TSTP Solution File: ALG273^5 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ALG273^5 : TPTP v8.2.0. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.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 : Mon May 20 18:14:42 EDT 2024
% Result : Theorem 3.97s 1.89s
% Output : Refutation 3.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of formulae : 9 ( 6 unt; 3 typ; 2 def)
% Number of atoms : 24 ( 11 equ; 0 cnn)
% Maximal formula atoms : 1 ( 4 avg)
% Number of connectives : 52 ( 2 ~; 0 |; 8 &; 42 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 22 ( 4 ^ 16 !; 2 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(g_type,type,
g: $tType ).
thf(cGROUP2_type,type,
cGROUP2: ( g > g > g ) > g > $o ).
thf(cGROUP2_def,definition,
( cGROUP2
= ( ^ [A: g > g > g,B: g] :
( ( cGRP_ASSOC @ A )
& ( cGRP_LEFT_UNIT @ A @ B )
& ( cGRP_LEFT_INVERSE @ A @ B ) ) ) ) ).
thf(cGROUP3_type,type,
cGROUP3: ( g > g > g ) > g > $o ).
thf(cGROUP3_def,definition,
( cGROUP3
= ( ^ [A: g > g > g,B: g] :
( ( cGRP_ASSOC @ A )
& ( cGRP_RIGHT_UNIT @ A @ B )
& ( cGRP_RIGHT_INVERSE @ A @ B ) ) ) ) ).
thf(1,conjecture,
! [A: g > g > g,B: g] :
( ( cGROUP2 @ A @ B )
= ( cGROUP3 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEQUIV_02_03) ).
thf(2,negated_conjecture,
~ ! [A: g > g > g,B: g] :
( ( cGROUP2 @ A @ B )
= ( cGROUP3 @ A @ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: g > g > g,B: g] :
( ( ! [C: g,D: g,E: g] :
( ( A @ ( A @ C @ D ) @ E )
= ( A @ C @ ( A @ D @ E ) ) )
& ! [C: g] :
( ( A @ B @ C )
= C )
& ! [C: g] :
? [D: g] :
( ( A @ D @ C )
= B ) )
= ( ! [C: g,D: g,E: g] :
( ( A @ ( A @ C @ D ) @ E )
= ( A @ C @ ( A @ D @ E ) ) )
& ! [C: g] :
( ( A @ C @ B )
= C )
& ! [C: g] :
? [D: g] :
( ( A @ C @ D )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(72,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG273^5 : TPTP v8.2.0. Bugfixed v5.3.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n026.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sat May 18 22:47:09 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.97/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.11/1.00 % [INFO] Parsing done (111ms).
% 1.11/1.00 % [INFO] Running in sequential loop mode.
% 1.66/1.21 % [INFO] eprover registered as external prover.
% 1.75/1.21 % [INFO] cvc4 registered as external prover.
% 1.75/1.21 % [INFO] Scanning for conjecture ...
% 1.86/1.28 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.86/1.30 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.86/1.30 % [INFO] Problem is higher-order (TPTP THF).
% 1.86/1.30 % [INFO] Type checking passed.
% 1.86/1.30 % [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 ...
% 3.97/1.89 % External prover 'e' found a proof!
% 3.97/1.89 % [INFO] Killing All external provers ...
% 3.97/1.89 % Time passed: 1354ms (effective reasoning time: 882ms)
% 3.97/1.89 % 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)>
% 3.97/1.89 % Axioms used in derivation (0):
% 3.97/1.89 % No. of inferences in proof: 4
% 3.97/1.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1354 ms resp. 882 ms w/o parsing
% 3.97/1.91 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.97/1.91 % [INFO] Killing All external provers ...
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