%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV121+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 : n011.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 13.03s 5.51s
% Output : Refutation 13.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 9 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 69 ( 12 equ; 0 cnn)
% Maximal formula atoms : 16 ( 7 avg)
% Number of connectives : 292 ( 16 ~; 12 |; 36 &; 216 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 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 : 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(true_decl,type,
true: $o ).
thf(48,axiom,
true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ttrue) ).
thf(339,plain,
true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
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 ) ) ) ) ) )
=> true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quaternion_ds1_symm_0014) ).
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 ) ) ) ) ) )
=> true ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(95,plain,
~ ( ( ! [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 ) ) ) ) ) )
=> true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(96,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ true
& ( ( ( F @ ( E @ ( pminus_ds1_filter @ a_select3 ) ) )
= ( E @ ( F @ ( pminus_ds1_filter @ a_select3 ) ) ) )
| ~ ( n1 @ ( n6 @ minus ) @ ( F @ leq ) )
| ~ ( n1 @ ( n6 @ minus ) @ ( E @ leq ) )
| ~ ( F @ ( n0 @ leq ) )
| ~ ( E @ ( n0 @ leq ) ) )
& ( ( ( D @ ( C @ ( r_ds1_filter @ a_select3 ) ) )
= ( C @ ( D @ ( r_ds1_filter @ a_select3 ) ) ) )
| ~ ( n1 @ ( n3 @ minus ) @ ( D @ leq ) )
| ~ ( n1 @ ( n3 @ minus ) @ ( C @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( C @ ( n0 @ leq ) ) )
& ( ( ( B @ ( A @ ( q_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( q_ds1_filter @ a_select3 ) ) ) )
| ~ ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
| ~ ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
| ~ ( B @ ( n0 @ leq ) )
| ~ ( A @ ( n0 @ leq ) ) ) ),
inference(cnf,[status(esa)],[95]) ).
thf(100,plain,
~ true,
inference(cnfConj,[status(thm)],[96]) ).
thf(574,plain,
$false,
inference(rewrite,[status(thm)],[339,100]) ).
thf(575,plain,
$false,
inference(simp,[status(thm)],[574]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV121+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.12 % 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
% 0.25/0.50 % Computer : n011.cluster.edu
% 0.25/0.50 % Model : x86_64 x86_64
% 0.25/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.50 % Memory : 8046.5625MB
% 0.25/0.50 % OS : Linux 6.8.0-71-generic
% 0.25/0.50 % CPULimit : 300
% 0.25/0.50 % WCLimit : 300
% 0.25/0.50 % DateTime : Sat Sep 26 13:14:14 UTC 2026
% 0.25/0.51 % CPUTime :
% 0.25/0.51 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
% 1.37/1.34 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.26/1.72 % [INFO] Parsing done (369ms).
% 2.26/1.74 % [INFO] Running in sequential loop mode.
% 3.31/2.34 % [INFO] eprover registered as external prover.
% 3.31/2.35 % [INFO] Scanning for conjecture ...
% 3.71/2.56 % [INFO] Found a conjecture (or negated_conjecture) and 93 axioms. Running axiom selection ...
% 4.10/2.73 % [INFO] Axiom selection finished. Selected 92 axioms (removed 1 axioms).
% 4.63/2.91 % [INFO] Problem is first-order (TPTP FOF).
% 4.63/2.94 % [INFO] Type checking passed.
% 4.63/2.95 % [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 ...
% 12.84/5.49 % [INFO] Killing All external provers ...
% 13.03/5.50 % Time passed: 4785ms (effective reasoning time: 3751ms)
% 13.03/5.50 % 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)>
% 13.03/5.50 % Axioms used in derivation (1): ttrue
% 13.03/5.50 % No. of inferences in proof: 9
% 13.03/5.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4785 ms resp. 3751 ms w/o parsing
% 13.03/5.56 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.03/5.56 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------