%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PUZ078+1 : TPTP v9.3.1. Released v3.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:21:18 AM UTC 2026
% Result : Theorem 4.83s 3.06s
% Output : Refutation 4.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 23
% Syntax : Number of formulae : 48 ( 26 unt; 0 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 : 0 ( 0 >; 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_decl,type,
truthday: $i > $o ).
thf(tuesday_decl,type,
tuesday: $i ).
thf(day1_decl,type,
day1: $i > $o ).
thf(consecutive_decl,type,
consecutive: $i > $i ).
thf(sunday_decl,type,
sunday: $i ).
thf(monday_decl,type,
monday: $i ).
thf(saturday_decl,type,
saturday: $i ).
thf(friday_decl,type,
friday: $i ).
thf(day3_decl,type,
day3: $i > $o ).
thf(wednesday_decl,type,
wednesday: $i ).
thf(thursday_decl,type,
thursday: $i ).
thf(day2_decl,type,
day2: $i > $o ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( B @ truthday )
& ( A @ truthday ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',truth_unique) ).
thf(69,plain,
! [A: $i,B: $i] :
( ( ( B @ truthday )
& ( A @ truthday ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ day1 )
<=> ( A @ consecutive @ day2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',day2_follows_day1) ).
thf(52,plain,
! [A: $i] :
( ( ( A @ consecutive @ day2 )
=> ( A @ day1 ) )
& ( ( A @ day1 )
=> ( A @ consecutive @ day2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(4,axiom,
( ( sunday @ consecutive )
= monday ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monday_follows_sunday) ).
thf(29,plain,
( ( sunday @ consecutive )
= monday ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ day1 )
=> ( ( A @ truthday )
<=> ( ~ ( tuesday @ truthday )
& ~ ( monday @ truthday ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',statement1) ).
thf(84,plain,
! [A: $i] :
( ( A @ day1 )
=> ( ( ( ~ ( tuesday @ truthday )
& ~ ( monday @ truthday ) )
=> ( A @ truthday ) )
& ( ( A @ truthday )
=> ( ~ ( tuesday @ truthday )
& ~ ( monday @ truthday ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( ( B @ day3 )
& ( A @ day3 ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',day3_unique) ).
thf(60,plain,
! [A: $i,B: $i] :
( ( ( B @ day3 )
& ( A @ day3 ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(6,axiom,
( ( saturday @ consecutive )
= sunday ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sunday_follows_saturday) ).
thf(33,plain,
( ( saturday @ consecutive )
= sunday ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(20,axiom,
( ( monday @ consecutive )
= tuesday ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tuesday_follows_monday) ).
thf(77,plain,
( ( monday @ consecutive )
= tuesday ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ day2 )
<=> ( A @ consecutive @ day3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',day3_follows_day2) ).
thf(41,plain,
! [A: $i] :
( ( ( A @ consecutive @ day3 )
=> ( A @ day2 ) )
& ( ( A @ day2 )
=> ( A @ consecutive @ day3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( B @ day2 )
& ( A @ day2 ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',day2_unique) ).
thf(49,plain,
! [A: $i,B: $i] :
( ( ( B @ day2 )
& ( A @ day2 ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
( ( wednesday @ consecutive )
= thursday ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thursday_follows_wednesday) ).
thf(39,plain,
( ( wednesday @ consecutive )
= thursday ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
( ( friday @ consecutive )
= saturday ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',saturday_follows_friday) ).
thf(35,plain,
( ( friday @ consecutive )
= saturday ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ day2 )
=> ( ( A @ truthday )
<=> ( ( sunday @ day2 )
| ( saturday @ day2 )
| ( thursday @ day2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',statement2) ).
thf(63,plain,
! [A: $i] :
( ( A @ day2 )
=> ( ( ( ( sunday @ day2 )
| ( saturday @ day2 )
| ( thursday @ day2 ) )
=> ( A @ truthday ) )
& ( ( A @ truthday )
=> ( ( sunday @ day2 )
| ( saturday @ day2 )
| ( thursday @ day2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(5,axiom,
? [A: $i] : ( A @ day1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',day1_once) ).
thf(31,plain,
? [A: $i] : ( A @ day1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(18,axiom,
! [A: $i] :
( ( A = sunday )
| ( A = saturday )
| ( A = friday )
| ( A = thursday )
| ( A = wednesday )
| ( A = tuesday )
| ( A = monday ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',days_of_week) ).
thf(72,plain,
! [A: $i] :
( ( A = sunday )
| ( A = saturday )
| ( A = friday )
| ( A = thursday )
| ( A = wednesday )
| ( A = tuesday )
| ( A = monday ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( B @ day1 )
& ( A @ day1 ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',day1_unique) ).
thf(26,plain,
! [A: $i,B: $i] :
( ( ( B @ day1 )
& ( A @ day1 ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ day3 )
=> ( ( A @ truthday )
<=> ( ~ ( friday @ truthday )
& ~ ( wednesday @ truthday ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',statement3) ).
thf(79,plain,
! [A: $i] :
( ( A @ day3 )
=> ( ( ( ~ ( friday @ truthday )
& ~ ( wednesday @ truthday ) )
=> ( A @ truthday ) )
& ( ( A @ truthday )
=> ( ~ ( friday @ truthday )
& ~ ( wednesday @ truthday ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(11,axiom,
( ( thursday @ consecutive )
= friday ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',friday_follows_thursday) ).
thf(47,plain,
( ( thursday @ consecutive )
= friday ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(8,axiom,
? [A: $i] : ( A @ day3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',day3_once) ).
thf(37,plain,
? [A: $i] : ( A @ day3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,conjecture,
tuesday @ truthday,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tuesday_leo_tells_truths) ).
thf(2,negated_conjecture,
~ ( tuesday @ truthday ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(25,plain,
~ ( tuesday @ truthday ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(23,axiom,
( ( saturday != sunday )
& ( friday != sunday )
& ( friday != saturday )
& ( thursday != sunday )
& ( thursday != saturday )
& ( thursday != friday )
& ( wednesday != sunday )
& ( wednesday != saturday )
& ( wednesday != friday )
& ( wednesday != thursday )
& ( tuesday != sunday )
& ( tuesday != saturday )
& ( tuesday != friday )
& ( tuesday != thursday )
& ( tuesday != wednesday )
& ( monday != sunday )
& ( monday != saturday )
& ( monday != friday )
& ( monday != thursday )
& ( monday != wednesday )
& ( monday != tuesday ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniquenames) ).
thf(89,plain,
( ( saturday != sunday )
& ( friday != sunday )
& ( friday != saturday )
& ( thursday != sunday )
& ( thursday != saturday )
& ( thursday != friday )
& ( wednesday != sunday )
& ( wednesday != saturday )
& ( wednesday != friday )
& ( wednesday != thursday )
& ( tuesday != sunday )
& ( tuesday != saturday )
& ( tuesday != friday )
& ( tuesday != thursday )
& ( tuesday != wednesday )
& ( monday != sunday )
& ( monday != saturday )
& ( monday != friday )
& ( monday != thursday )
& ( monday != wednesday )
& ( monday != tuesday ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(24,axiom,
? [A: $i] : ( A @ truthday ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',truth_once) ).
thf(133,plain,
? [A: $i] : ( A @ truthday ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(19,axiom,
( ( tuesday @ consecutive )
= wednesday ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wednesday_follows_tuesday) ).
thf(75,plain,
( ( tuesday @ consecutive )
= wednesday ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(14,axiom,
? [A: $i] : ( A @ day2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',day2_once) ).
thf(58,plain,
? [A: $i] : ( A @ day2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(214,plain,
$false,
inference(e,[status(thm)],[69,52,29,84,60,33,77,41,49,39,35,63,31,72,26,79,47,37,25,89,133,75,58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ078+1 : TPTP v9.3.1. Released v3.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.15/0.62 % Computer : n009.cluster.edu
% 0.15/0.62 % Model : x86_64 x86_64
% 0.15/0.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.62 % Memory : 8046.5625MB
% 0.15/0.62 % OS : Linux 6.8.0-71-generic
% 0.15/0.62 % CPULimit : 300
% 0.15/0.62 % WCLimit : 300
% 0.15/0.62 % DateTime : Sat Sep 26 05:14:00 UTC 2026
% 0.15/0.62 % CPUTime :
% 0.15/0.62 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.97/1.21 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.31/1.43 % [INFO] Parsing done (213ms).
% 1.31/1.44 % [INFO] Running in sequential loop mode.
% 1.98/1.83 % [INFO] eprover registered as external prover.
% 1.98/1.84 % [INFO] Scanning for conjecture ...
% 2.17/1.93 % [INFO] Found a conjecture (or negated_conjecture) and 22 axioms. Running axiom selection ...
% 2.17/1.99 % [INFO] Axiom selection finished. Selected 22 axioms (removed 0 axioms).
% 2.41/2.05 % [INFO] Problem is first-order (TPTP FOF).
% 2.41/2.05 % [INFO] Type checking passed.
% 2.41/2.06 % [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 ...
% 3.09/2.40 % [INFO] [Domain constraints] Detected constraint on $i
% 3.09/2.40 % [INFO] [Domain constraints] dom($i) ⊆ {sunday,tuesday,wednesday,monday,friday,thursday,saturday}
% 4.83/3.05 % External prover 'e' found a proof!
% 4.83/3.06 % [INFO] Killing All external provers ...
% 4.83/3.06 % Time passed: 2291ms (effective reasoning time: 1605ms)
% 4.83/3.06 % 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)>
% 4.83/3.06 % 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
% 4.83/3.06 % No. of inferences in proof: 48
% 4.83/3.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2291 ms resp. 1605 ms w/o parsing
% 4.83/3.09 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.83/3.09 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------