TSTP Solution File: SYO530^1 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SYO530^1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.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 09:00:50 EDT 2024
% Result : Theorem 3.15s 2.14s
% Output : Refutation 3.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 20 ( 4 unt; 5 typ; 0 def)
% Number of atoms : 31 ( 0 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 103 ( 10 ~; 5 |; 0 &; 84 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 46 ( 11 ^ 14 !; 21 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
thf(eps_type,type,
eps: ( $i > $o ) > $i ).
thf(sk1_type,type,
sk1: $i > $i > $o ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i > $i > $i ).
thf(1,conjecture,
! [A: $i > $i > $o] :
( ? [B: $i,C: $i] : ( A @ B @ C )
=> ( A @ ( epsa @ A ) @ ( epsb @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: $i > $i > $o] :
( ? [B: $i,C: $i] : ( A @ B @ C )
=> ( A @ ( epsa @ A ) @ ( epsb @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ! [A: $i > $i > $o] :
( ? [B: $i,C: $i] : ( A @ B @ C )
=> ( A
@ ( eps
@ ^ [B: $i] :
? [C: $i] : ( A @ B @ C ) )
@ ( eps
@ ( A
@ ( eps
@ ^ [B: $i] :
? [C: $i] : ( A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
sk1 @ sk2 @ sk3,
inference(cnf,[status(esa)],[4]) ).
thf(11,axiom,
? [A: ( $i > $o ) > $i] :
! [B: $i > $o] :
( ? [C: $i] : ( B @ C )
=> ( B @ ( A @ B ) ) ),
introduced(axiom_of_choice) ).
thf(12,plain,
! [A: $i] :
( ~ ? [B: $i] : ( sk1 @ A @ B )
| ? [B: $i] :
( sk1
@ ( eps
@ ^ [C: $i] :
? [D: $i] : ( sk1 @ C @ D ) )
@ B ) ),
inference(choice,[status(esa)],[11]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( sk1
@ ( eps
@ ^ [C: $i] :
? [D: $i] : ( sk1 @ C @ D ) )
@ ( sk4 @ B @ A ) )
| ~ ( sk1 @ A @ B ) ),
inference(cnf,[status(esa)],[12]) ).
thf(13,plain,
! [A: $i] :
( ~ ( sk1
@ ( eps
@ ^ [B: $i] :
? [C: $i] : ( sk1 @ B @ C ) )
@ A )
| ( sk1
@ ( eps
@ ^ [B: $i] :
? [C: $i] : ( sk1 @ B @ C ) )
@ ( eps
@ ( sk1
@ ( eps
@ ^ [B: $i] :
? [C: $i] : ( sk1 @ B @ C ) ) ) ) ) ),
inference(choice,[status(esa)],[11]) ).
thf(5,plain,
~ ( sk1
@ ( eps
@ ^ [A: $i] :
? [B: $i] : ( sk1 @ A @ B ) )
@ ( eps
@ ( sk1
@ ( eps
@ ^ [A: $i] :
? [B: $i] : ( sk1 @ A @ B ) ) ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(16,plain,
! [A: $i] :
( ~ ( sk1
@ ( eps
@ ^ [B: $i] :
? [C: $i] : ( sk1 @ B @ C ) )
@ A )
| $false ),
inference(rewrite,[status(thm)],[13,5]) ).
thf(17,plain,
! [A: $i] :
~ ( sk1
@ ( eps
@ ^ [B: $i] :
? [C: $i] : ( sk1 @ B @ C ) )
@ A ),
inference(simp,[status(thm)],[16]) ).
thf(23,plain,
! [B: $i,A: $i] :
( $false
| ~ ( sk1 @ A @ B ) ),
inference(rewrite,[status(thm)],[15,17]) ).
thf(24,plain,
! [B: $i,A: $i] :
~ ( sk1 @ A @ B ),
inference(simp,[status(thm)],[23]) ).
thf(26,plain,
$false,
inference(rewrite,[status(thm)],[6,24]) ).
thf(27,plain,
$false,
inference(simp,[status(thm)],[26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SYO530^1 : TPTP v8.2.0. Released v5.2.0.
% 0.10/0.12 % Command : run_Leo-III %s %d
% 0.11/0.32 % Computer : n015.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon May 20 11:04:39 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.99/0.94 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.30/1.10 % [INFO] Parsing done (161ms).
% 1.30/1.11 % [INFO] Running in sequential loop mode.
% 1.68/1.46 % [INFO] nitpick registered as external prover.
% 1.84/1.47 % [INFO] Scanning for conjecture ...
% 1.98/1.56 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 1.98/1.59 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 1.98/1.59 % [INFO] Problem is higher-order (TPTP THF).
% 1.98/1.60 % [INFO] Type checking passed.
% 1.98/1.60 % [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 ...
% 3.15/2.13 % [INFO] Killing All external provers ...
% 3.15/2.13 % Time passed: 1660ms (effective reasoning time: 1010ms)
% 3.15/2.13 % 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)>
% 3.15/2.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1660 ms resp. 1010 ms w/o parsing
% 3.15/2.19 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.15/2.19 % [INFO] Killing All external provers ...
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