%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PUZ018-1 : TPTP v9.3.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 08:23:06 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 23
% Syntax : Number of formulae : 88 ( 47 unt; 0 def)
% Number of atoms : 198 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 186 ( 76 ~; 110 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 10 con; 0-0 aty)
% Number of variables : 42 ( 5 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sunday_not_tuesday,axiom,
~ same_day(sunday,tuesday),
file('theBenchmark.p',sunday_not_tuesday) ).
cnf(c_4,plain,
~ same_day(sunday,tuesday),
inference(clausify,[status(thm)],[sunday_not_tuesday]) ).
fof(sunday_not_thursday,axiom,
~ same_day(sunday,thursday),
file('theBenchmark.p',sunday_not_thursday) ).
cnf(c_6,plain,
~ same_day(sunday,thursday),
inference(clausify,[status(thm)],[sunday_not_thursday]) ).
fof(tuesday_not_thursday,axiom,
~ same_day(tuesday,thursday),
file('theBenchmark.p',tuesday_not_thursday) ).
cnf(c_15,plain,
~ same_day(tuesday,thursday),
inference(clausify,[status(thm)],[tuesday_not_thursday]) ).
fof(no_two_off_twice_together,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( same_day(VAR_1,VAR_2)
| same_person(VAR_0,VAR_3)
| on(VAR_3,VAR_2)
| on(VAR_3,VAR_1)
| on(VAR_0,VAR_2)
| on(VAR_0,VAR_1) ),
file('theBenchmark.p',no_two_off_twice_together) ).
cnf(c_24,plain,
( same_day(B,C)
| same_person(A,D)
| on(D,C)
| on(D,B)
| on(A,C)
| on(A,B) ),
inference(clausify,[status(thm)],[no_two_off_twice_together]) ).
cnf(c_34,plain,
( same_person(A,B)
| on(B,thursday)
| on(B,tuesday)
| on(A,thursday)
| on(A,tuesday) ),
inference(resolve,[status(thm)],[c_24,c_15]) ).
cnf(c_43,plain,
( same_person(A,B)
| on(B,thursday)
| on(B,sunday)
| on(A,thursday)
| on(A,sunday) ),
inference(resolve,[status(thm)],[c_24,c_6]) ).
cnf(c_45,plain,
( same_person(A,B)
| on(B,tuesday)
| on(B,sunday)
| on(A,tuesday)
| on(A,sunday) ),
inference(resolve,[status(thm)],[c_24,c_4]) ).
fof(a_not_c,axiom,
~ same_person(a,c),
file('theBenchmark.p',a_not_c) ).
cnf(c_47,plain,
~ same_person(a,c),
inference(clausify,[status(thm)],[a_not_c]) ).
fof(a_not_b,axiom,
~ same_person(a,b),
file('theBenchmark.p',a_not_b) ).
cnf(c_48,plain,
~ same_person(a,b),
inference(clausify,[status(thm)],[a_not_b]) ).
cnf(c_53,plain,
( on(b,thursday)
| on(b,sunday)
| on(a,thursday)
| on(a,sunday) ),
inference(resolve,[status(thm)],[c_48,c_43]) ).
cnf(c_62,plain,
( on(b,thursday)
| on(b,tuesday)
| on(a,thursday)
| on(a,tuesday) ),
inference(resolve,[status(thm)],[c_48,c_34]) ).
cnf(c_72,plain,
( on(c,tuesday)
| on(c,sunday)
| on(a,tuesday)
| on(a,sunday) ),
inference(resolve,[status(thm)],[c_47,c_45]) ).
cnf(c_74,plain,
( on(c,thursday)
| on(c,sunday)
| on(a,thursday)
| on(a,sunday) ),
inference(resolve,[status(thm)],[c_47,c_43]) ).
fof(all_on_a_on,axiom,
! [VAR_0] :
( on(a,VAR_0)
| ~ all_on(VAR_0) ),
file('theBenchmark.p',all_on_a_on) ).
cnf(c_113,plain,
( on(a,A)
| ~ all_on(A) ),
inference(clausify,[status(thm)],[all_on_a_on]) ).
fof(all_on_b_on,axiom,
! [VAR_0] :
( on(b,VAR_0)
| ~ all_on(VAR_0) ),
file('theBenchmark.p',all_on_b_on) ).
cnf(c_114,plain,
( on(b,A)
| ~ all_on(A) ),
inference(clausify,[status(thm)],[all_on_b_on]) ).
fof(all_on_c_on,axiom,
! [VAR_0] :
( on(c,VAR_0)
| ~ all_on(VAR_0) ),
file('theBenchmark.p',all_on_c_on) ).
cnf(c_115,plain,
( on(c,A)
| ~ all_on(A) ),
inference(clausify,[status(thm)],[all_on_c_on]) ).
fof(monday_follows_sunday,axiom,
consecutive(sunday,monday),
file('theBenchmark.p',monday_follows_sunday) ).
cnf(c_117,plain,
consecutive(sunday,monday),
inference(clausify,[status(thm)],[monday_follows_sunday]) ).
fof(tuesday_follows_monday,axiom,
consecutive(monday,tuesday),
file('theBenchmark.p',tuesday_follows_monday) ).
cnf(c_118,plain,
consecutive(monday,tuesday),
inference(clausify,[status(thm)],[tuesday_follows_monday]) ).
fof(wednesday_follows_tuesday,axiom,
consecutive(tuesday,wednesday),
file('theBenchmark.p',wednesday_follows_tuesday) ).
cnf(c_119,plain,
consecutive(tuesday,wednesday),
inference(clausify,[status(thm)],[wednesday_follows_tuesday]) ).
fof(thursday_follows_wednesday,axiom,
consecutive(wednesday,thursday),
file('theBenchmark.p',thursday_follows_wednesday) ).
cnf(c_120,plain,
consecutive(wednesday,thursday),
inference(clausify,[status(thm)],[thursday_follows_wednesday]) ).
fof(friday_follows_thursday,axiom,
consecutive(thursday,friday),
file('theBenchmark.p',friday_follows_thursday) ).
cnf(c_121,plain,
consecutive(thursday,friday),
inference(clausify,[status(thm)],[friday_follows_thursday]) ).
fof(all_on_one_day,axiom,
( all_on(saturday)
| all_on(friday)
| all_on(thursday)
| all_on(wednesday)
| all_on(tuesday)
| all_on(monday)
| all_on(sunday) ),
file('theBenchmark.p',all_on_one_day) ).
cnf(c_124,plain,
( all_on(saturday)
| all_on(friday)
| all_on(thursday)
| all_on(wednesday)
| all_on(tuesday)
| all_on(monday)
| all_on(sunday) ),
inference(clausify,[status(thm)],[all_on_one_day]) ).
fof(not_on_for_3_days,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ~ on(VAR_4,VAR_2)
| ~ on(VAR_4,VAR_1)
| ~ on(VAR_4,VAR_0)
| ~ consecutive(VAR_2,VAR_3)
| ~ consecutive(VAR_1,VAR_2)
| ~ consecutive(VAR_0,VAR_1) ),
file('theBenchmark.p',not_on_for_3_days) ).
cnf(c_125,plain,
( ~ on(E,C)
| ~ on(E,B)
| ~ on(E,A)
| ~ consecutive(C,D)
| ~ consecutive(B,C)
| ~ consecutive(A,B) ),
inference(clausify,[status(thm)],[not_on_for_3_days]) ).
fof(a_off_sunday,axiom,
~ on(a,sunday),
file('theBenchmark.p',a_off_sunday) ).
cnf(c_126,plain,
~ on(a,sunday),
inference(clausify,[status(thm)],[a_off_sunday]) ).
fof(a_off_tuesday,axiom,
~ on(a,tuesday),
file('theBenchmark.p',a_off_tuesday) ).
cnf(c_127,plain,
~ on(a,tuesday),
inference(clausify,[status(thm)],[a_off_tuesday]) ).
fof(a_off_thursday,axiom,
~ on(a,thursday),
file('theBenchmark.p',a_off_thursday) ).
cnf(c_128,plain,
~ on(a,thursday),
inference(clausify,[status(thm)],[a_off_thursday]) ).
fof(b_off_thursday,axiom,
~ on(b,thursday),
file('theBenchmark.p',b_off_thursday) ).
cnf(c_129,plain,
~ on(b,thursday),
inference(clausify,[status(thm)],[b_off_thursday]) ).
fof(b_off_saturday,axiom,
~ on(b,saturday),
file('theBenchmark.p',b_off_saturday) ).
cnf(c_130,plain,
~ on(b,saturday),
inference(clausify,[status(thm)],[b_off_saturday]) ).
fof(c_off_sunday,axiom,
~ on(c,sunday),
file('theBenchmark.p',c_off_sunday) ).
cnf(c_131,plain,
~ on(c,sunday),
inference(clausify,[status(thm)],[c_off_sunday]) ).
fof(prove_all_on_friday,axiom,
~ all_on(friday),
file('theBenchmark.p',prove_all_on_friday) ).
cnf(c_132,plain,
~ all_on(friday),
inference(clausify,[status(thm)],[prove_all_on_friday]) ).
cnf(c_246,plain,
( on(c,thursday)
| on(c,sunday)
| on(a,thursday) ),
inference(resolve,[status(thm)],[c_126,c_74]) ).
cnf(c_247,plain,
( on(c,thursday)
| on(c,sunday) ),
inference(resolve,[status(thm)],[c_128,c_246]) ).
cnf(c_152,plain,
on(c,thursday),
inference(resolve,[status(thm)],[c_131,c_247]) ).
cnf(c_248,plain,
( on(c,tuesday)
| on(c,sunday)
| on(a,tuesday) ),
inference(resolve,[status(thm)],[c_126,c_72]) ).
cnf(c_249,plain,
( on(c,tuesday)
| on(c,sunday) ),
inference(resolve,[status(thm)],[c_127,c_248]) ).
cnf(c_154,plain,
on(c,tuesday),
inference(resolve,[status(thm)],[c_131,c_249]) ).
cnf(c_250,plain,
( on(b,thursday)
| on(b,sunday)
| on(a,thursday) ),
inference(resolve,[status(thm)],[c_126,c_53]) ).
cnf(c_251,plain,
( on(b,thursday)
| on(b,sunday) ),
inference(resolve,[status(thm)],[c_128,c_250]) ).
cnf(c_158,plain,
on(b,sunday),
inference(resolve,[status(thm)],[c_129,c_251]) ).
cnf(c_252,plain,
( on(b,thursday)
| on(b,tuesday)
| on(a,thursday) ),
inference(resolve,[status(thm)],[c_127,c_62]) ).
cnf(c_253,plain,
( on(b,thursday)
| on(b,tuesday) ),
inference(resolve,[status(thm)],[c_128,c_252]) ).
cnf(c_161,plain,
on(b,tuesday),
inference(resolve,[status(thm)],[c_129,c_253]) ).
cnf(c_169,plain,
( all_on(saturday)
| all_on(thursday)
| all_on(wednesday)
| all_on(tuesday)
| all_on(monday)
| all_on(sunday) ),
inference(resolve,[status(thm)],[c_132,c_124]) ).
cnf(c_206,plain,
~ all_on(sunday),
inference(resolve,[status(thm)],[c_113,c_126]) ).
cnf(c_207,plain,
( all_on(saturday)
| all_on(thursday)
| all_on(wednesday)
| all_on(tuesday)
| all_on(monday) ),
inference(resolve,[status(thm)],[c_206,c_169]) ).
cnf(c_208,plain,
~ all_on(tuesday),
inference(resolve,[status(thm)],[c_113,c_127]) ).
cnf(c_209,plain,
( all_on(saturday)
| all_on(thursday)
| all_on(wednesday)
| all_on(monday) ),
inference(resolve,[status(thm)],[c_208,c_207]) ).
cnf(c_210,plain,
~ all_on(thursday),
inference(resolve,[status(thm)],[c_113,c_128]) ).
cnf(c_211,plain,
( all_on(saturday)
| all_on(wednesday)
| all_on(monday) ),
inference(resolve,[status(thm)],[c_210,c_209]) ).
cnf(c_212,plain,
~ all_on(saturday),
inference(resolve,[status(thm)],[c_114,c_130]) ).
cnf(c_213,plain,
( all_on(wednesday)
| all_on(monday) ),
inference(resolve,[status(thm)],[c_212,c_211]) ).
cnf(c_254,plain,
( ~ on(C,A)
| ~ on(C,wednesday)
| ~ on(C,tuesday)
| ~ consecutive(A,B)
| ~ consecutive(wednesday,A) ),
inference(resolve,[status(thm)],[c_125,c_119]) ).
cnf(c_255,plain,
( ~ on(B,thursday)
| ~ on(B,wednesday)
| ~ on(B,tuesday)
| ~ consecutive(thursday,A) ),
inference(resolve,[status(thm)],[c_254,c_120]) ).
cnf(c_256,plain,
( ~ on(A,thursday)
| ~ on(A,wednesday)
| ~ on(A,tuesday) ),
inference(resolve,[status(thm)],[c_255,c_121]) ).
cnf(c_257,plain,
( ~ on(c,thursday)
| ~ on(c,wednesday) ),
inference(resolve,[status(thm)],[c_256,c_154]) ).
cnf(c_214,plain,
~ on(c,wednesday),
inference(resolve,[status(thm)],[c_257,c_152]) ).
cnf(c_258,plain,
( ~ on(C,A)
| ~ on(C,monday)
| ~ on(C,sunday)
| ~ consecutive(A,B)
| ~ consecutive(monday,A) ),
inference(resolve,[status(thm)],[c_125,c_117]) ).
cnf(c_259,plain,
( ~ on(B,tuesday)
| ~ on(B,monday)
| ~ on(B,sunday)
| ~ consecutive(tuesday,A) ),
inference(resolve,[status(thm)],[c_258,c_118]) ).
cnf(c_260,plain,
( ~ on(A,tuesday)
| ~ on(A,monday)
| ~ on(A,sunday) ),
inference(resolve,[status(thm)],[c_259,c_119]) ).
cnf(c_261,plain,
( ~ on(b,tuesday)
| ~ on(b,monday) ),
inference(resolve,[status(thm)],[c_260,c_158]) ).
cnf(c_219,plain,
~ on(b,monday),
inference(resolve,[status(thm)],[c_261,c_161]) ).
cnf(c_262,plain,
( on(c,wednesday)
| all_on(monday) ),
inference(resolve,[status(thm)],[c_213,c_115]) ).
cnf(c_242,plain,
all_on(monday),
inference(resolve,[status(thm)],[c_214,c_262]) ).
cnf(c_263,plain,
on(b,monday),
inference(resolve,[status(thm)],[c_242,c_114]) ).
cnf(c_245,plain,
$false,
inference(resolve,[status(thm)],[c_219,c_263]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ018-1 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 05:04:22 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 869645 was started by sandbox on n004,
% 0.09/0.36 % Sat Sep 26 05:04:22 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.38
% 0.14/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.38
% 0.14/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/0.38 % Length of proof is 47.
% 0.14/0.38 % Level of proof is 7.
% 0.14/0.38 % Maximum clause weight is 20.000.
% 0.14/0.38 % Given clauses 45.
% 0.14/0.38
% 0.14/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------