TSTP Solution File: SEU468^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEU468^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n020.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 03:37:44 EDT 2024
% Result : Theorem 3.19s 1.74s
% Output : Refutation 3.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of formulae : 8 ( 3 unt; 2 typ; 2 def)
% Number of atoms : 13 ( 2 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 59 ( 2 ~; 0 |; 5 &; 41 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 25 ( 4 ^ 21 !; 0 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(mono_type,type,
mono: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(mono_def,definition,
( mono
= ( ^ [A: ( $i > $i > $o ) > $i > $i > $o] :
! [B: $i > $i > $o,C: $i > $i > $o] :
( ( subrel @ B @ C )
=> ( subrel @ ( A @ B ) @ ( A @ C ) ) ) ) ) ).
thf(tc_type,type,
tc: ( $i > $i > $o ) > $i > $i > $o ).
thf(tc_def,definition,
( tc
= ( ^ [A: $i > $i > $o,B: $i,C: $i] :
! [D: $i > $i > $o] :
( ( ( trans @ D )
& ( subrel @ A @ D ) )
=> ( D @ B @ C ) ) ) ) ).
thf(1,conjecture,
mono @ tc,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive_closure_op_is_monotonic) ).
thf(2,negated_conjecture,
~ ( mono @ tc ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $i > $o,B: $i > $i > $o] :
( ! [C: $i,D: $i] :
( ( A @ C @ D )
=> ( B @ C @ D ) )
=> ! [C: $i,D: $i] :
( ! [E: $i > $i > $o] :
( ( ! [F: $i,G: $i,H: $i] :
( ( ( E @ F @ G )
& ( E @ G @ H ) )
=> ( E @ F @ H ) )
& ! [F: $i,G: $i] :
( ( A @ F @ G )
=> ( E @ F @ G ) ) )
=> ( E @ C @ D ) )
=> ! [E: $i > $i > $o] :
( ( ! [F: $i,G: $i,H: $i] :
( ( ( E @ F @ G )
& ( E @ G @ H ) )
=> ( E @ F @ H ) )
& ! [F: $i,G: $i] :
( ( B @ F @ G )
=> ( E @ F @ G ) ) )
=> ( E @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU468^1 : TPTP v8.2.0. Released v3.6.0.
% 0.03/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n020.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun May 19 15:50:24 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.96/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/1.04 % [INFO] Parsing done (149ms).
% 1.50/1.05 % [INFO] Running in sequential loop mode.
% 1.95/1.25 % [INFO] eprover registered as external prover.
% 1.95/1.26 % [INFO] cvc4 registered as external prover.
% 1.95/1.26 % [INFO] Scanning for conjecture ...
% 2.18/1.36 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.18/1.37 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.18/1.37 % [INFO] Problem is higher-order (TPTP THF).
% 2.32/1.37 % [INFO] Type checking passed.
% 2.32/1.38 % [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 ...
% 3.19/1.74 % External prover 'e' found a proof!
% 3.19/1.74 % [INFO] Killing All external provers ...
% 3.19/1.74 % Time passed: 1224ms (effective reasoning time: 686ms)
% 3.19/1.74 % 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)>
% 3.19/1.74 % Axioms used in derivation (0):
% 3.19/1.74 % No. of inferences in proof: 4
% 3.19/1.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1224 ms resp. 686 ms w/o parsing
% 3.45/1.76 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.45/1.76 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------