%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PUZ005+1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 : Theorem 0.11s 0.48s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 43 ( 12 unt; 0 def)
% Number of atoms : 95 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 94 ( 42 ~; 33 |; 6 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 32 ( 0 sgn 11 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(wednesday_is_a_day,axiom,
! [X] :
( wednesday(X)
=> day(X) ),
file('theBenchmark.p',wednesday_is_a_day) ).
fof(thursday_is_a_day,axiom,
! [X] :
( thursday(X)
=> day(X) ),
file('theBenchmark.p',thursday_is_a_day) ).
fof(thursday_follows_wednesday,axiom,
! [X] :
( thursday(X)
=> wednesday(yesterday(X)) ),
file('theBenchmark.p',thursday_follows_wednesday) ).
fof(lion_lies_wednesday,axiom,
! [X] :
( wednesday(X)
=> lion_lies(X) ),
file('theBenchmark.p',lion_lies_wednesday) ).
fof(lion_does_not_lie_thursday,axiom,
! [X] :
( thursday(X)
=> ~ lion_lies(X) ),
file('theBenchmark.p',lion_does_not_lie_thursday) ).
fof(unicorn_does_not_lie_wednesday,axiom,
! [X] :
( wednesday(X)
=> ~ unicorn_lies(X) ),
file('theBenchmark.p',unicorn_does_not_lie_wednesday) ).
fof(unicorn_lies_thursday,axiom,
! [X] :
( thursday(X)
=> unicorn_lies(X) ),
file('theBenchmark.p',unicorn_lies_thursday) ).
fof(lion_lies_on_neither,axiom,
! [X] :
( day(X)
=> ! [Y] :
( day(Y)
=> ( ( ~ lies_on_one_of(a_lion,X,Y)
& ~ lion_lies(X) )
=> ~ lion_lies(Y) ) ) ),
file('theBenchmark.p',lion_lies_on_neither) ).
fof(unicorn_lies_on_both,axiom,
! [X] :
( day(X)
=> ! [Y] :
( day(Y)
=> ( ( ~ lies_on_one_of(a_unicorn,X,Y)
& unicorn_lies(X) )
=> unicorn_lies(Y) ) ) ),
file('theBenchmark.p',unicorn_lies_on_both) ).
fof(prove_there_are_close_lying_days,conjecture,
? [X] :
( lies_on_one_of(a_unicorn,X,yesterday(X))
& lies_on_one_of(a_lion,X,yesterday(X))
& day(X) ),
file('theBenchmark.p',prove_there_are_close_lying_days) ).
fof(prove_there_are_close_lying_days_neg,negated_conjecture,
~ ? [X] :
( lies_on_one_of(a_unicorn,X,yesterday(X))
& lies_on_one_of(a_lion,X,yesterday(X))
& day(X) ),
inference(assume_negation,[status(cth)],[prove_there_are_close_lying_days]) ).
cnf(c_63,plain,
( day(A)
| ~ wednesday(A) ),
inference(clausify,[status(thm)],[wednesday_is_a_day]) ).
cnf(c_64,plain,
( wednesday(yesterday(A))
| ~ thursday(A) ),
inference(clausify,[status(thm)],[thursday_follows_wednesday]) ).
cnf(c_65,plain,
( lion_lies(A)
| ~ wednesday(A) ),
inference(clausify,[status(thm)],[lion_lies_wednesday]) ).
cnf(c_66,plain,
( ~ unicorn_lies(A)
| ~ wednesday(A) ),
inference(clausify,[status(thm)],[unicorn_does_not_lie_wednesday]) ).
cnf(c_68,plain,
( ~ lion_lies(A)
| ~ thursday(A) ),
inference(clausify,[status(thm)],[lion_does_not_lie_thursday]) ).
cnf(c_69,plain,
( unicorn_lies(A)
| ~ thursday(A) ),
inference(clausify,[status(thm)],[unicorn_lies_thursday]) ).
cnf(c_70,plain,
( day(yesterday(A))
| ~ thursday(A) ),
inference(resolve,[status(thm)],[c_64,c_63]) ).
cnf(c_78,plain,
( ~ thursday(A)
| lion_lies(yesterday(A)) ),
inference(resolve,[status(thm)],[c_65,c_64]) ).
cnf(c_79,plain,
( ~ thursday(A)
| ~ unicorn_lies(yesterday(A)) ),
inference(resolve,[status(thm)],[c_66,c_64]) ).
cnf(c_80,plain,
( day(A)
| ~ thursday(A) ),
inference(clausify,[status(thm)],[thursday_is_a_day]) ).
fof(thursday,axiom,
thursday(a_thursday),
file('theBenchmark.p',thursday) ).
cnf(c_81,plain,
thursday(a_thursday),
inference(clausify,[status(thm)],[thursday]) ).
cnf(c_159,plain,
~ unicorn_lies(yesterday(a_thursday)),
inference(resolve,[status(thm)],[c_81,c_79]) ).
cnf(c_160,plain,
lion_lies(yesterday(a_thursday)),
inference(resolve,[status(thm)],[c_81,c_78]) ).
cnf(c_168,plain,
day(yesterday(a_thursday)),
inference(resolve,[status(thm)],[c_81,c_70]) ).
cnf(c_169,plain,
unicorn_lies(a_thursday),
inference(resolve,[status(thm)],[c_81,c_69]) ).
cnf(c_170,plain,
~ lion_lies(a_thursday),
inference(resolve,[status(thm)],[c_81,c_68]) ).
cnf(c_171,plain,
day(a_thursday),
inference(resolve,[status(thm)],[c_81,c_80]) ).
cnf(c_187,plain,
( ~ lion_lies(B)
| lies_on_one_of(a_lion,A,B)
| lion_lies(A)
| ~ day(B)
| ~ day(A) ),
inference(clausify,[status(thm)],[lion_lies_on_neither]) ).
cnf(c_192,plain,
( unicorn_lies(B)
| lies_on_one_of(a_unicorn,A,B)
| ~ unicorn_lies(A)
| ~ day(B)
| ~ day(A) ),
inference(clausify,[status(thm)],[unicorn_lies_on_both]) ).
cnf(c_193,negated_conjecture,
( ~ lies_on_one_of(a_unicorn,A,yesterday(A))
| ~ lies_on_one_of(a_lion,A,yesterday(A))
| ~ day(A) ),
inference(clausify,[status(thm)],[prove_there_are_close_lying_days_neg]) ).
cnf(c_991,plain,
( ~ lion_lies(A)
| lies_on_one_of(a_lion,a_thursday,A)
| lion_lies(a_thursday)
| ~ day(A) ),
inference(resolve,[status(thm)],[c_187,c_171]) ).
cnf(c_348,plain,
( ~ lion_lies(A)
| lies_on_one_of(a_lion,a_thursday,A)
| ~ day(A) ),
inference(resolve,[status(thm)],[c_170,c_991]) ).
cnf(c_992,plain,
( unicorn_lies(A)
| lies_on_one_of(a_unicorn,a_thursday,A)
| ~ unicorn_lies(a_thursday)
| ~ day(A) ),
inference(resolve,[status(thm)],[c_192,c_171]) ).
cnf(c_408,plain,
( unicorn_lies(A)
| lies_on_one_of(a_unicorn,a_thursday,A)
| ~ day(A) ),
inference(resolve,[status(thm)],[c_169,c_992]) ).
cnf(c_422,plain,
( ~ lies_on_one_of(a_unicorn,a_thursday,yesterday(a_thursday))
| ~ lies_on_one_of(a_lion,a_thursday,yesterday(a_thursday)) ),
inference(resolve,[status(thm)],[c_193,c_171]) ).
cnf(c_993,plain,
( ~ lion_lies(yesterday(a_thursday))
| lies_on_one_of(a_lion,a_thursday,yesterday(a_thursday)) ),
inference(resolve,[status(thm)],[c_348,c_168]) ).
cnf(c_706,plain,
lies_on_one_of(a_lion,a_thursday,yesterday(a_thursday)),
inference(resolve,[status(thm)],[c_160,c_993]) ).
cnf(c_712,plain,
~ lies_on_one_of(a_unicorn,a_thursday,yesterday(a_thursday)),
inference(resolve,[status(thm)],[c_706,c_422]) ).
cnf(c_994,plain,
( unicorn_lies(yesterday(a_thursday))
| lies_on_one_of(a_unicorn,a_thursday,yesterday(a_thursday)) ),
inference(resolve,[status(thm)],[c_408,c_168]) ).
cnf(c_995,plain,
unicorn_lies(yesterday(a_thursday)),
inference(resolve,[status(thm)],[c_712,c_994]) ).
cnf(c_990,plain,
$false,
inference(resolve,[status(thm)],[c_159,c_995]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ005+1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n026.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 05:05:40 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 128944 was started by sandbox2 on n026,
% 0.11/0.38 % Sat Sep 26 05:05:40 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.39
% 0.11/0.39 % From the command line: assign(max_seconds, 300).
% 0.11/0.48
% 0.11/0.48 % Assigning unary symbol yesterday kb_weight 0 and highest precedence (15).
% 0.11/0.48
% 0.11/0.48 % SZS status Theorem for theBenchmark
% 0.11/0.48
% 0.11/0.48 % Proof 1 at 0.05 (+ 0.03) seconds.
% 0.11/0.48 % Length of proof is 36.
% 0.11/0.48 % Level of proof is 6.
% 0.11/0.48 % Maximum clause weight is 22.000.
% 0.11/0.48 % Given clauses 223.
% 0.11/0.48
% 0.11/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------