%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : PUZ078+1 : TPTP v9.3.1. Released v3.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 : Thu Sep 24 02:02:33 PM UTC 2026
% Result : Theorem 0.63s 0.59s
% Output : CNFRefutation 0.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 21
% Syntax : Number of formulae : 174 ( 46 unt; 0 def)
% Number of atoms : 503 ( 236 equ)
% Maximal formula atoms : 21 ( 2 avg)
% Number of connectives : 555 ( 226 ~; 238 |; 76 &)
% ( 7 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 11 con; 0-1 aty)
% Number of variables : 72 ( 1 sgn 26 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(tuesday_leo_tells_truths,conjecture,
truthday(tuesday),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tuesday_leo_tells_truths) ).
fof(statement1,axiom,
! [X1] :
( day1(X1)
=> ( truthday(X1)
<=> ( ~ truthday(tuesday)
& ~ truthday(monday) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',statement1) ).
fof(truth_unique,axiom,
! [X1,X2] :
( ( truthday(X2)
& truthday(X1) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',truth_unique) ).
fof(truth_once,axiom,
? [X1] : truthday(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',truth_once) ).
fof(day1_once,axiom,
? [X1] : day1(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',day1_once) ).
fof(statement3,axiom,
! [X1] :
( day3(X1)
=> ( truthday(X1)
<=> ( ~ truthday(friday)
& ~ truthday(wednesday) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',statement3) ).
fof(day3_once,axiom,
? [X1] : day3(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',day3_once) ).
fof(uniquenames,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) ).
fof(day3_follows_day2,axiom,
! [X1] :
( day2(X1)
<=> day3(consecutive(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',day3_follows_day2) ).
fof(day1_unique,axiom,
! [X1,X2] :
( ( day1(X2)
& day1(X1) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',day1_unique) ).
fof(day2_follows_day1,axiom,
! [X1] :
( day1(X1)
<=> day2(consecutive(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',day2_follows_day1) ).
fof(monday_follows_sunday,axiom,
consecutive(sunday) = monday,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monday_follows_sunday) ).
fof(days_of_week,axiom,
! [X1] :
( X1 = sunday
| X1 = saturday
| X1 = friday
| X1 = thursday
| X1 = wednesday
| X1 = tuesday
| X1 = monday ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',days_of_week) ).
fof(sunday_follows_saturday,axiom,
consecutive(saturday) = sunday,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sunday_follows_saturday) ).
fof(day3_unique,axiom,
! [X1,X2] :
( ( day3(X2)
& day3(X1) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',day3_unique) ).
fof(tuesday_follows_monday,axiom,
consecutive(monday) = tuesday,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tuesday_follows_monday) ).
fof(statement2,axiom,
! [X1] :
( day2(X1)
=> ( truthday(X1)
<=> ( day2(sunday)
| day2(saturday)
| day2(thursday) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',statement2) ).
fof(day2_once,axiom,
? [X1] : day2(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',day2_once) ).
fof(saturday_follows_friday,axiom,
consecutive(friday) = saturday,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',saturday_follows_friday) ).
fof(wednesday_follows_tuesday,axiom,
consecutive(tuesday) = wednesday,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wednesday_follows_tuesday) ).
fof(thursday_follows_wednesday,axiom,
consecutive(wednesday) = thursday,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thursday_follows_wednesday) ).
fof(c_0_21,negated_conjecture,
~ truthday(tuesday),
inference(assume_negation,[status(cth)],[tuesday_leo_tells_truths]) ).
fof(c_0_22,plain,
! [X1] :
( day1(X1)
=> ( truthday(X1)
<=> ( ~ truthday(tuesday)
& ~ truthday(monday) ) ) ),
inference(fof_simplification,[status(thm)],[statement1]) ).
fof(c_0_23,negated_conjecture,
~ truthday(tuesday),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_24,plain,
! [X6] :
( ( ~ day1(X6)
| truthday(X6)
| truthday(tuesday)
| truthday(monday) )
& ( ~ day1(X6)
| ~ truthday(X6)
| ~ truthday(tuesday) )
& ( ~ day1(X6)
| ~ truthday(X6)
| ~ truthday(monday) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])])]) ).
fof(c_0_25,negated_conjecture,
~ truthday(tuesday),
inference(fof_nnf,[status(thm)],[c_0_23]) ).
fof(c_0_26,plain,
! [X3,X4] :
( X3 = X4
| ~ truthday(X4)
| ~ truthday(X3) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[truth_unique])])]) ).
fof(c_0_27,plain,
truthday(esk1_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[truth_once])]) ).
cnf(c_0_28,plain,
( ~ day1(X1)
| truthday(X1)
| truthday(tuesday)
| truthday(monday) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,negated_conjecture,
~ truthday(tuesday),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_30,plain,
day1(esk2_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[day1_once])]) ).
fof(c_0_31,plain,
! [X1] :
( day3(X1)
=> ( truthday(X1)
<=> ( ~ truthday(friday)
& ~ truthday(wednesday) ) ) ),
inference(fof_simplification,[status(thm)],[statement3]) ).
cnf(c_0_32,plain,
( ~ truthday(X2)
| ~ truthday(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
truthday(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,plain,
( ~ day1(X1)
| truthday(X1)
| truthday(monday) ),
inference(sr,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,plain,
day1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_36,plain,
! [X8] :
( ( ~ day3(X8)
| truthday(X8)
| truthday(friday)
| truthday(wednesday) )
& ( ~ day3(X8)
| ~ truthday(X8)
| ~ truthday(friday) )
& ( ~ day3(X8)
| ~ truthday(X8)
| ~ truthday(wednesday) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])]) ).
fof(c_0_37,plain,
day3(esk4_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[day3_once])]) ).
cnf(c_0_38,plain,
( ~ truthday(X1)
| X1 = esk1_0 ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,plain,
( truthday(monday)
| truthday(esk2_0) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,plain,
( ~ day3(X1)
| truthday(X1)
| truthday(friday)
| truthday(wednesday) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_41,plain,
day3(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_42,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(fof_simplification,[status(thm)],[uniquenames]) ).
cnf(c_0_43,plain,
( truthday(monday)
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,plain,
( truthday(friday)
| truthday(wednesday)
| truthday(esk4_0) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
fof(c_0_45,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(fof_nnf,[status(thm)],[c_0_42]) ).
cnf(c_0_46,plain,
( ~ truthday(X1)
| X1 = monday
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_32,c_0_43]) ).
cnf(c_0_47,plain,
( truthday(wednesday)
| truthday(friday)
| esk4_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_38,c_0_44]) ).
cnf(c_0_48,plain,
monday != friday,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_49,plain,
( ~ day3(X1)
| ~ truthday(X1)
| ~ truthday(friday) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_50,plain,
( truthday(wednesday)
| esk2_0 = esk1_0
| esk4_0 = esk1_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_51,plain,
monday != wednesday,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_52,plain,
( ~ day3(X1)
| ~ truthday(X1)
| ~ truthday(wednesday) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_53,plain,
! [X17] :
( ( day2(X17)
| ~ day3(consecutive(X17)) )
& ( day3(consecutive(X17))
| ~ day2(X17) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[day3_follows_day2])])]) ).
cnf(c_0_54,plain,
( ~ truthday(esk4_0)
| ~ truthday(friday) ),
inference(spm,[status(thm)],[c_0_49,c_0_41]) ).
cnf(c_0_55,plain,
( esk2_0 = esk1_0
| esk4_0 = esk1_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_50]),c_0_51]) ).
cnf(c_0_56,plain,
( ~ truthday(esk4_0)
| ~ truthday(wednesday) ),
inference(spm,[status(thm)],[c_0_52,c_0_41]) ).
fof(c_0_57,plain,
! [X10,X11] :
( X10 = X11
| ~ day1(X11)
| ~ day1(X10) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[day1_unique])])]) ).
fof(c_0_58,plain,
! [X13] :
( ( day1(X13)
| ~ day2(consecutive(X13)) )
& ( day2(consecutive(X13))
| ~ day1(X13) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[day2_follows_day1])])]) ).
cnf(c_0_59,plain,
( ~ day3(consecutive(X1))
| day2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_60,plain,
consecutive(sunday) = monday,
inference(split_conjunct,[status(thm)],[monday_follows_sunday]) ).
fof(c_0_61,plain,
! [X9] :
( X9 = sunday
| X9 = saturday
| X9 = friday
| X9 = thursday
| X9 = wednesday
| X9 = tuesday
| X9 = monday ),
inference(variable_rename,[status(thm)],[days_of_week]) ).
cnf(c_0_62,plain,
( ~ truthday(friday)
| esk2_0 = esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_33])]) ).
cnf(c_0_63,plain,
( ~ truthday(wednesday)
| esk2_0 = esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_55]),c_0_33])]) ).
cnf(c_0_64,plain,
( ~ day1(X2)
| ~ day1(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_65,plain,
( ~ day2(consecutive(X1))
| day1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_66,plain,
consecutive(saturday) = sunday,
inference(split_conjunct,[status(thm)],[sunday_follows_saturday]) ).
cnf(c_0_67,plain,
( ~ day3(monday)
| day2(sunday) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_68,plain,
( X1 = sunday
| X1 = saturday
| X1 = friday
| X1 = thursday
| X1 = wednesday
| X1 = tuesday
| X1 = monday ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_69,plain,
( esk2_0 = esk1_0
| esk4_0 = monday ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_44]),c_0_62]),c_0_63]) ).
fof(c_0_70,plain,
! [X18,X19] :
( X18 = X19
| ~ day3(X19)
| ~ day3(X18) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[day3_unique])])]) ).
cnf(c_0_71,plain,
( ~ day1(X1)
| X1 = esk2_0 ),
inference(spm,[status(thm)],[c_0_64,c_0_35]) ).
cnf(c_0_72,plain,
( ~ day2(sunday)
| day1(saturday) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_73,plain,
( ~ day3(X1)
| day2(sunday)
| X1 = sunday
| X1 = saturday
| X1 = friday
| X1 = thursday
| X1 = wednesday
| X1 = tuesday ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_74,plain,
( day3(monday)
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_41,c_0_69]) ).
cnf(c_0_75,plain,
monday != tuesday,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_76,plain,
monday != thursday,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_77,plain,
monday != saturday,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_78,plain,
monday != sunday,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_79,plain,
( ~ day3(X2)
| ~ day3(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_80,plain,
consecutive(monday) = tuesday,
inference(split_conjunct,[status(thm)],[tuesday_follows_monday]) ).
cnf(c_0_81,plain,
( ~ day2(sunday)
| esk2_0 = saturday ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_82,plain,
( day2(sunday)
| esk2_0 = esk1_0 ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75]),c_0_51]),c_0_76]),c_0_48]),c_0_77]),c_0_78]) ).
cnf(c_0_83,plain,
( ~ day3(X1)
| X1 = esk4_0 ),
inference(spm,[status(thm)],[c_0_79,c_0_41]) ).
cnf(c_0_84,plain,
( ~ day2(X1)
| day3(consecutive(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_85,plain,
( ~ day1(X1)
| ~ truthday(X1)
| ~ truthday(monday) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_86,plain,
( ~ day2(tuesday)
| day1(monday) ),
inference(spm,[status(thm)],[c_0_65,c_0_80]) ).
cnf(c_0_87,plain,
( esk2_0 = saturday
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_88,plain,
( ~ day1(X1)
| day2(consecutive(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_89,plain,
( ~ day2(X1)
| consecutive(X1) = esk4_0 ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_90,plain,
( ~ truthday(monday)
| ~ day2(tuesday) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_91,plain,
( esk1_0 != saturday
| esk2_0 = saturday ),
inference(ef,[status(thm)],[c_0_87]) ).
cnf(c_0_92,plain,
( ~ day1(monday)
| day2(tuesday) ),
inference(spm,[status(thm)],[c_0_88,c_0_80]) ).
cnf(c_0_93,plain,
( ~ day2(X1)
| ~ day2(esk4_0)
| day1(X1) ),
inference(spm,[status(thm)],[c_0_65,c_0_89]) ).
cnf(c_0_94,plain,
~ day2(tuesday),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_86]),c_0_90]) ).
fof(c_0_95,plain,
! [X7] :
( ( ~ day2(X7)
| truthday(X7)
| ~ day2(sunday) )
& ( ~ day2(X7)
| truthday(X7)
| ~ day2(saturday) )
& ( ~ day2(X7)
| truthday(X7)
| ~ day2(thursday) )
& ( ~ day2(X7)
| day2(sunday)
| day2(saturday)
| day2(thursday)
| ~ truthday(X7) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[statement2])])])]) ).
cnf(c_0_96,plain,
( ~ day1(saturday)
| day2(sunday) ),
inference(spm,[status(thm)],[c_0_88,c_0_66]) ).
cnf(c_0_97,plain,
( esk1_0 != saturday
| day1(saturday) ),
inference(spm,[status(thm)],[c_0_35,c_0_91]) ).
cnf(c_0_98,plain,
( ~ day1(X1)
| ~ day2(X1)
| day2(esk4_0) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_99,plain,
( ~ day2(monday)
| day1(sunday) ),
inference(spm,[status(thm)],[c_0_65,c_0_60]) ).
cnf(c_0_100,plain,
( ~ day2(monday)
| ~ day2(esk4_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_94]) ).
cnf(c_0_101,plain,
( ~ day2(X1)
| ~ day2(sunday)
| truthday(X1) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_102,plain,
( esk1_0 != saturday
| day2(sunday) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
fof(c_0_103,plain,
day2(esk3_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[day2_once])]) ).
cnf(c_0_104,plain,
( ~ day1(sunday)
| day2(monday) ),
inference(spm,[status(thm)],[c_0_88,c_0_60]) ).
cnf(c_0_105,plain,
( ~ day2(monday)
| ~ day2(sunday) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_100]) ).
cnf(c_0_106,plain,
( ~ day2(X1)
| truthday(X1)
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_101,c_0_82]) ).
cnf(c_0_107,plain,
( ~ day2(X1)
| esk1_0 != saturday
| truthday(X1) ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_108,plain,
day2(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_109,plain,
( ~ day2(sunday)
| ~ day2(esk4_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_93]),c_0_105]) ).
cnf(c_0_110,plain,
( ~ day2(esk2_0)
| day2(esk4_0) ),
inference(spm,[status(thm)],[c_0_98,c_0_35]) ).
cnf(c_0_111,plain,
( truthday(sunday)
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_106,c_0_82]) ).
cnf(c_0_112,plain,
( esk1_0 != saturday
| truthday(esk3_0) ),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_113,plain,
( ~ day2(esk2_0)
| ~ day2(sunday) ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_114,plain,
esk2_0 = esk1_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_111]),c_0_78]) ).
cnf(c_0_115,plain,
( esk1_0 != saturday
| esk3_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_38,c_0_112]) ).
cnf(c_0_116,plain,
( ~ day2(esk1_0)
| ~ day2(sunday) ),
inference(rw,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_117,plain,
( esk1_0 != saturday
| day2(esk1_0) ),
inference(spm,[status(thm)],[c_0_108,c_0_115]) ).
cnf(c_0_118,plain,
( truthday(wednesday)
| esk1_0 = friday
| esk4_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_38,c_0_47]) ).
cnf(c_0_119,plain,
( ~ truthday(esk2_0)
| ~ truthday(monday) ),
inference(spm,[status(thm)],[c_0_85,c_0_35]) ).
cnf(c_0_120,plain,
( X2 = X1
| X2 = sunday
| X2 = saturday
| X2 = friday
| X2 = thursday
| X2 = wednesday
| X2 = tuesday
| X1 = sunday
| X1 = saturday
| X1 = friday
| X1 = thursday
| X1 = wednesday
| X1 = tuesday ),
inference(spm,[status(thm)],[c_0_68,c_0_68]) ).
cnf(c_0_121,plain,
esk1_0 != saturday,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_102]) ).
cnf(c_0_122,plain,
consecutive(friday) = saturday,
inference(split_conjunct,[status(thm)],[saturday_follows_friday]) ).
cnf(c_0_123,plain,
( esk1_0 = wednesday
| esk4_0 = esk1_0
| esk1_0 = friday ),
inference(spm,[status(thm)],[c_0_38,c_0_118]) ).
cnf(c_0_124,plain,
~ truthday(monday),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_119,c_0_114]),c_0_33])]) ).
cnf(c_0_125,plain,
( truthday(X1)
| X1 = tuesday
| X1 = wednesday
| X1 = thursday
| X1 = friday
| X1 = saturday
| X1 = sunday
| esk1_0 = tuesday
| esk1_0 = wednesday
| esk1_0 = thursday
| esk1_0 = friday
| esk1_0 = sunday ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_120]),c_0_121]) ).
cnf(c_0_126,plain,
( ~ day2(saturday)
| day1(friday) ),
inference(spm,[status(thm)],[c_0_65,c_0_122]) ).
cnf(c_0_127,plain,
( day3(esk1_0)
| esk1_0 = friday
| esk1_0 = wednesday ),
inference(spm,[status(thm)],[c_0_41,c_0_123]) ).
cnf(c_0_128,plain,
( esk1_0 = sunday
| esk1_0 = friday
| esk1_0 = thursday
| esk1_0 = wednesday
| esk1_0 = tuesday ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_78]),c_0_77]),c_0_48]),c_0_76]),c_0_51]),c_0_75]) ).
cnf(c_0_129,plain,
wednesday != sunday,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_130,plain,
friday != sunday,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_131,plain,
( ~ day2(saturday)
| esk2_0 = friday ),
inference(spm,[status(thm)],[c_0_71,c_0_126]) ).
cnf(c_0_132,plain,
( ~ day3(sunday)
| day2(saturday) ),
inference(spm,[status(thm)],[c_0_59,c_0_66]) ).
cnf(c_0_133,plain,
( day3(sunday)
| esk1_0 = tuesday
| esk1_0 = wednesday
| esk1_0 = thursday
| esk1_0 = friday ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_129]),c_0_130]) ).
cnf(c_0_134,plain,
( ~ day2(saturday)
| esk1_0 = friday ),
inference(rw,[status(thm)],[c_0_131,c_0_114]) ).
cnf(c_0_135,plain,
day1(esk1_0),
inference(rw,[status(thm)],[c_0_35,c_0_114]) ).
cnf(c_0_136,plain,
( esk1_0 = friday
| esk1_0 = thursday
| esk1_0 = wednesday
| esk1_0 = tuesday ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_134]) ).
cnf(c_0_137,plain,
( ~ day1(friday)
| day2(saturday) ),
inference(spm,[status(thm)],[c_0_88,c_0_122]) ).
cnf(c_0_138,plain,
( day1(friday)
| esk1_0 = tuesday
| esk1_0 = wednesday
| esk1_0 = thursday ),
inference(spm,[status(thm)],[c_0_135,c_0_136]) ).
cnf(c_0_139,plain,
( ~ day2(X1)
| ~ day2(saturday)
| truthday(X1) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_140,plain,
( day2(saturday)
| esk1_0 = thursday
| esk1_0 = wednesday
| esk1_0 = tuesday ),
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_141,plain,
( ~ day2(X1)
| truthday(X1)
| esk1_0 = tuesday
| esk1_0 = wednesday
| esk1_0 = thursday ),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_142,plain,
consecutive(tuesday) = wednesday,
inference(split_conjunct,[status(thm)],[wednesday_follows_tuesday]) ).
cnf(c_0_143,plain,
( truthday(saturday)
| esk1_0 = thursday
| esk1_0 = wednesday
| esk1_0 = tuesday ),
inference(spm,[status(thm)],[c_0_141,c_0_140]) ).
cnf(c_0_144,plain,
( ~ day2(wednesday)
| day1(tuesday) ),
inference(spm,[status(thm)],[c_0_65,c_0_142]) ).
cnf(c_0_145,plain,
( ~ day1(X1)
| ~ day2(X2)
| ~ day2(esk4_0)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_64,c_0_93]) ).
cnf(c_0_146,plain,
consecutive(wednesday) = thursday,
inference(split_conjunct,[status(thm)],[thursday_follows_wednesday]) ).
cnf(c_0_147,plain,
( esk1_0 = tuesday
| esk1_0 = wednesday
| esk1_0 = thursday ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_143]),c_0_121]) ).
cnf(c_0_148,plain,
wednesday != thursday,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_149,plain,
thursday != friday,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_150,plain,
( ~ day2(wednesday)
| esk2_0 = tuesday ),
inference(spm,[status(thm)],[c_0_71,c_0_144]) ).
cnf(c_0_151,plain,
( ~ day1(X2)
| ~ day1(X1)
| ~ day2(esk4_0)
| X1 = consecutive(X2) ),
inference(spm,[status(thm)],[c_0_145,c_0_88]) ).
cnf(c_0_152,plain,
( ~ day3(thursday)
| day2(wednesday) ),
inference(spm,[status(thm)],[c_0_59,c_0_146]) ).
cnf(c_0_153,plain,
( day3(thursday)
| esk1_0 = wednesday
| esk1_0 = tuesday ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_147]),c_0_148]),c_0_149]) ).
cnf(c_0_154,plain,
( ~ day2(wednesday)
| esk1_0 = tuesday ),
inference(rw,[status(thm)],[c_0_150,c_0_114]) ).
cnf(c_0_155,plain,
( ~ day1(X1)
| ~ day2(esk4_0)
| consecutive(X1) = esk1_0 ),
inference(spm,[status(thm)],[c_0_151,c_0_135]) ).
cnf(c_0_156,plain,
( esk1_0 = tuesday
| esk1_0 = wednesday ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_154]) ).
cnf(c_0_157,plain,
( ~ day2(X1)
| ~ day2(esk4_0)
| consecutive(X1) = esk1_0 ),
inference(spm,[status(thm)],[c_0_155,c_0_93]) ).
cnf(c_0_158,plain,
( ~ day1(wednesday)
| day2(thursday) ),
inference(spm,[status(thm)],[c_0_88,c_0_146]) ).
cnf(c_0_159,plain,
( day1(wednesday)
| esk1_0 = tuesday ),
inference(spm,[status(thm)],[c_0_135,c_0_156]) ).
cnf(c_0_160,plain,
( ~ day2(X1)
| ~ day2(esk4_0)
| day3(esk1_0) ),
inference(spm,[status(thm)],[c_0_84,c_0_157]) ).
cnf(c_0_161,plain,
( ~ day2(X1)
| ~ day2(thursday)
| truthday(X1) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_162,plain,
( day2(thursday)
| esk1_0 = tuesday ),
inference(spm,[status(thm)],[c_0_158,c_0_159]) ).
cnf(c_0_163,plain,
( ~ day2(esk4_0)
| day3(esk1_0) ),
inference(spm,[status(thm)],[c_0_160,c_0_108]) ).
cnf(c_0_164,plain,
( ~ day2(X1)
| truthday(X1)
| esk1_0 = tuesday ),
inference(spm,[status(thm)],[c_0_161,c_0_162]) ).
cnf(c_0_165,plain,
( ~ day3(wednesday)
| day2(tuesday) ),
inference(spm,[status(thm)],[c_0_59,c_0_142]) ).
cnf(c_0_166,plain,
( ~ day2(esk4_0)
| day3(wednesday)
| esk1_0 = tuesday ),
inference(spm,[status(thm)],[c_0_163,c_0_156]) ).
cnf(c_0_167,plain,
( truthday(esk3_0)
| esk1_0 = tuesday ),
inference(spm,[status(thm)],[c_0_164,c_0_108]) ).
cnf(c_0_168,plain,
( ~ day2(esk4_0)
| esk1_0 = tuesday ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_94]) ).
cnf(c_0_169,plain,
( ~ day2(esk1_0)
| day2(esk4_0) ),
inference(rw,[status(thm)],[c_0_110,c_0_114]) ).
cnf(c_0_170,plain,
( esk3_0 = esk1_0
| esk1_0 = tuesday ),
inference(spm,[status(thm)],[c_0_38,c_0_167]) ).
cnf(c_0_171,plain,
( ~ day2(esk1_0)
| esk1_0 = tuesday ),
inference(spm,[status(thm)],[c_0_168,c_0_169]) ).
cnf(c_0_172,plain,
esk1_0 = tuesday,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_170]),c_0_171]) ).
cnf(c_0_173,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_172]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ078+1 : TPTP v9.3.1. Released v3.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n003.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 : Mon Sep 21 03:51:46 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.63/0.59 % Version: 3.5.1
% 0.63/0.59 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.63/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.63/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.63/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.63/0.59 % Starting new_bool_1 with 300s (1) cores
% 0.63/0.59 % Starting sh5l with 300s (1) cores
% 0.63/0.59 % new_bool_1 with pid 3343141 completed with status 0
% 0.63/0.59 % Result found by new_bool_1
% 0.63/0.59 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.63/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.63/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.63/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.63/0.59 % Starting new_bool_1 with 300s (1) cores
% 0.63/0.59 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.63/0.59 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.63/0.59 % Search class: FGHSF-FFMM11-SFFFFFNN
% 0.63/0.59 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.63/0.59 % Starting SubtermCWHack with 31s (1) cores
% 0.63/0.59 % SubtermCWHack with pid 3343147 completed with status 0
% 0.63/0.59 % Result found by SubtermCWHack
% 0.63/0.59 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.63/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.63/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.63/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.63/0.59 % Starting new_bool_1 with 300s (1) cores
% 0.63/0.59 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.63/0.59 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.63/0.59 % Search class: FGHSF-FFMM11-SFFFFFNN
% 0.63/0.59 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.63/0.59 % Starting SubtermCWHack with 31s (1) cores
% 0.63/0.59 % Preprocessing time : 0.001 s
% 0.63/0.59
% 0.63/0.59 % Proof found!
% 0.63/0.59 % SZS status Theorem
% 0.63/0.59 % SZS output start CNFRefutation
% See solution above
% 0.63/0.59 % Parsed axioms : 23
% 0.63/0.59 % Removed by relevancy pruning/SinE : 0
% 0.63/0.59 % Initial clauses : 52
% 0.63/0.59 % Removed in clause preprocessing : 0
% 0.63/0.59 % Initial clauses in saturation : 52
% 0.63/0.59 % Processed clauses : 2236
% 0.63/0.59 % ...of these trivial : 1
% 0.63/0.59 % ...subsumed : 1618
% 0.63/0.59 % ...remaining for further processing : 617
% 0.63/0.59 % Other redundant clauses eliminated : 286
% 0.63/0.59 % Clauses deleted for lack of memory : 0
% 0.63/0.59 % Backward-subsumed : 168
% 0.63/0.59 % Backward-rewritten : 176
% 0.63/0.59 % Generated clauses : 9595
% 0.63/0.59 % ...of the previous two non-redundant : 8293
% 0.63/0.59 % ...aggressively subsumed : 0
% 0.63/0.59 % Contextual simplify-reflections : 41
% 0.63/0.59 % Paramodulations : 8656
% 0.63/0.59 % Factorizations : 648
% 0.63/0.59 % NegExts : 0
% 0.63/0.59 % Equation resolutions : 286
% 0.63/0.59 % Disequality decompositions : 0
% 0.63/0.59 % Total rewrite steps : 2610
% 0.63/0.59 % ...of those cached : 2594
% 0.63/0.59 % Propositional unsat checks : 0
% 0.63/0.59 % Propositional check models : 0
% 0.63/0.59 % Propositional check unsatisfiable : 0
% 0.63/0.59 % Propositional clauses : 0
% 0.63/0.59 % Propositional clauses after purity: 0
% 0.63/0.59 % Propositional unsat core size : 0
% 0.63/0.59 % Propositional preprocessing time : 0.000
% 0.63/0.59 % Propositional encoding time : 0.000
% 0.63/0.59 % Propositional solver time : 0.000
% 0.63/0.59 % Success case prop preproc time : 0.000
% 0.63/0.59 % Success case prop encoding time : 0.000
% 0.63/0.59 % Success case prop solver time : 0.000
% 0.63/0.59 % Current number of processed clauses : 268
% 0.63/0.59 % Positive orientable unit clauses : 10
% 0.63/0.59 % Positive unorientable unit clauses: 0
% 0.63/0.59 % Negative unit clauses : 24
% 0.63/0.59 % Non-unit-clauses : 234
% 0.63/0.59 % Current number of unprocessed clauses: 5325
% 0.63/0.59 % ...number of literals in the above : 94361
% 0.63/0.59 % Current number of archived formulas : 0
% 0.63/0.59 % Current number of archived clauses : 349
% 0.63/0.59 % Clause-clause subsumption calls (NU) : 51384
% 0.63/0.59 % Rec. Clause-clause subsumption calls : 26920
% 0.63/0.59 % Non-unit clause-clause subsumptions : 1704
% 0.63/0.59 % Unit Clause-clause subsumption calls : 393
% 0.63/0.59 % Rewrite failures with RHS unbound : 0
% 0.63/0.59 % BW rewrite match attempts : 4
% 0.63/0.59 % BW rewrite match successes : 4
% 0.63/0.59 % Condensation attempts : 0
% 0.63/0.59 % Condensation successes : 0
% 0.63/0.59 % Termbank termtop insertions : 82891
% 0.63/0.59 % Search garbage collected termcells : 359
% 0.63/0.59
% 0.63/0.59 % -------------------------------------------------
% 0.63/0.59 % User time : 0.149 s
% 0.63/0.59 % System time : 0.009 s
% 0.63/0.59 % Total time : 0.157 s
% 0.63/0.59 % Maximum resident set size: 3652 pages
% 0.63/0.59
% 0.63/0.59 % -------------------------------------------------
% 0.63/0.59 % User time : 0.150 s
% 0.63/0.59 % System time : 0.013 s
% 0.63/0.59 % Total time : 0.163 s
% 0.63/0.59 % Maximum resident set size: 4608 pages
% 0.63/0.59 % E exiting
%------------------------------------------------------------------------------