TSTP Solution File: PUZ086^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : PUZ086^1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.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 02:26:52 EDT 2024
% Result : Theorem 3.42s 1.88s
% Output : Refutation 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 34
% Syntax : Number of formulae : 49 ( 10 unt; 14 typ; 7 def)
% Number of atoms : 155 ( 7 equ; 0 cnn)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 240 ( 29 ~; 25 |; 4 &; 178 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 59 ( 59 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 4 con; 0-3 aty)
% Number of variables : 57 ( 12 ^ 45 !; 0 ?; 57 :)
% 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(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(mreflexive_type,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(mreflexive_def,definition,
( mreflexive
= ( ^ [A: $i > $i > $o] :
! [B: $i] : ( A @ B @ 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(peter_type,type,
peter: $i > $i > $o ).
thf(john_type,type,
john: $i > $i > $o ).
thf(wife_type,type,
wife: ( $i > $i > $o ) > $i > $i > $o ).
thf(time_type,type,
time: $i > $o ).
thf(place_type,type,
place: $i > $o ).
thf(appointment_type,type,
appointment: $i > $o ).
thf(8,axiom,
mtransitive @ ( wife @ peter ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trans_wife_peter) ).
thf(33,plain,
! [A: $i,B: $i,C: $i] :
( ( ( wife @ peter @ A @ B )
& ( wife @ peter @ B @ C ) )
=> ( wife @ peter @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(14,axiom,
mvalid @ ( mbox @ peter @ ( mbox @ john @ ( mimplies @ ( mand @ place @ time ) @ appointment ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_d) ).
thf(49,plain,
! [A: $i,B: $i] :
( ~ ( peter @ A @ B )
| ! [C: $i] :
( ~ ( john @ B @ C )
| ~ ( place @ C )
| ~ ( time @ C )
| ( appointment @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(10,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ ( wife @ peter ) @ A ) @ ( mbox @ peter @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_ii) ).
thf(39,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( wife @ peter @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( peter @ A @ C )
| ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(9,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ peter @ ( mbox @ john @ A ) ) @ ( mbox @ john @ ( mbox @ peter @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_i) ).
thf(35,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( peter @ A @ C )
| ! [D: $i] :
( ~ ( john @ C @ D )
| ( B @ D ) ) )
| ! [C: $i] :
( ~ ( john @ A @ C )
| ! [D: $i] :
( ~ ( peter @ C @ D )
| ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
mtransitive @ john,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trans_john) ).
thf(31,plain,
! [A: $i,B: $i,C: $i] :
( ( ( john @ A @ B )
& ( john @ B @ C ) )
=> ( john @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
mreflexive @ peter,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_peter) ).
thf(23,plain,
! [A: $i] : ( peter @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,conjecture,
mvalid @ ( mand @ ( mbox @ peter @ ( mbox @ john @ appointment ) ) @ ( mbox @ john @ ( mbox @ peter @ appointment ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ( mvalid @ ( mand @ ( mbox @ peter @ ( mbox @ john @ appointment ) ) @ ( mbox @ john @ ( mbox @ peter @ appointment ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(15,plain,
~ ! [A: $i] :
~ ( ~ ! [B: $i] :
( ~ ( peter @ A @ B )
| ! [C: $i] :
( ~ ( john @ B @ C )
| ( appointment @ C ) ) )
| ~ ! [B: $i] :
( ~ ( john @ A @ B )
| ! [C: $i] :
( ~ ( peter @ B @ C )
| ( appointment @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
mvalid @ ( mbox @ peter @ time ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_a) ).
thf(42,plain,
! [A: $i,B: $i] :
( ~ ( peter @ A @ B )
| ( time @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4,axiom,
mreflexive @ john,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_john) ).
thf(25,plain,
! [A: $i] : ( john @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,axiom,
mvalid @ ( mbox @ ( wife @ peter ) @ ( mimplies @ ( mbox @ peter @ time ) @ ( mbox @ john @ time ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_c) ).
thf(46,plain,
! [A: $i,B: $i] :
( ~ ( wife @ peter @ A @ B )
| ~ ! [C: $i] :
( ~ ( peter @ B @ C )
| ( time @ C ) )
| ! [C: $i] :
( ~ ( john @ B @ C )
| ( time @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6,axiom,
mtransitive @ peter,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trans_peter) ).
thf(29,plain,
! [A: $i,B: $i,C: $i] :
( ( ( peter @ A @ B )
& ( peter @ B @ C ) )
=> ( peter @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
mvalid @ ( mbox @ peter @ ( mbox @ john @ place ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_b) ).
thf(44,plain,
! [A: $i,B: $i] :
( ~ ( peter @ A @ B )
| ! [C: $i] :
( ~ ( john @ B @ C )
| ( place @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,axiom,
mreflexive @ ( wife @ peter ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_wife_peter) ).
thf(27,plain,
! [A: $i] : ( wife @ peter @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(51,plain,
$false,
inference(e,[status(thm)],[33,49,39,35,31,23,15,42,25,46,29,44,27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : PUZ086^1 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n016.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat May 18 10:37:39 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.86/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.32/0.99 % [INFO] Parsing done (155ms).
% 1.32/1.00 % [INFO] Running in sequential loop mode.
% 1.81/1.25 % [INFO] eprover registered as external prover.
% 1.81/1.25 % [INFO] cvc4 registered as external prover.
% 1.81/1.25 % [INFO] Scanning for conjecture ...
% 2.16/1.37 % [INFO] Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ...
% 2.16/1.39 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 2.16/1.39 % [INFO] Problem is higher-order (TPTP THF).
% 2.16/1.40 % [INFO] Type checking passed.
% 2.16/1.40 % [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 ...
% 3.42/1.88 % External prover 'e' found a proof!
% 3.42/1.88 % [INFO] Killing All external provers ...
% 3.42/1.88 % Time passed: 1370ms (effective reasoning time: 872ms)
% 3.42/1.88 % 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)>
% 3.42/1.88 % Axioms used in derivation (12): ax_i, trans_peter, ax_c, ax_b, trans_john, ax_ii, ax_a, refl_john, ax_d, refl_wife_peter, trans_wife_peter, refl_peter
% 3.42/1.88 % No. of inferences in proof: 28
% 3.42/1.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1370 ms resp. 872 ms w/o parsing
% 3.67/1.93 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.67/1.93 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------