%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV226+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 : 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 09:07:04 AM UTC 2026
% Result : Theorem 0.05s 5.39s
% Output : CNFRefutation 0.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 7 unt; 0 def)
% Number of atoms : 331 ( 282 equ)
% Maximal formula atoms : 81 ( 30 avg)
% Number of connectives : 527 ( 207 ~; 78 |; 232 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 45 ( 16 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_0601,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) )
=> ( ( n2 = F
& n2 = E
& n1 = F
& n1 = E
& ~ ( 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 )
& ~ ( n3 = F
& n2 = E )
& ~ ( n2 = F
& n2 = E )
& ~ ( n5 = E
& n1 = F )
& ~ ( n4 = E
& n1 = F )
& ~ ( n3 = E
& n1 = F )
& ~ ( n2 = E
& n1 = F )
& ~ ( n5 = F
& n1 = E )
& ~ ( n4 = F
& n1 = E )
& ~ ( n3 = F
& n1 = E )
& ~ ( n2 = F
& n1 = E )
& ~ ( n5 = E
& n0 = F )
& ~ ( n4 = E
& n0 = F )
& ~ ( n3 = E
& n0 = F )
& ~ ( n2 = E
& n0 = F )
& ~ ( n5 = F
& n0 = E )
& ~ ( n4 = F
& n0 = E )
& ~ ( n3 = F
& n0 = E ) )
=> a_select2(xinit_noise,n1) = a_select2(xinit_noise,n2) ) ) ),
file('theBenchmark.p',quaternion_ds1_symm_0601) ).
fof(quaternion_ds1_symm_0601_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) )
=> ( ( n2 = F
& n2 = E
& n1 = F
& n1 = E
& ~ ( 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 )
& ~ ( n3 = F
& n2 = E )
& ~ ( n2 = F
& n2 = E )
& ~ ( n5 = E
& n1 = F )
& ~ ( n4 = E
& n1 = F )
& ~ ( n3 = E
& n1 = F )
& ~ ( n2 = E
& n1 = F )
& ~ ( n5 = F
& n1 = E )
& ~ ( n4 = F
& n1 = E )
& ~ ( n3 = F
& n1 = E )
& ~ ( n2 = F
& n1 = E )
& ~ ( n5 = E
& n0 = F )
& ~ ( n4 = E
& n0 = F )
& ~ ( n3 = E
& n0 = F )
& ~ ( n2 = E
& n0 = F )
& ~ ( n5 = F
& n0 = E )
& ~ ( n4 = F
& n0 = E )
& ~ ( n3 = F
& n0 = E ) )
=> a_select2(xinit_noise,n1) = a_select2(xinit_noise,n2) ) ) ),
inference(assume_negation,[status(cth)],[quaternion_ds1_symm_0601]) ).
fof(nnf_56,plain,
( ? [E,F] :
( a_select2(xinit_noise,n2) != a_select2(xinit_noise,n1)
& n2 = F
& n2 = E
& n1 = F
& n1 = E
& ( 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 )
& ( n3 != F
| n2 != E )
& ( n2 != F
| n2 != E )
& ( n5 != E
| n1 != F )
& ( n4 != E
| n1 != F )
& ( n3 != E
| n1 != F )
& ( n2 != E
| n1 != F )
& ( n5 != F
| n1 != E )
& ( n4 != F
| n1 != E )
& ( n3 != F
| n1 != E )
& ( n2 != F
| n1 != E )
& ( n5 != E
| F != n0 )
& ( n4 != E
| F != n0 )
& ( n3 != E
| F != n0 )
& ( n2 != E
| F != n0 )
& ( n5 != F
| E != n0 )
& ( n4 != F
| E != n0 )
& ( n3 != 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_0601_neg]) ).
fof(sk_quaternion_ds1_symm_0601_neg,plain,
( a_select2(xinit_noise,n2) != a_select2(xinit_noise,n1)
& n2 = sK1
& n2 = sK0
& n1 = sK1
& n1 = sK0
& ( 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 )
& ( n3 != sK1
| n2 != sK0 )
& ( n2 != sK1
| n2 != sK0 )
& ( n5 != sK0
| n1 != sK1 )
& ( n4 != sK0
| n1 != sK1 )
& ( n3 != sK0
| n1 != sK1 )
& ( n2 != sK0
| n1 != sK1 )
& ( n5 != sK1
| n1 != sK0 )
& ( n4 != sK1
| n1 != sK0 )
& ( n3 != sK1
| n1 != sK0 )
& ( n2 != sK1
| n1 != sK0 )
& ( n5 != sK0
| sK1 != n0 )
& ( n4 != sK0
| sK1 != n0 )
& ( n3 != sK0
| sK1 != n0 )
& ( n2 != sK0
| sK1 != n0 )
& ( n5 != sK1
| sK0 != n0 )
& ( n4 != sK1
| sK0 != n0 )
& ( n3 != 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_435,negated_conjecture,
n1 = sK0,
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_symm_0601_neg]) ).
cnf(c_436,negated_conjecture,
sK0 = n1,
inference(copy,[status(thm)],[c_435]) ).
cnf(c_439,negated_conjecture,
n2 = sK0,
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_symm_0601_neg]) ).
cnf(c_440,negated_conjecture,
n2 = n1,
inference(paramod,[status(thm)],[c_436,c_439]) ).
cnf(c_442,negated_conjecture,
a_select2(xinit_noise,n2) != a_select2(xinit_noise,n1),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_symm_0601_neg]) ).
cnf(c_444,negated_conjecture,
a_select2(xinit_noise,n1) != a_select2(xinit_noise,n1),
inference(paramod,[status(thm)],[c_440,c_442]) ).
cnf(c_443,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_444]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWV226+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/5.32 % Computer : n012.cluster.edu
% 0.05/5.32 % Model : x86_64 x86_64
% 0.05/5.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/5.32 % Memory : 8046.5625MB
% 0.05/5.32 % OS : Linux 6.8.0-71-generic
% 0.05/5.32 % CPULimit : 300
% 0.05/5.32 % WCLimit : 300
% 0.05/5.32 % DateTime : Sat Sep 26 13:20:40 UTC 2026
% 0.05/5.32 % CPUTime :
% 0.05/5.32 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.05/5.32 % Process 702203 was started by sandbox on n012,
% 0.05/5.32 % Sat Sep 26 13:20:40 2026
% 0.05/5.32 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.05/5.35
% 0.05/5.35 % From the command line: assign(max_seconds, 300).
% 0.05/5.39
% 0.05/5.39 % SZS status Theorem for theBenchmark
% 0.05/5.39
% 0.05/5.39 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.05/5.39 % Length of proof is 7.
% 0.05/5.39 % Level of proof is 4.
% 0.05/5.39 % Maximum clause weight is 3.000.
% 0.05/5.39 % Given clauses 0.
% 0.05/5.39
% 0.05/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------