TSTP Solution File: LCL707^1 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : LCL707^1 : TPTP v8.2.0. Bugfixed v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n017.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 : Mon Jun 24 11:15:27 EDT 2024
% Result : Theorem 2.87s 1.50s
% Output : Refutation 2.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 8
% Syntax : Number of formulae : 11 ( 9 unt; 0 typ; 7 def)
% Number of atoms : 50 ( 9 equ; 0 cnn)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 122 ( 11 ~; 15 |; 2 &; 89 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 34 ( 16 ^ 18 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(mor_type,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mor_def,definition,
( mor
= ( ^ [A: $i > $o,B: $i > $o,C: $i] :
( ( A @ C )
| ( B @ C ) ) ) ) ).
thf(mand_type,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mand_def,definition,
( mand
= ( ^ [A: $i > $o,B: $i > $o] : ( mnot @ ( mor @ ( mnot @ A ) @ ( mnot @ B ) ) ) ) ) ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mimplies_def,definition,
( mimplies
= ( ^ [A: $i > $o] : ( mor @ ( mnot @ A ) ) ) ) ).
thf(mforall_prop_type,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(mforall_prop_def,definition,
( mforall_prop
= ( ^ [A: ( $i > $o ) > $i > $o,B: $i] :
! [C: $i > $o] : ( A @ C @ B ) ) ) ).
thf(mbox_type,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mbox_def,definition,
( mbox
= ( ^ [A: $i > $i > $o,B: $i > $o,C: $i] :
! [D: $i] :
( ~ ( A @ C @ D )
| ( B @ D ) ) ) ) ).
thf(mweakly_connected_type,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(mweakly_connected_def,definition,
( mweakly_connected
= ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ B @ D ) )
=> ( ( A @ C @ D )
| ( C = D )
| ( A @ D @ C ) ) ) ) ) ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mvalid_def,definition,
( mvalid
= ( '!' @ $i ) ) ).
thf(1,conjecture,
! [A: $i > $i > $o] :
( ( mweakly_connected @ A )
=> ( mvalid
@ ( mforall_prop
@ ^ [B: $i > $o] :
( mforall_prop
@ ^ [C: $i > $o] : ( mor @ ( mbox @ A @ ( mimplies @ ( mand @ B @ ( mbox @ A @ B ) ) @ C ) ) @ ( mbox @ A @ ( mimplies @ ( mand @ C @ ( mbox @ A @ C ) ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: $i > $i > $o] :
( ( mweakly_connected @ A )
=> ( mvalid
@ ( mforall_prop
@ ^ [B: $i > $o] :
( mforall_prop
@ ^ [C: $i > $o] : ( mor @ ( mbox @ A @ ( mimplies @ ( mand @ B @ ( mbox @ A @ B ) ) @ C ) ) @ ( mbox @ A @ ( mimplies @ ( mand @ C @ ( mbox @ A @ C ) ) @ B ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $i > $o] :
( ! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ B @ D ) )
=> ( ( A @ C @ D )
| ( C = D )
| ( A @ D @ C ) ) )
=> ! [B: $i,C: $i > $o,D: $i > $o] :
( ! [E: $i] :
( ~ ( A @ B @ E )
| ~ ( C @ E )
| ~ ! [F: $i] :
( ~ ( A @ E @ F )
| ( C @ F ) )
| ( D @ E ) )
| ! [E: $i] :
( ~ ( A @ B @ E )
| ~ ( D @ E )
| ~ ! [F: $i] :
( ~ ( A @ E @ F )
| ( D @ F ) )
| ( C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : LCL707^1 : TPTP v8.2.0. Bugfixed v5.1.0.
% 0.00/0.07 % Command : run_Leo-III %s %d THM
% 0.07/0.26 % Computer : n017.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Sat Jun 22 16:51:25 EDT 2024
% 0.07/0.26 % CPUTime :
% 0.65/0.70 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.97/0.85 % [INFO] Parsing done (150ms).
% 0.97/0.86 % [INFO] Running in sequential loop mode.
% 1.61/1.06 % [INFO] eprover registered as external prover.
% 1.61/1.07 % [INFO] Scanning for conjecture ...
% 1.80/1.17 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.10/1.19 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.10/1.19 % [INFO] Problem is higher-order (TPTP THF).
% 2.10/1.19 % [INFO] Type checking passed.
% 2.10/1.19 % [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 ...
% 2.87/1.50 % External prover 'e' found a proof!
% 2.87/1.50 % [INFO] Killing All external provers ...
% 2.87/1.50 % Time passed: 1130ms (effective reasoning time: 633ms)
% 2.87/1.50 % 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)>
% 2.87/1.50 % Axioms used in derivation (0):
% 2.87/1.50 % No. of inferences in proof: 4
% 2.87/1.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1130 ms resp. 633 ms w/o parsing
% 2.87/1.53 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.87/1.53 % [INFO] Killing All external provers ...
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