TSTP Solution File: SEU458^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEU458^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:37:42 EDT 2024
% Result : Theorem 3.76s 1.78s
% Output : Refutation 3.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 18 ( 9 unt; 5 typ; 2 def)
% Number of atoms : 48 ( 8 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 119 ( 11 ~; 27 |; 0 &; 81 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 18 ( 16 ^ 2 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(idem_type,type,
idem: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(idem_def,definition,
( idem
= ( ^ [A: ( $i > $i > $o ) > $i > $i > $o] :
! [B: $i > $i > $o] :
( ( A @ ( A @ B ) )
= ( A @ B ) ) ) ) ).
thf(sc_type,type,
sc: ( $i > $i > $o ) > $i > $i > $o ).
thf(sc_def,definition,
( sc
= ( ^ [A: $i > $i > $o,B: $i,C: $i] :
( ( A @ C @ B )
| ( A @ B @ C ) ) ) ) ).
thf(sk1_type,type,
sk1: $i > $i > $o ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(1,conjecture,
idem @ sc,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_closure_op_is_idempotent) ).
thf(2,negated_conjecture,
~ ( idem @ sc ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $i > $o] :
( ( ^ [B: $i,C: $i] :
( ( A @ B @ C )
| ( A @ C @ B )
| ( A @ C @ B )
| ( A @ B @ C ) ) )
= ( ^ [B: $i,C: $i] :
( ( A @ C @ B )
| ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
| ( sk1 @ B @ A )
| ( sk1 @ B @ A )
| ( sk1 @ A @ B ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ B @ A )
| ( sk1 @ A @ B ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
| ( sk1 @ B @ A )
| ( sk1 @ B @ A )
| ( sk1 @ A @ B ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ B @ A )
| ( sk1 @ A @ B ) ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(7,plain,
( ( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk2 @ sk3 ) )
!= ( ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk2 @ sk3 ) ) ),
inference(func_ext,[status(esa)],[5]) ).
thf(9,plain,
( ~ ( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk2 @ sk3 ) )
| ~ ( ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk2 @ sk3 ) ) ),
inference(bool_ext,[status(thm)],[7]) ).
thf(11,plain,
( ~ ( sk1 @ sk2 @ sk3 )
| ~ ( sk1 @ sk2 @ sk3 ) ),
inference(cnf,[status(esa)],[9]) ).
thf(14,plain,
~ ( sk1 @ sk2 @ sk3 ),
inference(simp,[status(thm)],[11]) ).
thf(18,plain,
( ( $false
| ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk3 @ sk2 )
| $false )
!= ( ( sk1 @ sk3 @ sk2 )
| $false ) ),
inference(rewrite,[status(thm)],[7,14]) ).
thf(19,plain,
$false,
inference(simp,[status(thm)],[18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU458^1 : TPTP v8.2.0. Released v3.6.0.
% 0.15/0.16 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n025.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sun May 19 17:02:24 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.96/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.29/1.01 % [INFO] Parsing done (133ms).
% 1.29/1.02 % [INFO] Running in sequential loop mode.
% 1.80/1.23 % [INFO] eprover registered as external prover.
% 1.80/1.23 % [INFO] cvc4 registered as external prover.
% 1.80/1.23 % [INFO] Scanning for conjecture ...
% 2.23/1.33 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.23/1.35 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.23/1.35 % [INFO] Problem is higher-order (TPTP THF).
% 2.23/1.35 % [INFO] Type checking passed.
% 2.23/1.35 % [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 ...
% 3.76/1.77 % [INFO] Killing All external provers ...
% 3.76/1.77 % Time passed: 1229ms (effective reasoning time: 748ms)
% 3.76/1.77 % 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)>
% 3.76/1.77 % Axioms used in derivation (0):
% 3.76/1.77 % No. of inferences in proof: 11
% 3.76/1.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1229 ms resp. 748 ms w/o parsing
% 3.76/1.80 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.76/1.80 % [INFO] Killing All external provers ...
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