TSTP Solution File: SEU462^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEU462^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n011.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 03:37:43 EDT 2024
% Result : Theorem 3.50s 2.23s
% Output : Refutation 3.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 7
% Syntax : Number of formulae : 10 ( 4 unt; 3 typ; 3 def)
% Number of atoms : 15 ( 3 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 79 ( 2 ~; 0 |; 11 &; 55 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 1 con; 0-3 aty)
% Number of variables : 35 ( 6 ^ 29 !; 0 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
thf(subrel_type,type,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(subrel_def,definition,
( subrel
= ( ^ [A: $i > $i > $o,B: $i > $i > $o] :
! [C: $i,D: $i] :
( ( A @ C @ D )
=> ( B @ C @ D ) ) ) ) ).
thf(trans_type,type,
trans: ( $i > $i > $o ) > $o ).
thf(trans_def,definition,
( trans
= ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ) ) ).
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,
! [A: $i > $i > $o,B: $i,C: $i,D: $i > $i > $o] :
( ( ( trans @ D )
& ( subrel @ A @ D )
& ( tc @ A @ B @ C ) )
=> ( D @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive_closure_is_transitive2) ).
thf(2,negated_conjecture,
~ ! [A: $i > $i > $o,B: $i,C: $i,D: $i > $i > $o] :
( ( ( trans @ D )
& ( subrel @ A @ D )
& ( tc @ A @ B @ C ) )
=> ( D @ B @ C ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $i > $o,B: $i,C: $i,D: $i > $i > $o] :
( ( ! [E: $i,F: $i,G: $i] :
( ( ( D @ E @ F )
& ( D @ F @ G ) )
=> ( D @ E @ G ) )
& ! [E: $i,F: $i] :
( ( A @ E @ F )
=> ( D @ E @ F ) )
& ! [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 @ B @ C ) ) )
=> ( D @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SEU462^1 : TPTP v8.2.0. Released v3.6.0.
% 0.02/0.11 % Command : run_Leo-III %s %d
% 0.11/0.31 % Computer : n011.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Sun May 19 17:45:09 EDT 2024
% 0.11/0.31 % CPUTime :
% 0.92/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.37/1.13 % [INFO] Parsing done (229ms).
% 1.37/1.15 % [INFO] Running in sequential loop mode.
% 2.02/1.50 % [INFO] eprover registered as external prover.
% 2.02/1.51 % [INFO] cvc4 registered as external prover.
% 2.02/1.51 % [INFO] Scanning for conjecture ...
% 2.36/1.67 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.47/1.70 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.47/1.70 % [INFO] Problem is higher-order (TPTP THF).
% 2.47/1.71 % [INFO] Type checking passed.
% 2.47/1.71 % [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 ...
% 3.50/2.22 % External prover 'e' found a proof!
% 3.50/2.22 % [INFO] Killing All external provers ...
% 3.50/2.22 % Time passed: 1787ms (effective reasoning time: 1074ms)
% 3.50/2.22 % 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)>
% 3.50/2.23 % Axioms used in derivation (0):
% 3.50/2.23 % No. of inferences in proof: 4
% 3.50/2.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1787 ms resp. 1074 ms w/o parsing
% 3.79/2.26 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.79/2.26 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------