%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : TIM012_1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n027.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 : Tue May 5 07:15:46 PM UTC 2026
% Result : Theorem 17.98s 5.75s
% Output : CNFRefutation 17.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 97 ( 20 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 113 ( 44 ~; 52 |; 11 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 274 ( 31 atm; 59 fun; 134 num; 50 var)
% Number of types : 5 ( 3 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 18 ( 13 usr; 1 prp; 0-9 aty)
% Number of functors : 24 ( 9 usr; 18 con; 0-5 aty)
% Number of variables : 53 ( 50 !; 3 ?; 53 :)
% Comments :
%------------------------------------------------------------------------------
%$ calc_datetime > normalize_time > zeller_prep > nth_weekday_date > calc_date > is_days_in_month > calc_nth_offset > weekday > map_name_to_int > map_iso > is_days_in_year > valid_day > is_leap_year > dt > ymd > #nlpp > wednesday > tuesday > thursday > sunday > saturday > monday > friday
%Foreground sorts:
tff(date,type,
date: $tType ).
tff(time,type,
time: $tType ).
tff(day_name,type,
day_name: $tType ).
%Background operators:
%Foreground operators:
tff(friday,type,
friday: day_name ).
tff(calc_date,type,
calc_date: ( $int * $int * $int * date ) > $o ).
tff(tuesday,type,
tuesday: day_name ).
tff(nth_weekday_date,type,
nth_weekday_date: ( $int * day_name * $int * $int * date ) > $o ).
tff(zeller_prep,type,
zeller_prep: ( $int * $int * $int * $int * $int * $int ) > $o ).
tff(is_leap_year,type,
is_leap_year: $int > $o ).
tff(thursday,type,
thursday: day_name ).
tff(calc_nth_offset,type,
calc_nth_offset: ( $int * $int * $int ) > $o ).
tff(weekday,type,
weekday: ( date * day_name ) > $o ).
tff(is_days_in_month,type,
is_days_in_month: ( $int * $int * $int ) > $o ).
tff(is_days_in_year,type,
is_days_in_year: ( $int * $int ) > $o ).
tff(ymd,type,
ymd: ( $int * $int * $int ) > date ).
tff(saturday,type,
saturday: day_name ).
tff(sunday,type,
sunday: day_name ).
tff(map_iso,type,
map_iso: ( $int * day_name ) > $o ).
tff(wednesday,type,
wednesday: day_name ).
tff(valid_day,type,
valid_day: $int > $o ).
tff(monday,type,
monday: day_name ).
tff(map_name_to_int,type,
map_name_to_int: ( day_name * $int ) > $o ).
tff(calc_datetime,type,
calc_datetime: ( $int * $int * $int * $int * $int * $int * $int * $int * time ) > $o ).
tff(dt,type,
dt: ( $int * $int * $int * $int * $int ) > time ).
tff(normalize_time,type,
normalize_time: ( $int * $int * $int * $int * $int * $int * $int ) > $o ).
tff(f_307,axiom,
! [Ya: $int] :
( ( ( ( $remainder_e(Ya,4) = 0 )
& ( ( $remainder_e(Ya,100) != 0 )
| ( $remainder_e(Ya,400) = 0 ) ) )
=> is_days_in_month(2,Ya,29) )
& ( ( ( $remainder_e(Ya,4) != 0 )
| ( ( $remainder_e(Ya,100) = 0 )
& ( $remainder_e(Ya,400) != 0 ) ) )
=> is_days_in_month(2,Ya,28) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/TIM001_0.ax',m2) ).
tff(f_501,axiom,
is_days_in_month(2,2024,29),
file('/export/starexec/sandbox/benchmark/Axioms/TIM001_0.ax',hint_leap_2024_feb) ).
tff(f_335,axiom,
! [Da: $int,Ma: $int,Ya: $int,Limita: $int] :
( ( is_days_in_month(Ma,Ya,Limita)
& $greater(Da,0)
& $lesseq(Da,Limita) )
=> calc_date(Da,Ma,Ya,ymd(Ya,Ma,Da)) ),
file('/export/starexec/sandbox/benchmark/Axioms/TIM001_0.ax',rule_base) ).
tff(f_367,axiom,
! [Da: $int,Ma: $int,Ya: $int,Limita: $int,Res: date] :
( ( $lesseq(Da,0)
& ( Ma != 1 ) )
=> ( ( is_days_in_month($difference(Ma,1),Ya,Limita)
& calc_date($sum(Da,Limita),$difference(Ma,1),Ya,Res) )
=> calc_date(Da,Ma,Ya,Res) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/TIM001_0.ax',rule_back_std) ).
tff(f_72,axiom,
! [Da: $int] :
( valid_day(Da)
<=> ( $greater(Da,0)
& $lesseq(Da,31) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/TIM001_0.ax',trap_ax) ).
tff(f_564,negated_conjecture,
~ ? [Ya: $int,Ma: $int,Da: $int] :
( calc_date($sum(1,$uminus(2)),3,2024,ymd(Ya,Ma,Da))
& ( Ma = 2 )
& ( Da = 28 )
& valid_day(Da) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_back_leap) ).
tff(c_341,plain,
! [Y_76a: $int] :
( ( $remainder_e(Y_76a,100) = 0 )
| is_days_in_month(2,Y_76a,29)
| ( $remainder_e(Y_76a,4) != 0 ) ),
inference(cnfTransformation,[status(thm)],[f_307]) ).
tff(c_254,plain,
is_days_in_month(2,2024,29),
inference(cnfTransformation,[status(thm)],[f_501]) ).
tff(c_125,plain,
! [D_87a: $int,M_88a: $int,Y_89a: $int,Limit_90a: $int] :
( calc_date(D_87a,M_88a,Y_89a,ymd(Y_89a,M_88a,D_87a))
| ~ is_days_in_month(M_88a,Y_89a,Limit_90a)
| ~ $greater(D_87a,0)
| ~ $lesseq(D_87a,Limit_90a) ),
inference(cnfTransformation,[status(thm)],[f_335]) ).
tff(c_328,plain,
! [D_87a: $int,M_88a: $int,Y_89a: $int,Limit_90a: $int] :
( calc_date(D_87a,M_88a,Y_89a,ymd(Y_89a,M_88a,D_87a))
| ~ is_days_in_month(M_88a,Y_89a,Limit_90a)
| ~ $less(0,D_87a)
| $less(Limit_90a,D_87a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_125]) ).
tff(c_132,plain,
! [Y_103a: $int,Res_105: date,Limit_104a: $int,D_101a: $int,M_102a: $int] :
( calc_date(D_101a,M_102a,Y_103a,Res_105)
| ~ calc_date($sum(D_101a,Limit_104a),$difference(M_102a,1),Y_103a,Res_105)
| ~ is_days_in_month($difference(M_102a,1),Y_103a,Limit_104a)
| ~ $lesseq(D_101a,0)
| ( M_102a = 1 ) ),
inference(cnfTransformation,[status(thm)],[f_367]) ).
tff(c_1502,plain,
! [Limit_672a: $int,M_673a: $int,D_674a: $int,Res_679: date,Y_675a: $int] :
( calc_date(D_674a,M_673a,Y_675a,Res_679)
| ~ calc_date($sum(D_674a,Limit_672a),$sum($uminus(1),M_673a),Y_675a,Res_679)
| ~ is_days_in_month($sum($uminus(1),M_673a),Y_675a,Limit_672a)
| $less(0,D_674a)
| ( M_673a = 1 ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_132]) ).
tff(c_1553,plain,
! [Limit_672a: $int,Y_89a: $int,Limit_90a: $int,M_673a: $int,D_674a: $int] :
( calc_date(D_674a,M_673a,Y_89a,ymd(Y_89a,$sum($uminus(1),M_673a),$sum(D_674a,Limit_672a)))
| ~ is_days_in_month($sum($uminus(1),M_673a),Y_89a,Limit_672a)
| $less(0,D_674a)
| ( M_673a = 1 )
| ~ is_days_in_month($sum($uminus(1),M_673a),Y_89a,Limit_90a)
| ~ $less(0,$sum(D_674a,Limit_672a))
| $less(Limit_90a,$sum(D_674a,Limit_672a)) ),
inference(resolution,[status(thm)],[c_328,c_1502]) ).
tff(c_22167,plain,
! [M_4001a: $int,D_4006a: $int,Limit_4008a: $int,Y_4005a: $int,Limit_4002a: $int] :
( calc_date(D_4006a,M_4001a,Y_4005a,ymd(Y_4005a,$sum($uminus(1),M_4001a),$sum(Limit_4008a,D_4006a)))
| ~ is_days_in_month($sum($uminus(1),M_4001a),Y_4005a,Limit_4008a)
| $less(0,D_4006a)
| ( M_4001a = 1 )
| ~ is_days_in_month($sum($uminus(1),M_4001a),Y_4005a,Limit_4002a)
| ~ $less(0,$sum(D_4006a,Limit_4008a))
| $less(Limit_4002a,$sum(D_4006a,Limit_4008a)) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1553]) ).
tff(c_5,plain,
! [D_1a: $int] :
( valid_day(D_1a)
| ~ $greater(D_1a,0)
| ~ $lesseq(D_1a,31) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_593,plain,
! [D_350a: $int] :
( valid_day(D_350a)
| ~ $less(0,D_350a)
| $less(31,D_350a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_5]) ).
tff(c_230,plain,
! [Y_164a: $int] :
( ~ valid_day(28)
| ~ calc_date($sum(1,$uminus(2)),3,2024,ymd(Y_164a,2,28)) ),
inference(cnfTransformation,[status(thm)],[f_564]) ).
tff(c_232,plain,
! [Y_164a: $int] :
( ~ valid_day(28)
| ~ calc_date($uminus(1),3,2024,ymd(Y_164a,2,28)) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_230]) ).
tff(c_493,plain,
~ valid_day(28),
inference(splitLeft,[status(thm)],[c_232]) ).
tff(c_607,plain,
( ~ $less(0,28)
| $less(31,28) ),
inference(resolution,[status(thm)],[c_593,c_493]) ).
tff(c_610,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_607]) ).
tff(c_613,plain,
! [Y_164a: $int] : ~ calc_date($uminus(1),3,2024,ymd(Y_164a,2,28)),
inference(splitRight,[status(thm)],[c_232]) ).
tff(c_23155,plain,
! [Limit_4008a: $int,Limit_4002a: $int] :
( ( $sum(Limit_4008a,$uminus(1)) != 28 )
| ( $sum($uminus(1),3) != 2 )
| ~ is_days_in_month($sum($uminus(1),3),2024,Limit_4008a)
| $less(0,$uminus(1))
| ( 3 = 1 )
| ~ is_days_in_month($sum($uminus(1),3),2024,Limit_4002a)
| ~ $less(0,$sum($uminus(1),Limit_4008a))
| $less(Limit_4002a,$sum($uminus(1),Limit_4008a)) ),
inference(resolution,[status(thm)],[c_22167,c_613]) ).
tff(c_23157,plain,
! [Limit_4002a: $int] :
( ~ is_days_in_month(2,2024,29)
| ~ is_days_in_month(2,2024,Limit_4002a)
| ~ $less(1,29)
| $less($sum(1,Limit_4002a),29) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_23155]) ).
tff(c_23159,plain,
! [Limit_4002a: $int] :
( ~ is_days_in_month(2,2024,29)
| ~ is_days_in_month(2,2024,Limit_4002a)
| $less(Limit_4002a,28) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_23157]) ).
tff(c_23163,plain,
! [Limit_4333a: $int] :
( ~ is_days_in_month(2,2024,Limit_4333a)
| $less(Limit_4333a,28) ),
inference(demodulation,[status(thm),theory(equality)],[c_254,c_23159]) ).
tff(c_23189,plain,
( $less(29,28)
| ( $remainder_e(2024,100) = 0 )
| ( $remainder_e(2024,4) != 0 ) ),
inference(resolution,[status(thm)],[c_341,c_23163]) ).
tff(c_23192,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_23189]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : TIM012_1 : TPTP v9.3.0. Released v9.3.0.
% 0.13/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.17/0.34 % Computer : n027.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Mon May 4 18:08:34 EDT 2026
% 0.17/0.34 % CPUTime :
% 17.98/5.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.98/5.75
% 17.98/5.75 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------