TSTP Solution File: LCL725^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : LCL725^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.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 00:07:21 EDT 2024
% Result : Theorem 3.77s 2.25s
% Output : Refutation 3.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 21
% Syntax : Number of formulae : 27 ( 9 unt; 10 typ; 7 def)
% Number of atoms : 82 ( 7 equ; 0 cnn)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 120 ( 14 ~; 10 |; 8 &; 84 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 29 ( 7 ^ 22 !; 0 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mimplies_def,definition,
( mimplies
= ( ^ [A: $i > $o] : ( mor @ ( mnot @ A ) ) ) ) ).
thf(mreflexive_type,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(mreflexive_def,definition,
( mreflexive
= ( ^ [A: $i > $i > $o] :
! [B: $i] : ( A @ B @ B ) ) ) ).
thf(msymmetric_type,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(msymmetric_def,definition,
( msymmetric
= ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i] :
( ( A @ B @ C )
=> ( A @ C @ B ) ) ) ) ).
thf(mtransitive_type,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(mtransitive_def,definition,
( mtransitive
= ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ) ) ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mvalid_def,definition,
( mvalid
= ( '!' @ $i ) ) ).
thf(rel_s5_type,type,
rel_s5: $i > $i > $o ).
thf(mbox_s5_type,type,
mbox_s5: ( $i > $o ) > $i > $o ).
thf(mbox_s5_def,definition,
( mbox_s5
= ( ^ [A: $i > $o,B: $i] :
! [C: $i] :
( ~ ( rel_s5 @ B @ C )
| ( A @ C ) ) ) ) ).
thf(mdia_s5_type,type,
mdia_s5: ( $i > $o ) > $i > $o ).
thf(mdia_s5_def,definition,
( mdia_s5
= ( ^ [A: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ A ) ) ) ) ) ).
thf(phi_type,type,
phi: $i > $o ).
thf(1,conjecture,
( ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ phi ) )
& ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ ( mbox_s5 @ ( mbox_s5 @ phi ) ) ) )
& ( mvalid @ ( mimplies @ phi @ ( mbox_s5 @ ( mdia_s5 @ phi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ( ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ phi ) )
& ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ ( mbox_s5 @ ( mbox_s5 @ phi ) ) ) )
& ( mvalid @ ( mimplies @ phi @ ( mbox_s5 @ ( mdia_s5 @ phi ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ( ! [A: $i] :
( ~ ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ( phi @ B ) )
| ( phi @ A ) )
& ! [A: $i] :
( ~ ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ( phi @ B ) )
| ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ! [C: $i] :
( ~ ( rel_s5 @ B @ C )
| ( phi @ C ) ) ) )
& ! [A: $i] :
( ~ ( phi @ A )
| ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ~ ! [C: $i] :
( ~ ( rel_s5 @ B @ C )
| ~ ( phi @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
mreflexive @ rel_s5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
thf(18,plain,
! [A: $i] : ( rel_s5 @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
mtransitive @ rel_s5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
thf(20,plain,
! [A: $i,B: $i,C: $i] :
( ( ( rel_s5 @ A @ B )
& ( rel_s5 @ B @ C ) )
=> ( rel_s5 @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
msymmetric @ rel_s5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3) ).
thf(22,plain,
! [A: $i,B: $i] :
( ( rel_s5 @ A @ B )
=> ( rel_s5 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(24,plain,
$false,
inference(e,[status(thm)],[6,18,20,22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : LCL725^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% 0.03/0.12 % Command : run_Leo-III %s %d
% 0.12/0.32 % Computer : n004.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon May 20 03:03:39 EDT 2024
% 0.12/0.33 % CPUTime :
% 1.00/0.95 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.51/1.16 % [INFO] Parsing done (213ms).
% 1.51/1.18 % [INFO] Running in sequential loop mode.
% 2.05/1.54 % [INFO] eprover registered as external prover.
% 2.14/1.54 % [INFO] cvc4 registered as external prover.
% 2.14/1.54 % [INFO] Scanning for conjecture ...
% 2.48/1.72 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.48/1.75 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.48/1.75 % [INFO] Problem is higher-order (TPTP THF).
% 2.48/1.75 % [INFO] Type checking passed.
% 2.48/1.76 % [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 ...
% 3.77/2.24 % External prover 'e' found a proof!
% 3.77/2.24 % [INFO] Killing All external provers ...
% 3.77/2.25 % Time passed: 1766ms (effective reasoning time: 1063ms)
% 3.77/2.25 % 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)>
% 3.77/2.25 % Axioms used in derivation (3): a1, a2, a3
% 3.77/2.25 % No. of inferences in proof: 10
% 3.77/2.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1766 ms resp. 1063 ms w/o parsing
% 3.92/2.30 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.92/2.30 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------