%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV220+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 : n003.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 08:58:27 AM UTC 2026
% Result : Theorem 12.93s 5.05s
% Output : Refutation 12.93s
% 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 : 251 ( 226 equ; 0 cnn)
% Maximal formula atoms : 39 ( 13 avg)
% Number of connectives : 431 ( 116 ~; 18 |; 203 &; 84 @)
% ( 0 <=>; 10 =>; 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; 11 con; 0-2 aty)
% Number of variables : 9 ( 0 ^; 7 !; 0 ?; 9 :)
% ( 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(n4_decl,type,
n4: $i ).
thf(n1_decl,type,
n1: $i ).
thf(n2_decl,type,
n2: $i ).
thf(n3_decl,type,
n3: $i ).
thf(times_decl,type,
times: $i > $i > $i ).
thf(divide_decl,type,
divide: $i > $i > $i ).
thf(n400_decl,type,
n400: $i ).
thf(a_select2_decl,type,
a_select2: $i > $i > $i ).
thf(sigma_decl,type,
sigma: $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 = B )
& ( n3 = B )
& ( n3 = A )
& ( n1 = A )
& ~ ( ( n5 = B )
& ( n5 = A ) )
& ~ ( ( n5 = A )
& ( n4 = B ) )
& ~ ( ( n5 = B )
& ( n4 = A ) )
& ~ ( ( n4 = B )
& ( n4 = A ) )
& ~ ( ( n5 = A )
& ( n3 = B ) )
& ~ ( ( n4 = A )
& ( n3 = B ) )
& ~ ( ( n5 = B )
& ( n3 = A ) )
& ~ ( ( n4 = B )
& ( n3 = A ) )
& ~ ( ( n5 = A )
& ( n2 = B ) )
& ~ ( ( n4 = A )
& ( n2 = B ) )
& ~ ( ( n5 = B )
& ( n2 = A ) )
& ~ ( ( n5 = A )
& ( n1 = B ) )
& ~ ( ( n4 = A )
& ( n1 = B ) )
& ~ ( ( n5 = A )
& ( n0 = B ) )
& ~ ( ( n4 = A )
& ( n0 = B ) ) )
=> ( ( n3 @ ( sigma @ a_select2 ) @ ( n400 @ ( n1 @ divide ) @ times ) )
= n0 ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( ( n5 @ ( A @ leq ) )
& ( n5 @ ( sk1 @ leq ) )
& ( A @ ( n0 @ leq ) )
& ( sk1 @ ( n0 @ leq ) ) )
=> ( ( ( n5 = A )
& ( n3 = A )
& ( n3 = sk1 )
& ( n1 = sk1 )
& ~ ( ( n5 = A )
& ( n5 = sk1 ) )
& ~ ( ( n5 = sk1 )
& ( n4 = A ) )
& ~ ( ( n5 = A )
& ( n4 = sk1 ) )
& ~ ( ( n4 = A )
& ( n4 = sk1 ) )
& ~ ( ( n5 = sk1 )
& ( n3 = A ) )
& ~ ( ( n4 = sk1 )
& ( n3 = A ) )
& ~ ( ( n5 = A )
& ( n3 = sk1 ) )
& ~ ( ( n4 = A )
& ( n3 = sk1 ) )
& ~ ( ( n5 = sk1 )
& ( n2 = A ) )
& ~ ( ( n4 = sk1 )
& ( n2 = A ) )
& ~ ( ( n5 = A )
& ( n2 = sk1 ) )
& ~ ( ( n5 = sk1 )
& ( n1 = A ) )
& ~ ( ( n4 = sk1 )
& ( n1 = A ) )
& ~ ( ( n5 = sk1 )
& ( n0 = A ) )
& ~ ( ( n4 = sk1 )
& ( n0 = A ) ) )
=> ( ( n3 @ ( sigma @ a_select2 ) @ ( n400 @ ( n1 @ divide ) @ times ) )
= n0 ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( ( n5 = B )
& ( n3 = B )
& ( n3 = A )
& ( n1 = A )
& ~ ( ( n5 = B )
& ( n5 = A ) )
& ~ ( ( n5 = A )
& ( n4 = B ) )
& ~ ( ( n5 = B )
& ( n4 = A ) )
& ~ ( ( n4 = B )
& ( n4 = A ) )
& ~ ( ( n5 = A )
& ( n3 = B ) )
& ~ ( ( n4 = A )
& ( n3 = B ) )
& ~ ( ( n5 = B )
& ( n3 = A ) )
& ~ ( ( n4 = B )
& ( n3 = A ) )
& ~ ( ( n5 = A )
& ( n2 = B ) )
& ~ ( ( n4 = A )
& ( n2 = B ) )
& ~ ( ( n5 = B )
& ( n2 = A ) )
& ~ ( ( n5 = A )
& ( n1 = B ) )
& ~ ( ( n4 = A )
& ( n1 = B ) )
& ~ ( ( n5 = A )
& ( n0 = B ) )
& ~ ( ( n4 = A )
& ( n0 = B ) ) )
=> ( ( n3 @ ( sigma @ a_select2 ) @ ( n400 @ ( n1 @ divide ) @ times ) )
= n0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quaternion_ds1_symm_0361) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( ( n5 = B )
& ( n3 = B )
& ( n3 = A )
& ( n1 = A )
& ~ ( ( n5 = B )
& ( n5 = A ) )
& ~ ( ( n5 = A )
& ( n4 = B ) )
& ~ ( ( n5 = B )
& ( n4 = A ) )
& ~ ( ( n4 = B )
& ( n4 = A ) )
& ~ ( ( n5 = A )
& ( n3 = B ) )
& ~ ( ( n4 = A )
& ( n3 = B ) )
& ~ ( ( n5 = B )
& ( n3 = A ) )
& ~ ( ( n4 = B )
& ( n3 = A ) )
& ~ ( ( n5 = A )
& ( n2 = B ) )
& ~ ( ( n4 = A )
& ( n2 = B ) )
& ~ ( ( n5 = B )
& ( n2 = A ) )
& ~ ( ( n5 = A )
& ( n1 = B ) )
& ~ ( ( n4 = A )
& ( n1 = B ) )
& ~ ( ( n5 = A )
& ( n0 = B ) )
& ~ ( ( n4 = A )
& ( n0 = B ) ) )
=> ( ( n3 @ ( sigma @ a_select2 ) @ ( n400 @ ( n1 @ divide ) @ times ) )
= n0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(92,plain,
~ ! [A: $i,B: $i] :
( ( ( n5 @ ( B @ leq ) )
& ( n5 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( ( n5 = B )
& ( n3 = B )
& ( n3 = A )
& ( n1 = A )
& ~ ( ( n5 = B )
& ( n5 = A ) )
& ~ ( ( n5 = A )
& ( n4 = B ) )
& ~ ( ( n5 = B )
& ( n4 = A ) )
& ~ ( ( n4 = B )
& ( n4 = A ) )
& ~ ( ( n5 = A )
& ( n3 = B ) )
& ~ ( ( n4 = A )
& ( n3 = B ) )
& ~ ( ( n5 = B )
& ( n3 = A ) )
& ~ ( ( n4 = B )
& ( n3 = A ) )
& ~ ( ( n5 = A )
& ( n2 = B ) )
& ~ ( ( n4 = A )
& ( n2 = B ) )
& ~ ( ( n5 = B )
& ( n2 = A ) )
& ~ ( ( n5 = A )
& ( n1 = B ) )
& ~ ( ( n4 = A )
& ( n1 = B ) )
& ~ ( ( n5 = A )
& ( n0 = B ) )
& ~ ( ( n4 = A )
& ( n0 = B ) ) )
=> ( ( n3 @ ( sigma @ a_select2 ) @ ( n400 @ ( n1 @ divide ) @ times ) )
= n0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(93,plain,
( ( ( n3 @ ( sigma @ a_select2 ) @ ( n400 @ ( n1 @ divide ) @ times ) )
!= n0 )
& ( n5 = sk2 )
& ( n3 = sk2 )
& ( n3 = sk1 )
& ( n1 = sk1 )
& ( ( n5 != sk2 )
| ( n5 != sk1 ) )
& ( ( n5 != sk1 )
| ( n4 != sk2 ) )
& ( ( n5 != sk2 )
| ( n4 != sk1 ) )
& ( ( n4 != sk2 )
| ( n4 != sk1 ) )
& ( ( n5 != sk1 )
| ( n3 != sk2 ) )
& ( ( n4 != sk1 )
| ( n3 != sk2 ) )
& ( ( n5 != sk2 )
| ( n3 != sk1 ) )
& ( ( n4 != sk2 )
| ( n3 != sk1 ) )
& ( ( n5 != sk1 )
| ( n2 != sk2 ) )
& ( ( n4 != sk1 )
| ( n2 != sk2 ) )
& ( ( n5 != sk2 )
| ( n2 != sk1 ) )
& ( ( n5 != sk1 )
| ( n1 != sk2 ) )
& ( ( n4 != sk1 )
| ( n1 != sk2 ) )
& ( ( n5 != sk1 )
| ( n0 != sk2 ) )
& ( ( n4 != sk1 )
| ( n0 != sk2 ) )
& ( n5 @ ( sk2 @ leq ) )
& ( n5 @ ( sk1 @ leq ) )
& ( sk2 @ ( n0 @ leq ) )
& ( sk1 @ ( n0 @ leq ) ) ),
inference(cnf,[status(esa)],[92]) ).
thf(97,plain,
( ( n5 != sk1 )
| ( n3 != sk2 ) ),
inference(cnfConj,[status(thm)],[93]) ).
thf(121,plain,
( ( sk1 != n5 )
| ( sk2 != n3 ) ),
inference(lifteq,[status(thm)],[97]) ).
thf(106,plain,
n5 = sk2,
inference(cnfConj,[status(thm)],[93]) ).
thf(119,plain,
sk2 = n5,
inference(lifteq,[status(thm)],[106]) ).
thf(116,plain,
n3 = sk2,
inference(cnfConj,[status(thm)],[93]) ).
thf(120,plain,
sk2 = n3,
inference(lifteq,[status(thm)],[116]) ).
thf(600,plain,
n3 = n5,
inference(rewrite,[status(thm)],[120,119]) ).
thf(112,plain,
n3 = sk1,
inference(cnfConj,[status(thm)],[93]) ).
thf(123,plain,
sk1 = n3,
inference(lifteq,[status(thm)],[112]) ).
thf(601,plain,
sk1 = n5,
inference(rewrite,[status(thm)],[123,600]) ).
thf(603,plain,
( ( n5 != n5 )
| ( n5 != n5 ) ),
inference(rewrite,[status(thm)],[121,119,600,601]) ).
thf(604,plain,
$false,
inference(simp,[status(thm)],[603]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV220+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.07 % 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
% 0.12/0.38 % Computer : n003.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 13:22:10 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.39 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
% 1.17/1.12 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.29/1.50 % [INFO] Parsing done (375ms).
% 2.29/1.52 % [INFO] Running in sequential loop mode.
% 3.09/2.03 % [INFO] eprover registered as external prover.
% 3.09/2.04 % [INFO] Scanning for conjecture ...
% 3.73/2.28 % [INFO] Found a conjecture (or negated_conjecture) and 91 axioms. Running axiom selection ...
% 4.27/2.46 % [INFO] Axiom selection finished. Selected 89 axioms (removed 2 axioms).
% 4.78/2.64 % [INFO] Problem is first-order (TPTP FOF).
% 4.78/2.67 % [INFO] Type checking passed.
% 4.78/2.68 % [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 ...
% 12.93/5.04 % [INFO] Killing All external provers ...
% 12.93/5.04 % Time passed: 4458ms (effective reasoning time: 3508ms)
% 12.93/5.04 % 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)>
% 12.93/5.05 % Axioms used in derivation (0):
% 12.93/5.05 % No. of inferences in proof: 16
% 12.93/5.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4458 ms resp. 3508 ms w/o parsing
% 12.93/5.10 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.93/5.10 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------