TSTP Solution File: SEU473^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEU473^1 : 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 03:37:45 EDT 2024
% Result : Theorem 3.80s 1.88s
% Output : Refutation 3.80s
% 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 : 18 ( 6 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 95 ( 2 ~; 6 |; 8 &; 63 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 5 con; 0-3 aty)
% Number of variables : 34 ( 2 ^ 32 !; 0 ?; 34 :)
% 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(trsc_type,type,
trsc: ( $i > $i > $o ) > $i > $i > $o ).
thf(trsc_def,definition,
( trsc
= ( ^ [A: $i > $i > $o] : ( sc @ ( rc @ ( tc @ A ) ) ) ) ) ).
thf(1,conjecture,
mono @ trsc,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive_reflexive_symmetric_closure_op_is_monotonic) ).
thf(2,negated_conjecture,
~ ( mono @ trsc ),
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] :
( ( ( D = C )
| ! [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 @ D @ C ) )
| ( 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] :
( ( A @ F @ G )
=> ( E @ F @ G ) ) )
=> ( E @ C @ D ) ) )
=> ( ( D = C )
| ! [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 @ D @ C ) )
| ( 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(66,plain,
$false,
inference(cvc4,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU473^1 : TPTP v8.2.0. Released v3.6.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n011.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Sun May 19 15:24:39 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.98/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.45/1.01 % [INFO] Parsing done (139ms).
% 1.45/1.02 % [INFO] Running in sequential loop mode.
% 1.87/1.23 % [INFO] eprover registered as external prover.
% 1.87/1.23 % [INFO] cvc4 registered as external prover.
% 1.87/1.23 % [INFO] Scanning for conjecture ...
% 1.96/1.33 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.27/1.34 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.27/1.34 % [INFO] Problem is higher-order (TPTP THF).
% 2.27/1.34 % [INFO] Type checking passed.
% 2.27/1.35 % [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 ...
% 3.80/1.88 % External prover 'cvc4' found a proof!
% 3.80/1.88 % [INFO] Killing All external provers ...
% 3.80/1.88 % Time passed: 1341ms (effective reasoning time: 857ms)
% 3.80/1.88 % 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)>
% 3.80/1.88 % Axioms used in derivation (0):
% 3.80/1.88 % No. of inferences in proof: 4
% 3.80/1.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1341 ms resp. 857 ms w/o parsing
% 3.80/1.90 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.80/1.90 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------