TSTP Solution File: SEV299^5 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEV299^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n022.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 Jun 24 15:58:44 EDT 2024
% Result : Theorem 3.65s 1.83s
% Output : Refutation 3.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 2
% Syntax : Number of formulae : 5 ( 2 unt; 0 typ; 1 def)
% Number of atoms : 13 ( 3 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 61 ( 6 ~; 0 |; 9 &; 33 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 24 ( 7 ^ 13 !; 4 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(cNAT_type,type,
cNAT: ( ( $i > $o ) > $o ) > $o ).
thf(cNAT_def,definition,
( cNAT
= ( ^ [A: ( $i > $o ) > $o] :
! [B: ( ( $i > $o ) > $o ) > $o] :
( ( ( B @ cZERO )
& ! [C: ( $i > $o ) > $o] :
( ( B @ C )
=> ( B @ ( cSUCC @ C ) ) ) )
=> ( B @ A ) ) ) ) ).
thf(1,conjecture,
! [A: ( ( $i > $o ) > $o ) > $o] :
( ( ( A @ cZERO )
& ! [B: ( $i > $o ) > $o] :
( ( A @ B )
=> ( A @ ( cSUCC @ B ) ) ) )
=> ! [B: ( $i > $o ) > $o] :
( ( cNAT @ B )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cINDUCTION) ).
thf(2,negated_conjecture,
~ ! [A: ( ( $i > $o ) > $o ) > $o] :
( ( ( A @ cZERO )
& ! [B: ( $i > $o ) > $o] :
( ( A @ B )
=> ( A @ ( cSUCC @ B ) ) ) )
=> ! [B: ( $i > $o ) > $o] :
( ( cNAT @ B )
=> ( A @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: ( ( $i > $o ) > $o ) > $o] :
( ( ( A
@ ^ [B: $i > $o] :
~ ? [C: $i] : ( B @ C ) )
& ! [B: ( $i > $o ) > $o] :
( ( A @ B )
=> ( A
@ ^ [C: $i > $o] :
? [D: $i] :
( ( C @ D )
& ( B
@ ^ [E: $i] :
( ( E != D )
& ( C @ E ) ) ) ) ) ) )
=> ! [B: ( $i > $o ) > $o] :
( ! [C: ( ( $i > $o ) > $o ) > $o] :
( ( ( C
@ ^ [D: $i > $o] :
~ ? [E: $i] : ( D @ E ) )
& ! [D: ( $i > $o ) > $o] :
( ( C @ D )
=> ( C
@ ^ [E: $i > $o] :
? [F: $i] :
( ( E @ F )
& ( D
@ ^ [G: $i] :
( ( G != F )
& ( E @ G ) ) ) ) ) ) )
=> ( C @ B ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(17,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV299^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n022.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 21 19:07:40 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.97/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.37/1.04 % [INFO] Parsing done (123ms).
% 1.37/1.04 % [INFO] Running in sequential loop mode.
% 1.77/1.25 % [INFO] eprover registered as external prover.
% 1.77/1.26 % [INFO] Scanning for conjecture ...
% 1.99/1.32 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.99/1.34 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.99/1.34 % [INFO] Problem is higher-order (TPTP THF).
% 1.99/1.34 % [INFO] Type checking passed.
% 1.99/1.35 % [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 ...
% 3.65/1.83 % External prover 'e' found a proof!
% 3.65/1.83 % [INFO] Killing All external provers ...
% 3.65/1.83 % Time passed: 1307ms (effective reasoning time: 784ms)
% 3.65/1.83 % 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)>
% 3.65/1.83 % Axioms used in derivation (0):
% 3.65/1.83 % No. of inferences in proof: 4
% 3.65/1.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1307 ms resp. 784 ms w/o parsing
% 3.65/1.86 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.65/1.86 % [INFO] Killing All external provers ...
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