TSTP Solution File: PUZ078+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : PUZ078+1 : TPTP v8.1.2. Released v3.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.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 : Fri May 19 11:47:38 EDT 2023
% Result : Theorem 3.22s 1.74s
% Output : Refutation 3.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 35
% Syntax : Number of formulae : 60 ( 26 unt; 12 typ; 0 def)
% Number of atoms : 154 ( 78 equ; 0 cnn)
% Maximal formula atoms : 21 ( 3 avg)
% Number of connectives : 257 ( 56 ~; 18 |; 59 &; 95 @)
% ( 5 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 36 ( 0 ^; 28 !; 8 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(truthday_type,type,
truthday: $i > $o ).
thf(tuesday_type,type,
tuesday: $i ).
thf(day1_type,type,
day1: $i > $o ).
thf(consecutive_type,type,
consecutive: $i > $i ).
thf(sunday_type,type,
sunday: $i ).
thf(monday_type,type,
monday: $i ).
thf(saturday_type,type,
saturday: $i ).
thf(friday_type,type,
friday: $i ).
thf(day3_type,type,
day3: $i > $o ).
thf(wednesday_type,type,
wednesday: $i ).
thf(thursday_type,type,
thursday: $i ).
thf(day2_type,type,
day2: $i > $o ).
thf(18,axiom,
! [A: $i] :
( ( A = monday )
| ( A = tuesday )
| ( A = wednesday )
| ( A = thursday )
| ( A = friday )
| ( A = saturday )
| ( A = sunday ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',days_of_week) ).
thf(69,plain,
! [A: $i] :
( ( A = monday )
| ( A = tuesday )
| ( A = wednesday )
| ( A = thursday )
| ( A = friday )
| ( A = saturday )
| ( A = sunday ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(14,axiom,
? [A: $i] : ( day2 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',day2_once) ).
thf(56,plain,
? [A: $i] : ( day2 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(23,axiom,
( ( monday != tuesday )
& ( monday != wednesday )
& ( monday != thursday )
& ( monday != friday )
& ( monday != saturday )
& ( monday != sunday )
& ( tuesday != wednesday )
& ( tuesday != thursday )
& ( tuesday != friday )
& ( tuesday != saturday )
& ( tuesday != sunday )
& ( wednesday != thursday )
& ( wednesday != friday )
& ( wednesday != saturday )
& ( wednesday != sunday )
& ( thursday != friday )
& ( thursday != saturday )
& ( thursday != sunday )
& ( friday != saturday )
& ( friday != sunday )
& ( saturday != sunday ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniquenames) ).
thf(84,plain,
( ( monday != tuesday )
& ( monday != wednesday )
& ( monday != thursday )
& ( monday != friday )
& ( monday != saturday )
& ( monday != sunday )
& ( tuesday != wednesday )
& ( tuesday != thursday )
& ( tuesday != friday )
& ( tuesday != saturday )
& ( tuesday != sunday )
& ( wednesday != thursday )
& ( wednesday != friday )
& ( wednesday != saturday )
& ( wednesday != sunday )
& ( thursday != friday )
& ( thursday != saturday )
& ( thursday != sunday )
& ( friday != saturday )
& ( friday != sunday )
& ( saturday != sunday ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(6,axiom,
( ( consecutive @ saturday )
= sunday ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sunday_follows_saturday) ).
thf(33,plain,
( ( consecutive @ saturday )
= sunday ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(10,axiom,
! [A: $i] :
( ( day2 @ A )
<=> ( day3 @ ( consecutive @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',day3_follows_day2) ).
thf(41,plain,
! [A: $i] :
( ( ( day2 @ A )
=> ( day3 @ ( consecutive @ A ) ) )
& ( ( day3 @ ( consecutive @ A ) )
=> ( day2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( truthday @ A )
& ( truthday @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',truth_unique) ).
thf(66,plain,
! [A: $i,B: $i] :
( ( ( truthday @ A )
& ( truthday @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( day2 @ A )
& ( day2 @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',day2_unique) ).
thf(48,plain,
! [A: $i,B: $i] :
( ( ( day2 @ A )
& ( day2 @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(19,axiom,
( ( consecutive @ tuesday )
= wednesday ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wednesday_follows_tuesday) ).
thf(72,plain,
( ( consecutive @ tuesday )
= wednesday ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( day1 @ A )
& ( day1 @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',day1_unique) ).
thf(26,plain,
! [A: $i,B: $i] :
( ( ( day1 @ A )
& ( day1 @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( ( day3 @ A )
& ( day3 @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',day3_unique) ).
thf(58,plain,
! [A: $i,B: $i] :
( ( ( day3 @ A )
& ( day3 @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(13,axiom,
! [A: $i] :
( ( day1 @ A )
<=> ( day2 @ ( consecutive @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',day2_follows_day1) ).
thf(51,plain,
! [A: $i] :
( ( ( day1 @ A )
=> ( day2 @ ( consecutive @ A ) ) )
& ( ( day2 @ ( consecutive @ A ) )
=> ( day1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(8,axiom,
? [A: $i] : ( day3 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',day3_once) ).
thf(37,plain,
? [A: $i] : ( day3 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,conjecture,
truthday @ tuesday,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tuesday_leo_tells_truths) ).
thf(2,negated_conjecture,
~ ( truthday @ tuesday ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(25,plain,
~ ( truthday @ tuesday ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
( ( consecutive @ thursday )
= friday ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',friday_follows_thursday) ).
thf(46,plain,
( ( consecutive @ thursday )
= friday ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4,axiom,
( ( consecutive @ sunday )
= monday ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monday_follows_sunday) ).
thf(29,plain,
( ( consecutive @ sunday )
= monday ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,axiom,
! [A: $i] :
( ( day2 @ A )
=> ( ( truthday @ A )
<=> ( ( day2 @ thursday )
| ( day2 @ saturday )
| ( day2 @ sunday ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',statement2) ).
thf(61,plain,
! [A: $i] :
( ( day2 @ A )
=> ( ( ( truthday @ A )
=> ( ( day2 @ thursday )
| ( day2 @ saturday )
| ( day2 @ sunday ) ) )
& ( ( ( day2 @ thursday )
| ( day2 @ saturday )
| ( day2 @ sunday ) )
=> ( truthday @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(20,axiom,
( ( consecutive @ monday )
= tuesday ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tuesday_follows_monday) ).
thf(74,plain,
( ( consecutive @ monday )
= tuesday ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(21,axiom,
! [A: $i] :
( ( day3 @ A )
=> ( ( truthday @ A )
<=> ( ~ ( truthday @ wednesday )
& ~ ( truthday @ friday ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',statement3) ).
thf(76,plain,
! [A: $i] :
( ( day3 @ A )
=> ( ( ( truthday @ A )
=> ( ~ ( truthday @ wednesday )
& ~ ( truthday @ friday ) ) )
& ( ( ~ ( truthday @ wednesday )
& ~ ( truthday @ friday ) )
=> ( truthday @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(9,axiom,
( ( consecutive @ wednesday )
= thursday ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thursday_follows_wednesday) ).
thf(39,plain,
( ( consecutive @ wednesday )
= thursday ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(22,axiom,
! [A: $i] :
( ( day1 @ A )
=> ( ( truthday @ A )
<=> ( ~ ( truthday @ monday )
& ~ ( truthday @ tuesday ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',statement1) ).
thf(80,plain,
! [A: $i] :
( ( day1 @ A )
=> ( ( ( truthday @ A )
=> ( ~ ( truthday @ monday )
& ~ ( truthday @ tuesday ) ) )
& ( ( ~ ( truthday @ monday )
& ~ ( truthday @ tuesday ) )
=> ( truthday @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(7,axiom,
( ( consecutive @ friday )
= saturday ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',saturday_follows_friday) ).
thf(35,plain,
( ( consecutive @ friday )
= saturday ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(24,axiom,
? [A: $i] : ( truthday @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',truth_once) ).
thf(127,plain,
? [A: $i] : ( truthday @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(5,axiom,
? [A: $i] : ( day1 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',day1_once) ).
thf(31,plain,
? [A: $i] : ( day1 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(129,plain,
$false,
inference(cvc4,[status(thm)],[69,56,84,33,41,66,48,72,26,58,51,37,25,46,29,61,74,76,39,80,35,127,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : PUZ078+1 : TPTP v8.1.2. Released v3.5.0.
% 0.15/0.15 % Command : run_Leo-III %s %d
% 0.15/0.34 % Computer : n018.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Thu May 18 20:03:44 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.93/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/0.95 % [INFO] Parsing done (120ms).
% 1.23/0.96 % [INFO] Running in sequential loop mode.
% 1.68/1.15 % [INFO] eprover registered as external prover.
% 1.68/1.15 % [INFO] cvc4 registered as external prover.
% 1.68/1.15 % [INFO] Scanning for conjecture ...
% 1.76/1.20 % [INFO] Found a conjecture and 22 axioms. Running axiom selection ...
% 1.94/1.24 % [INFO] Axiom selection finished. Selected 22 axioms (removed 0 axioms).
% 2.00/1.28 % [INFO] Problem is first-order (TPTP FOF).
% 2.00/1.28 % [INFO] Type checking passed.
% 2.00/1.28 % [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 ...
% 2.50/1.47 % [INFO] [Domain constraints] Detected constraint on $i
% 2.50/1.47 % [INFO] [Domain constraints] dom($i) ⊆ {sunday,tuesday,wednesday,monday,friday,thursday,saturday}
% 3.22/1.74 % External prover 'cvc4' found a proof!
% 3.22/1.74 % [INFO] Killing All external provers ...
% 3.22/1.74 % Time passed: 1229ms (effective reasoning time: 776ms)
% 3.22/1.74 % 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)>
% 3.22/1.74 % Axioms used in derivation (22): truth_unique, statement1, thursday_follows_wednesday, wednesday_follows_tuesday, tuesday_follows_monday, day3_once, day1_unique, monday_follows_sunday, statement3, day2_unique, day3_follows_day2, friday_follows_thursday, day3_unique, truth_once, day2_once, sunday_follows_saturday, days_of_week, day1_once, statement2, saturday_follows_friday, day2_follows_day1, uniquenames
% 3.22/1.74 % No. of inferences in proof: 48
% 3.22/1.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1229 ms resp. 776 ms w/o parsing
% 3.59/1.78 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.59/1.78 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------