%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV232+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 : n004.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 11.80s 5.25s
% Output : Refutation 12.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 15 unt; 0 typ; 2 def)
% Number of atoms : 179 ( 138 equ; 0 cnn)
% Maximal formula atoms : 28 ( 8 avg)
% Number of connectives : 336 ( 65 ~; 14 |; 125 &; 116 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 9 con; 0-3 aty)
% Number of variables : 17 ( 0 ^; 15 !; 0 ?; 17 :)
% ( 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(n1_decl,type,
n1: $i ).
thf(a_select2_decl,type,
a_select2: $i > $i > $i ).
thf(rho_decl,type,
rho: $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( n2 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( ( n2 = A )
& ( n1 = B )
& ( n1 = A )
& ( n0 = B )
& ~ ( ( n2 = B )
& ( n2 = A ) )
& ~ ( ( n2 = A )
& ( n1 = B ) )
& ~ ( ( n2 = B )
& ( n1 = A ) )
& ~ ( ( n1 = B )
& ( n1 = A ) )
& ~ ( ( n2 = A )
& ( n0 = B ) )
& ~ ( ( n2 = B )
& ( n0 = A ) )
& ~ ( ( n1 = B )
& ( n0 = A ) ) )
=> ( ( n1 @ ( rho @ a_select2 ) )
= n0 ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( ( n2 @ ( A @ leq ) )
& ( n2 @ ( sk1 @ leq ) )
& ( A @ ( n0 @ leq ) )
& ( sk1 @ ( n0 @ leq ) ) )
=> ( ( ( n2 = sk1 )
& ( n1 = A )
& ( n1 = sk1 )
& ( n0 = A )
& ~ ( ( n2 = A )
& ( n2 = sk1 ) )
& ~ ( ( n2 = sk1 )
& ( n1 = A ) )
& ~ ( ( n2 = A )
& ( n1 = sk1 ) )
& ~ ( ( n1 = A )
& ( n1 = sk1 ) )
& ~ ( ( n2 = sk1 )
& ( n0 = A ) )
& ~ ( ( n2 = A )
& ( n0 = sk1 ) )
& ~ ( ( n1 = A )
& ( n0 = sk1 ) ) )
=> ( ( n1 @ ( rho @ a_select2 ) )
= n0 ) ) ) ) ) ).
thf(1,conjecture,
( ! [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] :
( ( ( n2 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( ( n2 = A )
& ( n1 = B )
& ( n1 = A )
& ( n0 = B )
& ~ ( ( n2 = B )
& ( n2 = A ) )
& ~ ( ( n2 = A )
& ( n1 = B ) )
& ~ ( ( n2 = B )
& ( n1 = A ) )
& ~ ( ( n1 = B )
& ( n1 = A ) )
& ~ ( ( n2 = A )
& ( n0 = B ) )
& ~ ( ( n2 = B )
& ( n0 = A ) )
& ~ ( ( n1 = B )
& ( n0 = A ) ) )
=> ( ( n1 @ ( rho @ a_select2 ) )
= n0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quaternion_ds1_symm_0841) ).
thf(2,negated_conjecture,
~ ( ! [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] :
( ( ( n2 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( ( n2 = A )
& ( n1 = B )
& ( n1 = A )
& ( n0 = B )
& ~ ( ( n2 = B )
& ( n2 = A ) )
& ~ ( ( n2 = A )
& ( n1 = B ) )
& ~ ( ( n2 = B )
& ( n1 = A ) )
& ~ ( ( n1 = B )
& ( n1 = A ) )
& ~ ( ( n2 = A )
& ( n0 = B ) )
& ~ ( ( n2 = B )
& ( n0 = A ) )
& ~ ( ( n1 = B )
& ( n0 = A ) ) )
=> ( ( n1 @ ( rho @ a_select2 ) )
= n0 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(85,plain,
~ ( ! [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] :
( ( ( n2 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( ( n2 = A )
& ( n1 = B )
& ( n1 = A )
& ( n0 = B )
& ~ ( ( n2 = B )
& ( n2 = A ) )
& ~ ( ( n2 = A )
& ( n1 = B ) )
& ~ ( ( n2 = B )
& ( n1 = A ) )
& ~ ( ( n1 = B )
& ( n1 = A ) )
& ~ ( ( n2 = A )
& ( n0 = B ) )
& ~ ( ( n2 = B )
& ( n0 = A ) )
& ~ ( ( n1 = B )
& ( n0 = A ) ) )
=> ( ( n1 @ ( rho @ a_select2 ) )
= n0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(86,plain,
! [B: $i,A: $i] :
( ( ( n1 @ ( rho @ a_select2 ) )
!= n0 )
& ( n2 = sk1 )
& ( n1 = sk2 )
& ( n1 = sk1 )
& ( n0 = sk2 )
& ( ( n2 != sk2 )
| ( n2 != sk1 ) )
& ( ( n2 != sk1 )
| ( n1 != sk2 ) )
& ( ( n2 != sk2 )
| ( n1 != sk1 ) )
& ( ( n1 != sk2 )
| ( n1 != sk1 ) )
& ( ( n2 != sk1 )
| ( n0 != sk2 ) )
& ( ( n2 != sk2 )
| ( n0 != sk1 ) )
& ( ( n1 != sk2 )
| ( n0 != sk1 ) )
& ( n2 @ ( sk2 @ leq ) )
& ( n2 @ ( sk1 @ leq ) )
& ( sk2 @ ( n0 @ leq ) )
& ( sk1 @ ( 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,
n2 = sk1,
inference(cnfConj,[status(thm)],[86]) ).
thf(104,plain,
sk1 = n2,
inference(lifteq,[status(thm)],[93]) ).
thf(103,plain,
n1 = sk2,
inference(cnfConj,[status(thm)],[86]) ).
thf(113,plain,
sk2 = n1,
inference(lifteq,[status(thm)],[103]) ).
thf(95,plain,
n0 = sk2,
inference(cnfConj,[status(thm)],[86]) ).
thf(108,plain,
sk2 = n0,
inference(lifteq,[status(thm)],[95]) ).
thf(92,plain,
n1 = sk1,
inference(cnfConj,[status(thm)],[86]) ).
thf(111,plain,
sk1 = n1,
inference(lifteq,[status(thm)],[92]) ).
thf(572,plain,
n1 = n2,
inference(rewrite,[status(thm)],[111,104]) ).
thf(573,plain,
n2 = n0,
inference(rewrite,[status(thm)],[113,108,572]) ).
thf(574,plain,
sk1 = n0,
inference(rewrite,[status(thm)],[104,573]) ).
thf(96,plain,
( ( n2 != sk2 )
| ( n2 != sk1 ) ),
inference(cnfConj,[status(thm)],[86]) ).
thf(106,plain,
( ( sk2 != n2 )
| ( sk1 != n2 ) ),
inference(lifteq,[status(thm)],[96]) ).
thf(576,plain,
( ( n0 != n0 )
| ( sk1 != n0 ) ),
inference(rewrite,[status(thm)],[106,108,573]) ).
thf(577,plain,
sk1 != n0,
inference(simp,[status(thm)],[576]) ).
thf(578,plain,
$false,
inference(simplifyReflect,[status(thm)],[574,577]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV232+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.11 % 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
% 0.24/0.49 % Computer : n004.cluster.edu
% 0.24/0.49 % Model : x86_64 x86_64
% 0.24/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.49 % Memory : 8046.5625MB
% 0.24/0.49 % OS : Linux 6.8.0-71-generic
% 0.24/0.49 % CPULimit : 300
% 0.24/0.49 % WCLimit : 300
% 0.24/0.49 % DateTime : Sat Sep 26 13:20:51 UTC 2026
% 0.24/0.50 % CPUTime :
% 0.24/0.50 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
% 1.35/1.33 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.88/1.69 % [INFO] Parsing done (361ms).
% 2.30/1.71 % [INFO] Running in sequential loop mode.
% 3.21/2.31 % [INFO] eprover registered as external prover.
% 3.21/2.32 % [INFO] Scanning for conjecture ...
% 3.61/2.52 % [INFO] Found a conjecture (or negated_conjecture) and 84 axioms. Running axiom selection ...
% 3.78/2.67 % [INFO] Axiom selection finished. Selected 82 axioms (removed 2 axioms).
% 4.23/2.83 % [INFO] Problem is first-order (TPTP FOF).
% 4.23/2.85 % [INFO] Type checking passed.
% 4.23/2.86 % [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 ...
% 11.80/5.24 % [INFO] Killing All external provers ...
% 11.80/5.25 % Time passed: 4546ms (effective reasoning time: 3527ms)
% 11.80/5.25 % 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)>
% 11.80/5.25 % Axioms used in derivation (0):
% 11.80/5.25 % No. of inferences in proof: 20
% 11.80/5.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4546 ms resp. 3527 ms w/o parsing
% 12.28/5.32 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.28/5.32 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------