%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV230+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n002.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 08:58:28 AM UTC 2026
% Result : Theorem 12.61s 5.44s
% Output : Refutation 12.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 11 unt; 0 typ; 2 def)
% Number of atoms : 219 ( 162 equ; 0 cnn)
% Maximal formula atoms : 37 ( 12 avg)
% Number of connectives : 453 ( 82 ~; 20 |; 160 &; 172 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 12 con; 0-3 aty)
% Number of variables : 25 ( 0 ^; 23 !; 0 ?; 25 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(n0_decl,type,
n0: $i ).
thf(n5_decl,type,
n5: $i ).
thf(a_select3_decl,type,
a_select3: $i > $i > $i > $i ).
thf(q_ds1_filter_decl,type,
q_ds1_filter: $i ).
thf(n2_decl,type,
n2: $i ).
thf(r_ds1_filter_decl,type,
r_ds1_filter: $i ).
thf(n1_decl,type,
n1: $i ).
thf(n3_decl,type,
n3: $i ).
thf(n4_decl,type,
n4: $i ).
thf(a_select2_decl,type,
a_select2: $i > $i > $i ).
thf(xinit_noise_decl,type,
xinit_noise: $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( ( n5 = A )
& ( n4 = B )
& ( n4 = A )
& ( n1 = B )
& ~ ( ( n5 = B )
& ( n5 = A ) )
& ~ ( ( n5 = A )
& ( n4 = B ) )
& ~ ( ( n5 = B )
& ( n4 = A ) )
& ~ ( ( n5 = A )
& ( n3 = B ) )
& ~ ( ( n5 = B )
& ( n3 = A ) )
& ~ ( ( n5 = A )
& ( n2 = B ) )
& ~ ( ( n5 = B )
& ( n2 = A ) )
& ~ ( ( n5 = B )
& ( n1 = A ) )
& ~ ( ( n5 = B )
& ( n0 = A ) ) )
=> ( n0
= ( n4 @ ( xinit_noise @ a_select2 ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( ( n5 @ ( A @ leq ) )
& ( n5 @ ( sk1 @ leq ) )
& ( A @ ( n0 @ leq ) )
& ( sk1 @ ( n0 @ leq ) ) )
=> ( ( ( n5 = sk1 )
& ( n4 = A )
& ( n4 = sk1 )
& ( n1 = A )
& ~ ( ( n5 = A )
& ( n5 = sk1 ) )
& ~ ( ( n5 = sk1 )
& ( n4 = A ) )
& ~ ( ( n5 = A )
& ( n4 = sk1 ) )
& ~ ( ( n5 = sk1 )
& ( n3 = A ) )
& ~ ( ( n5 = A )
& ( n3 = sk1 ) )
& ~ ( ( n5 = sk1 )
& ( n2 = A ) )
& ~ ( ( n5 = A )
& ( n2 = sk1 ) )
& ~ ( ( n5 = A )
& ( n1 = sk1 ) )
& ~ ( ( n5 = A )
& ( n0 = sk1 ) ) )
=> ( n0
= ( n4 @ ( xinit_noise @ a_select2 ) ) ) ) ) ) ) ).
thf(1,conjecture,
( ( ! [A: $i,B: $i] :
( ( ( n2 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( r_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( r_ds1_filter @ a_select3 ) ) ) ) )
& ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( q_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( q_ds1_filter @ a_select3 ) ) ) ) ) )
=> ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( ( n5 = A )
& ( n4 = B )
& ( n4 = A )
& ( n1 = B )
& ~ ( ( n5 = B )
& ( n5 = A ) )
& ~ ( ( n5 = A )
& ( n4 = B ) )
& ~ ( ( n5 = B )
& ( n4 = A ) )
& ~ ( ( n5 = A )
& ( n3 = B ) )
& ~ ( ( n5 = B )
& ( n3 = A ) )
& ~ ( ( n5 = A )
& ( n2 = B ) )
& ~ ( ( n5 = B )
& ( n2 = A ) )
& ~ ( ( n5 = B )
& ( n1 = A ) )
& ~ ( ( n5 = B )
& ( n0 = A ) ) )
=> ( n0
= ( n4 @ ( xinit_noise @ a_select2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quaternion_ds1_symm_0761) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i,B: $i] :
( ( ( n2 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( r_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( r_ds1_filter @ a_select3 ) ) ) ) )
& ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( q_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( q_ds1_filter @ a_select3 ) ) ) ) ) )
=> ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( ( n5 = A )
& ( n4 = B )
& ( n4 = A )
& ( n1 = B )
& ~ ( ( n5 = B )
& ( n5 = A ) )
& ~ ( ( n5 = A )
& ( n4 = B ) )
& ~ ( ( n5 = B )
& ( n4 = A ) )
& ~ ( ( n5 = A )
& ( n3 = B ) )
& ~ ( ( n5 = B )
& ( n3 = A ) )
& ~ ( ( n5 = A )
& ( n2 = B ) )
& ~ ( ( n5 = B )
& ( n2 = A ) )
& ~ ( ( n5 = B )
& ( n1 = A ) )
& ~ ( ( n5 = B )
& ( n0 = A ) ) )
=> ( n0
= ( n4 @ ( xinit_noise @ a_select2 ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(85,plain,
~ ( ( ! [A: $i,B: $i] :
( ( ( n2 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( r_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( r_ds1_filter @ a_select3 ) ) ) ) )
& ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( q_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( q_ds1_filter @ a_select3 ) ) ) ) ) )
=> ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( ( n5 = A )
& ( n4 = B )
& ( n4 = A )
& ( n1 = B )
& ~ ( ( n5 = B )
& ( n5 = A ) )
& ~ ( ( n5 = A )
& ( n4 = B ) )
& ~ ( ( n5 = B )
& ( n4 = A ) )
& ~ ( ( n5 = A )
& ( n3 = B ) )
& ~ ( ( n5 = B )
& ( n3 = A ) )
& ~ ( ( n5 = A )
& ( n2 = B ) )
& ~ ( ( n5 = B )
& ( n2 = A ) )
& ~ ( ( n5 = B )
& ( n1 = A ) )
& ~ ( ( n5 = B )
& ( n0 = A ) ) )
=> ( n0
= ( n4 @ ( xinit_noise @ a_select2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(86,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( n0
!= ( n4 @ ( xinit_noise @ a_select2 ) ) )
& ( n5 = sk1 )
& ( n4 = sk2 )
& ( n4 = sk1 )
& ( n1 = sk2 )
& ( ( n5 != sk2 )
| ( n5 != sk1 ) )
& ( ( n5 != sk1 )
| ( n4 != sk2 ) )
& ( ( n5 != sk2 )
| ( n4 != sk1 ) )
& ( ( n5 != sk1 )
| ( n3 != sk2 ) )
& ( ( n5 != sk2 )
| ( n3 != sk1 ) )
& ( ( n5 != sk1 )
| ( n2 != sk2 ) )
& ( ( n5 != sk2 )
| ( n2 != sk1 ) )
& ( ( n5 != sk2 )
| ( n1 != sk1 ) )
& ( ( n5 != sk2 )
| ( n0 != sk1 ) )
& ( n5 @ ( sk2 @ leq ) )
& ( n5 @ ( sk1 @ leq ) )
& ( sk2 @ ( n0 @ leq ) )
& ( sk1 @ ( n0 @ leq ) )
& ( ( ( D @ ( C @ ( r_ds1_filter @ a_select3 ) ) )
= ( C @ ( D @ ( r_ds1_filter @ a_select3 ) ) ) )
| ~ ( n2 @ ( D @ leq ) )
| ~ ( n2 @ ( C @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( C @ ( n0 @ leq ) ) )
& ( ( ( B @ ( A @ ( q_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( q_ds1_filter @ a_select3 ) ) ) )
| ~ ( n5 @ ( B @ leq ) )
| ~ ( n5 @ ( A @ leq ) )
| ~ ( B @ ( n0 @ leq ) )
| ~ ( A @ ( n0 @ leq ) ) ) ),
inference(cnf,[status(esa)],[85]) ).
thf(93,plain,
( ( n5 != sk2 )
| ( n5 != sk1 ) ),
inference(cnfConj,[status(thm)],[86]) ).
thf(107,plain,
( ( sk2 != n5 )
| ( sk1 != n5 ) ),
inference(lifteq,[status(thm)],[93]) ).
thf(102,plain,
n4 = sk2,
inference(cnfConj,[status(thm)],[86]) ).
thf(110,plain,
sk2 = n4,
inference(lifteq,[status(thm)],[102]) ).
thf(89,plain,
n4 = sk1,
inference(cnfConj,[status(thm)],[86]) ).
thf(109,plain,
sk1 = n4,
inference(lifteq,[status(thm)],[89]) ).
thf(106,plain,
n5 = sk1,
inference(cnfConj,[status(thm)],[86]) ).
thf(108,plain,
sk1 = n5,
inference(lifteq,[status(thm)],[106]) ).
thf(579,plain,
n4 = n5,
inference(rewrite,[status(thm)],[109,108]) ).
thf(580,plain,
sk2 = n5,
inference(rewrite,[status(thm)],[110,579]) ).
thf(582,plain,
( ( n5 != n5 )
| ( n5 != n5 ) ),
inference(rewrite,[status(thm)],[107,580,108]) ).
thf(583,plain,
$false,
inference(simp,[status(thm)],[582]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV230+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.23/0.49 % Computer : n002.cluster.edu
% 0.23/0.49 % Model : x86_64 x86_64
% 0.23/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.49 % Memory : 8046.5625MB
% 0.23/0.49 % OS : Linux 6.8.0-71-generic
% 0.23/0.49 % CPULimit : 300
% 0.23/0.49 % WCLimit : 300
% 0.23/0.49 % DateTime : Sat Sep 26 13:23:20 UTC 2026
% 0.23/0.49 % CPUTime :
% 0.23/0.49 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.46/1.32 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.02/1.69 % [INFO] Parsing done (369ms).
% 2.44/1.71 % [INFO] Running in sequential loop mode.
% 3.53/2.30 % [INFO] eprover registered as external prover.
% 3.53/2.32 % [INFO] Scanning for conjecture ...
% 3.91/2.54 % [INFO] Found a conjecture (or negated_conjecture) and 84 axioms. Running axiom selection ...
% 4.32/2.71 % [INFO] Axiom selection finished. Selected 82 axioms (removed 2 axioms).
% 4.56/2.88 % [INFO] Problem is first-order (TPTP FOF).
% 4.79/2.91 % [INFO] Type checking passed.
% 4.79/2.91 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 12.61/5.43 % [INFO] Killing All external provers ...
% 12.61/5.44 % Time passed: 4751ms (effective reasoning time: 3709ms)
% 12.61/5.44 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 12.61/5.44 % Axioms used in derivation (0):
% 12.61/5.44 % No. of inferences in proof: 16
% 12.61/5.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4751 ms resp. 3709 ms w/o parsing
% 12.98/5.52 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.98/5.52 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------