%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV122+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 : n001.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 08:58:11 AM UTC 2026
% Result : Theorem 7.12s 3.23s
% Output : Refutation 7.12s
% 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 : 62 ( 12 equ; 0 cnn)
% Maximal formula atoms : 30 ( 15 avg)
% Number of connectives : 276 ( 2 ~; 0 |; 44 &; 216 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 9 con; 0-3 aty)
% Number of variables : 24 ( 0 ^; 24 !; 0 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(n0_decl,type,
n0: $i ).
thf(minus_decl,type,
minus: $i > $i > $i ).
thf(n6_decl,type,
n6: $i ).
thf(n1_decl,type,
n1: $i ).
thf(a_select3_decl,type,
a_select3: $i > $i > $i > $i ).
thf(q_ds1_filter_decl,type,
q_ds1_filter: $i ).
thf(n3_decl,type,
n3: $i ).
thf(r_ds1_filter_decl,type,
r_ds1_filter: $i ).
thf(pminus_ds1_filter_decl,type,
pminus_ds1_filter: $i ).
thf(1,conjecture,
( ( ! [A: $i,B: $i] :
( ( ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
& ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( pminus_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( pminus_ds1_filter @ a_select3 ) ) ) ) )
& ! [A: $i,B: $i] :
( ( ( n1 @ ( n3 @ minus ) @ ( B @ leq ) )
& ( n1 @ ( n3 @ minus ) @ ( 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] :
( ( ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
& ( n1 @ ( n6 @ minus ) @ ( 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] :
( ( ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
& ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( pminus_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( pminus_ds1_filter @ a_select3 ) ) ) ) )
& ! [A: $i,B: $i] :
( ( ( n1 @ ( n3 @ minus ) @ ( B @ leq ) )
& ( n1 @ ( n3 @ minus ) @ ( 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] :
( ( ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
& ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( q_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( q_ds1_filter @ a_select3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quaternion_ds1_symm_0015) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i,B: $i] :
( ( ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
& ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( pminus_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( pminus_ds1_filter @ a_select3 ) ) ) ) )
& ! [A: $i,B: $i] :
( ( ( n1 @ ( n3 @ minus ) @ ( B @ leq ) )
& ( n1 @ ( n3 @ minus ) @ ( 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] :
( ( ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
& ( n1 @ ( n6 @ minus ) @ ( 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] :
( ( ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
& ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( pminus_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( pminus_ds1_filter @ a_select3 ) ) ) ) )
& ! [A: $i,B: $i] :
( ( ( n1 @ ( n3 @ minus ) @ ( B @ leq ) )
& ( n1 @ ( n3 @ minus ) @ ( 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] :
( ( ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
& ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( q_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( q_ds1_filter @ a_select3 ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(94,plain,
~ $true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(95,plain,
$false,
inference(simp,[status(thm)],[94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV122+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.08 % 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
% 0.14/0.40 % Computer : n001.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 13:19:57 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 0.88/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.56/1.23 % [INFO] Parsing done (257ms).
% 1.56/1.24 % [INFO] Running in sequential loop mode.
% 2.45/1.62 % [INFO] eprover registered as external prover.
% 2.45/1.63 % [INFO] Scanning for conjecture ...
% 2.65/1.78 % [INFO] Found a conjecture (or negated_conjecture) and 93 axioms. Running axiom selection ...
% 2.86/1.88 % [INFO] Axiom selection finished. Selected 91 axioms (removed 2 axioms).
% 3.12/2.00 % [INFO] Problem is first-order (TPTP FOF).
% 3.12/2.02 % [INFO] Type checking passed.
% 3.12/2.03 % [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 ...
% 7.12/3.23 % [INFO] Killing All external provers ...
% 7.12/3.23 % Time passed: 2684ms (effective reasoning time: 1980ms)
% 7.12/3.23 % 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)>
% 7.12/3.23 % Axioms used in derivation (0):
% 7.12/3.23 % No. of inferences in proof: 4
% 7.12/3.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2684 ms resp. 1980 ms w/o parsing
% 7.12/3.28 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.12/3.28 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------