%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV213+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 : n018.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 09:07:02 AM UTC 2026
% Result : Theorem 0.44s 0.57s
% Output : CNFRefutation 0.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 22 ( 10 unt; 0 def)
% Number of atoms : 326 ( 309 equ)
% Maximal formula atoms : 75 ( 14 avg)
% Number of connectives : 522 ( 218 ~; 74 |; 226 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 45 ( 9 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_0081,conjecture,
! [A,B] :
( ( leq(B,n5)
& leq(A,n5)
& leq(n0,B)
& leq(n0,A) )
=> ( ( n3 = A
& n2 = B
& n2 = A
& n0 = B
& ~ ( 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 )
& ~ ( n5 = B
& n0 = A )
& ~ ( n4 = B
& n0 = A )
& ~ ( n3 = B
& n0 = A )
& ~ ( n2 = B
& n0 = A )
& ~ ( n1 = B
& n0 = A ) )
=> times(divide(n1,n400),a_select2(sigma,n2)) = n0 ) ),
file('theBenchmark.p',quaternion_ds1_symm_0081) ).
fof(quaternion_ds1_symm_0081_neg,negated_conjecture,
~ ! [A,B] :
( ( leq(B,n5)
& leq(A,n5)
& leq(n0,B)
& leq(n0,A) )
=> ( ( n3 = A
& n2 = B
& n2 = A
& n0 = B
& ~ ( 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 )
& ~ ( n5 = B
& n0 = A )
& ~ ( n4 = B
& n0 = A )
& ~ ( n3 = B
& n0 = A )
& ~ ( n2 = B
& n0 = A )
& ~ ( n1 = B
& n0 = A ) )
=> times(divide(n1,n400),a_select2(sigma,n2)) = n0 ) ),
inference(assume_negation,[status(cth)],[quaternion_ds1_symm_0081]) ).
fof(nnf_56,plain,
? [A,B] :
( times(divide(n1,n400),a_select2(sigma,n2)) != n0
& n3 = A
& n2 = B
& n2 = A
& B = 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 )
& ( n5 != B
| A != n0 )
& ( n4 != B
| A != n0 )
& ( n3 != B
| A != n0 )
& ( n2 != B
| A != n0 )
& ( n1 != B
| A != n0 )
& leq(B,n5)
& leq(A,n5)
& leq(n0,B)
& leq(n0,A) ),
inference(fof_nnf,[status(thm)],[quaternion_ds1_symm_0081_neg]) ).
fof(sk_quaternion_ds1_symm_0081_neg,plain,
( times(divide(n1,n400),a_select2(sigma,n2)) != n0
& n3 = sK0
& n2 = sK1
& n2 = 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 )
& ( 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 )
& ( n5 != sK1
| sK0 != n0 )
& ( n4 != sK1
| sK0 != n0 )
& ( n3 != sK1
| sK0 != n0 )
& ( n2 != sK1
| sK0 != n0 )
& ( n1 != 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_417,negated_conjecture,
( n3 != sK1
| n3 != sK0 ),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_symm_0081_neg]) ).
cnf(c_909,negated_conjecture,
( n3 != sK1
| sK0 != n3 ),
inference(copy,[status(thm)],[c_417]) ).
cnf(c_418,negated_conjecture,
( sK1 != n3
| sK0 != n3 ),
inference(copy,[status(thm)],[c_909]) ).
cnf(c_435,negated_conjecture,
sK1 = n0,
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_symm_0081_neg]) ).
cnf(c_436,negated_conjecture,
n2 = sK0,
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_symm_0081_neg]) ).
cnf(c_437,negated_conjecture,
sK0 = n2,
inference(copy,[status(thm)],[c_436]) ).
cnf(c_438,negated_conjecture,
n2 = sK1,
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_symm_0081_neg]) ).
cnf(c_439,negated_conjecture,
n2 = n0,
inference(paramod,[status(thm)],[c_435,c_438]) ).
cnf(c_440,negated_conjecture,
n3 = sK0,
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_symm_0081_neg]) ).
cnf(c_910,negated_conjecture,
n3 = n2,
inference(paramod,[status(thm)],[c_437,c_440]) ).
cnf(c_441,negated_conjecture,
n3 = n0,
inference(paramod,[status(thm)],[c_439,c_910]) ).
cnf(c_911,negated_conjecture,
( sK1 != n3
| n2 != n3 ),
inference(paramod,[status(thm)],[c_437,c_418]) ).
cnf(c_912,negated_conjecture,
( sK1 != n3
| n0 != n3 ),
inference(paramod,[status(thm)],[c_439,c_911]) ).
cnf(c_913,negated_conjecture,
( sK1 != n3
| n0 != n0 ),
inference(paramod,[status(thm)],[c_441,c_912]) ).
cnf(c_914,negated_conjecture,
( n0 != n3
| n0 != n0 ),
inference(paramod,[status(thm)],[c_435,c_913]) ).
cnf(c_915,negated_conjecture,
( n0 != n0
| n0 != n0 ),
inference(paramod,[status(thm)],[c_441,c_914]) ).
cnf(c_916,negated_conjecture,
n0 != n0,
inference(copy,[status(thm)],[c_915]) ).
cnf(c_908,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_916]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV213+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n018.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 26 13:22:06 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 542900 was started by sandbox on n018,
% 0.08/0.35 % Sat Sep 26 13:22:06 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.41
% 0.15/0.41 % From the command line: assign(max_seconds, 300).
% 0.44/0.57
% 0.44/0.57 % SZS status Theorem for theBenchmark
% 0.44/0.57
% 0.44/0.57 % Proof 1 at 0.11 (+ 0.01) seconds.
% 0.44/0.57 % Length of proof is 11.
% 0.44/0.57 % Level of proof is 4.
% 0.44/0.57 % Maximum clause weight is 11.000.
% 0.44/0.57 % Given clauses 0.
% 0.44/0.57
% 0.44/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------