TSTP Solution File: SYO048^1 by Leo-III---1.7.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SYO048^1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n006.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 08:55:35 EDT 2024
% Result : Theorem 3.33s 1.71s
% Output : Refutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 12
% Syntax : Number of formulae : 15 ( 6 unt; 6 typ; 5 def)
% Number of atoms : 37 ( 5 equ; 0 cnn)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 105 ( 24 ~; 14 |; 0 &; 67 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 46 ( 46 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 27 ( 13 ^ 14 !; 0 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
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(mequiv_type,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mequiv_def,definition,
( mequiv
= ( ^ [A: $i > $o,B: $i > $o] : ( mand @ ( mimplies @ A @ B ) @ ( mimplies @ B @ 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(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mvalid_def,definition,
( mvalid
= ( '!' @ $i ) ) ).
thf(1,conjecture,
! [A: $i > $i > $o] :
( mvalid
@ ( mforall_prop
@ ^ [B: $i > $o] :
( mforall_prop
@ ^ [C: $i > $o] : ( mequiv @ ( mbox @ A @ ( mand @ B @ C ) ) @ ( mand @ ( mbox @ A @ B ) @ ( mbox @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: $i > $i > $o] :
( mvalid
@ ( mforall_prop
@ ^ [B: $i > $o] :
( mforall_prop
@ ^ [C: $i > $o] : ( mequiv @ ( mbox @ A @ ( mand @ B @ C ) ) @ ( mand @ ( mbox @ A @ B ) @ ( mbox @ A @ C ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $i > $o,B: $i,C: $i > $o,D: $i > $o] :
~ ( ~ ( ~ ! [E: $i] :
( ~ ( A @ B @ E )
| ~ ( ~ ( C @ E )
| ~ ( D @ E ) ) )
| ~ ( ~ ! [E: $i] :
( ~ ( A @ B @ E )
| ( C @ E ) )
| ~ ! [E: $i] :
( ~ ( A @ B @ E )
| ( D @ E ) ) ) )
| ~ ( ~ ! [E: $i] :
( ~ ( A @ B @ E )
| ( C @ E ) )
| ~ ! [E: $i] :
( ~ ( A @ B @ E )
| ( D @ E ) )
| ! [E: $i] :
( ~ ( A @ B @ E )
| ~ ( ~ ( C @ E )
| ~ ( D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(17,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO048^1 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n006.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon May 20 08:40:54 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.99/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.42/1.01 % [INFO] Parsing done (145ms).
% 1.42/1.02 % [INFO] Running in sequential loop mode.
% 1.90/1.23 % [INFO] eprover registered as external prover.
% 1.90/1.23 % [INFO] cvc4 registered as external prover.
% 1.90/1.23 % [INFO] Scanning for conjecture ...
% 2.10/1.34 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.10/1.35 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.10/1.35 % [INFO] Problem is higher-order (TPTP THF).
% 2.10/1.36 % [INFO] Type checking passed.
% 2.10/1.36 % [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 ...
% 3.33/1.71 % External prover 'e' found a proof!
% 3.33/1.71 % [INFO] Killing All external provers ...
% 3.33/1.71 % Time passed: 1182ms (effective reasoning time: 689ms)
% 3.33/1.71 % 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)>
% 3.33/1.71 % Axioms used in derivation (0):
% 3.33/1.71 % No. of inferences in proof: 4
% 3.33/1.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1182 ms resp. 689 ms w/o parsing
% 3.51/1.74 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.51/1.74 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------