TSTP Solution File: SYO068^4.001 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SYO068^4.001 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% 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 : Tue May 21 08:55:41 EDT 2024
% Result : Theorem 2.77s 1.54s
% Output : Refutation 2.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 14
% Syntax : Number of formulae : 21 ( 8 unt; 6 typ; 3 def)
% Number of atoms : 46 ( 3 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 62 ( 4 ~; 2 |; 2 &; 48 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 18 ( 3 ^ 15 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(irel_type,type,
irel: $i > $i > $o ).
thf(iatom_type,type,
iatom: ( $i > $o ) > $i > $o ).
thf(iatom_def,definition,
( iatom
= ( ^ [A: $i > $o] : A ) ) ).
thf(iimplies_type,type,
iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(iimplies_def,definition,
( iimplies
= ( ^ [A: $i > $o,B: $i > $o] : ( mimplies @ ( mbox_s4 @ A ) @ ( mbox_s4 @ B ) ) ) ) ).
thf(ivalid_type,type,
ivalid: ( $i > $o ) > $o ).
thf(ivalid_def,definition,
( ivalid
= ( '!' @ $i ) ) ).
thf(p0_type,type,
p0: $i > $o ).
thf(p1_type,type,
p1: $i > $o ).
thf(3,axiom,
! [A: $i] : ( irel @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_axiom) ).
thf(9,plain,
! [A: $i] : ( irel @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
ivalid @ ( iatom @ p1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom1) ).
thf(13,plain,
! [A: $i] : ( p1 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
ivalid @ ( iatom @ p0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ( ivalid @ ( iatom @ p0 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ! [A: $i] : ( p0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( irel @ A @ B )
& ( irel @ B @ C ) )
=> ( irel @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trans_axiom) ).
thf(11,plain,
! [A: $i,B: $i,C: $i] :
( ( ( irel @ A @ B )
& ( irel @ B @ C ) )
=> ( irel @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
ivalid @ ( iimplies @ ( iatom @ p1 ) @ ( iimplies @ ( iatom @ p1 ) @ ( iatom @ p0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom2) ).
thf(15,plain,
! [A: $i] :
( ~ ! [B: $i] :
( ( irel @ A @ B )
=> ( p1 @ B ) )
| ! [B: $i] :
( ( irel @ A @ B )
=> ( ~ ! [C: $i] :
( ( irel @ B @ C )
=> ( p1 @ C ) )
| ! [C: $i] :
( ( irel @ B @ C )
=> ( p0 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(20,plain,
$false,
inference(cvc4,[status(thm)],[9,13,7,11,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYO068^4.001 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.14 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon May 20 10:41:39 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.94/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/0.97 % [INFO] Parsing done (121ms).
% 1.19/0.98 % [INFO] Running in sequential loop mode.
% 1.73/1.18 % [INFO] eprover registered as external prover.
% 1.73/1.18 % [INFO] cvc4 registered as external prover.
% 1.73/1.19 % [INFO] Scanning for conjecture ...
% 1.93/1.26 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.05/1.27 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.05/1.28 % [INFO] Problem is higher-order (TPTP THF).
% 2.05/1.28 % [INFO] Type checking passed.
% 2.05/1.28 % [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 ...
% 2.77/1.54 % External prover 'cvc4' found a proof!
% 2.77/1.54 % [INFO] Killing All external provers ...
% 2.77/1.54 % Time passed: 1024ms (effective reasoning time: 559ms)
% 2.77/1.54 % 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)>
% 2.77/1.54 % Axioms used in derivation (4): refl_axiom, axiom1, trans_axiom, axiom2
% 2.77/1.54 % No. of inferences in proof: 12
% 2.77/1.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1024 ms resp. 559 ms w/o parsing
% 2.96/1.61 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.96/1.61 % [INFO] Killing All external provers ...
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