%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV232+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 09:07:05 AM UTC 2026
% Result : Theorem 1.24s 0.70s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 5 unt; 0 def)
% Number of atoms : 121 ( 88 equ)
% Maximal formula atoms : 28 ( 11 avg)
% Number of connectives : 168 ( 58 ~; 24 |; 78 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-3 aty)
% Number of variables : 14 ( 0 sgn 12 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(quaternion_ds1_symm_0841,conjecture,
( ! [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) )
=> ! [C,D] :
( ( leq(D,n2)
& leq(C,n2)
& leq(n0,D)
& leq(n0,C) )
=> ( ( n2 = C
& n1 = D
& n1 = C
& n0 = D
& ~ ( n2 = D
& n2 = C )
& ~ ( n2 = C
& n1 = D )
& ~ ( n2 = D
& n1 = C )
& ~ ( n1 = D
& n1 = C )
& ~ ( n2 = C
& n0 = D )
& ~ ( n2 = D
& n0 = C )
& ~ ( n1 = D
& n0 = C ) )
=> a_select2(rho,n1) = n0 ) ) ),
file('theBenchmark.p',quaternion_ds1_symm_0841) ).
fof(quaternion_ds1_symm_0841_neg,negated_conjecture,
~ ( ! [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) )
=> ! [C,D] :
( ( leq(D,n2)
& leq(C,n2)
& leq(n0,D)
& leq(n0,C) )
=> ( ( n2 = C
& n1 = D
& n1 = C
& n0 = D
& ~ ( n2 = D
& n2 = C )
& ~ ( n2 = C
& n1 = D )
& ~ ( n2 = D
& n1 = C )
& ~ ( n1 = D
& n1 = C )
& ~ ( n2 = C
& n0 = D )
& ~ ( n2 = D
& n0 = C )
& ~ ( n1 = D
& n0 = C ) )
=> a_select2(rho,n1) = n0 ) ) ),
inference(assume_negation,[status(cth)],[quaternion_ds1_symm_0841]) ).
fof(nnf_56,plain,
( ? [C,D] :
( a_select2(rho,n1) != n0
& n2 = C
& n1 = D
& n1 = C
& D = n0
& ( n2 != D
| n2 != C )
& ( n2 != C
| n1 != D )
& ( n2 != D
| n1 != C )
& ( n1 != D
| n1 != C )
& ( n2 != C
| D != n0 )
& ( n2 != D
| C != n0 )
& ( n1 != D
| C != n0 )
& 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_0841_neg]) ).
fof(sk_quaternion_ds1_symm_0841_neg,plain,
( a_select2(rho,n1) != n0
& n2 = sK1
& n1 = sK0
& n1 = sK1
& sK0 = n0
& ( n2 != sK0
| n2 != sK1 )
& ( n2 != sK1
| n1 != sK0 )
& ( n2 != sK0
| n1 != sK1 )
& ( n1 != sK0
| n1 != sK1 )
& ( n2 != sK1
| sK0 != n0 )
& ( n2 != sK0
| sK1 != n0 )
& ( n1 != sK0
| sK1 != n0 )
& leq(sK0,n2)
& leq(sK1,n2)
& leq(n0,sK0)
& leq(n0,sK1)
& ! [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,[sK1,sK0]),skolemize(C,sK1),skolemize(D,sK0)],[nnf_56]) ).
cnf(c_365,negated_conjecture,
( n2 != sK1
| sK0 != n0 ),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_symm_0841_neg]) ).
cnf(c_366,negated_conjecture,
( sK1 != n2
| sK0 != n0 ),
inference(copy,[status(thm)],[c_365]) ).
cnf(c_375,negated_conjecture,
sK0 = n0,
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_symm_0841_neg]) ).
cnf(c_380,negated_conjecture,
n2 = sK1,
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_symm_0841_neg]) ).
cnf(c_381,negated_conjecture,
sK1 = n2,
inference(copy,[status(thm)],[c_380]) ).
cnf(c_847,negated_conjecture,
sK1 != n2,
inference(resolve,[status(thm)],[c_375,c_366]) ).
cnf(c_846,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_381,c_847]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV232+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n017.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 13:16:03 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 798474 was started by sandbox2 on n017,
% 0.19/0.45 % Sat Sep 26 13:16:03 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.27/0.55
% 0.27/0.55 % From the command line: assign(max_seconds, 300).
% 1.24/0.70
% 1.24/0.70 % SZS status Theorem for theBenchmark
% 1.24/0.70
% 1.24/0.70 % Proof 1 at 0.11 (+ 0.01) seconds.
% 1.24/0.70 % Length of proof is 7.
% 1.24/0.70 % Level of proof is 3.
% 1.24/0.70 % Maximum clause weight is 11.000.
% 1.24/0.70 % Given clauses 0.
% 1.24/0.70
% 1.24/0.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------