%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV106+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n006.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 08:58:09 AM UTC 2026
% Result : Theorem 8.49s 3.66s
% Output : Refutation 8.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 9 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 109 ( 28 equ; 0 cnn)
% Maximal formula atoms : 26 ( 12 avg)
% Number of connectives : 394 ( 22 ~; 18 |; 58 &; 272 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 19 usr; 16 con; 0-3 aty)
% Number of variables : 36 ( 0 ^; 36 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(n0_decl,type,
n0: $i ).
thf(minus_decl,type,
minus: $i > $i > $i ).
thf(m_measvars_decl,type,
m_measvars: $i ).
thf(n1_decl,type,
n1: $i ).
thf(a_select2_decl,type,
a_select2: $i > $i > $i ).
thf(rho_defuse_decl,type,
rho_defuse: $i ).
thf(use_decl,type,
use: $i ).
thf(n_statevars_decl,type,
n_statevars: $i ).
thf(sigma_defuse_decl,type,
sigma_defuse: $i ).
thf(n2_decl,type,
n2: $i ).
thf(n_steps_decl,type,
n_steps: $i ).
thf(a_select3_decl,type,
a_select3: $i > $i > $i > $i ).
thf(u_defuse_decl,type,
u_defuse: $i ).
thf(xinit_defuse_decl,type,
xinit_defuse: $i ).
thf(xinit_mean_defuse_decl,type,
xinit_mean_defuse: $i ).
thf(xinit_noise_defuse_decl,type,
xinit_noise_defuse: $i ).
thf(z_defuse_decl,type,
z_defuse: $i ).
thf(true_decl,type,
true: $o ).
thf(42,axiom,
true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ttrue) ).
thf(322,plain,
true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(1,conjecture,
( ( ! [A: $i,B: $i] :
( ( ( n1 @ ( n_steps @ minus ) @ ( B @ leq ) )
& ( n1 @ ( m_measvars @ minus ) @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( z_defuse @ a_select3 ) ) )
= use ) )
& ! [A: $i] :
( ( ( n1 @ ( n_statevars @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( xinit_noise_defuse @ a_select2 ) )
= use ) )
& ! [A: $i] :
( ( ( n1 @ ( n_statevars @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( xinit_mean_defuse @ a_select2 ) )
= use ) )
& ! [A: $i] :
( ( ( n1 @ ( n_statevars @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( xinit_defuse @ a_select2 ) )
= use ) )
& ! [A: $i,B: $i] :
( ( ( n1 @ ( n_steps @ minus ) @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( u_defuse @ a_select3 ) ) )
= use ) )
& ! [A: $i] :
( ( ( n1 @ ( n_statevars @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( sigma_defuse @ a_select2 ) )
= use ) )
& ! [A: $i] :
( ( ( n1 @ ( m_measvars @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( rho_defuse @ a_select2 ) )
= use ) ) )
=> true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quaternion_ds1_inuse_0018) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i,B: $i] :
( ( ( n1 @ ( n_steps @ minus ) @ ( B @ leq ) )
& ( n1 @ ( m_measvars @ minus ) @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( z_defuse @ a_select3 ) ) )
= use ) )
& ! [A: $i] :
( ( ( n1 @ ( n_statevars @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( xinit_noise_defuse @ a_select2 ) )
= use ) )
& ! [A: $i] :
( ( ( n1 @ ( n_statevars @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( xinit_mean_defuse @ a_select2 ) )
= use ) )
& ! [A: $i] :
( ( ( n1 @ ( n_statevars @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( xinit_defuse @ a_select2 ) )
= use ) )
& ! [A: $i,B: $i] :
( ( ( n1 @ ( n_steps @ minus ) @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( u_defuse @ a_select3 ) ) )
= use ) )
& ! [A: $i] :
( ( ( n1 @ ( n_statevars @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( sigma_defuse @ a_select2 ) )
= use ) )
& ! [A: $i] :
( ( ( n1 @ ( m_measvars @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( rho_defuse @ a_select2 ) )
= use ) ) )
=> true ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(87,plain,
~ ( ( ! [A: $i,B: $i] :
( ( ( n1 @ ( n_steps @ minus ) @ ( B @ leq ) )
& ( n1 @ ( m_measvars @ minus ) @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( z_defuse @ a_select3 ) ) )
= use ) )
& ! [A: $i] :
( ( ( n1 @ ( n_statevars @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( xinit_noise_defuse @ a_select2 ) )
= use ) )
& ! [A: $i] :
( ( ( n1 @ ( n_statevars @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( xinit_mean_defuse @ a_select2 ) )
= use ) )
& ! [A: $i] :
( ( ( n1 @ ( n_statevars @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( xinit_defuse @ a_select2 ) )
= use ) )
& ! [A: $i,B: $i] :
( ( ( n1 @ ( n_steps @ minus ) @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( u_defuse @ a_select3 ) ) )
= use ) )
& ! [A: $i] :
( ( ( n1 @ ( n_statevars @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( sigma_defuse @ a_select2 ) )
= use ) )
& ! [A: $i] :
( ( ( n1 @ ( m_measvars @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( rho_defuse @ a_select2 ) )
= use ) ) )
=> true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(88,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ true
& ( ( ( I @ ( H @ ( z_defuse @ a_select3 ) ) )
= use )
| ~ ( n1 @ ( n_steps @ minus ) @ ( I @ leq ) )
| ~ ( n1 @ ( m_measvars @ minus ) @ ( H @ leq ) )
| ~ ( I @ ( n0 @ leq ) )
| ~ ( H @ ( n0 @ leq ) ) )
& ( ( ( G @ ( xinit_noise_defuse @ a_select2 ) )
= use )
| ~ ( n1 @ ( n_statevars @ minus ) @ ( G @ leq ) )
| ~ ( G @ ( n0 @ leq ) ) )
& ( ( ( F @ ( xinit_mean_defuse @ a_select2 ) )
= use )
| ~ ( n1 @ ( n_statevars @ minus ) @ ( F @ leq ) )
| ~ ( F @ ( n0 @ leq ) ) )
& ( ( ( E @ ( xinit_defuse @ a_select2 ) )
= use )
| ~ ( n1 @ ( n_statevars @ minus ) @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) ) )
& ( ( ( D @ ( C @ ( u_defuse @ a_select3 ) ) )
= use )
| ~ ( n1 @ ( n_steps @ minus ) @ ( D @ leq ) )
| ~ ( n2 @ ( C @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( C @ ( n0 @ leq ) ) )
& ( ( ( B @ ( sigma_defuse @ a_select2 ) )
= use )
| ~ ( n1 @ ( n_statevars @ minus ) @ ( B @ leq ) )
| ~ ( B @ ( n0 @ leq ) ) )
& ( ( ( A @ ( rho_defuse @ a_select2 ) )
= use )
| ~ ( n1 @ ( m_measvars @ minus ) @ ( A @ leq ) )
| ~ ( A @ ( n0 @ leq ) ) ) ),
inference(cnf,[status(esa)],[87]) ).
thf(93,plain,
~ true,
inference(cnfConj,[status(thm)],[88]) ).
thf(569,plain,
$false,
inference(rewrite,[status(thm)],[322,93]) ).
thf(570,plain,
$false,
inference(simp,[status(thm)],[569]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV106+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.39 % Computer : n006.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sat Sep 26 13:12:41 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.83/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.41/1.25 % [INFO] Parsing done (264ms).
% 1.41/1.27 % [INFO] Running in sequential loop mode.
% 2.34/1.67 % [INFO] eprover registered as external prover.
% 2.34/1.68 % [INFO] Scanning for conjecture ...
% 2.77/1.83 % [INFO] Found a conjecture (or negated_conjecture) and 84 axioms. Running axiom selection ...
% 3.01/1.96 % [INFO] Axiom selection finished. Selected 84 axioms (removed 0 axioms).
% 3.31/2.08 % [INFO] Problem is first-order (TPTP FOF).
% 3.31/2.10 % [INFO] Type checking passed.
% 3.31/2.10 % [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 ...
% 8.49/3.66 % [INFO] Killing All external provers ...
% 8.49/3.66 % Time passed: 3123ms (effective reasoning time: 2386ms)
% 8.49/3.66 % 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)>
% 8.49/3.66 % Axioms used in derivation (1): ttrue
% 8.49/3.66 % No. of inferences in proof: 9
% 8.49/3.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3123 ms resp. 2386 ms w/o parsing
% 8.89/3.71 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.89/3.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------