%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV115+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 : 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 08:58:10 AM UTC 2026
% Result : Theorem 6.58s 4.46s
% Output : Refutation 6.88s
% 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 : 110 ( 20 equ; 0 cnn)
% Maximal formula atoms : 54 ( 27 avg)
% Number of connectives : 492 ( 2 ~; 0 |; 80 &; 384 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 12 con; 0-3 aty)
% Number of variables : 40 ( 0 ^; 40 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(n0_decl,type,
n0: $i ).
thf(pv5_decl,type,
pv5: $i ).
thf(minus_decl,type,
minus: $i > $i > $i ).
thf(n999_decl,type,
n999: $i ).
thf(n1_decl,type,
n1: $i ).
thf(n6_decl,type,
n6: $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(id_ds1_filter_decl,type,
id_ds1_filter: $i ).
thf(1,conjecture,
( ( ! [A: $i] :
( ( ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ! [B: $i] :
( ( ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
& ( B @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( id_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( id_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 @ ( 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 ) ) ) ) )
& ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
& ( pv5 @ ( n0 @ leq ) ) )
=> ( ! [A: $i] :
( ( ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ! [B: $i] :
( ( ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
& ( B @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( id_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( id_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 @ ( 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 ) ) ) ) )
& ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
& ( pv5 @ ( n0 @ leq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quaternion_ds1_symm_0008) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i] :
( ( ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ! [B: $i] :
( ( ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
& ( B @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( id_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( id_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 @ ( 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 ) ) ) ) )
& ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
& ( pv5 @ ( n0 @ leq ) ) )
=> ( ! [A: $i] :
( ( ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ! [B: $i] :
( ( ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
& ( B @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( id_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( id_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 @ ( 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 ) ) ) ) )
& ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
& ( pv5 @ ( n0 @ leq ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(102,plain,
~ $true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(103,plain,
$false,
inference(simp,[status(thm)],[102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV115+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.13 % 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
% 0.16/0.50 % Computer : n001.cluster.edu
% 0.16/0.50 % Model : x86_64 x86_64
% 0.16/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.50 % Memory : 8046.5625MB
% 0.16/0.50 % OS : Linux 6.8.0-71-generic
% 0.16/0.51 % CPULimit : 300
% 0.16/0.51 % WCLimit : 300
% 0.16/0.51 % DateTime : Sat Sep 26 13:19:27 UTC 2026
% 0.16/0.51 % CPUTime :
% 0.16/0.51 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
% 0.83/1.29 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.42/1.64 % [INFO] Parsing done (340ms).
% 1.42/1.66 % [INFO] Running in sequential loop mode.
% 2.24/2.20 % [INFO] eprover registered as external prover.
% 2.33/2.21 % [INFO] Scanning for conjecture ...
% 2.64/2.44 % [INFO] Found a conjecture (or negated_conjecture) and 101 axioms. Running axiom selection ...
% 3.00/2.60 % [INFO] Axiom selection finished. Selected 99 axioms (removed 2 axioms).
% 3.19/2.76 % [INFO] Problem is first-order (TPTP FOF).
% 3.19/2.79 % [INFO] Type checking passed.
% 3.19/2.79 % [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 ...
% 6.58/4.46 % [INFO] Killing All external provers ...
% 6.58/4.46 % Time passed: 3764ms (effective reasoning time: 2786ms)
% 6.58/4.46 % 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)>
% 6.58/4.46 % Axioms used in derivation (0):
% 6.58/4.46 % No. of inferences in proof: 4
% 6.58/4.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3764 ms resp. 2786 ms w/o parsing
% 6.88/4.54 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.88/4.54 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------