds1_symm_0681_neg,negated_conjecture,
~ ( ( ! [C,D] :
( ( leq(D,n2)
& leq(C,n2)
& leq(n0,D)
& leq(n0,C) )
=> a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C) )
& ! [A,B] :
( ( leq(B,n5)
& leq(A,n5)
& leq(n0,B)
& leq(n0,A) )
=> a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A) ) )
=> ! [E,F] :
( ( leq(F,n5)
& leq(E,n5)
& leq(n0,F)
& leq(n0,E) )
=> ( ( n3 = F
& n3 = E
& n0 = F
& ~ ( n5 = F
& n5 = E )
& ~ ( n5 = E
& n4 = F )
& ~ ( n5 = F
& n4 = E )
& ~ ( n4 = F
& n4 = E )
& ~ ( n5 = E
& n3 = F )
& ~ ( n4 = E
& n3 = F )
& ~ ( n5 = F
& n3 = E )
& ~ ( n4 = F
& n3 = E )
& ~ ( n3 = F
& n3 = E )
& ~ ( n5 = E
& n2 = F )
& ~ ( n4 = E
& n2 = F )
& ~ ( n3 = E
& n2 = F )
& ~ ( n5 = F
& n2 = E )
& ~ ( n4 = F
& n2 = E )
& ~ ( n5 = E
& n1 = F )
& ~ ( n4 = E
& n1 = F )
& ~ ( n3 = E
& n1 = F )
& ~ ( n5 = F
& n1 = E )
& ~ ( n4 = F
& n1 = E )
& ~ ( n5 = E
& n0 = F )
& ~ ( n4 = E
& n0 = F )
& ~ ( n5 = F
& n0 = E )
& ~ ( n4 = F
& n0 = E ) )
=> n0 = a_select2(xinit_noise,n3) ) ) ),
inference(assume_negation,[status(cth)],[quaternion_ds1_symm_0681]) ).
fof(nnf_56,plain,
( ? [E,F] :
( a_select2(xinit_noise,n3) != n0
& n3 = F
& n3 = E
& F = n0
& ( n5 != F
| n5 != E )
& ( n5 != E
| n4 != F )
& ( n5 != F
| n4 != E )
& ( n4 != F
| n4 != E )
& ( n5 != E
| n3 != F )
& ( n4 != E
| n3 != F )
& ( n5 != F
| n3 != E )
& ( n4 != F
| n3 != E )
& ( n3 != F
| n3 != E )
& ( n5 != E
| n2 != F )
& ( n4 != E
| n2 != F )
& ( n3 != E
| n2 != F )
& ( n5 != F
| n2 != E )
& ( n4 != F
| n2 != E )
& ( n5 != E
| n1 != F )
& ( n4 != E
| n1 != F )
& ( n3 != E
| n1 != F )
& ( n5 != F
| n1 != E )
& ( n4 != F
| n1 != E )
& ( n5 != E
| F != n0 )
& ( n4 != E
| F != n0 )
& ( n5 != F
| E != n0 )
& ( n4 != F
| E != n0 )
& leq(F,n5)
& leq(E,n5)
& leq(n0,F)
& leq(n0,E) )
& ! [C,D] :
( a_select3(r_ds1_filter,D,C) = a_select3(r_ds1_filter,C,D)
| ~ leq(D,n2)
| ~ leq(C,n2)
| ~ leq(n0,D)
| ~ leq(n0,C) )
& ! [A,B] :
( a_select3(q_ds1_filter,B,A) = a_select3(q_ds1_filter,A,B)
| ~ leq(B,n5)
| ~ leq(A,n5)
| ~ leq(n0,B)
| ~ leq(n0,A) ) ),
inference(fof_nnf,[status(thm)],[quaternion_ds1_symm_0681_neg]) ).
fof(sk_quaternion_ds1_symm_0681_neg,plain,
( a_select2(xinit_noise,n3) != n0
& n3 = sK1
& n3 = sK0
& sK1 = n0
& ( n5 != sK1
| n5 != sK0 )
& ( n5 != sK0
| n4 != sK1 )
& ( n5 != sK1
| n4 != sK0 )
& ( n4 != sK1
| n4 != sK0 )
& ( n5 != sK0
| n3 != sK1 )
& ( n4 != sK0
| n3 != sK1 )
& ( n5 != sK1
| n3 != sK0 )
& ( n4 != sK1
| n3 != sK0 )
& ( n3 != sK1
| n3 != sK0 )
& ( n5 != sK0
| n2 != sK1 )
& ( n4 != sK0
| n2 != sK1 )
& ( n3 != sK0
| n2 != sK1 )
& ( n5 != sK1
| n2 != sK0 )
& ( n4 != sK1
| n2 != sK0 )
& ( n5 != sK0
| n1 != sK1 )
& ( n4 != sK0
| n1 != sK1 )
& ( n3 != sK0
| n1 != sK1 )
& ( n5 != sK1
| n1 != sK0 )
& ( n4 != sK1
| n1 != sK0 )
& ( n5 != sK0
| sK1 != n0 )
& ( n4 != sK0
| sK1 != n0 )
& ( n5 != sK1
| sK0 != n0 )
& ( n4 != sK1
| sK0 != n0 )
& leq(sK1,n5)
& leq(sK0,n5)
& leq(n0,sK1)
& leq(n0,sK0)
& ! [C,D] :
( a_select3(r_ds1_filter,D,C) = a_select3(r_ds1_filter,C,D)
| ~ leq(D,n2)
| ~ leq(C,n2)
| ~ leq(n0,D)
| ~ leq(n0,C) )
& ! [A,B] :
( a_select3(q_ds1_filter,B,A) = a_select3(q_ds1_filter,A,B)
| ~ leq(B,n5)
| ~ leq(A,n5)
| ~ leq(n0,B)
| ~ leq(n0,A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(E,sK0),skolemize(F,sK1)],[nnf_56]) ).
cnf(c_401,negated_conjecture,
( n3 != sK1
| n3 != sK0 ),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_symm_0681_neg]) ).
cnf(c_901,negated_conjecture,
( n3 != sK1
| sK0 != n3 ),
inference(copy,[status(thm)],[c_401]) ).
cnf(c_402,negated_conjecture,
( sK1 != n3
| sK0 != n3 ),
inference(copy,[status(thm)],[c_901]) ).
cnf(c_419,negated_conjecture,
sK1 = n0,
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_symm_0681_neg]) ).
cnf(c_420,negated_conjecture,
n3 = sK0,
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_symm_0681_neg]) ).
cnf(c_421,negated_conjecture,
sK0 = n3,
inference(copy,[status(thm)],[c_420]) ).
cnf(c_422,negated_conjecture,
n3 = sK1,
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_symm_0681_neg]) ).
cnf(c_423,negated_conjecture,
n3 = n0,
inference(paramod,[status(thm)],[c_419,c_422]) ).
cnf(c_902,negated_conjecture,
( sK1 != n3
| n3 != n3 ),
inference(paramod,[status(thm)],[c_421,c_402]) ).
cnf(c_903,negated_conjecture,
( sK1 != n3
| n0 != n3 ),
inference(paramod,[status(thm)],[c_423,c_902]) ).
cnf(c_904,negated_conjecture,
( sK1 != n3
| n0 != n0 ),
inference(paramod,[status(thm)],[c_423,c_903]) ).
cnf(c_905,negated_conjecture,
( n0 != n3
| n0 != n0 ),
inference(paramod,[status(thm)],[c_419,c_904]) ).
cnf(c_906,negated_conjecture,
( n0 != n0
| n0 != n0 ),
inference(paramod,[status(thm)],[c_423,c_905]) ).
cnf(c_907,negated_conjecture,
n0 != n0,
inference(copy,[status(thm)],[c_906]) ).
cnf(c_900,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_907]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV228+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n009.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 13:20:44 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 244363 was started by sandbox2 on n009,
% 0.10/0.36 % Sat Sep 26 13:20:44 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.42
% 0.14/0.42 % From the command line: assign(max_seconds, 300).
% 1.26/0.60
% 1.26/0.60 % SZS status Theorem for theBenchmark
% 1.26/0.60
% 1.26/0.60 % Proof 1 at 0.14 (+ 0.02) seconds.
% 1.26/0.60 % Length of proof is 9.
% 1.26/0.60 % Level of proof is 3.
% 1.26/0.60 % Maximum clause weight is 8.000.
% 1.26/0.60 % Given clauses 0.
% 1.26/0.60
% 1.26/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------