%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV225+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 : n017.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 0.19s 0.55s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 6
% Syntax : Number of formulae : 50 ( 39 unt; 0 def)
% Number of atoms : 369 ( 320 equ)
% Maximal formula atoms : 79 ( 7 avg)
% Number of connectives : 533 ( 214 ~; 83 |; 226 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 44 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 11 con; 0-3 aty)
% Number of variables : 28 ( 0 sgn 22 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(succ_plus_1_r,axiom,
! [X] : plus(X,n1) = succ(X),
file('theBenchmark.p',succ_plus_1_r) ).
fof(succ_plus_1_l,axiom,
! [X] : plus(n1,X) = succ(X),
file('theBenchmark.p',succ_plus_1_l) ).
fof(quaternion_ds1_symm_0561,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 = E
& n2 = F
& 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 )
& ~ ( n5 = F
& n0 = E )
& ~ ( n4 = F
& n0 = E )
& ~ ( n3 = F
& n0 = E )
& ~ ( n2 = F
& n0 = E ) )
=> n0 = a_select2(xinit_noise,n1) ) ) ),
file('theBenchmark.p',quaternion_ds1_symm_0561) ).
fof(quaternion_ds1_symm_0561_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 = E
& n2 = F
& 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 )
& ~ ( n5 = F
& n0 = E )
& ~ ( n4 = F
& n0 = E )
& ~ ( n3 = F
& n0 = E )
& ~ ( n2 = F
& n0 = E ) )
=> n0 = a_select2(xinit_noise,n1) ) ) ),
inference(assume_negation,[status(cth)],[quaternion_ds1_symm_0561]) ).
cnf(c_282,plain,
plus(A,n1) = succ(A),
inference(clausify,[status(thm)],[succ_plus_1_r]) ).
cnf(c_283,plain,
succ(A) = plus(A,n1),
inference(copy,[status(thm)],[c_282]) ).
cnf(c_284,plain,
plus(n1,A) = succ(A),
inference(clausify,[status(thm)],[succ_plus_1_l]) ).
cnf(c_285,plain,
plus(n1,A) = plus(A,n1),
inference(paramod,[status(thm)],[c_283,c_284]) ).
fof(successor_4,axiom,
succ(succ(succ(succ(n0)))) = n4,
file('theBenchmark.p',successor_4) ).
cnf(c_357,plain,
succ(succ(succ(succ(n0)))) = n4,
inference(clausify,[status(thm)],[successor_4]) ).
cnf(c_916,plain,
succ(succ(succ(plus(n0,n1)))) = n4,
inference(paramod,[status(thm)],[c_283,c_357]) ).
cnf(c_917,plain,
succ(succ(plus(plus(n0,n1),n1))) = n4,
inference(paramod,[status(thm)],[c_283,c_916]) ).
cnf(c_918,plain,
succ(succ(plus(n1,plus(n0,n1)))) = n4,
inference(paramod,[status(thm)],[c_285,c_917]) ).
cnf(c_919,plain,
succ(plus(plus(n1,plus(n0,n1)),n1)) = n4,
inference(paramod,[status(thm)],[c_283,c_918]) ).
cnf(c_920,plain,
succ(plus(n1,plus(n1,plus(n0,n1)))) = n4,
inference(paramod,[status(thm)],[c_285,c_919]) ).
cnf(c_921,plain,
plus(plus(n1,plus(n1,plus(n0,n1))),n1) = n4,
inference(paramod,[status(thm)],[c_283,c_920]) ).
cnf(c_358,plain,
plus(n1,plus(n1,plus(n1,plus(n0,n1)))) = n4,
inference(paramod,[status(thm)],[c_285,c_921]) ).
fof(successor_1,axiom,
succ(n0) = n1,
file('theBenchmark.p',successor_1) ).
cnf(c_361,plain,
succ(n0) = n1,
inference(clausify,[status(thm)],[successor_1]) ).
cnf(c_362,plain,
plus(n0,n1) = n1,
inference(paramod,[status(thm)],[c_283,c_361]) ).
fof(successor_2,axiom,
succ(succ(n0)) = n2,
file('theBenchmark.p',successor_2) ).
cnf(c_363,plain,
succ(succ(n0)) = n2,
inference(clausify,[status(thm)],[successor_2]) ).
cnf(c_922,plain,
succ(plus(n0,n1)) = n2,
inference(paramod,[status(thm)],[c_283,c_363]) ).
cnf(c_923,plain,
succ(n1) = n2,
inference(paramod,[status(thm)],[c_362,c_922]) ).
cnf(c_364,plain,
plus(n1,n1) = n2,
inference(paramod,[status(thm)],[c_283,c_923]) ).
fof(nnf_56,plain,
( ? [E,F] :
( a_select2(xinit_noise,n1) != n0
& n3 = E
& n2 = F
& 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 )
& ( n5 != F
| E != n0 )
& ( n4 != F
| E != n0 )
& ( n3 != F
| E != n0 )
& ( n2 != 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_0561_neg]) ).
fof(sk_quaternion_ds1_symm_0561_neg,plain,
( a_select2(xinit_noise,n1) != n0
& n3 = sK0
& n2 = sK1
& 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 )
& ( n5 != sK1
| sK0 != n0 )
& ( n4 != sK1
| sK0 != n0 )
& ( n3 != sK1
| sK0 != n0 )
& ( n2 != 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_425,negated_conjecture,
( n4 != sK1
| n4 != sK0 ),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_symm_0561_neg]) ).
cnf(c_924,negated_conjecture,
( n4 != sK1
| sK0 != n4 ),
inference(copy,[status(thm)],[c_425]) ).
cnf(c_426,negated_conjecture,
( sK1 != n4
| sK0 != n4 ),
inference(copy,[status(thm)],[c_924]) ).
cnf(c_433,negated_conjecture,
n1 = sK0,
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_symm_0561_neg]) ).
cnf(c_434,negated_conjecture,
sK0 = n1,
inference(copy,[status(thm)],[c_433]) ).
cnf(c_435,negated_conjecture,
n1 = sK1,
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_symm_0561_neg]) ).
cnf(c_436,negated_conjecture,
sK1 = n1,
inference(copy,[status(thm)],[c_435]) ).
cnf(c_437,negated_conjecture,
n2 = sK1,
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_symm_0561_neg]) ).
cnf(c_438,negated_conjecture,
n2 = n1,
inference(paramod,[status(thm)],[c_436,c_437]) ).
cnf(c_925,plain,
plus(n1,plus(n1,plus(n1,n1))) = n4,
inference(paramod,[status(thm)],[c_362,c_358]) ).
cnf(c_926,plain,
plus(n1,plus(n1,n2)) = n4,
inference(paramod,[status(thm)],[c_364,c_925]) ).
cnf(c_927,plain,
plus(n1,plus(n1,n1)) = n4,
inference(paramod,[status(thm)],[c_438,c_926]) ).
cnf(c_928,plain,
plus(n1,n2) = n4,
inference(paramod,[status(thm)],[c_364,c_927]) ).
cnf(c_929,plain,
plus(n1,n1) = n4,
inference(paramod,[status(thm)],[c_438,c_928]) ).
cnf(c_930,plain,
n2 = n4,
inference(paramod,[status(thm)],[c_364,c_929]) ).
cnf(c_931,plain,
n1 = n4,
inference(paramod,[status(thm)],[c_438,c_930]) ).
cnf(c_911,plain,
n4 = n1,
inference(copy,[status(thm)],[c_931]) ).
cnf(c_932,negated_conjecture,
( sK1 != n4
| n1 != n4 ),
inference(paramod,[status(thm)],[c_434,c_426]) ).
cnf(c_933,negated_conjecture,
( sK1 != n4
| n1 != n1 ),
inference(paramod,[status(thm)],[c_911,c_932]) ).
cnf(c_934,negated_conjecture,
( n1 != n4
| n1 != n1 ),
inference(paramod,[status(thm)],[c_436,c_933]) ).
cnf(c_935,negated_conjecture,
( n1 != n1
| n1 != n1 ),
inference(paramod,[status(thm)],[c_911,c_934]) ).
cnf(c_936,negated_conjecture,
n1 != n1,
inference(copy,[status(thm)],[c_935]) ).
cnf(c_915,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_936]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV225+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n017.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 13:16:19 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 799023 was started by sandbox2 on n017,
% 0.09/0.37 % Sat Sep 26 13:16:19 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.43
% 0.09/0.43 % From the command line: assign(max_seconds, 300).
% 0.19/0.55
% 0.19/0.55 % SZS status Theorem for theBenchmark
% 0.19/0.55
% 0.19/0.55 % Proof 1 at 0.09 (+ 0.02) seconds.
% 0.19/0.55 % Length of proof is 23.
% 0.19/0.55 % Level of proof is 6.
% 0.19/0.55 % Maximum clause weight is 11.000.
% 0.19/0.55 % Given clauses 0.
% 0.19/0.55
% 0.19/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------