%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV215+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 : n019.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 09:07:03 AM UTC 2026
% Result : Theorem 0.19s 10.61s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 21 ( 10 unt; 0 def)
% Number of atoms : 324 ( 307 equ)
% Maximal formula atoms : 75 ( 15 avg)
% Number of connectives : 519 ( 216 ~; 73 |; 226 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 45 ( 10 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 6 ( 0 sgn 4 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(quaternion_ds1_symm_0161,conjecture,
! [A,B] :
( ( leq(B,n5)
& leq(A,n5)
& leq(n0,B)
& leq(n0,A) )
=> ( ( n4 = B
& n2 = B
& n2 = A
& n0 = A
& ~ ( n5 = B
& n5 = A )
& ~ ( n5 = A
& n4 = B )
& ~ ( n5 = B
& n4 = A )
& ~ ( n4 = B
& n4 = A )
& ~ ( n5 = A
& n3 = B )
& ~ ( n4 = A
& n3 = B )
& ~ ( n5 = B
& n3 = A )
& ~ ( n4 = B
& n3 = A )
& ~ ( n3 = B
& n3 = A )
& ~ ( n5 = A
& n2 = B )
& ~ ( n4 = A
& n2 = B )
& ~ ( n3 = A
& n2 = B )
& ~ ( n5 = B
& n2 = A )
& ~ ( n4 = B
& n2 = A )
& ~ ( n3 = B
& n2 = A )
& ~ ( n2 = B
& n2 = A )
& ~ ( n5 = A
& n1 = B )
& ~ ( n4 = A
& n1 = B )
& ~ ( n3 = A
& n1 = B )
& ~ ( n2 = A
& n1 = B )
& ~ ( n5 = B
& n1 = A )
& ~ ( n4 = B
& n1 = A )
& ~ ( n3 = B
& n1 = A )
& ~ ( n2 = B
& n1 = A )
& ~ ( n1 = B
& n1 = A )
& ~ ( n5 = A
& n0 = B )
& ~ ( n4 = A
& n0 = B )
& ~ ( n3 = A
& n0 = B )
& ~ ( n2 = A
& n0 = B )
& ~ ( n1 = A
& n0 = B )
& ~ ( n5 = B
& n0 = A )
& ~ ( n4 = B
& n0 = A )
& ~ ( n3 = B
& n0 = A ) )
=> n0 = times(divide(n1,n400),a_select2(sigma,n2)) ) ),
file('theBenchmark.p',quaternion_ds1_symm_0161) ).
fof(quaternion_ds1_symm_0161_neg,negated_conjecture,
~ ! [A,B] :
( ( leq(B,n5)
& leq(A,n5)
& leq(n0,B)
& leq(n0,A) )
=> ( ( n4 = B
& n2 = B
& n2 = A
& n0 = A
& ~ ( n5 = B
& n5 = A )
& ~ ( n5 = A
& n4 = B )
& ~ ( n5 = B
& n4 = A )
& ~ ( n4 = B
& n4 = A )
& ~ ( n5 = A
& n3 = B )
& ~ ( n4 = A
& n3 = B )
& ~ ( n5 = B
& n3 = A )
& ~ ( n4 = B
& n3 = A )
& ~ ( n3 = B
& n3 = A )
& ~ ( n5 = A
& n2 = B )
& ~ ( n4 = A
& n2 = B )
& ~ ( n3 = A
& n2 = B )
& ~ ( n5 = B
& n2 = A )
& ~ ( n4 = B
& n2 = A )
& ~ ( n3 = B
& n2 = A )
& ~ ( n2 = B
& n2 = A )
& ~ ( n5 = A
& n1 = B )
& ~ ( n4 = A
& n1 = B )
& ~ ( n3 = A
& n1 = B )
& ~ ( n2 = A
& n1 = B )
& ~ ( n5 = B
& n1 = A )
& ~ ( n4 = B
& n1 = A )
& ~ ( n3 = B
& n1 = A )
& ~ ( n2 = B
& n1 = A )
& ~ ( n1 = B
& n1 = A )
& ~ ( n5 = A
& n0 = B )
& ~ ( n4 = A
& n0 = B )
& ~ ( n3 = A
& n0 = B )
& ~ ( n2 = A
& n0 = B )
& ~ ( n1 = A
& n0 = B )
& ~ ( n5 = B
& n0 = A )
& ~ ( n4 = B
& n0 = A )
& ~ ( n3 = B
& n0 = A ) )
=> n0 = times(divide(n1,n400),a_select2(sigma,n2)) ) ),
inference(assume_negation,[status(cth)],[quaternion_ds1_symm_0161]) ).
fof(nnf_56,plain,
? [A,B] :
( times(divide(n1,n400),a_select2(sigma,n2)) != n0
& n4 = B
& n2 = B
& n2 = A
& A = n0
& ( n5 != B
| n5 != A )
& ( n5 != A
| n4 != B )
& ( n5 != B
| n4 != A )
& ( n4 != B
| n4 != A )
& ( n5 != A
| n3 != B )
& ( n4 != A
| n3 != B )
& ( n5 != B
| n3 != A )
& ( n4 != B
| n3 != A )
& ( n3 != B
| n3 != A )
& ( n5 != A
| n2 != B )
& ( n4 != A
| n2 != B )
& ( n3 != A
| n2 != B )
& ( n5 != B
| n2 != A )
& ( n4 != B
| n2 != A )
& ( n3 != B
| n2 != A )
& ( n2 != B
| n2 != A )
& ( n5 != A
| n1 != B )
& ( n4 != A
| n1 != B )
& ( n3 != A
| n1 != B )
& ( n2 != A
| n1 != B )
& ( n5 != B
| n1 != A )
& ( n4 != B
| n1 != A )
& ( n3 != B
| n1 != A )
& ( n2 != B
| n1 != A )
& ( n1 != B
| n1 != A )
& ( n5 != A
| B != n0 )
& ( n4 != A
| B != n0 )
& ( n3 != A
| B != n0 )
& ( n2 != A
| B != n0 )
& ( n1 != A
| B != n0 )
& ( n5 != B
| A != n0 )
& ( n4 != B
| A != n0 )
& ( n3 != B
| A != n0 )
& leq(B,n5)
& leq(A,n5)
& leq(n0,B)
& leq(n0,A) ),
inference(fof_nnf,[status(thm)],[quaternion_ds1_symm_0161_neg]) ).
fof(sk_quaternion_ds1_symm_0161_neg,plain,
( times(divide(n1,n400),a_select2(sigma,n2)) != n0
& n4 = sK1
& n2 = sK1
& n2 = sK0
& sK0 = 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 )
& ( 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 )
& ( n1 != sK1
| n1 != sK0 )
& ( n5 != sK0
| sK1 != n0 )
& ( n4 != sK0
| sK1 != n0 )
& ( n3 != sK0
| sK1 != n0 )
& ( n2 != sK0
| sK1 != n0 )
& ( n1 != 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) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_56]) ).
cnf(c_427,negated_conjecture,
( n4 != sK1
| n4 != sK0 ),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_symm_0161_neg]) ).
cnf(c_908,negated_conjecture,
( n4 != sK1
| sK0 != n4 ),
inference(copy,[status(thm)],[c_427]) ).
cnf(c_428,negated_conjecture,
( sK1 != n4
| sK0 != n4 ),
inference(copy,[status(thm)],[c_908]) ).
cnf(c_435,negated_conjecture,
sK0 = n0,
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_symm_0161_neg]) ).
cnf(c_436,negated_conjecture,
n2 = sK0,
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_symm_0161_neg]) ).
cnf(c_437,negated_conjecture,
n2 = n0,
inference(paramod,[status(thm)],[c_435,c_436]) ).
cnf(c_438,negated_conjecture,
n2 = sK1,
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_symm_0161_neg]) ).
cnf(c_909,negated_conjecture,
n0 = sK1,
inference(paramod,[status(thm)],[c_437,c_438]) ).
cnf(c_439,negated_conjecture,
sK1 = n0,
inference(copy,[status(thm)],[c_909]) ).
cnf(c_440,negated_conjecture,
n4 = sK1,
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_symm_0161_neg]) ).
cnf(c_441,negated_conjecture,
n4 = n0,
inference(paramod,[status(thm)],[c_439,c_440]) ).
cnf(c_910,negated_conjecture,
( sK1 != n4
| n0 != n4 ),
inference(paramod,[status(thm)],[c_435,c_428]) ).
cnf(c_911,negated_conjecture,
( sK1 != n4
| n0 != n0 ),
inference(paramod,[status(thm)],[c_441,c_910]) ).
cnf(c_912,negated_conjecture,
( n0 != n4
| n0 != n0 ),
inference(paramod,[status(thm)],[c_439,c_911]) ).
cnf(c_913,negated_conjecture,
( n0 != n0
| n0 != n0 ),
inference(paramod,[status(thm)],[c_441,c_912]) ).
cnf(c_914,negated_conjecture,
n0 != n0,
inference(copy,[status(thm)],[c_913]) ).
cnf(c_907,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_914]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV215+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/10.42 % Computer : n019.cluster.edu
% 0.16/10.42 % Model : x86_64 x86_64
% 0.16/10.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/10.42 % Memory : 8046.5625MB
% 0.16/10.42 % OS : Linux 6.8.0-71-generic
% 0.16/10.42 % CPULimit : 300
% 0.16/10.42 % WCLimit : 300
% 0.16/10.43 % DateTime : Sat Sep 26 13:20:29 UTC 2026
% 0.16/10.43 % CPUTime :
% 0.16/10.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/10.43 % Process 1411912 was started by sandbox2 on n019,
% 0.16/10.43 % Sat Sep 26 13:20:29 2026
% 0.16/10.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/10.49
% 0.16/10.49 % From the command line: assign(max_seconds, 300).
% 0.19/10.61
% 0.19/10.61 % SZS status Theorem for theBenchmark
% 0.19/10.61
% 0.19/10.61 % Proof 1 at 0.10 (+ 0.01) seconds.
% 0.19/10.61 % Length of proof is 11.
% 0.19/10.61 % Level of proof is 5.
% 0.19/10.61 % Maximum clause weight is 11.000.
% 0.19/10.61 % Given clauses 0.
% 0.19/10.61
% 0.19/10.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------