%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV097+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 : n014.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 08:58:08 AM UTC 2026
% Result : Theorem 6.97s 3.31s
% Output : Refutation 6.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1
% Syntax : Number of formulae : 4 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 166 ( 124 equ; 0 cnn)
% Maximal formula atoms : 82 ( 41 avg)
% Number of connectives : 536 ( 2 ~; 0 |; 152 &; 372 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 42 ( 22 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 18 con; 0-3 aty)
% Number of variables : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_select2_decl,type,
a_select2: $i > $i > $i ).
thf(rho_defuse_decl,type,
rho_defuse: $i ).
thf(n0_decl,type,
n0: $i ).
thf(use_decl,type,
use: $i ).
thf(n1_decl,type,
n1: $i ).
thf(n2_decl,type,
n2: $i ).
thf(sigma_defuse_decl,type,
sigma_defuse: $i ).
thf(n3_decl,type,
n3: $i ).
thf(n4_decl,type,
n4: $i ).
thf(n5_decl,type,
n5: $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(leq_decl,type,
leq: $i > $i > $o ).
thf(pv5_decl,type,
pv5: $i ).
thf(minus_decl,type,
minus: $i > $i > $i ).
thf(n999_decl,type,
n999: $i ).
thf(z_defuse_decl,type,
z_defuse: $i ).
thf(1,conjecture,
( ( ! [A: $i,B: $i] :
( ( ( n1 @ ( pv5 @ minus ) @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( ( B @ ( A @ ( z_defuse @ a_select3 ) ) )
= use )
& ( ( B @ ( A @ ( u_defuse @ a_select3 ) ) )
= use ) ) )
& ! [A: $i,B: $i] :
( ( ( pv5 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( ( B @ ( A @ ( z_defuse @ a_select3 ) ) )
= use )
& ( ( B @ ( A @ ( u_defuse @ a_select3 ) ) )
= use ) ) )
& ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
& ( pv5 @ ( n0 @ leq ) )
& ( ( n5 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n4 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n3 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n2 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n1 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n5 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n4 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n3 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n2 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n1 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n5 @ ( xinit_defuse @ a_select2 ) )
= use )
& ( ( n4 @ ( xinit_defuse @ a_select2 ) )
= use )
& ( ( n3 @ ( xinit_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( n2 @ ( u_defuse @ a_select3 ) ) )
= use )
& ( ( n0 @ ( n1 @ ( u_defuse @ a_select3 ) ) )
= use )
& ( ( n0 @ ( n0 @ ( u_defuse @ a_select3 ) ) )
= use )
& ( ( n5 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n4 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n3 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n2 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n1 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n2 @ ( rho_defuse @ a_select2 ) )
= use )
& ( ( n1 @ ( rho_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( rho_defuse @ a_select2 ) )
= use ) )
=> ( ! [A: $i,B: $i] :
( ( ( n1 @ ( pv5 @ minus ) @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( ( B @ ( A @ ( z_defuse @ a_select3 ) ) )
= use )
& ( ( B @ ( A @ ( u_defuse @ a_select3 ) ) )
= use ) ) )
& ! [A: $i,B: $i] :
( ( ( pv5 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( ( B @ ( A @ ( z_defuse @ a_select3 ) ) )
= use )
& ( ( B @ ( A @ ( u_defuse @ a_select3 ) ) )
= use ) ) )
& ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
& ( pv5 @ ( n0 @ leq ) )
& ( ( n5 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n4 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n3 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n2 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n1 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n5 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n4 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n3 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n2 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n1 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n5 @ ( xinit_defuse @ a_select2 ) )
= use )
& ( ( n4 @ ( xinit_defuse @ a_select2 ) )
= use )
& ( ( n3 @ ( xinit_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( n2 @ ( u_defuse @ a_select3 ) ) )
= use )
& ( ( n0 @ ( n1 @ ( u_defuse @ a_select3 ) ) )
= use )
& ( ( n0 @ ( n0 @ ( u_defuse @ a_select3 ) ) )
= use )
& ( ( n5 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n4 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n3 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n2 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n1 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n2 @ ( rho_defuse @ a_select2 ) )
= use )
& ( ( n1 @ ( rho_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( rho_defuse @ a_select2 ) )
= use ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quaternion_ds1_inuse_0009) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i,B: $i] :
( ( ( n1 @ ( pv5 @ minus ) @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( ( B @ ( A @ ( z_defuse @ a_select3 ) ) )
= use )
& ( ( B @ ( A @ ( u_defuse @ a_select3 ) ) )
= use ) ) )
& ! [A: $i,B: $i] :
( ( ( pv5 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( ( B @ ( A @ ( z_defuse @ a_select3 ) ) )
= use )
& ( ( B @ ( A @ ( u_defuse @ a_select3 ) ) )
= use ) ) )
& ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
& ( pv5 @ ( n0 @ leq ) )
& ( ( n5 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n4 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n3 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n2 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n1 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n5 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n4 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n3 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n2 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n1 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n5 @ ( xinit_defuse @ a_select2 ) )
= use )
& ( ( n4 @ ( xinit_defuse @ a_select2 ) )
= use )
& ( ( n3 @ ( xinit_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( n2 @ ( u_defuse @ a_select3 ) ) )
= use )
& ( ( n0 @ ( n1 @ ( u_defuse @ a_select3 ) ) )
= use )
& ( ( n0 @ ( n0 @ ( u_defuse @ a_select3 ) ) )
= use )
& ( ( n5 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n4 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n3 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n2 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n1 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n2 @ ( rho_defuse @ a_select2 ) )
= use )
& ( ( n1 @ ( rho_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( rho_defuse @ a_select2 ) )
= use ) )
=> ( ! [A: $i,B: $i] :
( ( ( n1 @ ( pv5 @ minus ) @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( ( B @ ( A @ ( z_defuse @ a_select3 ) ) )
= use )
& ( ( B @ ( A @ ( u_defuse @ a_select3 ) ) )
= use ) ) )
& ! [A: $i,B: $i] :
( ( ( pv5 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( ( B @ ( A @ ( z_defuse @ a_select3 ) ) )
= use )
& ( ( B @ ( A @ ( u_defuse @ a_select3 ) ) )
= use ) ) )
& ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
& ( pv5 @ ( n0 @ leq ) )
& ( ( n5 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n4 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n3 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n2 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n1 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n5 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n4 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n3 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n2 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n1 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n5 @ ( xinit_defuse @ a_select2 ) )
= use )
& ( ( n4 @ ( xinit_defuse @ a_select2 ) )
= use )
& ( ( n3 @ ( xinit_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( n2 @ ( u_defuse @ a_select3 ) ) )
= use )
& ( ( n0 @ ( n1 @ ( u_defuse @ a_select3 ) ) )
= use )
& ( ( n0 @ ( n0 @ ( u_defuse @ a_select3 ) ) )
= use )
& ( ( n5 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n4 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n3 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n2 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n1 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n2 @ ( rho_defuse @ a_select2 ) )
= use )
& ( ( n1 @ ( rho_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( rho_defuse @ a_select2 ) )
= use ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(93,plain,
~ $true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(94,plain,
$false,
inference(simp,[status(thm)],[93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV097+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
% 0.12/0.38 % Computer : n014.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sat Sep 26 13:12:16 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 0.87/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.46/1.26 % [INFO] Parsing done (277ms).
% 1.46/1.27 % [INFO] Running in sequential loop mode.
% 2.23/1.66 % [INFO] eprover registered as external prover.
% 2.23/1.67 % [INFO] Scanning for conjecture ...
% 2.62/1.87 % [INFO] Found a conjecture (or negated_conjecture) and 91 axioms. Running axiom selection ...
% 2.82/2.00 % [INFO] Axiom selection finished. Selected 90 axioms (removed 1 axioms).
% 3.15/2.10 % [INFO] Problem is first-order (TPTP FOF).
% 3.15/2.12 % [INFO] Type checking passed.
% 3.15/2.12 % [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 ...
% 6.97/3.31 % [INFO] Killing All external provers ...
% 6.97/3.31 % Time passed: 2778ms (effective reasoning time: 2030ms)
% 6.97/3.31 % 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)>
% 6.97/3.31 % Axioms used in derivation (0):
% 6.97/3.31 % No. of inferences in proof: 4
% 6.97/3.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2778 ms resp. 2030 ms w/o parsing
% 6.97/3.37 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.97/3.37 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------