%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV220+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 : n008.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 0.13s 5.54s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 13 ( 6 unt; 0 def)
% Number of atoms : 168 ( 151 equ)
% Maximal formula atoms : 39 ( 12 avg)
% Number of connectives : 255 ( 100 ~; 33 |; 118 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 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_0361,conjecture,
! [A,B] :
( ( leq(B,n5)
& leq(A,n5)
& leq(n0,B)
& leq(n0,A) )
=> ( ( n5 = B
& n3 = B
& n3 = A
& n1 = 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 )
& ~ ( n5 = A
& n2 = B )
& ~ ( n4 = A
& n2 = B )
& ~ ( n5 = B
& n2 = A )
& ~ ( n5 = A
& n1 = B )
& ~ ( n4 = A
& n1 = B )
& ~ ( n5 = A
& n0 = B )
& ~ ( n4 = A
& n0 = B ) )
=> times(divide(n1,n400),a_select2(sigma,n3)) = n0 ) ),
file('theBenchmark.p',quaternion_ds1_symm_0361) ).
fof(quaternion_ds1_symm_0361_neg,negated_conjecture,
~ ! [A,B] :
( ( leq(B,n5)
& leq(A,n5)
& leq(n0,B)
& leq(n0,A) )
=> ( ( n5 = B
& n3 = B
& n3 = A
& n1 = 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 )
& ~ ( n5 = A
& n2 = B )
& ~ ( n4 = A
& n2 = B )
& ~ ( n5 = B
& n2 = A )
& ~ ( n5 = A
& n1 = B )
& ~ ( n4 = A
& n1 = B )
& ~ ( n5 = A
& n0 = B )
& ~ ( n4 = A
& n0 = B ) )
=> times(divide(n1,n400),a_select2(sigma,n3)) = n0 ) ),
inference(assume_negation,[status(cth)],[quaternion_ds1_symm_0361]) ).
fof(nnf_56,plain,
? [A,B] :
( times(divide(n1,n400),a_select2(sigma,n3)) != n0
& n5 = B
& n3 = B
& n3 = A
& n1 = 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 )
& ( n5 != A
| n2 != B )
& ( n4 != A
| n2 != B )
& ( n5 != B
| n2 != A )
& ( n5 != A
| n1 != B )
& ( n4 != A
| n1 != B )
& ( n5 != A
| B != n0 )
& ( n4 != A
| B != n0 )
& leq(B,n5)
& leq(A,n5)
& leq(n0,B)
& leq(n0,A) ),
inference(fof_nnf,[status(thm)],[quaternion_ds1_symm_0361_neg]) ).
fof(sk_quaternion_ds1_symm_0361_neg,plain,
( times(divide(n1,n400),a_select2(sigma,n3)) != n0
& n5 = sK1
& n3 = sK1
& n3 = sK0
& 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 )
& ( n5 != sK0
| n2 != sK1 )
& ( n4 != sK0
| n2 != sK1 )
& ( n5 != sK1
| n2 != sK0 )
& ( n5 != sK0
| n1 != sK1 )
& ( n4 != sK0
| n1 != sK1 )
& ( n5 != sK0
| sK1 != n0 )
& ( n4 != sK0
| sK1 != 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_383,negated_conjecture,
( n5 != sK1
| n3 != sK0 ),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_symm_0361_neg]) ).
cnf(c_869,negated_conjecture,
( n5 != sK1
| sK0 != n3 ),
inference(copy,[status(thm)],[c_383]) ).
cnf(c_384,negated_conjecture,
( sK1 != n5
| sK0 != n3 ),
inference(copy,[status(thm)],[c_869]) ).
cnf(c_399,negated_conjecture,
n3 = sK0,
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_symm_0361_neg]) ).
cnf(c_400,negated_conjecture,
sK0 = n3,
inference(copy,[status(thm)],[c_399]) ).
cnf(c_403,negated_conjecture,
n5 = sK1,
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_symm_0361_neg]) ).
cnf(c_404,negated_conjecture,
sK1 = n5,
inference(copy,[status(thm)],[c_403]) ).
cnf(c_870,negated_conjecture,
sK1 != n5,
inference(resolve,[status(thm)],[c_400,c_384]) ).
cnf(c_868,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_404,c_870]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV220+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n008.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Sat Sep 26 13:21:15 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.37 % Process 3762244 was started by sandbox on n008,
% 0.09/5.37 % Sat Sep 26 13:21:15 2026
% 0.09/5.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/5.43
% 0.13/5.43 % From the command line: assign(max_seconds, 300).
% 0.13/5.54
% 0.13/5.54 % SZS status Theorem for theBenchmark
% 0.13/5.54
% 0.13/5.54 % Proof 1 at 0.08 (+ 0.01) seconds.
% 0.13/5.54 % Length of proof is 8.
% 0.13/5.54 % Level of proof is 3.
% 0.13/5.54 % Maximum clause weight is 11.000.
% 0.13/5.54 % Given clauses 0.
% 0.13/5.54
% 0.13/5.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------