%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PUZ005-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 08:22:43 AM UTC 2026
% Result : Unsatisfiable 0.14s 5.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 23
% Syntax : Number of formulae : 93 ( 17 unt; 0 def)
% Number of atoms : 216 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 226 ( 103 ~; 123 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 61 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(monday_not_friday,axiom,
! [VAR_0] :
( ~ friday(VAR_0)
| ~ monday(VAR_0) ),
file('theBenchmark.p',monday_not_friday) ).
cnf(c_5,plain,
( ~ friday(A)
| ~ monday(A) ),
inference(clausify,[status(thm)],[monday_not_friday]) ).
fof(monday_not_saturday,axiom,
! [VAR_0] :
( ~ saturday(VAR_0)
| ~ monday(VAR_0) ),
file('theBenchmark.p',monday_not_saturday) ).
cnf(c_6,plain,
( ~ saturday(A)
| ~ monday(A) ),
inference(clausify,[status(thm)],[monday_not_saturday]) ).
fof(monday_not_sunday,axiom,
! [VAR_0] :
( ~ sunday(VAR_0)
| ~ monday(VAR_0) ),
file('theBenchmark.p',monday_not_sunday) ).
cnf(c_7,plain,
( ~ sunday(A)
| ~ monday(A) ),
inference(clausify,[status(thm)],[monday_not_sunday]) ).
fof(monday_yesterday,axiom,
! [VAR_0] :
( tuesday(VAR_0)
| ~ monday(yesterday(VAR_0)) ),
file('theBenchmark.p',monday_yesterday) ).
cnf(c_8,plain,
( tuesday(A)
| ~ monday(yesterday(A)) ),
inference(clausify,[status(thm)],[monday_yesterday]) ).
fof(yesterday_monday,axiom,
! [VAR_0] :
( ~ tuesday(VAR_0)
| monday(yesterday(VAR_0)) ),
file('theBenchmark.p',yesterday_monday) ).
cnf(c_10,plain,
( ~ tuesday(A)
| monday(yesterday(A)) ),
inference(clausify,[status(thm)],[yesterday_monday]) ).
fof(lions_lying_days,axiom,
! [VAR_0] :
( wednesday(VAR_0)
| tuesday(VAR_0)
| monday(VAR_0)
| ~ member(VAR_0,lying_days(lion)) ),
file('theBenchmark.p',lions_lying_days) ).
cnf(c_12,plain,
( wednesday(A)
| tuesday(A)
| monday(A)
| ~ member(A,lying_days(lion)) ),
inference(clausify,[status(thm)],[lions_lying_days]) ).
fof(lion_lies_on_monday,axiom,
! [VAR_0] :
( member(VAR_0,lying_days(lion))
| ~ monday(VAR_0) ),
file('theBenchmark.p',lion_lies_on_monday) ).
cnf(c_13,plain,
( member(A,lying_days(lion))
| ~ monday(A) ),
inference(clausify,[status(thm)],[lion_lies_on_monday]) ).
cnf(c_17,plain,
( tuesday(A)
| wednesday(yesterday(A))
| tuesday(yesterday(A))
| ~ member(yesterday(A),lying_days(lion)) ),
inference(resolve,[status(thm)],[c_12,c_8]) ).
cnf(c_18,plain,
( ~ sunday(A)
| wednesday(A)
| tuesday(A)
| ~ member(A,lying_days(lion)) ),
inference(resolve,[status(thm)],[c_12,c_7]) ).
cnf(c_19,plain,
( ~ saturday(A)
| wednesday(A)
| tuesday(A)
| ~ member(A,lying_days(lion)) ),
inference(resolve,[status(thm)],[c_12,c_6]) ).
cnf(c_20,plain,
( ~ friday(A)
| wednesday(A)
| tuesday(A)
| ~ member(A,lying_days(lion)) ),
inference(resolve,[status(thm)],[c_12,c_5]) ).
fof(lion_lies_on_wednesday,axiom,
! [VAR_0] :
( member(VAR_0,lying_days(lion))
| ~ wednesday(VAR_0) ),
file('theBenchmark.p',lion_lies_on_wednesday) ).
cnf(c_25,plain,
( member(A,lying_days(lion))
| ~ wednesday(A) ),
inference(clausify,[status(thm)],[lion_lies_on_wednesday]) ).
fof(wednesday_yesterday,axiom,
! [VAR_0] :
( thursday(VAR_0)
| ~ wednesday(yesterday(VAR_0)) ),
file('theBenchmark.p',wednesday_yesterday) ).
cnf(c_28,plain,
( thursday(A)
| ~ wednesday(yesterday(A)) ),
inference(clausify,[status(thm)],[wednesday_yesterday]) ).
fof(tuesday_yesterday,axiom,
! [VAR_0] :
( wednesday(VAR_0)
| ~ tuesday(yesterday(VAR_0)) ),
file('theBenchmark.p',tuesday_yesterday) ).
cnf(c_29,plain,
( wednesday(A)
| ~ tuesday(yesterday(A)) ),
inference(clausify,[status(thm)],[tuesday_yesterday]) ).
fof(wednesday_not_sunday,axiom,
! [VAR_0] :
( ~ sunday(VAR_0)
| ~ wednesday(VAR_0) ),
file('theBenchmark.p',wednesday_not_sunday) ).
cnf(c_30,plain,
( ~ sunday(A)
| ~ wednesday(A) ),
inference(clausify,[status(thm)],[wednesday_not_sunday]) ).
fof(wednesday_not_saturday,axiom,
! [VAR_0] :
( ~ saturday(VAR_0)
| ~ wednesday(VAR_0) ),
file('theBenchmark.p',wednesday_not_saturday) ).
cnf(c_31,plain,
( ~ saturday(A)
| ~ wednesday(A) ),
inference(clausify,[status(thm)],[wednesday_not_saturday]) ).
fof(wednesday_not_friday,axiom,
! [VAR_0] :
( ~ friday(VAR_0)
| ~ wednesday(VAR_0) ),
file('theBenchmark.p',wednesday_not_friday) ).
cnf(c_32,plain,
( ~ friday(A)
| ~ wednesday(A) ),
inference(clausify,[status(thm)],[wednesday_not_friday]) ).
fof(admissions1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_2,lying_days(VAR_1))
| ~ admits(VAR_1,VAR_0,VAR_2)
| member(VAR_0,lying_days(VAR_1)) ),
file('theBenchmark.p',admissions1) ).
cnf(c_36,plain,
( member(C,lying_days(B))
| ~ admits(B,A,C)
| member(A,lying_days(B)) ),
inference(clausify,[status(thm)],[admissions1]) ).
fof(admissions3,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ member(VAR_2,lying_days(VAR_1))
| ~ admits(VAR_1,VAR_0,VAR_2)
| ~ member(VAR_0,lying_days(VAR_1)) ),
file('theBenchmark.p',admissions3) ).
cnf(c_37,plain,
( ~ member(C,lying_days(B))
| ~ admits(B,A,C)
| ~ member(A,lying_days(B)) ),
inference(clausify,[status(thm)],[admissions3]) ).
fof(admissions5,axiom,
admits(lion,today,yesterday(today)),
file('theBenchmark.p',admissions5) ).
cnf(c_39,plain,
admits(lion,today,yesterday(today)),
inference(clausify,[status(thm)],[admissions5]) ).
fof(admissions6,axiom,
admits(unicorn,today,yesterday(today)),
file('theBenchmark.p',admissions6) ).
cnf(c_40,plain,
admits(unicorn,today,yesterday(today)),
inference(clausify,[status(thm)],[admissions6]) ).
cnf(c_41,plain,
( member(yesterday(today),lying_days(unicorn))
| member(today,lying_days(unicorn)) ),
inference(resolve,[status(thm)],[c_40,c_36]) ).
cnf(c_42,plain,
( ~ member(yesterday(today),lying_days(unicorn))
| ~ member(today,lying_days(unicorn)) ),
inference(resolve,[status(thm)],[c_40,c_37]) ).
cnf(c_43,plain,
( member(yesterday(today),lying_days(lion))
| member(today,lying_days(lion)) ),
inference(resolve,[status(thm)],[c_39,c_36]) ).
cnf(c_44,plain,
( ~ member(yesterday(today),lying_days(lion))
| ~ member(today,lying_days(lion)) ),
inference(resolve,[status(thm)],[c_39,c_37]) ).
cnf(c_46,plain,
( ~ tuesday(A)
| member(yesterday(A),lying_days(lion)) ),
inference(resolve,[status(thm)],[c_13,c_10]) ).
fof(prove_today_is_thursday,axiom,
~ thursday(today),
file('theBenchmark.p',prove_today_is_thursday) ).
cnf(c_58,plain,
~ thursday(today),
inference(clausify,[status(thm)],[prove_today_is_thursday]) ).
fof(lion_lies_on_tuesday,axiom,
! [VAR_0] :
( member(VAR_0,lying_days(lion))
| ~ tuesday(VAR_0) ),
file('theBenchmark.p',lion_lies_on_tuesday) ).
cnf(c_62,plain,
( member(A,lying_days(lion))
| ~ tuesday(A) ),
inference(clausify,[status(thm)],[lion_lies_on_tuesday]) ).
fof(unicorns_lying_days,axiom,
! [VAR_0] :
( saturday(VAR_0)
| friday(VAR_0)
| thursday(VAR_0)
| ~ member(VAR_0,lying_days(unicorn)) ),
file('theBenchmark.p',unicorns_lying_days) ).
cnf(c_63,plain,
( saturday(A)
| friday(A)
| thursday(A)
| ~ member(A,lying_days(unicorn)) ),
inference(clausify,[status(thm)],[unicorns_lying_days]) ).
fof(saturday_yesterday,axiom,
! [VAR_0] :
( sunday(VAR_0)
| ~ saturday(yesterday(VAR_0)) ),
file('theBenchmark.p',saturday_yesterday) ).
cnf(c_67,plain,
( sunday(A)
| ~ saturday(yesterday(A)) ),
inference(clausify,[status(thm)],[saturday_yesterday]) ).
fof(friday_yesterday,axiom,
! [VAR_0] :
( saturday(VAR_0)
| ~ friday(yesterday(VAR_0)) ),
file('theBenchmark.p',friday_yesterday) ).
cnf(c_68,plain,
( saturday(A)
| ~ friday(yesterday(A)) ),
inference(clausify,[status(thm)],[friday_yesterday]) ).
fof(thursday_yesterday,axiom,
! [VAR_0] :
( friday(VAR_0)
| ~ thursday(yesterday(VAR_0)) ),
file('theBenchmark.p',thursday_yesterday) ).
cnf(c_69,plain,
( friday(A)
| ~ thursday(yesterday(A)) ),
inference(clausify,[status(thm)],[thursday_yesterday]) ).
cnf(c_98,plain,
( tuesday(A)
| tuesday(yesterday(A))
| ~ member(yesterday(A),lying_days(lion))
| thursday(A) ),
inference(resolve,[status(thm)],[c_28,c_17]) ).
cnf(c_104,plain,
( member(A,lying_days(lion))
| ~ tuesday(yesterday(A)) ),
inference(resolve,[status(thm)],[c_29,c_25]) ).
cnf(c_109,plain,
( ~ sunday(A)
| tuesday(A)
| ~ member(A,lying_days(lion))
| ~ sunday(A) ),
inference(resolve,[status(thm)],[c_30,c_18]) ).
cnf(c_110,plain,
( tuesday(A)
| ~ member(A,lying_days(lion))
| ~ sunday(A) ),
inference(copy,[status(thm)],[c_109]) ).
cnf(c_115,plain,
( ~ saturday(A)
| tuesday(A)
| ~ member(A,lying_days(lion))
| ~ saturday(A) ),
inference(resolve,[status(thm)],[c_31,c_19]) ).
cnf(c_116,plain,
( tuesday(A)
| ~ member(A,lying_days(lion))
| ~ saturday(A) ),
inference(copy,[status(thm)],[c_115]) ).
cnf(c_121,plain,
( ~ friday(A)
| tuesday(A)
| ~ member(A,lying_days(lion))
| ~ friday(A) ),
inference(resolve,[status(thm)],[c_32,c_20]) ).
cnf(c_122,plain,
( tuesday(A)
| ~ member(A,lying_days(lion))
| ~ friday(A) ),
inference(copy,[status(thm)],[c_121]) ).
cnf(c_129,plain,
( member(today,lying_days(unicorn))
| saturday(yesterday(today))
| friday(yesterday(today))
| thursday(yesterday(today)) ),
inference(resolve,[status(thm)],[c_63,c_41]) ).
cnf(c_416,plain,
( member(yesterday(today),lying_days(unicorn))
| saturday(today)
| friday(today)
| thursday(today) ),
inference(resolve,[status(thm)],[c_63,c_41]) ).
cnf(c_130,plain,
( member(yesterday(today),lying_days(unicorn))
| saturday(today)
| friday(today) ),
inference(resolve,[status(thm)],[c_58,c_416]) ).
cnf(c_417,plain,
( member(today,lying_days(lion))
| tuesday(today)
| tuesday(yesterday(today))
| thursday(today) ),
inference(resolve,[status(thm)],[c_98,c_43]) ).
cnf(c_226,plain,
( member(today,lying_days(lion))
| tuesday(today)
| tuesday(yesterday(today)) ),
inference(resolve,[status(thm)],[c_58,c_417]) ).
cnf(c_253,plain,
( friday(today)
| member(today,lying_days(unicorn))
| saturday(yesterday(today))
| friday(yesterday(today)) ),
inference(resolve,[status(thm)],[c_129,c_69]) ).
cnf(c_279,plain,
( ~ member(today,lying_days(unicorn))
| saturday(today)
| friday(today) ),
inference(resolve,[status(thm)],[c_130,c_42]) ).
cnf(c_418,plain,
( member(today,lying_days(lion))
| member(today,lying_days(lion))
| tuesday(today) ),
inference(resolve,[status(thm)],[c_226,c_104]) ).
cnf(c_302,plain,
( member(today,lying_days(lion))
| tuesday(today) ),
inference(copy,[status(thm)],[c_418]) ).
cnf(c_419,plain,
( member(today,lying_days(lion))
| member(today,lying_days(lion)) ),
inference(resolve,[status(thm)],[c_302,c_62]) ).
cnf(c_308,plain,
member(today,lying_days(lion)),
inference(copy,[status(thm)],[c_419]) ).
cnf(c_420,plain,
( tuesday(today)
| ~ friday(today)
| tuesday(today) ),
inference(resolve,[status(thm)],[c_302,c_122]) ).
cnf(c_309,plain,
( ~ friday(today)
| tuesday(today) ),
inference(copy,[status(thm)],[c_420]) ).
cnf(c_421,plain,
( tuesday(today)
| ~ saturday(today)
| tuesday(today) ),
inference(resolve,[status(thm)],[c_302,c_116]) ).
cnf(c_310,plain,
( ~ saturday(today)
| tuesday(today) ),
inference(copy,[status(thm)],[c_421]) ).
cnf(c_422,plain,
( tuesday(today)
| ~ sunday(today)
| tuesday(today) ),
inference(resolve,[status(thm)],[c_302,c_110]) ).
cnf(c_311,plain,
( ~ sunday(today)
| tuesday(today) ),
inference(copy,[status(thm)],[c_422]) ).
cnf(c_313,plain,
~ member(yesterday(today),lying_days(lion)),
inference(resolve,[status(thm)],[c_308,c_44]) ).
cnf(c_392,plain,
~ tuesday(today),
inference(resolve,[status(thm)],[c_46,c_313]) ).
cnf(c_400,plain,
~ sunday(today),
inference(resolve,[status(thm)],[c_392,c_311]) ).
cnf(c_401,plain,
~ saturday(today),
inference(resolve,[status(thm)],[c_392,c_310]) ).
cnf(c_402,plain,
~ friday(today),
inference(resolve,[status(thm)],[c_392,c_309]) ).
cnf(c_423,plain,
( ~ member(today,lying_days(unicorn))
| saturday(today) ),
inference(resolve,[status(thm)],[c_402,c_279]) ).
cnf(c_407,plain,
~ member(today,lying_days(unicorn)),
inference(resolve,[status(thm)],[c_401,c_423]) ).
cnf(c_424,plain,
( friday(today)
| saturday(yesterday(today))
| friday(yesterday(today)) ),
inference(resolve,[status(thm)],[c_407,c_253]) ).
cnf(c_410,plain,
( saturday(yesterday(today))
| friday(yesterday(today)) ),
inference(resolve,[status(thm)],[c_402,c_424]) ).
cnf(c_412,plain,
~ saturday(yesterday(today)),
inference(resolve,[status(thm)],[c_67,c_400]) ).
cnf(c_413,plain,
friday(yesterday(today)),
inference(resolve,[status(thm)],[c_412,c_410]) ).
cnf(c_425,plain,
~ friday(yesterday(today)),
inference(resolve,[status(thm)],[c_68,c_401]) ).
cnf(c_415,plain,
$false,
inference(resolve,[status(thm)],[c_413,c_425]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ005-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n014.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sat Sep 26 05:02:52 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.38 % Process 2197680 was started by sandbox on n014,
% 0.10/5.38 % Sat Sep 26 05:02:52 2026
% 0.10/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.38
% 0.10/5.38 % From the command line: assign(max_seconds, 300).
% 0.14/5.42
% 0.14/5.42 % SZS status Unsatisfiable for theBenchmark
% 0.14/5.42
% 0.14/5.42 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.14/5.42 % Length of proof is 60.
% 0.14/5.42 % Level of proof is 12.
% 0.14/5.42 % Maximum clause weight is 23.000.
% 0.14/5.42 % Given clauses 85.
% 0.14/5.42
% 0.14/5.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------