%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CSR007+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 07:06:31 AM UTC 2026
% Result : Theorem 13.56s 2.42s
% Output : CNFRefutation 13.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 21
% Syntax : Number of formulae : 235 ( 61 unt; 0 def)
% Number of atoms : 798 ( 356 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 766 ( 203 ~; 511 |; 38 &)
% ( 11 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-4 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-3 aty)
% Number of variables : 316 ( 23 sgn 80 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(stoppedin_defn,axiom,
! [Time1,Fluent,Time2] :
( stoppedIn(Time1,Fluent,Time2)
<=> ? [Event,Time] :
( terminates(Event,Fluent,Time)
& less(Time,Time2)
& less(Time1,Time)
& happens(Event,Time) ) ),
file('theBenchmark.p',stoppedin_defn) ).
fof(change_holding,axiom,
! [Event,Time,Fluent,Fluent2,Offset] :
( ( ~ stoppedIn(Time,Fluent,plus(Time,Offset))
& trajectory(Fluent,Time,Fluent2,Offset)
& less(n0,Offset)
& initiates(Event,Fluent,Time)
& happens(Event,Time) )
=> holdsAt(Fluent2,plus(Time,Offset)) ),
file('theBenchmark.p',change_holding) ).
fof(initiates_all_defn,axiom,
! [Event,Fluent,Time] :
( initiates(Event,Fluent,Time)
<=> ( ? [Height] :
( Fluent = waterLevel(Height)
& Event = overflow
& holdsAt(waterLevel(Height),Time) )
| ? [Height] :
( Fluent = waterLevel(Height)
& Event = tapOff
& holdsAt(waterLevel(Height),Time) )
| ( Fluent = spilling
& Event = overflow )
| ( Fluent = filling
& Event = tapOn ) ) ),
file('theBenchmark.p',initiates_all_defn) ).
fof(releases_all_defn,axiom,
! [Event,Fluent,Time] :
( releases(Event,Fluent,Time)
<=> ? [Height] :
( Fluent = waterLevel(Height)
& Event = tapOn ) ),
file('theBenchmark.p',releases_all_defn) ).
fof(happens_all_defn,axiom,
! [Event,Time] :
( happens(Event,Time)
<=> ( ( Event = overflow
& holdsAt(filling,Time)
& holdsAt(waterLevel(n3),Time) )
| ( Time = n0
& Event = tapOn ) ) ),
file('theBenchmark.p',happens_all_defn) ).
fof(change_of_waterLevel,axiom,
! [Height1,Time,Height2,Offset] :
( ( Height2 = plus(Height1,Offset)
& holdsAt(waterLevel(Height1),Time) )
=> trajectory(filling,Time,waterLevel(Height2),Offset) ),
file('theBenchmark.p',change_of_waterLevel) ).
fof(same_waterLevel,axiom,
! [Time,Height1,Height2] :
( ( holdsAt(waterLevel(Height2),Time)
& holdsAt(waterLevel(Height1),Time) )
=> Height1 = Height2 ),
file('theBenchmark.p',same_waterLevel) ).
fof(distinct_waterLevels,axiom,
! [X,Y] :
( waterLevel(X) = waterLevel(Y)
<=> X = Y ),
file('theBenchmark.p',distinct_waterLevels) ).
fof(symmetry_of_plus,axiom,
! [X,Y] : plus(X,Y) = plus(Y,X),
file('theBenchmark.p',symmetry_of_plus) ).
fof(less_or_equal,axiom,
! [X,Y] :
( less_or_equal(X,Y)
<=> ( X = Y
| less(X,Y) ) ),
file('theBenchmark.p',less_or_equal) ).
fof(less0,axiom,
~ ? [X] : less(X,n0),
file('theBenchmark.p',less0) ).
fof(less1,axiom,
! [X] :
( less(X,n1)
<=> less_or_equal(X,n0) ),
file('theBenchmark.p',less1) ).
fof(less2,axiom,
! [X] :
( less(X,n2)
<=> less_or_equal(X,n1) ),
file('theBenchmark.p',less2) ).
fof(less3,axiom,
! [X] :
( less(X,n3)
<=> less_or_equal(X,n2) ),
file('theBenchmark.p',less3) ).
fof(less4,axiom,
! [X] :
( less(X,n4)
<=> less_or_equal(X,n3) ),
file('theBenchmark.p',less4) ).
fof(less_property,axiom,
! [X,Y] :
( less(X,Y)
<=> ( Y != X
& ~ less(Y,X) ) ),
file('theBenchmark.p',less_property) ).
fof(waterlevel_not_3,conjecture,
~ holdsAt(waterLevel(n3),n2),
file('theBenchmark.p',waterlevel_not_3) ).
fof(waterlevel_not_3_neg,negated_conjecture,
~ ~ holdsAt(waterLevel(n3),n2),
inference(assume_negation,[status(cth)],[waterlevel_not_3]) ).
fof(nnf_1,plain,
! [Time1,Fluent,Time2] :
( ( ! [Event,Time] :
( ~ terminates(Event,Fluent,Time)
| ~ less(Time,Time2)
| ~ less(Time1,Time)
| ~ happens(Event,Time) )
| stoppedIn(Time1,Fluent,Time2) )
& ( ? [X0,X1] :
( terminates(X0,Fluent,X1)
& less(X1,Time2)
& less(Time1,X1)
& happens(X0,X1) )
| ~ stoppedIn(Time1,Fluent,Time2) ) ),
inference(fof_nnf,[status(thm)],[stoppedin_defn]) ).
fof(sk_stoppedin_defn_sk,plain,
! [Time1,Fluent,Time2] :
( ( ! [Event,Time] :
( ~ terminates(Event,Fluent,Time)
| ~ less(Time,Time2)
| ~ less(Time1,Time)
| ~ happens(Event,Time) )
| stoppedIn(Time1,Fluent,Time2) )
& ( ( terminates(sK1(Time1,Fluent,Time2),Fluent,sK0(Time1,Fluent,Time2))
& less(sK0(Time1,Fluent,Time2),Time2)
& less(Time1,sK0(Time1,Fluent,Time2))
& happens(sK1(Time1,Fluent,Time2),sK0(Time1,Fluent,Time2)) )
| ~ stoppedIn(Time1,Fluent,Time2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0]),skolemize(X0,sK1(Time1,Fluent,Time2)),skolemize(X1,sK0(Time1,Fluent,Time2))],[nnf_1]) ).
fof(sk_stoppedin_defn,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ~ terminates(VAR_3,VAR_1,VAR_4)
| ~ less(VAR_4,VAR_2)
| ~ less(VAR_0,VAR_4)
| ~ happens(VAR_3,VAR_4)
| stoppedIn(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1,VAR_2] :
( terminates(sK1(VAR_0,VAR_1,VAR_2),VAR_1,sK0(VAR_0,VAR_1,VAR_2))
| ~ stoppedIn(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1,VAR_2] :
( less(sK0(VAR_0,VAR_1,VAR_2),VAR_2)
| ~ stoppedIn(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1,VAR_2] :
( less(VAR_0,sK0(VAR_0,VAR_1,VAR_2))
| ~ stoppedIn(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1,VAR_2] :
( happens(sK1(VAR_0,VAR_1,VAR_2),sK0(VAR_0,VAR_1,VAR_2))
| ~ stoppedIn(VAR_0,VAR_1,VAR_2) ) ),
inference(cnf_transformation,[status(thm)],[sk_stoppedin_defn_sk]) ).
cnf(c_39,plain,
( less(sK0(A,B,C),C)
| ~ stoppedIn(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_stoppedin_defn]) ).
cnf(c_40,plain,
( less(A,sK0(A,B,C))
| ~ stoppedIn(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_stoppedin_defn]) ).
cnf(c_41,plain,
( happens(sK1(A,B,C),sK0(A,B,C))
| ~ stoppedIn(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_stoppedin_defn]) ).
cnf(c_42,plain,
( holdsAt(E,plus(B,D))
| stoppedIn(B,C,plus(B,D))
| ~ trajectory(C,B,E,D)
| ~ less(n0,D)
| ~ initiates(A,C,B)
| ~ happens(A,B) ),
inference(clausify,[status(thm)],[change_holding]) ).
cnf(c_50,plain,
( trajectory(filling,B,waterLevel(D),C)
| plus(A,C) != D
| ~ holdsAt(waterLevel(A),B) ),
inference(clausify,[status(thm)],[change_of_waterLevel]) ).
cnf(c_51,plain,
( less(sK0(B,C,plus(B,D)),plus(B,D))
| holdsAt(E,plus(B,D))
| ~ trajectory(C,B,E,D)
| ~ less(n0,D)
| ~ initiates(A,C,B)
| ~ happens(A,B) ),
inference(resolve,[status(thm)],[c_42,c_39]) ).
cnf(c_52,plain,
( less(B,sK0(B,C,plus(B,D)))
| holdsAt(E,plus(B,D))
| ~ trajectory(C,B,E,D)
| ~ less(n0,D)
| ~ initiates(A,C,B)
| ~ happens(A,B) ),
inference(resolve,[status(thm)],[c_42,c_40]) ).
cnf(c_53,plain,
( happens(sK1(B,C,plus(B,D)),sK0(B,C,plus(B,D)))
| holdsAt(E,plus(B,D))
| ~ trajectory(C,B,E,D)
| ~ less(n0,D)
| ~ initiates(A,C,B)
| ~ happens(A,B) ),
inference(resolve,[status(thm)],[c_42,c_41]) ).
fof(nnf_15,plain,
! [Event,Fluent,Time] :
( ( ! [Height] :
( waterLevel(Height) != Fluent
| tapOn != Event )
| releases(Event,Fluent,Time) )
& ( ? [X0] :
( waterLevel(X0) = Fluent
& tapOn = Event )
| ~ releases(Event,Fluent,Time) ) ),
inference(fof_nnf,[status(thm)],[releases_all_defn]) ).
fof(sk_releases_all_defn_sk,plain,
! [Event,Fluent,Time] :
( ( ! [Height] :
( waterLevel(Height) != Fluent
| tapOn != Event )
| releases(Event,Fluent,Time) )
& ( ( waterLevel(sK2(Event,Fluent,Time)) = Fluent
& tapOn = Event )
| ~ releases(Event,Fluent,Time) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2(Event,Fluent,Time))],[nnf_15]) ).
fof(sk_releases_all_defn,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( waterLevel(VAR_3) != VAR_1
| tapOn != VAR_0
| releases(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1,VAR_2] :
( waterLevel(sK2(VAR_0,VAR_1,VAR_2)) = VAR_1
| ~ releases(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1,VAR_2] :
( tapOn = VAR_0
| ~ releases(VAR_0,VAR_1,VAR_2) ) ),
inference(cnf_transformation,[status(thm)],[sk_releases_all_defn_sk]) ).
cnf(c_57,plain,
( waterLevel(sK2(A,B,C)) = B
| ~ releases(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_releases_all_defn]) ).
cnf(c_58,plain,
( waterLevel(D) != B
| tapOn != A
| releases(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_releases_all_defn]) ).
cnf(c_60,plain,
( waterLevel(sK2(A,C,D)) = C
| waterLevel(B) != C
| tapOn != A ),
inference(resolve,[status(thm)],[c_58,c_57]) ).
cnf(c_64,plain,
( plus(E,C) != D
| ~ holdsAt(waterLevel(E),B)
| happens(sK1(B,filling,plus(B,C)),sK0(B,filling,plus(B,C)))
| holdsAt(waterLevel(D),plus(B,C))
| ~ less(n0,C)
| ~ initiates(A,filling,B)
| ~ happens(A,B) ),
inference(resolve,[status(thm)],[c_53,c_50]) ).
cnf(c_65,plain,
( plus(E,C) != D
| ~ holdsAt(waterLevel(E),B)
| less(B,sK0(B,filling,plus(B,C)))
| holdsAt(waterLevel(D),plus(B,C))
| ~ less(n0,C)
| ~ initiates(A,filling,B)
| ~ happens(A,B) ),
inference(resolve,[status(thm)],[c_52,c_50]) ).
cnf(c_66,plain,
( plus(E,C) != D
| ~ holdsAt(waterLevel(E),B)
| less(sK0(B,filling,plus(B,C)),plus(B,C))
| holdsAt(waterLevel(D),plus(B,C))
| ~ less(n0,C)
| ~ initiates(A,filling,B)
| ~ happens(A,B) ),
inference(resolve,[status(thm)],[c_51,c_50]) ).
cnf(c_72,negated_conjecture,
holdsAt(waterLevel(n3),n2),
inference(clausify,[status(thm)],[waterlevel_not_3_neg]) ).
fof(waterLevel_0,axiom,
holdsAt(waterLevel(n0),n0),
file('theBenchmark.p',waterLevel_0) ).
cnf(c_78,plain,
holdsAt(waterLevel(n0),n0),
inference(clausify,[status(thm)],[waterLevel_0]) ).
cnf(c_79,plain,
( B = A
| less(B,A)
| less(A,B) ),
inference(clausify,[status(thm)],[less_property]) ).
cnf(c_80,plain,
( B != A
| ~ less(A,B) ),
inference(clausify,[status(thm)],[less_property]) ).
cnf(c_81,plain,
( ~ less(B,A)
| ~ less(A,B) ),
inference(clausify,[status(thm)],[less_property]) ).
cnf(c_92,plain,
( ~ less_or_equal(A,n3)
| less(A,n4) ),
inference(clausify,[status(thm)],[less4]) ).
cnf(c_93,plain,
( less_or_equal(A,n3)
| ~ less(A,n4) ),
inference(clausify,[status(thm)],[less4]) ).
cnf(c_94,plain,
( ~ less_or_equal(A,n2)
| less(A,n3) ),
inference(clausify,[status(thm)],[less3]) ).
cnf(c_95,plain,
( less_or_equal(A,n2)
| ~ less(A,n3) ),
inference(clausify,[status(thm)],[less3]) ).
cnf(c_96,plain,
( ~ less_or_equal(A,n1)
| less(A,n2) ),
inference(clausify,[status(thm)],[less2]) ).
cnf(c_97,plain,
( less_or_equal(A,n1)
| ~ less(A,n2) ),
inference(clausify,[status(thm)],[less2]) ).
cnf(c_98,plain,
( ~ less_or_equal(A,n0)
| less(A,n1) ),
inference(clausify,[status(thm)],[less1]) ).
cnf(c_99,plain,
( less_or_equal(A,n0)
| ~ less(A,n1) ),
inference(clausify,[status(thm)],[less1]) ).
cnf(c_100,plain,
~ less(A,n0),
inference(clausify,[status(thm)],[less0]) ).
cnf(c_101,plain,
( B != A
| less_or_equal(A,B) ),
inference(clausify,[status(thm)],[less_or_equal]) ).
cnf(c_102,plain,
( ~ less(A,B)
| less_or_equal(A,B) ),
inference(clausify,[status(thm)],[less_or_equal]) ).
cnf(c_103,plain,
( B = A
| less(A,B)
| ~ less_or_equal(A,B) ),
inference(clausify,[status(thm)],[less_or_equal]) ).
cnf(c_104,plain,
plus(A,B) = plus(B,A),
inference(clausify,[status(thm)],[symmetry_of_plus]) ).
fof(plus0_2,axiom,
plus(n0,n2) = n2,
file('theBenchmark.p',plus0_2) ).
cnf(c_113,plain,
plus(n0,n2) = n2,
inference(clausify,[status(thm)],[plus0_2]) ).
fof(plus0_1,axiom,
plus(n0,n1) = n1,
file('theBenchmark.p',plus0_1) ).
cnf(c_114,plain,
plus(n0,n1) = n1,
inference(clausify,[status(thm)],[plus0_1]) ).
cnf(c_115,plain,
plus(n1,n0) = n1,
inference(paramod,[status(thm)],[c_104,c_114]) ).
fof(plus0_0,axiom,
plus(n0,n0) = n0,
file('theBenchmark.p',plus0_0) ).
cnf(c_116,plain,
plus(n0,n0) = n0,
inference(clausify,[status(thm)],[plus0_0]) ).
cnf(c_118,plain,
( A = B
| waterLevel(A) != waterLevel(B) ),
inference(clausify,[status(thm)],[distinct_waterLevels]) ).
cnf(c_126,plain,
( C = A
| ~ holdsAt(waterLevel(C),B)
| ~ holdsAt(waterLevel(A),B) ),
inference(clausify,[status(thm)],[same_waterLevel]) ).
cnf(c_128,plain,
( n0 != B
| tapOn != A
| happens(A,B) ),
inference(clausify,[status(thm)],[happens_all_defn]) ).
cnf(c_131,plain,
( holdsAt(waterLevel(n3),B)
| n0 = B
| ~ happens(A,B) ),
inference(clausify,[status(thm)],[happens_all_defn]) ).
cnf(c_142,plain,
( filling != B
| tapOn != A
| initiates(A,B,C) ),
inference(clausify,[status(thm)],[initiates_all_defn]) ).
cnf(c_180,plain,
~ less(A,A),
inference(factor,[status(thm)],[c_81]) ).
cnf(c_181,plain,
( waterLevel(sK2(tapOn,B,C)) = B
| waterLevel(A) != B ),
inference(xxres,[status(thm)],[c_60]) ).
cnf(c_4043,plain,
( A = n4
| less(n4,A)
| less_or_equal(A,n3) ),
inference(resolve,[status(thm)],[c_93,c_79]) ).
cnf(c_189,plain,
( n4 = A
| less(n4,A)
| less_or_equal(A,n3) ),
inference(copy,[status(thm)],[c_4043]) ).
cnf(c_4044,plain,
( A = n3
| less(n3,A)
| less_or_equal(A,n2) ),
inference(resolve,[status(thm)],[c_95,c_79]) ).
cnf(c_190,plain,
( n3 = A
| less(n3,A)
| less_or_equal(A,n2) ),
inference(copy,[status(thm)],[c_4044]) ).
cnf(c_4045,plain,
( A = n2
| less(n2,A)
| less_or_equal(A,n1) ),
inference(resolve,[status(thm)],[c_97,c_79]) ).
cnf(c_191,plain,
( n2 = A
| less(n2,A)
| less_or_equal(A,n1) ),
inference(copy,[status(thm)],[c_4045]) ).
cnf(c_4046,plain,
( A = n1
| less(n1,A)
| less_or_equal(A,n0) ),
inference(resolve,[status(thm)],[c_99,c_79]) ).
cnf(c_192,plain,
( n1 = A
| less(n1,A)
| less_or_equal(A,n0) ),
inference(copy,[status(thm)],[c_4046]) ).
cnf(c_194,plain,
less_or_equal(A,A),
inference(xxres,[status(thm)],[c_101]) ).
cnf(c_4047,negated_conjecture,
( A = n3
| ~ holdsAt(waterLevel(A),n2) ),
inference(resolve,[status(thm)],[c_126,c_72]) ).
cnf(c_203,negated_conjecture,
( n3 = A
| ~ holdsAt(waterLevel(A),n2) ),
inference(copy,[status(thm)],[c_4047]) ).
cnf(c_205,plain,
( n0 != A
| happens(tapOn,A) ),
inference(xxres,[status(thm)],[c_128]) ).
cnf(c_217,plain,
( filling != A
| initiates(tapOn,A,B) ),
inference(xxres,[status(thm)],[c_142]) ).
cnf(c_229,plain,
waterLevel(sK2(tapOn,waterLevel(A),B)) = waterLevel(A),
inference(xxres,[status(thm)],[c_181]) ).
cnf(c_230,plain,
less(n0,n1),
inference(resolve,[status(thm)],[c_194,c_98]) ).
cnf(c_231,plain,
less(n1,n2),
inference(resolve,[status(thm)],[c_194,c_96]) ).
cnf(c_232,plain,
less(n2,n3),
inference(resolve,[status(thm)],[c_194,c_94]) ).
cnf(c_239,plain,
less_or_equal(n0,n1),
inference(resolve,[status(thm)],[c_230,c_102]) ).
cnf(c_4048,plain,
n1 != n0,
inference(resolve,[status(thm)],[c_230,c_80]) ).
cnf(c_240,plain,
n0 != n1,
inference(copy,[status(thm)],[c_4048]) ).
cnf(c_241,plain,
less_or_equal(n1,n2),
inference(resolve,[status(thm)],[c_231,c_102]) ).
cnf(c_4049,plain,
n3 != n2,
inference(resolve,[status(thm)],[c_232,c_80]) ).
cnf(c_246,plain,
n2 != n3,
inference(copy,[status(thm)],[c_4049]) ).
cnf(c_265,plain,
less(n0,n2),
inference(resolve,[status(thm)],[c_239,c_96]) ).
cnf(c_266,plain,
less(n1,n3),
inference(resolve,[status(thm)],[c_241,c_94]) ).
cnf(c_275,plain,
less_or_equal(n0,n2),
inference(resolve,[status(thm)],[c_265,c_102]) ).
cnf(c_276,plain,
n2 != n0,
inference(resolve,[status(thm)],[c_265,c_80]) ).
cnf(c_280,plain,
n3 != n1,
inference(resolve,[status(thm)],[c_266,c_80]) ).
cnf(c_300,plain,
less(n0,n3),
inference(resolve,[status(thm)],[c_275,c_94]) ).
cnf(c_306,plain,
( n3 = A
| less(A,n3)
| n4 = A
| less(n4,A) ),
inference(resolve,[status(thm)],[c_189,c_103]) ).
cnf(c_309,plain,
less_or_equal(n0,n3),
inference(resolve,[status(thm)],[c_300,c_102]) ).
cnf(c_310,plain,
n3 != n0,
inference(resolve,[status(thm)],[c_300,c_80]) ).
cnf(c_311,plain,
( n2 = A
| less(A,n2)
| n3 = A
| less(n3,A) ),
inference(resolve,[status(thm)],[c_190,c_103]) ).
cnf(c_324,plain,
( n1 = A
| less(A,n1)
| n2 = A
| less(n2,A) ),
inference(resolve,[status(thm)],[c_191,c_103]) ).
cnf(c_331,plain,
less(n0,n4),
inference(resolve,[status(thm)],[c_309,c_92]) ).
cnf(c_4050,plain,
( n0 = A
| less(A,n0)
| n1 = A
| less(n1,A) ),
inference(resolve,[status(thm)],[c_192,c_103]) ).
cnf(c_333,plain,
( n0 = A
| n1 = A
| less(n1,A) ),
inference(resolve,[status(thm)],[c_100,c_4050]) ).
cnf(c_345,plain,
n4 != n0,
inference(resolve,[status(thm)],[c_331,c_80]) ).
cnf(c_4051,plain,
n0 = plus(n0,n0),
inference(copy,[status(thm)],[c_116]) ).
cnf(c_4052,plain,
happens(tapOn,plus(n0,n0)),
inference(resolve,[status(thm)],[c_205,c_4051]) ).
cnf(c_430,plain,
happens(tapOn,n0),
inference(paramod,[status(thm)],[c_116,c_4052]) ).
cnf(c_460,plain,
initiates(tapOn,filling,A),
inference(xxres,[status(thm)],[c_217]) ).
cnf(c_468,plain,
( plus(D,B) != C
| ~ holdsAt(waterLevel(D),A)
| less(sK0(A,filling,plus(A,B)),plus(A,B))
| holdsAt(waterLevel(C),plus(A,B))
| ~ less(n0,B)
| ~ happens(tapOn,A) ),
inference(resolve,[status(thm)],[c_460,c_66]) ).
cnf(c_469,plain,
( plus(D,B) != C
| ~ holdsAt(waterLevel(D),A)
| less(A,sK0(A,filling,plus(A,B)))
| holdsAt(waterLevel(C),plus(A,B))
| ~ less(n0,B)
| ~ happens(tapOn,A) ),
inference(resolve,[status(thm)],[c_460,c_65]) ).
cnf(c_470,plain,
( plus(D,B) != C
| ~ holdsAt(waterLevel(D),A)
| happens(sK1(A,filling,plus(A,B)),sK0(A,filling,plus(A,B)))
| holdsAt(waterLevel(C),plus(A,B))
| ~ less(n0,B)
| ~ happens(tapOn,A) ),
inference(resolve,[status(thm)],[c_460,c_64]) ).
cnf(c_535,plain,
sK2(tapOn,waterLevel(A),B) = A,
inference(resolve,[status(thm)],[c_229,c_118]) ).
cnf(c_537,plain,
( ~ less(A,n1)
| n0 = A
| n1 = A ),
inference(resolve,[status(thm)],[c_333,c_81]) ).
cnf(c_619,plain,
( less_or_equal(A,n2)
| n3 = A
| n4 = A
| less(n4,A) ),
inference(resolve,[status(thm)],[c_306,c_95]) ).
cnf(c_623,plain,
( less_or_equal(A,n1)
| n2 = A
| n3 = A
| less(n3,A) ),
inference(resolve,[status(thm)],[c_311,c_97]) ).
cnf(c_4053,plain,
( n0 = A
| n1 = A
| n1 = A
| n2 = A
| less(n2,A) ),
inference(resolve,[status(thm)],[c_324,c_537]) ).
cnf(c_628,plain,
( n0 = A
| n1 = A
| n2 = A
| less(n2,A) ),
inference(copy,[status(thm)],[c_4053]) ).
cnf(c_778,plain,
( plus(C,A) != B
| ~ holdsAt(waterLevel(C),n0)
| less(sK0(n0,filling,plus(n0,A)),plus(n0,A))
| holdsAt(waterLevel(B),plus(n0,A))
| ~ less(n0,A) ),
inference(resolve,[status(thm)],[c_468,c_430]) ).
cnf(c_796,plain,
( plus(C,A) != B
| ~ holdsAt(waterLevel(C),n0)
| less(n0,sK0(n0,filling,plus(n0,A)))
| holdsAt(waterLevel(B),plus(n0,A))
| ~ less(n0,A) ),
inference(resolve,[status(thm)],[c_469,c_430]) ).
cnf(c_799,plain,
( plus(C,A) != B
| ~ holdsAt(waterLevel(C),n0)
| happens(sK1(n0,filling,plus(n0,A)),sK0(n0,filling,plus(n0,A)))
| holdsAt(waterLevel(B),plus(n0,A))
| ~ less(n0,A) ),
inference(resolve,[status(thm)],[c_470,c_430]) ).
cnf(c_990,plain,
( n2 = A
| less(A,n2)
| n3 = A
| n4 = A
| less(n4,A) ),
inference(resolve,[status(thm)],[c_619,c_103]) ).
cnf(c_991,plain,
( n1 = A
| less(A,n1)
| n2 = A
| n3 = A
| less(n3,A) ),
inference(resolve,[status(thm)],[c_623,c_103]) ).
cnf(c_994,plain,
( ~ less(A,n2)
| n0 = A
| n1 = A
| n2 = A ),
inference(resolve,[status(thm)],[c_628,c_81]) ).
cnf(c_1038,plain,
( plus(n0,A) != B
| less(sK0(n0,filling,plus(n0,A)),plus(n0,A))
| holdsAt(waterLevel(B),plus(n0,A))
| ~ less(n0,A) ),
inference(resolve,[status(thm)],[c_778,c_78]) ).
cnf(c_1046,plain,
( plus(n0,A) != B
| less(n0,sK0(n0,filling,plus(n0,A)))
| holdsAt(waterLevel(B),plus(n0,A))
| ~ less(n0,A) ),
inference(resolve,[status(thm)],[c_796,c_78]) ).
cnf(c_1071,plain,
( plus(n0,A) != B
| happens(sK1(n0,filling,plus(n0,A)),sK0(n0,filling,plus(n0,A)))
| holdsAt(waterLevel(B),plus(n0,A))
| ~ less(n0,A) ),
inference(resolve,[status(thm)],[c_799,c_78]) ).
cnf(c_4054,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| plus(n0,n1) != A
| less(sK0(n0,filling,plus(n0,n1)),plus(n0,n1))
| holdsAt(waterLevel(A),plus(n0,n1)) ),
inference(resolve,[status(thm)],[c_1038,c_991]) ).
cnf(c_4055,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| plus(n0,n1) != A
| less(sK0(n0,filling,plus(n0,n1)),plus(n0,n1))
| holdsAt(waterLevel(A),plus(n1,n0)) ),
inference(paramod,[status(thm)],[c_104,c_4054]) ).
cnf(c_4056,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| plus(n0,n1) != A
| less(sK0(n0,filling,plus(n0,n1)),plus(n0,n1))
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_115,c_4055]) ).
cnf(c_4057,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| plus(n0,n1) != A
| less(sK0(n0,filling,plus(n1,n0)),plus(n0,n1))
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_104,c_4056]) ).
cnf(c_4058,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| plus(n0,n1) != A
| less(sK0(n0,filling,n1),plus(n0,n1))
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_115,c_4057]) ).
cnf(c_4059,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| plus(n0,n1) != A
| less(sK0(n0,filling,n1),plus(n1,n0))
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_104,c_4058]) ).
cnf(c_4060,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| plus(n0,n1) != A
| less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_115,c_4059]) ).
cnf(c_4061,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| plus(n1,n0) != A
| less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_104,c_4060]) ).
cnf(c_4062,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| n1 != A
| less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_115,c_4061]) ).
cnf(c_4063,plain,
( n0 = n1
| n2 = n0
| n3 = n0
| less(n3,n0)
| n1 != A
| less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(A),n1) ),
inference(copy,[status(thm)],[c_4062]) ).
cnf(c_4064,plain,
( n0 = n1
| n2 = n0
| n3 = n0
| n1 != A
| less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(A),n1) ),
inference(resolve,[status(thm)],[c_100,c_4063]) ).
cnf(c_4065,plain,
( n0 = n1
| n2 = n0
| n1 != A
| less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(A),n1) ),
inference(resolve,[status(thm)],[c_310,c_4064]) ).
cnf(c_4066,plain,
( n0 = n1
| n1 != A
| less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(A),n1) ),
inference(resolve,[status(thm)],[c_276,c_4065]) ).
cnf(c_3077,plain,
( n1 != A
| less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(A),n1) ),
inference(resolve,[status(thm)],[c_240,c_4066]) ).
cnf(c_4067,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| less(n4,n0)
| plus(n0,n2) != A
| less(sK0(n0,filling,plus(n0,n2)),plus(n0,n2))
| holdsAt(waterLevel(A),plus(n0,n2)) ),
inference(resolve,[status(thm)],[c_1038,c_990]) ).
cnf(c_4068,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| less(n4,n0)
| plus(n0,n2) != A
| less(sK0(n0,filling,plus(n0,n2)),plus(n0,n2))
| holdsAt(waterLevel(A),n2) ),
inference(paramod,[status(thm)],[c_113,c_4067]) ).
cnf(c_4069,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| less(n4,n0)
| plus(n0,n2) != A
| less(sK0(n0,filling,n2),plus(n0,n2))
| holdsAt(waterLevel(A),n2) ),
inference(paramod,[status(thm)],[c_113,c_4068]) ).
cnf(c_4070,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| less(n4,n0)
| plus(n0,n2) != A
| less(sK0(n0,filling,n2),n2)
| holdsAt(waterLevel(A),n2) ),
inference(paramod,[status(thm)],[c_113,c_4069]) ).
cnf(c_4071,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| less(n4,n0)
| n2 != A
| less(sK0(n0,filling,n2),n2)
| holdsAt(waterLevel(A),n2) ),
inference(paramod,[status(thm)],[c_113,c_4070]) ).
cnf(c_4072,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| n2 != A
| less(sK0(n0,filling,n2),n2)
| holdsAt(waterLevel(A),n2) ),
inference(resolve,[status(thm)],[c_100,c_4071]) ).
cnf(c_4073,plain,
( n2 = n0
| n3 = n0
| n2 != A
| less(sK0(n0,filling,n2),n2)
| holdsAt(waterLevel(A),n2) ),
inference(resolve,[status(thm)],[c_345,c_4072]) ).
cnf(c_4074,plain,
( n2 = n0
| n2 != A
| less(sK0(n0,filling,n2),n2)
| holdsAt(waterLevel(A),n2) ),
inference(resolve,[status(thm)],[c_310,c_4073]) ).
cnf(c_3078,plain,
( n2 != A
| less(sK0(n0,filling,n2),n2)
| holdsAt(waterLevel(A),n2) ),
inference(resolve,[status(thm)],[c_276,c_4074]) ).
cnf(c_4075,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| plus(n0,n1) != A
| less(n0,sK0(n0,filling,plus(n0,n1)))
| holdsAt(waterLevel(A),plus(n0,n1)) ),
inference(resolve,[status(thm)],[c_1046,c_991]) ).
cnf(c_4076,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| plus(n0,n1) != A
| less(n0,sK0(n0,filling,plus(n0,n1)))
| holdsAt(waterLevel(A),plus(n1,n0)) ),
inference(paramod,[status(thm)],[c_104,c_4075]) ).
cnf(c_4077,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| plus(n0,n1) != A
| less(n0,sK0(n0,filling,plus(n0,n1)))
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_115,c_4076]) ).
cnf(c_4078,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| plus(n0,n1) != A
| less(n0,sK0(n0,filling,plus(n1,n0)))
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_104,c_4077]) ).
cnf(c_4079,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| plus(n0,n1) != A
| less(n0,sK0(n0,filling,n1))
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_115,c_4078]) ).
cnf(c_4080,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| plus(n1,n0) != A
| less(n0,sK0(n0,filling,n1))
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_104,c_4079]) ).
cnf(c_4081,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| n1 != A
| less(n0,sK0(n0,filling,n1))
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_115,c_4080]) ).
cnf(c_4082,plain,
( n0 = n1
| n2 = n0
| n3 = n0
| less(n3,n0)
| n1 != A
| less(n0,sK0(n0,filling,n1))
| holdsAt(waterLevel(A),n1) ),
inference(copy,[status(thm)],[c_4081]) ).
cnf(c_4083,plain,
( n0 = n1
| n2 = n0
| n3 = n0
| n1 != A
| less(n0,sK0(n0,filling,n1))
| holdsAt(waterLevel(A),n1) ),
inference(resolve,[status(thm)],[c_100,c_4082]) ).
cnf(c_4084,plain,
( n0 = n1
| n2 = n0
| n1 != A
| less(n0,sK0(n0,filling,n1))
| holdsAt(waterLevel(A),n1) ),
inference(resolve,[status(thm)],[c_310,c_4083]) ).
cnf(c_4085,plain,
( n0 = n1
| n1 != A
| less(n0,sK0(n0,filling,n1))
| holdsAt(waterLevel(A),n1) ),
inference(resolve,[status(thm)],[c_276,c_4084]) ).
cnf(c_3179,plain,
( n1 != A
| less(n0,sK0(n0,filling,n1))
| holdsAt(waterLevel(A),n1) ),
inference(resolve,[status(thm)],[c_240,c_4085]) ).
cnf(c_4086,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| less(n4,n0)
| plus(n0,n2) != A
| less(n0,sK0(n0,filling,plus(n0,n2)))
| holdsAt(waterLevel(A),plus(n0,n2)) ),
inference(resolve,[status(thm)],[c_1046,c_990]) ).
cnf(c_4087,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| less(n4,n0)
| plus(n0,n2) != A
| less(n0,sK0(n0,filling,plus(n0,n2)))
| holdsAt(waterLevel(A),n2) ),
inference(paramod,[status(thm)],[c_113,c_4086]) ).
cnf(c_4088,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| less(n4,n0)
| plus(n0,n2) != A
| less(n0,sK0(n0,filling,n2))
| holdsAt(waterLevel(A),n2) ),
inference(paramod,[status(thm)],[c_113,c_4087]) ).
cnf(c_4089,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| less(n4,n0)
| n2 != A
| less(n0,sK0(n0,filling,n2))
| holdsAt(waterLevel(A),n2) ),
inference(paramod,[status(thm)],[c_113,c_4088]) ).
cnf(c_4090,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| n2 != A
| less(n0,sK0(n0,filling,n2))
| holdsAt(waterLevel(A),n2) ),
inference(resolve,[status(thm)],[c_100,c_4089]) ).
cnf(c_4091,plain,
( n2 = n0
| n3 = n0
| n2 != A
| less(n0,sK0(n0,filling,n2))
| holdsAt(waterLevel(A),n2) ),
inference(resolve,[status(thm)],[c_345,c_4090]) ).
cnf(c_4092,plain,
( n2 = n0
| n2 != A
| less(n0,sK0(n0,filling,n2))
| holdsAt(waterLevel(A),n2) ),
inference(resolve,[status(thm)],[c_310,c_4091]) ).
cnf(c_3180,plain,
( n2 != A
| less(n0,sK0(n0,filling,n2))
| holdsAt(waterLevel(A),n2) ),
inference(resolve,[status(thm)],[c_276,c_4092]) ).
cnf(c_4093,plain,
A = sK2(tapOn,waterLevel(A),B),
inference(copy,[status(thm)],[c_535]) ).
cnf(c_4094,plain,
( less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(sK2(tapOn,waterLevel(n1),A)),n1) ),
inference(resolve,[status(thm)],[c_3077,c_4093]) ).
cnf(c_3477,plain,
( less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(n1),n1) ),
inference(paramod,[status(thm)],[c_535,c_4094]) ).
cnf(c_3484,plain,
( n1 = A
| ~ holdsAt(waterLevel(A),n1)
| less(sK0(n0,filling,n1),n1) ),
inference(resolve,[status(thm)],[c_3477,c_126]) ).
cnf(c_4095,plain,
A = sK2(tapOn,waterLevel(A),B),
inference(copy,[status(thm)],[c_535]) ).
cnf(c_4096,plain,
( less(sK0(n0,filling,n2),n2)
| holdsAt(waterLevel(sK2(tapOn,waterLevel(n2),A)),n2) ),
inference(resolve,[status(thm)],[c_3078,c_4095]) ).
cnf(c_3565,plain,
( less(sK0(n0,filling,n2),n2)
| holdsAt(waterLevel(n2),n2) ),
inference(paramod,[status(thm)],[c_535,c_4096]) ).
cnf(c_4097,plain,
( n3 = n2
| less(sK0(n0,filling,n2),n2) ),
inference(resolve,[status(thm)],[c_3565,c_203]) ).
cnf(c_4098,plain,
( n2 = n3
| less(sK0(n0,filling,n2),n2) ),
inference(copy,[status(thm)],[c_4097]) ).
cnf(c_3568,plain,
less(sK0(n0,filling,n2),n2),
inference(resolve,[status(thm)],[c_246,c_4098]) ).
cnf(c_4099,plain,
( n0 = sK0(n0,filling,n2)
| n1 = sK0(n0,filling,n2)
| n2 = sK0(n0,filling,n2) ),
inference(resolve,[status(thm)],[c_3568,c_994]) ).
cnf(c_4100,plain,
( n0 = sK0(n0,filling,n2)
| n1 = sK0(n0,filling,n2)
| sK0(n0,filling,n2) = n2 ),
inference(copy,[status(thm)],[c_4099]) ).
cnf(c_4101,plain,
( n0 = sK0(n0,filling,n2)
| sK0(n0,filling,n2) = n1
| sK0(n0,filling,n2) = n2 ),
inference(copy,[status(thm)],[c_4100]) ).
cnf(c_3580,plain,
( sK0(n0,filling,n2) = n0
| sK0(n0,filling,n2) = n1
| sK0(n0,filling,n2) = n2 ),
inference(copy,[status(thm)],[c_4101]) ).
cnf(c_4102,plain,
n2 != sK0(n0,filling,n2),
inference(resolve,[status(thm)],[c_3568,c_80]) ).
cnf(c_3604,plain,
sK0(n0,filling,n2) != n2,
inference(copy,[status(thm)],[c_4102]) ).
cnf(c_3613,plain,
( sK0(n0,filling,n2) = n0
| sK0(n0,filling,n2) = n1 ),
inference(resolve,[status(thm)],[c_3604,c_3580]) ).
cnf(c_4103,plain,
A = sK2(tapOn,waterLevel(A),B),
inference(copy,[status(thm)],[c_535]) ).
cnf(c_4104,plain,
( less(n0,sK0(n0,filling,n1))
| holdsAt(waterLevel(sK2(tapOn,waterLevel(n1),A)),n1) ),
inference(resolve,[status(thm)],[c_3179,c_4103]) ).
cnf(c_3742,plain,
( less(n0,sK0(n0,filling,n1))
| holdsAt(waterLevel(n1),n1) ),
inference(paramod,[status(thm)],[c_535,c_4104]) ).
cnf(c_3749,plain,
( n1 = A
| ~ holdsAt(waterLevel(A),n1)
| less(n0,sK0(n0,filling,n1)) ),
inference(resolve,[status(thm)],[c_3742,c_126]) ).
cnf(c_4105,plain,
A = sK2(tapOn,waterLevel(A),B),
inference(copy,[status(thm)],[c_535]) ).
cnf(c_4106,plain,
( less(n0,sK0(n0,filling,n2))
| holdsAt(waterLevel(sK2(tapOn,waterLevel(n2),A)),n2) ),
inference(resolve,[status(thm)],[c_3180,c_4105]) ).
cnf(c_3784,plain,
( less(n0,sK0(n0,filling,n2))
| holdsAt(waterLevel(n2),n2) ),
inference(paramod,[status(thm)],[c_535,c_4106]) ).
cnf(c_4107,plain,
( n3 = n2
| less(n0,sK0(n0,filling,n2)) ),
inference(resolve,[status(thm)],[c_3784,c_203]) ).
cnf(c_4108,plain,
( n2 = n3
| less(n0,sK0(n0,filling,n2)) ),
inference(copy,[status(thm)],[c_4107]) ).
cnf(c_3787,plain,
less(n0,sK0(n0,filling,n2)),
inference(resolve,[status(thm)],[c_246,c_4108]) ).
cnf(c_4109,plain,
( less(n0,n0)
| sK0(n0,filling,n2) = n1 ),
inference(paramod,[status(thm)],[c_3613,c_3787]) ).
cnf(c_3795,plain,
sK0(n0,filling,n2) = n1,
inference(resolve,[status(thm)],[c_180,c_4109]) ).
cnf(c_4110,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| less(n4,n0)
| plus(n0,n2) != A
| happens(sK1(n0,filling,plus(n0,n2)),sK0(n0,filling,plus(n0,n2)))
| holdsAt(waterLevel(A),plus(n0,n2)) ),
inference(resolve,[status(thm)],[c_1071,c_990]) ).
cnf(c_4111,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| less(n4,n0)
| plus(n0,n2) != A
| happens(sK1(n0,filling,plus(n0,n2)),sK0(n0,filling,plus(n0,n2)))
| holdsAt(waterLevel(A),n2) ),
inference(paramod,[status(thm)],[c_113,c_4110]) ).
cnf(c_4112,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| less(n4,n0)
| plus(n0,n2) != A
| happens(sK1(n0,filling,n2),sK0(n0,filling,plus(n0,n2)))
| holdsAt(waterLevel(A),n2) ),
inference(paramod,[status(thm)],[c_113,c_4111]) ).
cnf(c_4113,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| less(n4,n0)
| plus(n0,n2) != A
| happens(sK1(n0,filling,n2),sK0(n0,filling,n2))
| holdsAt(waterLevel(A),n2) ),
inference(paramod,[status(thm)],[c_113,c_4112]) ).
cnf(c_4114,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| less(n4,n0)
| plus(n0,n2) != A
| happens(sK1(n0,filling,n2),n1)
| holdsAt(waterLevel(A),n2) ),
inference(paramod,[status(thm)],[c_3795,c_4113]) ).
cnf(c_4115,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| less(n4,n0)
| n2 != A
| happens(sK1(n0,filling,n2),n1)
| holdsAt(waterLevel(A),n2) ),
inference(paramod,[status(thm)],[c_113,c_4114]) ).
cnf(c_4116,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| n2 != A
| happens(sK1(n0,filling,n2),n1)
| holdsAt(waterLevel(A),n2) ),
inference(resolve,[status(thm)],[c_100,c_4115]) ).
cnf(c_4117,plain,
( n2 = n0
| n3 = n0
| n2 != A
| happens(sK1(n0,filling,n2),n1)
| holdsAt(waterLevel(A),n2) ),
inference(resolve,[status(thm)],[c_345,c_4116]) ).
cnf(c_4118,plain,
( n2 = n0
| n2 != A
| happens(sK1(n0,filling,n2),n1)
| holdsAt(waterLevel(A),n2) ),
inference(resolve,[status(thm)],[c_310,c_4117]) ).
cnf(c_3841,plain,
( n2 != A
| happens(sK1(n0,filling,n2),n1)
| holdsAt(waterLevel(A),n2) ),
inference(resolve,[status(thm)],[c_276,c_4118]) ).
cnf(c_4119,plain,
A = sK2(tapOn,waterLevel(A),B),
inference(copy,[status(thm)],[c_535]) ).
cnf(c_4120,plain,
( happens(sK1(n0,filling,n2),n1)
| holdsAt(waterLevel(sK2(tapOn,waterLevel(n2),A)),n2) ),
inference(resolve,[status(thm)],[c_3841,c_4119]) ).
cnf(c_3971,plain,
( happens(sK1(n0,filling,n2),n1)
| holdsAt(waterLevel(n2),n2) ),
inference(paramod,[status(thm)],[c_535,c_4120]) ).
cnf(c_4121,plain,
( holdsAt(waterLevel(n3),n1)
| n0 = n1
| holdsAt(waterLevel(n2),n2) ),
inference(resolve,[status(thm)],[c_3971,c_131]) ).
cnf(c_3974,plain,
( holdsAt(waterLevel(n3),n1)
| holdsAt(waterLevel(n2),n2) ),
inference(resolve,[status(thm)],[c_240,c_4121]) ).
cnf(c_4122,plain,
( n3 = n2
| holdsAt(waterLevel(n3),n1) ),
inference(resolve,[status(thm)],[c_3974,c_203]) ).
cnf(c_4123,plain,
( n2 = n3
| holdsAt(waterLevel(n3),n1) ),
inference(copy,[status(thm)],[c_4122]) ).
cnf(c_3979,plain,
holdsAt(waterLevel(n3),n1),
inference(resolve,[status(thm)],[c_246,c_4123]) ).
cnf(c_4124,plain,
( n1 = n3
| less(n0,sK0(n0,filling,n1)) ),
inference(resolve,[status(thm)],[c_3979,c_3749]) ).
cnf(c_4125,plain,
( n3 = n1
| less(n0,sK0(n0,filling,n1)) ),
inference(copy,[status(thm)],[c_4124]) ).
cnf(c_3980,plain,
less(n0,sK0(n0,filling,n1)),
inference(resolve,[status(thm)],[c_280,c_4125]) ).
cnf(c_4126,plain,
( n1 = n3
| less(sK0(n0,filling,n1),n1) ),
inference(resolve,[status(thm)],[c_3979,c_3484]) ).
cnf(c_4127,plain,
( n3 = n1
| less(sK0(n0,filling,n1),n1) ),
inference(copy,[status(thm)],[c_4126]) ).
cnf(c_3981,plain,
less(sK0(n0,filling,n1),n1),
inference(resolve,[status(thm)],[c_280,c_4127]) ).
cnf(c_3991,plain,
sK0(n0,filling,n1) != n0,
inference(resolve,[status(thm)],[c_3980,c_80]) ).
cnf(c_4128,plain,
( n0 = sK0(n0,filling,n1)
| n1 = sK0(n0,filling,n1) ),
inference(resolve,[status(thm)],[c_3981,c_537]) ).
cnf(c_4129,plain,
( n0 = sK0(n0,filling,n1)
| sK0(n0,filling,n1) = n1 ),
inference(copy,[status(thm)],[c_4128]) ).
cnf(c_4130,plain,
( sK0(n0,filling,n1) = n0
| sK0(n0,filling,n1) = n1 ),
inference(copy,[status(thm)],[c_4129]) ).
cnf(c_4040,plain,
sK0(n0,filling,n1) = n1,
inference(resolve,[status(thm)],[c_3991,c_4130]) ).
cnf(c_4131,plain,
n1 != sK0(n0,filling,n1),
inference(resolve,[status(thm)],[c_3981,c_80]) ).
cnf(c_4132,plain,
n1 != n1,
inference(paramod,[status(thm)],[c_4040,c_4131]) ).
cnf(c_4042,plain,
$false,
inference(copy,[status(thm)],[c_4132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : CSR007+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.42 % Computer : n016.cluster.edu
% 0.18/0.42 % Model : x86_64 x86_64
% 0.18/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.42 % Memory : 8046.5625MB
% 0.18/0.42 % OS : Linux 6.8.0-71-generic
% 0.18/0.42 % CPULimit : 300
% 0.18/0.42 % WCLimit : 300
% 0.18/0.42 % DateTime : Sat Sep 26 23:59:31 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.43 % Process 2024220 was started by sandbox on n016,
% 0.18/0.43 % Sat Sep 26 23:59:31 2026
% 0.18/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 13.56/2.42
% 13.56/2.42 % given #500 (T,wt=9): 668 less(n5,A) | n5 = A | n7 != A. [resolve(625,c,80,a)].
% 13.56/2.42
% 13.56/2.42 % given #1000 (T,wt=9): 2016 holdsAt(filling,n2) | less(n0,f2(n0,filling,n2)). [resolve(1350,b,311,c),unit_del(c,279),unit_del(d,280),unit_del(e,243)].
% 13.56/2.42
% 13.56/2.42 % given #1500 (T,wt=12): 3916 f5(filling,n1) = overflow | less_or_equal(f10(overflow,waterLevel(n3),n3),n5). [resolve(3911,b,102,b)].
% 13.56/2.42
% 13.56/2.42 % SZS status Theorem for theBenchmark
% 13.56/2.42
% 13.56/2.42 % Proof 1 at 1.45 (+ 0.48) seconds.
% 13.56/2.42 % Length of proof is 134.
% 13.56/2.42 % Level of proof is 24.
% 13.56/2.42 % Maximum clause weight is 38.000.
% 13.56/2.42 % Given clauses 1536.
% 13.56/2.42
% 13.56/2.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------