%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CSR002+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 07:06:30 AM UTC 2026
% Result : Theorem 15.59s 2.45s
% Output : CNFRefutation 15.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 62
% Number of leaves : 30
% Syntax : Number of formulae : 294 ( 70 unt; 0 def)
% Number of atoms : 897 ( 319 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 860 ( 257 ~; 532 |; 52 &)
% ( 13 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-4 aty)
% Number of functors : 18 ( 18 usr; 11 con; 0-3 aty)
% Number of variables : 368 ( 29 sgn 108 !; 13 ?)
% 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(keep_not_holding,axiom,
! [Fluent,Time] :
( ( ~ ? [Event] :
( initiates(Event,Fluent,Time)
& happens(Event,Time) )
& ~ releasedAt(Fluent,plus(Time,n1))
& ~ holdsAt(Fluent,Time) )
=> ~ holdsAt(Fluent,plus(Time,n1)) ),
file('theBenchmark.p',keep_not_holding) ).
fof(keep_not_released,axiom,
! [Fluent,Time] :
( ( ~ ? [Event] :
( releases(Event,Fluent,Time)
& happens(Event,Time) )
& ~ releasedAt(Fluent,Time) )
=> ~ releasedAt(Fluent,plus(Time,n1)) ),
file('theBenchmark.p',keep_not_released) ).
fof(happens_terminates_not_holds,axiom,
! [Event,Time,Fluent] :
( ( terminates(Event,Fluent,Time)
& happens(Event,Time) )
=> ~ holdsAt(Fluent,plus(Time,n1)) ),
file('theBenchmark.p',happens_terminates_not_holds) ).
fof(happens_not_released,axiom,
! [Event,Time,Fluent] :
( ( ( terminates(Event,Fluent,Time)
| initiates(Event,Fluent,Time) )
& happens(Event,Time) )
=> ~ releasedAt(Fluent,plus(Time,n1)) ),
file('theBenchmark.p',happens_not_released) ).
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(terminates_all_defn,axiom,
! [Event,Fluent,Time] :
( terminates(Event,Fluent,Time)
<=> ( ( Fluent = filling
& Event = overflow )
| ( Fluent = filling
& Event = tapOff ) ) ),
file('theBenchmark.p',terminates_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(filling_not_waterLevel,axiom,
! [X] : filling != waterLevel(X),
file('theBenchmark.p',filling_not_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(less5,axiom,
! [X] :
( less(X,n5)
<=> less_or_equal(X,n4) ),
file('theBenchmark.p',less5) ).
fof(less_property,axiom,
! [X,Y] :
( less(X,Y)
<=> ( Y != X
& ~ less(Y,X) ) ),
file('theBenchmark.p',less_property) ).
fof(not_filling_4,conjecture,
~ holdsAt(filling,n4),
file('theBenchmark.p',not_filling_4) ).
fof(not_filling_4_neg,negated_conjecture,
~ ~ holdsAt(filling,n4),
inference(assume_negation,[status(cth)],[not_filling_4]) ).
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_8,plain,
! [Fluent,Time] :
( ~ releasedAt(Fluent,plus(Time,n1))
| ? [Event] :
( releases(Event,Fluent,Time)
& happens(Event,Time) )
| releasedAt(Fluent,Time) ),
inference(fof_nnf,[status(thm)],[keep_not_released]) ).
fof(sk_keep_not_released_sk,plain,
! [Fluent,Time] :
( ~ releasedAt(Fluent,plus(Time,n1))
| ( releases(sK2(Fluent,Time),Fluent,Time)
& happens(sK2(Fluent,Time),Time) )
| releasedAt(Fluent,Time) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(Event,sK2(Fluent,Time))],[nnf_8]) ).
fof(sk_keep_not_released,plain,
( ! [VAR_0,VAR_1] :
( ~ releasedAt(VAR_0,plus(VAR_1,n1))
| releases(sK2(VAR_0,VAR_1),VAR_0,VAR_1)
| releasedAt(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( ~ releasedAt(VAR_0,plus(VAR_1,n1))
| happens(sK2(VAR_0,VAR_1),VAR_1)
| releasedAt(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_keep_not_released_sk]) ).
cnf(c_55,plain,
( ~ releasedAt(A,plus(B,n1))
| releases(sK2(A,B),A,B)
| releasedAt(A,B) ),
inference(split_conjunct,[status(thm)],[sk_keep_not_released]) ).
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(sK3(Event,Fluent,Time)) = Fluent
& tapOn = Event )
| ~ releases(Event,Fluent,Time) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3(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(sK3(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(sK3(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(sK3(A,C,D)) = C
| waterLevel(B) != C
| tapOn != A ),
inference(resolve,[status(thm)],[c_58,c_57]) ).
cnf(c_61,plain,
( ~ releasedAt(A,plus(B,n1))
| releasedAt(A,B)
| waterLevel(sK3(sK2(A,B),A,B)) = A ),
inference(resolve,[status(thm)],[c_57,c_55]) ).
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(filling,n4),
inference(clausify,[status(thm)],[not_filling_4_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_90,plain,
( ~ less_or_equal(A,n4)
| less(A,n5) ),
inference(clausify,[status(thm)],[less5]) ).
cnf(c_91,plain,
( less_or_equal(A,n4)
| ~ less(A,n5) ),
inference(clausify,[status(thm)],[less5]) ).
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(plus1_3,axiom,
plus(n1,n3) = n4,
file('theBenchmark.p',plus1_3) ).
cnf(c_109,plain,
plus(n1,n3) = n4,
inference(clausify,[status(thm)],[plus1_3]) ).
fof(plus1_2,axiom,
plus(n1,n2) = n3,
file('theBenchmark.p',plus1_2) ).
cnf(c_110,plain,
plus(n1,n2) = n3,
inference(clausify,[status(thm)],[plus1_2]) ).
fof(plus1_1,axiom,
plus(n1,n1) = n2,
file('theBenchmark.p',plus1_1) ).
cnf(c_111,plain,
plus(n1,n1) = n2,
inference(clausify,[status(thm)],[plus1_1]) ).
fof(plus0_3,axiom,
plus(n0,n3) = n3,
file('theBenchmark.p',plus0_3) ).
cnf(c_112,plain,
plus(n0,n3) = n3,
inference(clausify,[status(thm)],[plus0_3]) ).
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_122,plain,
waterLevel(A) != filling,
inference(clausify,[status(thm)],[filling_not_waterLevel]) ).
cnf(c_127,plain,
( overflow != A
| ~ holdsAt(filling,B)
| ~ holdsAt(waterLevel(n3),B)
| happens(A,B) ),
inference(clausify,[status(thm)],[happens_all_defn]) ).
cnf(c_128,plain,
( n0 != B
| tapOn != A
| happens(A,B) ),
inference(clausify,[status(thm)],[happens_all_defn]) ).
cnf(c_129,plain,
( overflow = A
| n0 = B
| ~ happens(A,B) ),
inference(clausify,[status(thm)],[happens_all_defn]) ).
cnf(c_130,plain,
( holdsAt(filling,B)
| n0 = B
| ~ happens(A,B) ),
inference(clausify,[status(thm)],[happens_all_defn]) ).
cnf(c_135,plain,
( filling != B
| overflow != A
| terminates(A,B,C) ),
inference(clausify,[status(thm)],[terminates_all_defn]) ).
cnf(c_142,plain,
( filling != B
| tapOn != A
| initiates(A,B,C) ),
inference(clausify,[status(thm)],[initiates_all_defn]) ).
cnf(c_162,plain,
( ~ releasedAt(C,plus(B,n1))
| ~ initiates(A,C,B)
| ~ happens(A,B) ),
inference(clausify,[status(thm)],[happens_not_released]) ).
cnf(c_163,plain,
( ~ holdsAt(C,plus(B,n1))
| ~ terminates(A,C,B)
| ~ happens(A,B) ),
inference(clausify,[status(thm)],[happens_terminates_not_holds]) ).
fof(nnf_6,plain,
! [Fluent,Time] :
( ~ holdsAt(Fluent,plus(Time,n1))
| ? [Event] :
( initiates(Event,Fluent,Time)
& happens(Event,Time) )
| releasedAt(Fluent,plus(Time,n1))
| holdsAt(Fluent,Time) ),
inference(fof_nnf,[status(thm)],[keep_not_holding]) ).
fof(sk_keep_not_holding_sk,plain,
! [Fluent,Time] :
( ~ holdsAt(Fluent,plus(Time,n1))
| ( initiates(sK4(Fluent,Time),Fluent,Time)
& happens(sK4(Fluent,Time),Time) )
| releasedAt(Fluent,plus(Time,n1))
| holdsAt(Fluent,Time) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(Event,sK4(Fluent,Time))],[nnf_6]) ).
fof(sk_keep_not_holding,plain,
( ! [VAR_0,VAR_1] :
( ~ holdsAt(VAR_0,plus(VAR_1,n1))
| initiates(sK4(VAR_0,VAR_1),VAR_0,VAR_1)
| releasedAt(VAR_0,plus(VAR_1,n1))
| holdsAt(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( ~ holdsAt(VAR_0,plus(VAR_1,n1))
| happens(sK4(VAR_0,VAR_1),VAR_1)
| releasedAt(VAR_0,plus(VAR_1,n1))
| holdsAt(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_keep_not_holding_sk]) ).
cnf(c_169,plain,
( ~ holdsAt(A,plus(B,n1))
| happens(sK4(A,B),B)
| releasedAt(A,plus(B,n1))
| holdsAt(A,B) ),
inference(split_conjunct,[status(thm)],[sk_keep_not_holding]) ).
cnf(c_181,plain,
( waterLevel(sK3(tapOn,B,C)) = B
| waterLevel(A) != B ),
inference(xxres,[status(thm)],[c_60]) ).
cnf(c_2396,plain,
( A = n5
| less(n5,A)
| less_or_equal(A,n4) ),
inference(resolve,[status(thm)],[c_91,c_79]) ).
cnf(c_188,plain,
( n5 = A
| less(n5,A)
| less_or_equal(A,n4) ),
inference(copy,[status(thm)],[c_2396]) ).
cnf(c_2397,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_2397]) ).
cnf(c_2398,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_2398]) ).
cnf(c_2399,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_2399]) ).
cnf(c_194,plain,
less_or_equal(A,A),
inference(xxres,[status(thm)],[c_101]) ).
cnf(c_198,plain,
( ~ releasedAt(A,plus(n1,B))
| releasedAt(A,B)
| waterLevel(sK3(sK2(A,B),A,B)) = A ),
inference(paramod,[status(thm)],[c_104,c_61]) ).
cnf(c_200,plain,
( ~ releasedAt(A,n2)
| releasedAt(A,n1)
| waterLevel(sK3(sK2(A,n1),A,n1)) = A ),
inference(paramod,[status(thm)],[c_111,c_61]) ).
cnf(c_203,plain,
( n0 != A
| happens(tapOn,A) ),
inference(xxres,[status(thm)],[c_128]) ).
cnf(c_205,plain,
( filling != A
| terminates(overflow,A,B) ),
inference(xxres,[status(thm)],[c_135]) ).
cnf(c_213,plain,
( filling != A
| initiates(tapOn,A,B) ),
inference(xxres,[status(thm)],[c_142]) ).
cnf(c_219,plain,
( ~ holdsAt(A,plus(n1,B))
| happens(sK4(A,B),B)
| releasedAt(A,plus(B,n1))
| holdsAt(A,B) ),
inference(paramod,[status(thm)],[c_104,c_169]) ).
cnf(c_225,plain,
waterLevel(sK3(tapOn,waterLevel(A),B)) = waterLevel(A),
inference(xxres,[status(thm)],[c_181]) ).
cnf(c_226,plain,
less(n0,n1),
inference(resolve,[status(thm)],[c_194,c_98]) ).
cnf(c_235,plain,
less_or_equal(n0,n1),
inference(resolve,[status(thm)],[c_226,c_102]) ).
cnf(c_261,plain,
less(n0,n2),
inference(resolve,[status(thm)],[c_235,c_96]) ).
cnf(c_271,plain,
less_or_equal(n0,n2),
inference(resolve,[status(thm)],[c_261,c_102]) ).
cnf(c_272,plain,
n2 != n0,
inference(resolve,[status(thm)],[c_261,c_80]) ).
cnf(c_296,plain,
less(n0,n3),
inference(resolve,[status(thm)],[c_271,c_94]) ).
cnf(c_297,plain,
( n4 = A
| less(A,n4)
| n5 = A
| less(n5,A) ),
inference(resolve,[status(thm)],[c_188,c_103]) ).
cnf(c_305,plain,
less_or_equal(n0,n3),
inference(resolve,[status(thm)],[c_296,c_102]) ).
cnf(c_306,plain,
n3 != n0,
inference(resolve,[status(thm)],[c_296,c_80]) ).
cnf(c_307,plain,
( n2 = A
| less(A,n2)
| n3 = A
| less(n3,A) ),
inference(resolve,[status(thm)],[c_190,c_103]) ).
cnf(c_320,plain,
( n1 = A
| less(A,n1)
| n2 = A
| less(n2,A) ),
inference(resolve,[status(thm)],[c_191,c_103]) ).
cnf(c_327,plain,
less(n0,n4),
inference(resolve,[status(thm)],[c_305,c_92]) ).
cnf(c_2400,plain,
( n0 = A
| less(A,n0)
| n1 = A
| less(n1,A) ),
inference(resolve,[status(thm)],[c_192,c_103]) ).
cnf(c_329,plain,
( n0 = A
| n1 = A
| less(n1,A) ),
inference(resolve,[status(thm)],[c_100,c_2400]) ).
cnf(c_340,plain,
less_or_equal(n0,n4),
inference(resolve,[status(thm)],[c_327,c_102]) ).
cnf(c_341,plain,
n4 != n0,
inference(resolve,[status(thm)],[c_327,c_80]) ).
cnf(c_365,plain,
less(n0,n5),
inference(resolve,[status(thm)],[c_340,c_90]) ).
cnf(c_371,plain,
n5 != n0,
inference(resolve,[status(thm)],[c_365,c_80]) ).
cnf(c_378,plain,
( ~ releasedAt(A,n4)
| releasedAt(A,n3)
| waterLevel(sK3(sK2(A,n3),A,n3)) = A ),
inference(paramod,[status(thm)],[c_109,c_198]) ).
cnf(c_379,plain,
( ~ releasedAt(A,n3)
| releasedAt(A,n2)
| waterLevel(sK3(sK2(A,n2),A,n2)) = A ),
inference(paramod,[status(thm)],[c_110,c_198]) ).
cnf(c_2401,plain,
n0 = plus(n0,n0),
inference(copy,[status(thm)],[c_116]) ).
cnf(c_2402,plain,
happens(tapOn,plus(n0,n0)),
inference(resolve,[status(thm)],[c_203,c_2401]) ).
cnf(c_418,plain,
happens(tapOn,n0),
inference(paramod,[status(thm)],[c_116,c_2402]) ).
cnf(c_428,plain,
terminates(overflow,filling,A),
inference(xxres,[status(thm)],[c_205]) ).
cnf(c_429,plain,
( ~ holdsAt(filling,plus(A,n1))
| ~ happens(overflow,A) ),
inference(resolve,[status(thm)],[c_428,c_163]) ).
cnf(c_456,plain,
initiates(tapOn,filling,A),
inference(xxres,[status(thm)],[c_213]) ).
cnf(c_462,plain,
( ~ releasedAt(filling,plus(A,n1))
| ~ happens(tapOn,A) ),
inference(resolve,[status(thm)],[c_456,c_162]) ).
cnf(c_464,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_456,c_66]) ).
cnf(c_465,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_456,c_65]) ).
cnf(c_466,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_456,c_64]) ).
cnf(c_486,plain,
( ~ releasedAt(filling,plus(n1,A))
| ~ happens(tapOn,A) ),
inference(paramod,[status(thm)],[c_104,c_462]) ).
cnf(c_501,plain,
sK3(tapOn,waterLevel(A),B) = A,
inference(resolve,[status(thm)],[c_225,c_118]) ).
cnf(c_2403,plain,
( ~ releasedAt(filling,n1)
| ~ happens(tapOn,n0) ),
inference(paramod,[status(thm)],[c_115,c_486]) ).
cnf(c_507,plain,
~ releasedAt(filling,n1),
inference(resolve,[status(thm)],[c_418,c_2403]) ).
cnf(c_509,plain,
( ~ less(A,n1)
| n0 = A
| n1 = A ),
inference(resolve,[status(thm)],[c_329,c_81]) ).
cnf(c_2404,plain,
( ~ holdsAt(A,n4)
| happens(sK4(A,n3),n3)
| releasedAt(A,plus(n3,n1))
| holdsAt(A,n3) ),
inference(paramod,[status(thm)],[c_109,c_219]) ).
cnf(c_2405,plain,
( ~ holdsAt(A,n4)
| happens(sK4(A,n3),n3)
| releasedAt(A,plus(n1,n3))
| holdsAt(A,n3) ),
inference(paramod,[status(thm)],[c_104,c_2404]) ).
cnf(c_545,plain,
( ~ holdsAt(A,n4)
| happens(sK4(A,n3),n3)
| releasedAt(A,n4)
| holdsAt(A,n3) ),
inference(paramod,[status(thm)],[c_109,c_2405]) ).
cnf(c_2406,plain,
( ~ holdsAt(A,n3)
| happens(sK4(A,n2),n2)
| releasedAt(A,plus(n2,n1))
| holdsAt(A,n2) ),
inference(paramod,[status(thm)],[c_110,c_219]) ).
cnf(c_2407,plain,
( ~ holdsAt(A,n3)
| happens(sK4(A,n2),n2)
| releasedAt(A,plus(n1,n2))
| holdsAt(A,n2) ),
inference(paramod,[status(thm)],[c_104,c_2406]) ).
cnf(c_546,plain,
( ~ holdsAt(A,n3)
| happens(sK4(A,n2),n2)
| releasedAt(A,n3)
| holdsAt(A,n2) ),
inference(paramod,[status(thm)],[c_110,c_2407]) ).
cnf(c_591,plain,
( less_or_equal(A,n3)
| n4 = A
| n5 = A
| less(n5,A) ),
inference(resolve,[status(thm)],[c_297,c_93]) ).
cnf(c_602,plain,
( ~ less(n2,A)
| n2 = A
| n3 = A
| less(n3,A) ),
inference(resolve,[status(thm)],[c_307,c_81]) ).
cnf(c_2408,plain,
( n0 = A
| n1 = A
| n1 = A
| n2 = A
| less(n2,A) ),
inference(resolve,[status(thm)],[c_320,c_509]) ).
cnf(c_605,plain,
( n0 = A
| n1 = A
| n2 = A
| less(n2,A) ),
inference(copy,[status(thm)],[c_2408]) ).
cnf(c_771,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_464,c_418]) ).
cnf(c_773,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_465,c_418]) ).
cnf(c_774,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_466,c_418]) ).
cnf(c_885,plain,
( happens(sK4(filling,n3),n3)
| releasedAt(filling,n4)
| holdsAt(filling,n3) ),
inference(resolve,[status(thm)],[c_545,c_72]) ).
cnf(c_2409,plain,
( releasedAt(filling,n3)
| waterLevel(sK3(sK2(filling,n3),filling,n3)) = filling
| happens(sK4(filling,n3),n3)
| holdsAt(filling,n3) ),
inference(resolve,[status(thm)],[c_885,c_378]) ).
cnf(c_919,plain,
( releasedAt(filling,n3)
| happens(sK4(filling,n3),n3)
| holdsAt(filling,n3) ),
inference(resolve,[status(thm)],[c_122,c_2409]) ).
cnf(c_2410,plain,
( releasedAt(filling,n2)
| waterLevel(sK3(sK2(filling,n2),filling,n2)) = filling
| happens(sK4(filling,n3),n3)
| holdsAt(filling,n3) ),
inference(resolve,[status(thm)],[c_919,c_379]) ).
cnf(c_927,plain,
( releasedAt(filling,n2)
| happens(sK4(filling,n3),n3)
| holdsAt(filling,n3) ),
inference(resolve,[status(thm)],[c_122,c_2410]) ).
cnf(c_2411,plain,
( releasedAt(filling,n1)
| waterLevel(sK3(sK2(filling,n1),filling,n1)) = filling
| happens(sK4(filling,n3),n3)
| holdsAt(filling,n3) ),
inference(resolve,[status(thm)],[c_927,c_200]) ).
cnf(c_2412,plain,
( releasedAt(filling,n1)
| happens(sK4(filling,n3),n3)
| holdsAt(filling,n3) ),
inference(resolve,[status(thm)],[c_122,c_2411]) ).
cnf(c_939,plain,
( happens(sK4(filling,n3),n3)
| holdsAt(filling,n3) ),
inference(resolve,[status(thm)],[c_507,c_2412]) ).
cnf(c_2413,plain,
( holdsAt(filling,n3)
| n0 = n3
| holdsAt(filling,n3) ),
inference(resolve,[status(thm)],[c_939,c_130]) ).
cnf(c_2414,plain,
( holdsAt(filling,n3)
| n3 = n0
| holdsAt(filling,n3) ),
inference(copy,[status(thm)],[c_2413]) ).
cnf(c_2415,plain,
( n3 = n0
| holdsAt(filling,n3) ),
inference(copy,[status(thm)],[c_2414]) ).
cnf(c_943,plain,
holdsAt(filling,n3),
inference(resolve,[status(thm)],[c_306,c_2415]) ).
cnf(c_944,plain,
( happens(sK4(filling,n2),n2)
| releasedAt(filling,n3)
| holdsAt(filling,n2) ),
inference(resolve,[status(thm)],[c_943,c_546]) ).
cnf(c_2416,plain,
( releasedAt(filling,n2)
| waterLevel(sK3(sK2(filling,n2),filling,n2)) = filling
| happens(sK4(filling,n2),n2)
| holdsAt(filling,n2) ),
inference(resolve,[status(thm)],[c_944,c_379]) ).
cnf(c_962,plain,
( releasedAt(filling,n2)
| happens(sK4(filling,n2),n2)
| holdsAt(filling,n2) ),
inference(resolve,[status(thm)],[c_122,c_2416]) ).
cnf(c_2417,plain,
( releasedAt(filling,n1)
| waterLevel(sK3(sK2(filling,n1),filling,n1)) = filling
| happens(sK4(filling,n2),n2)
| holdsAt(filling,n2) ),
inference(resolve,[status(thm)],[c_962,c_200]) ).
cnf(c_2418,plain,
( releasedAt(filling,n1)
| happens(sK4(filling,n2),n2)
| holdsAt(filling,n2) ),
inference(resolve,[status(thm)],[c_122,c_2417]) ).
cnf(c_970,plain,
( happens(sK4(filling,n2),n2)
| holdsAt(filling,n2) ),
inference(resolve,[status(thm)],[c_507,c_2418]) ).
cnf(c_2419,plain,
( holdsAt(filling,n2)
| n0 = n2
| holdsAt(filling,n2) ),
inference(resolve,[status(thm)],[c_970,c_130]) ).
cnf(c_2420,plain,
( holdsAt(filling,n2)
| n2 = n0
| holdsAt(filling,n2) ),
inference(copy,[status(thm)],[c_2419]) ).
cnf(c_2421,plain,
( n2 = n0
| holdsAt(filling,n2) ),
inference(copy,[status(thm)],[c_2420]) ).
cnf(c_974,plain,
holdsAt(filling,n2),
inference(resolve,[status(thm)],[c_272,c_2421]) ).
cnf(c_979,plain,
( n3 = A
| less(A,n3)
| n4 = A
| n5 = A
| less(n5,A) ),
inference(resolve,[status(thm)],[c_591,c_103]) ).
cnf(c_2422,plain,
( n2 = A
| n3 = A
| less(n3,A)
| n0 = A
| n1 = A
| n2 = A ),
inference(resolve,[status(thm)],[c_605,c_602]) ).
cnf(c_982,plain,
( n3 = A
| less(n3,A)
| n0 = A
| n1 = A
| n2 = A ),
inference(copy,[status(thm)],[c_2422]) ).
cnf(c_1009,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_771,c_78]) ).
cnf(c_1010,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_773,c_78]) ).
cnf(c_1011,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_774,c_78]) ).
cnf(c_1098,plain,
( ~ less(A,n3)
| n3 = A
| n0 = A
| n1 = A
| n2 = A ),
inference(resolve,[status(thm)],[c_982,c_81]) ).
cnf(c_2423,plain,
( n3 = n0
| n4 = n0
| n5 = n0
| less(n5,n0)
| plus(n0,n3) != A
| less(sK0(n0,filling,plus(n0,n3)),plus(n0,n3))
| holdsAt(waterLevel(A),plus(n0,n3)) ),
inference(resolve,[status(thm)],[c_1009,c_979]) ).
cnf(c_2424,plain,
( n3 = n0
| n4 = n0
| n5 = n0
| less(n5,n0)
| plus(n0,n3) != A
| less(sK0(n0,filling,plus(n0,n3)),plus(n0,n3))
| holdsAt(waterLevel(A),n3) ),
inference(paramod,[status(thm)],[c_112,c_2423]) ).
cnf(c_2425,plain,
( n3 = n0
| n4 = n0
| n5 = n0
| less(n5,n0)
| plus(n0,n3) != A
| less(sK0(n0,filling,n3),plus(n0,n3))
| holdsAt(waterLevel(A),n3) ),
inference(paramod,[status(thm)],[c_112,c_2424]) ).
cnf(c_2426,plain,
( n3 = n0
| n4 = n0
| n5 = n0
| less(n5,n0)
| plus(n0,n3) != A
| less(sK0(n0,filling,n3),n3)
| holdsAt(waterLevel(A),n3) ),
inference(paramod,[status(thm)],[c_112,c_2425]) ).
cnf(c_2427,plain,
( n3 = n0
| n4 = n0
| n5 = n0
| less(n5,n0)
| n3 != A
| less(sK0(n0,filling,n3),n3)
| holdsAt(waterLevel(A),n3) ),
inference(paramod,[status(thm)],[c_112,c_2426]) ).
cnf(c_2428,plain,
( n3 = n0
| n4 = n0
| n5 = n0
| n3 != A
| less(sK0(n0,filling,n3),n3)
| holdsAt(waterLevel(A),n3) ),
inference(resolve,[status(thm)],[c_100,c_2427]) ).
cnf(c_2429,plain,
( n3 = n0
| n4 = n0
| n3 != A
| less(sK0(n0,filling,n3),n3)
| holdsAt(waterLevel(A),n3) ),
inference(resolve,[status(thm)],[c_371,c_2428]) ).
cnf(c_2430,plain,
( n3 = n0
| n3 != A
| less(sK0(n0,filling,n3),n3)
| holdsAt(waterLevel(A),n3) ),
inference(resolve,[status(thm)],[c_341,c_2429]) ).
cnf(c_1838,plain,
( n3 != A
| less(sK0(n0,filling,n3),n3)
| holdsAt(waterLevel(A),n3) ),
inference(resolve,[status(thm)],[c_306,c_2430]) ).
cnf(c_2431,plain,
( n3 = n0
| n4 = n0
| n5 = n0
| less(n5,n0)
| plus(n0,n3) != A
| less(n0,sK0(n0,filling,plus(n0,n3)))
| holdsAt(waterLevel(A),plus(n0,n3)) ),
inference(resolve,[status(thm)],[c_1010,c_979]) ).
cnf(c_2432,plain,
( n3 = n0
| n4 = n0
| n5 = n0
| less(n5,n0)
| plus(n0,n3) != A
| less(n0,sK0(n0,filling,plus(n0,n3)))
| holdsAt(waterLevel(A),n3) ),
inference(paramod,[status(thm)],[c_112,c_2431]) ).
cnf(c_2433,plain,
( n3 = n0
| n4 = n0
| n5 = n0
| less(n5,n0)
| plus(n0,n3) != A
| less(n0,sK0(n0,filling,n3))
| holdsAt(waterLevel(A),n3) ),
inference(paramod,[status(thm)],[c_112,c_2432]) ).
cnf(c_2434,plain,
( n3 = n0
| n4 = n0
| n5 = n0
| less(n5,n0)
| n3 != A
| less(n0,sK0(n0,filling,n3))
| holdsAt(waterLevel(A),n3) ),
inference(paramod,[status(thm)],[c_112,c_2433]) ).
cnf(c_2435,plain,
( n3 = n0
| n4 = n0
| n5 = n0
| n3 != A
| less(n0,sK0(n0,filling,n3))
| holdsAt(waterLevel(A),n3) ),
inference(resolve,[status(thm)],[c_100,c_2434]) ).
cnf(c_2436,plain,
( n3 = n0
| n4 = n0
| n3 != A
| less(n0,sK0(n0,filling,n3))
| holdsAt(waterLevel(A),n3) ),
inference(resolve,[status(thm)],[c_371,c_2435]) ).
cnf(c_2437,plain,
( n3 = n0
| n3 != A
| less(n0,sK0(n0,filling,n3))
| holdsAt(waterLevel(A),n3) ),
inference(resolve,[status(thm)],[c_341,c_2436]) ).
cnf(c_1862,plain,
( n3 != A
| less(n0,sK0(n0,filling,n3))
| holdsAt(waterLevel(A),n3) ),
inference(resolve,[status(thm)],[c_306,c_2437]) ).
cnf(c_2438,plain,
A = sK3(tapOn,waterLevel(A),B),
inference(copy,[status(thm)],[c_501]) ).
cnf(c_2439,plain,
( less(sK0(n0,filling,n3),n3)
| holdsAt(waterLevel(sK3(tapOn,waterLevel(n3),A)),n3) ),
inference(resolve,[status(thm)],[c_1838,c_2438]) ).
cnf(c_1870,plain,
( less(sK0(n0,filling,n3),n3)
| holdsAt(waterLevel(n3),n3) ),
inference(paramod,[status(thm)],[c_501,c_2439]) ).
cnf(c_2440,plain,
( overflow != A
| ~ holdsAt(filling,n3)
| happens(A,n3)
| less(sK0(n0,filling,n3),n3) ),
inference(resolve,[status(thm)],[c_1870,c_127]) ).
cnf(c_1877,plain,
( overflow != A
| happens(A,n3)
| less(sK0(n0,filling,n3),n3) ),
inference(resolve,[status(thm)],[c_943,c_2440]) ).
cnf(c_2441,plain,
A = sK3(tapOn,waterLevel(A),B),
inference(copy,[status(thm)],[c_501]) ).
cnf(c_2442,plain,
( happens(sK3(tapOn,waterLevel(overflow),A),n3)
| less(sK0(n0,filling,n3),n3) ),
inference(resolve,[status(thm)],[c_1877,c_2441]) ).
cnf(c_1879,plain,
( happens(overflow,n3)
| less(sK0(n0,filling,n3),n3) ),
inference(paramod,[status(thm)],[c_501,c_2442]) ).
cnf(c_2443,plain,
( ~ holdsAt(filling,plus(n3,n1))
| less(sK0(n0,filling,n3),n3) ),
inference(resolve,[status(thm)],[c_1879,c_429]) ).
cnf(c_2444,plain,
( ~ holdsAt(filling,plus(n1,n3))
| less(sK0(n0,filling,n3),n3) ),
inference(paramod,[status(thm)],[c_104,c_2443]) ).
cnf(c_2445,plain,
( ~ holdsAt(filling,n4)
| less(sK0(n0,filling,n3),n3) ),
inference(paramod,[status(thm)],[c_109,c_2444]) ).
cnf(c_1889,negated_conjecture,
less(sK0(n0,filling,n3),n3),
inference(resolve,[status(thm)],[c_72,c_2445]) ).
cnf(c_2446,plain,
( n3 = n0
| n4 = n0
| n5 = n0
| less(n5,n0)
| plus(n0,n3) != A
| happens(sK1(n0,filling,plus(n0,n3)),sK0(n0,filling,plus(n0,n3)))
| holdsAt(waterLevel(A),plus(n0,n3)) ),
inference(resolve,[status(thm)],[c_1011,c_979]) ).
cnf(c_2447,plain,
( n3 = n0
| n4 = n0
| n5 = n0
| less(n5,n0)
| plus(n0,n3) != A
| happens(sK1(n0,filling,plus(n0,n3)),sK0(n0,filling,plus(n0,n3)))
| holdsAt(waterLevel(A),n3) ),
inference(paramod,[status(thm)],[c_112,c_2446]) ).
cnf(c_2448,plain,
( n3 = n0
| n4 = n0
| n5 = n0
| less(n5,n0)
| plus(n0,n3) != A
| happens(sK1(n0,filling,n3),sK0(n0,filling,plus(n0,n3)))
| holdsAt(waterLevel(A),n3) ),
inference(paramod,[status(thm)],[c_112,c_2447]) ).
cnf(c_2449,plain,
( n3 = n0
| n4 = n0
| n5 = n0
| less(n5,n0)
| plus(n0,n3) != A
| happens(sK1(n0,filling,n3),sK0(n0,filling,n3))
| holdsAt(waterLevel(A),n3) ),
inference(paramod,[status(thm)],[c_112,c_2448]) ).
cnf(c_2450,plain,
( n3 = n0
| n4 = n0
| n5 = n0
| less(n5,n0)
| n3 != A
| happens(sK1(n0,filling,n3),sK0(n0,filling,n3))
| holdsAt(waterLevel(A),n3) ),
inference(paramod,[status(thm)],[c_112,c_2449]) ).
cnf(c_2451,plain,
( n3 = n0
| n4 = n0
| n5 = n0
| n3 != A
| happens(sK1(n0,filling,n3),sK0(n0,filling,n3))
| holdsAt(waterLevel(A),n3) ),
inference(resolve,[status(thm)],[c_100,c_2450]) ).
cnf(c_2452,plain,
( n3 = n0
| n4 = n0
| n3 != A
| happens(sK1(n0,filling,n3),sK0(n0,filling,n3))
| holdsAt(waterLevel(A),n3) ),
inference(resolve,[status(thm)],[c_371,c_2451]) ).
cnf(c_2453,plain,
( n3 = n0
| n3 != A
| happens(sK1(n0,filling,n3),sK0(n0,filling,n3))
| holdsAt(waterLevel(A),n3) ),
inference(resolve,[status(thm)],[c_341,c_2452]) ).
cnf(c_1892,plain,
( n3 != A
| happens(sK1(n0,filling,n3),sK0(n0,filling,n3))
| holdsAt(waterLevel(A),n3) ),
inference(resolve,[status(thm)],[c_306,c_2453]) ).
cnf(c_2454,plain,
( n3 = sK0(n0,filling,n3)
| n0 = sK0(n0,filling,n3)
| n1 = sK0(n0,filling,n3)
| n2 = sK0(n0,filling,n3) ),
inference(resolve,[status(thm)],[c_1889,c_1098]) ).
cnf(c_2455,plain,
( n3 = sK0(n0,filling,n3)
| n0 = sK0(n0,filling,n3)
| n1 = sK0(n0,filling,n3)
| sK0(n0,filling,n3) = n2 ),
inference(copy,[status(thm)],[c_2454]) ).
cnf(c_2456,plain,
( n3 = sK0(n0,filling,n3)
| n0 = sK0(n0,filling,n3)
| sK0(n0,filling,n3) = n1
| sK0(n0,filling,n3) = n2 ),
inference(copy,[status(thm)],[c_2455]) ).
cnf(c_2457,plain,
( n3 = sK0(n0,filling,n3)
| sK0(n0,filling,n3) = n0
| sK0(n0,filling,n3) = n1
| sK0(n0,filling,n3) = n2 ),
inference(copy,[status(thm)],[c_2456]) ).
cnf(c_1900,plain,
( sK0(n0,filling,n3) = n3
| sK0(n0,filling,n3) = n0
| sK0(n0,filling,n3) = n1
| sK0(n0,filling,n3) = n2 ),
inference(copy,[status(thm)],[c_2457]) ).
cnf(c_2458,plain,
n3 != sK0(n0,filling,n3),
inference(resolve,[status(thm)],[c_1889,c_80]) ).
cnf(c_1912,plain,
sK0(n0,filling,n3) != n3,
inference(copy,[status(thm)],[c_2458]) ).
cnf(c_1921,plain,
( sK0(n0,filling,n3) = n0
| sK0(n0,filling,n3) = n1
| sK0(n0,filling,n3) = n2 ),
inference(resolve,[status(thm)],[c_1912,c_1900]) ).
cnf(c_2459,plain,
A = sK3(tapOn,waterLevel(A),B),
inference(copy,[status(thm)],[c_501]) ).
cnf(c_2460,plain,
( less(n0,sK0(n0,filling,n3))
| holdsAt(waterLevel(sK3(tapOn,waterLevel(n3),A)),n3) ),
inference(resolve,[status(thm)],[c_1862,c_2459]) ).
cnf(c_2015,plain,
( less(n0,sK0(n0,filling,n3))
| holdsAt(waterLevel(n3),n3) ),
inference(paramod,[status(thm)],[c_501,c_2460]) ).
cnf(c_2461,plain,
( overflow != A
| ~ holdsAt(filling,n3)
| happens(A,n3)
| less(n0,sK0(n0,filling,n3)) ),
inference(resolve,[status(thm)],[c_2015,c_127]) ).
cnf(c_2022,plain,
( overflow != A
| happens(A,n3)
| less(n0,sK0(n0,filling,n3)) ),
inference(resolve,[status(thm)],[c_943,c_2461]) ).
cnf(c_2462,plain,
A = sK3(tapOn,waterLevel(A),B),
inference(copy,[status(thm)],[c_501]) ).
cnf(c_2463,plain,
( happens(sK3(tapOn,waterLevel(overflow),A),n3)
| less(n0,sK0(n0,filling,n3)) ),
inference(resolve,[status(thm)],[c_2022,c_2462]) ).
cnf(c_2024,plain,
( happens(overflow,n3)
| less(n0,sK0(n0,filling,n3)) ),
inference(paramod,[status(thm)],[c_501,c_2463]) ).
cnf(c_2464,plain,
( ~ holdsAt(filling,plus(n3,n1))
| less(n0,sK0(n0,filling,n3)) ),
inference(resolve,[status(thm)],[c_2024,c_429]) ).
cnf(c_2465,plain,
( ~ holdsAt(filling,plus(n1,n3))
| less(n0,sK0(n0,filling,n3)) ),
inference(paramod,[status(thm)],[c_104,c_2464]) ).
cnf(c_2466,plain,
( ~ holdsAt(filling,n4)
| less(n0,sK0(n0,filling,n3)) ),
inference(paramod,[status(thm)],[c_109,c_2465]) ).
cnf(c_2034,negated_conjecture,
less(n0,sK0(n0,filling,n3)),
inference(resolve,[status(thm)],[c_72,c_2466]) ).
cnf(c_2040,plain,
sK0(n0,filling,n3) != n0,
inference(resolve,[status(thm)],[c_2034,c_80]) ).
cnf(c_2041,plain,
( sK0(n0,filling,n3) = n1
| sK0(n0,filling,n3) = n2 ),
inference(resolve,[status(thm)],[c_2040,c_1921]) ).
cnf(c_2467,plain,
A = sK3(tapOn,waterLevel(A),B),
inference(copy,[status(thm)],[c_501]) ).
cnf(c_2468,plain,
( happens(sK1(n0,filling,n3),sK0(n0,filling,n3))
| holdsAt(waterLevel(sK3(tapOn,waterLevel(n3),A)),n3) ),
inference(resolve,[status(thm)],[c_1892,c_2467]) ).
cnf(c_2207,plain,
( happens(sK1(n0,filling,n3),sK0(n0,filling,n3))
| holdsAt(waterLevel(n3),n3) ),
inference(paramod,[status(thm)],[c_501,c_2468]) ).
cnf(c_2469,plain,
( overflow = sK1(n0,filling,n3)
| n0 = sK0(n0,filling,n3)
| holdsAt(waterLevel(n3),n3) ),
inference(resolve,[status(thm)],[c_2207,c_129]) ).
cnf(c_2470,plain,
( overflow = sK1(n0,filling,n3)
| sK0(n0,filling,n3) = n0
| holdsAt(waterLevel(n3),n3) ),
inference(copy,[status(thm)],[c_2469]) ).
cnf(c_2471,plain,
( sK1(n0,filling,n3) = overflow
| sK0(n0,filling,n3) = n0
| holdsAt(waterLevel(n3),n3) ),
inference(copy,[status(thm)],[c_2470]) ).
cnf(c_2213,plain,
( sK1(n0,filling,n3) = overflow
| holdsAt(waterLevel(n3),n3) ),
inference(resolve,[status(thm)],[c_2040,c_2471]) ).
cnf(c_2472,plain,
( overflow != A
| ~ holdsAt(filling,n3)
| happens(A,n3)
| sK1(n0,filling,n3) = overflow ),
inference(resolve,[status(thm)],[c_2213,c_127]) ).
cnf(c_2230,plain,
( overflow != A
| happens(A,n3)
| sK1(n0,filling,n3) = overflow ),
inference(resolve,[status(thm)],[c_943,c_2472]) ).
cnf(c_2473,plain,
A = sK3(tapOn,waterLevel(A),B),
inference(copy,[status(thm)],[c_501]) ).
cnf(c_2474,plain,
( happens(sK3(tapOn,waterLevel(overflow),A),n3)
| sK1(n0,filling,n3) = overflow ),
inference(resolve,[status(thm)],[c_2230,c_2473]) ).
cnf(c_2261,plain,
( happens(overflow,n3)
| sK1(n0,filling,n3) = overflow ),
inference(paramod,[status(thm)],[c_501,c_2474]) ).
cnf(c_2475,plain,
( ~ holdsAt(filling,plus(n3,n1))
| sK1(n0,filling,n3) = overflow ),
inference(resolve,[status(thm)],[c_2261,c_429]) ).
cnf(c_2476,plain,
( ~ holdsAt(filling,plus(n1,n3))
| sK1(n0,filling,n3) = overflow ),
inference(paramod,[status(thm)],[c_104,c_2475]) ).
cnf(c_2477,plain,
( ~ holdsAt(filling,n4)
| sK1(n0,filling,n3) = overflow ),
inference(paramod,[status(thm)],[c_109,c_2476]) ).
cnf(c_2276,negated_conjecture,
sK1(n0,filling,n3) = overflow,
inference(resolve,[status(thm)],[c_72,c_2477]) ).
cnf(c_2278,plain,
( happens(overflow,sK0(n0,filling,n3))
| holdsAt(waterLevel(n3),n3) ),
inference(paramod,[status(thm)],[c_2276,c_2207]) ).
cnf(c_2478,plain,
( ~ holdsAt(filling,plus(sK0(n0,filling,n3),n1))
| holdsAt(waterLevel(n3),n3) ),
inference(resolve,[status(thm)],[c_2278,c_429]) ).
cnf(c_2289,plain,
( ~ holdsAt(filling,plus(n1,sK0(n0,filling,n3)))
| holdsAt(waterLevel(n3),n3) ),
inference(paramod,[status(thm)],[c_104,c_2478]) ).
cnf(c_2479,plain,
( ~ holdsAt(filling,plus(n1,n2))
| holdsAt(waterLevel(n3),n3)
| sK0(n0,filling,n3) = n1 ),
inference(paramod,[status(thm)],[c_2041,c_2289]) ).
cnf(c_2480,plain,
( ~ holdsAt(filling,n3)
| holdsAt(waterLevel(n3),n3)
| sK0(n0,filling,n3) = n1 ),
inference(paramod,[status(thm)],[c_110,c_2479]) ).
cnf(c_2322,plain,
( holdsAt(waterLevel(n3),n3)
| sK0(n0,filling,n3) = n1 ),
inference(resolve,[status(thm)],[c_943,c_2480]) ).
cnf(c_2481,plain,
( overflow != A
| ~ holdsAt(filling,n3)
| happens(A,n3)
| sK0(n0,filling,n3) = n1 ),
inference(resolve,[status(thm)],[c_2322,c_127]) ).
cnf(c_2329,plain,
( overflow != A
| happens(A,n3)
| sK0(n0,filling,n3) = n1 ),
inference(resolve,[status(thm)],[c_943,c_2481]) ).
cnf(c_2482,plain,
overflow = sK1(n0,filling,n3),
inference(copy,[status(thm)],[c_2276]) ).
cnf(c_2483,plain,
( happens(sK1(n0,filling,n3),n3)
| sK0(n0,filling,n3) = n1 ),
inference(resolve,[status(thm)],[c_2329,c_2482]) ).
cnf(c_2331,plain,
( happens(overflow,n3)
| sK0(n0,filling,n3) = n1 ),
inference(paramod,[status(thm)],[c_2276,c_2483]) ).
cnf(c_2484,plain,
( ~ holdsAt(filling,plus(n3,n1))
| sK0(n0,filling,n3) = n1 ),
inference(resolve,[status(thm)],[c_2331,c_429]) ).
cnf(c_2485,plain,
( ~ holdsAt(filling,plus(n1,n3))
| sK0(n0,filling,n3) = n1 ),
inference(paramod,[status(thm)],[c_104,c_2484]) ).
cnf(c_2486,plain,
( ~ holdsAt(filling,n4)
| sK0(n0,filling,n3) = n1 ),
inference(paramod,[status(thm)],[c_109,c_2485]) ).
cnf(c_2341,negated_conjecture,
sK0(n0,filling,n3) = n1,
inference(resolve,[status(thm)],[c_72,c_2486]) ).
cnf(c_2487,plain,
( ~ holdsAt(filling,plus(n1,n1))
| holdsAt(waterLevel(n3),n3) ),
inference(paramod,[status(thm)],[c_2341,c_2289]) ).
cnf(c_2488,plain,
( ~ holdsAt(filling,n2)
| holdsAt(waterLevel(n3),n3) ),
inference(paramod,[status(thm)],[c_111,c_2487]) ).
cnf(c_2350,plain,
holdsAt(waterLevel(n3),n3),
inference(resolve,[status(thm)],[c_974,c_2488]) ).
cnf(c_2489,plain,
( overflow != A
| ~ holdsAt(filling,n3)
| happens(A,n3) ),
inference(resolve,[status(thm)],[c_2350,c_127]) ).
cnf(c_2381,plain,
( overflow != A
| happens(A,n3) ),
inference(resolve,[status(thm)],[c_943,c_2489]) ).
cnf(c_2490,plain,
overflow = sK1(n0,filling,n3),
inference(copy,[status(thm)],[c_2276]) ).
cnf(c_2491,plain,
happens(sK1(n0,filling,n3),n3),
inference(resolve,[status(thm)],[c_2381,c_2490]) ).
cnf(c_2383,plain,
happens(overflow,n3),
inference(paramod,[status(thm)],[c_2276,c_2491]) ).
cnf(c_2492,plain,
~ holdsAt(filling,plus(n3,n1)),
inference(resolve,[status(thm)],[c_2383,c_429]) ).
cnf(c_2493,plain,
~ holdsAt(filling,plus(n1,n3)),
inference(paramod,[status(thm)],[c_104,c_2492]) ).
cnf(c_2494,plain,
~ holdsAt(filling,n4),
inference(paramod,[status(thm)],[c_109,c_2493]) ).
cnf(c_2395,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_72,c_2494]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CSR002+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 23:57:00 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 1066711 was started by sandbox2 on n015,
% 0.11/0.38 % Sat Sep 26 23:57:00 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.39
% 0.11/0.39 % From the command line: assign(max_seconds, 300).
% 15.59/2.45
% 15.59/2.45 % given #500 (T,wt=9): 669 n1 = A | less(A,n4) | -less(A,n1). [resolve(656,a,81,b)].
% 15.59/2.45
% 15.59/2.45 % given #1000 (T,wt=11): 1381 holdsAt(filling,plus(n1,n4)) | less(n2,f4(n2,n7,spilling)). [resolve(1313,c,975,d),unit_del(c,385),unit_del(d,386),unit_del(e,361),unit_del(f,319)].
% 15.59/2.45
% 15.59/2.45 % SZS status Theorem for theBenchmark
% 15.59/2.45
% 15.59/2.45 % Proof 1 at 1.32 (+ 0.59) seconds.
% 15.59/2.45 % Length of proof is 175.
% 15.59/2.45 % Level of proof is 32.
% 15.59/2.45 % Maximum clause weight is 38.000.
% 15.59/2.45 % Given clauses 1252.
% 15.59/2.45
% 15.59/2.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------