%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CSR006+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 : n017.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 17.83s 2.75s
% Output : CNFRefutation 17.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 70
% Number of leaves : 30
% Syntax : Number of formulae : 310 ( 75 unt; 0 def)
% Number of atoms : 939 ( 305 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 885 ( 256 ~; 556 |; 53 &)
% ( 13 <=>; 7 =>; 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 : 392 ( 38 sgn 111 !; 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_holding,axiom,
! [Fluent,Time] :
( ( ~ ? [Event] :
( terminates(Event,Fluent,Time)
& happens(Event,Time) )
& ~ releasedAt(Fluent,plus(Time,n1))
& holdsAt(Fluent,Time) )
=> holdsAt(Fluent,plus(Time,n1)) ),
file('theBenchmark.p',keep_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_holds,axiom,
! [Event,Time,Fluent] :
( ( initiates(Event,Fluent,Time)
& happens(Event,Time) )
=> holdsAt(Fluent,plus(Time,n1)) ),
file('theBenchmark.p',happens_holds) ).
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(waterLevel_3,conjecture,
holdsAt(waterLevel(n3),n3),
file('theBenchmark.p',waterLevel_3) ).
fof(waterLevel_3_neg,negated_conjecture,
~ holdsAt(waterLevel(n3),n3),
inference(assume_negation,[status(cth)],[waterLevel_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_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(waterLevel(n3),n3),
inference(clausify,[status(thm)],[waterLevel_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_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_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_131,plain,
( holdsAt(waterLevel(n3),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_137,plain,
( filling = B
| ~ terminates(A,B,C) ),
inference(clausify,[status(thm)],[terminates_all_defn]) ).
cnf(c_139,plain,
( waterLevel(D) != B
| overflow != A
| ~ holdsAt(waterLevel(D),C)
| initiates(A,B,C) ),
inference(clausify,[status(thm)],[initiates_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]) ).
cnf(c_164,plain,
( holdsAt(C,plus(B,n1))
| ~ initiates(A,C,B)
| ~ happens(A,B) ),
inference(clausify,[status(thm)],[happens_holds]) ).
cnf(c_165,plain,
( ~ releasedAt(A,plus(B,n1))
| happens(sK2(A,B),B)
| releasedAt(A,B) ),
inference(split_conjunct,[status(thm)],[sk_keep_not_released]) ).
fof(nnf_5,plain,
! [Fluent,Time] :
( holdsAt(Fluent,plus(Time,n1))
| ? [Event] :
( terminates(Event,Fluent,Time)
& happens(Event,Time) )
| releasedAt(Fluent,plus(Time,n1))
| ~ holdsAt(Fluent,Time) ),
inference(fof_nnf,[status(thm)],[keep_holding]) ).
fof(sk_keep_holding_sk,plain,
! [Fluent,Time] :
( holdsAt(Fluent,plus(Time,n1))
| ( terminates(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_5]) ).
fof(sk_keep_holding,plain,
( ! [VAR_0,VAR_1] :
( holdsAt(VAR_0,plus(VAR_1,n1))
| terminates(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_holding_sk]) ).
cnf(c_170,plain,
( holdsAt(A,plus(B,n1))
| terminates(sK4(A,B),A,B)
| releasedAt(A,plus(B,n1))
| ~ holdsAt(A,B) ),
inference(split_conjunct,[status(thm)],[sk_keep_holding]) ).
cnf(c_171,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_holding]) ).
cnf(c_181,plain,
( waterLevel(sK3(tapOn,B,C)) = B
| waterLevel(A) != B ),
inference(xxres,[status(thm)],[c_60]) ).
cnf(c_2088,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_2088]) ).
cnf(c_2089,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_2089]) ).
cnf(c_2090,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_2090]) ).
cnf(c_2091,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_2091]) ).
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_215,plain,
( ~ releasedAt(A,plus(n1,B))
| happens(sK2(A,B),B)
| releasedAt(A,B) ),
inference(paramod,[status(thm)],[c_104,c_165]) ).
cnf(c_223,plain,
waterLevel(sK3(tapOn,waterLevel(A),B)) = waterLevel(A),
inference(xxres,[status(thm)],[c_181]) ).
cnf(c_224,plain,
less(n0,n1),
inference(resolve,[status(thm)],[c_194,c_98]) ).
cnf(c_233,plain,
less_or_equal(n0,n1),
inference(resolve,[status(thm)],[c_224,c_102]) ).
cnf(c_2092,plain,
n1 != n0,
inference(resolve,[status(thm)],[c_224,c_80]) ).
cnf(c_234,plain,
n0 != n1,
inference(copy,[status(thm)],[c_2092]) ).
cnf(c_259,plain,
less(n0,n2),
inference(resolve,[status(thm)],[c_233,c_96]) ).
cnf(c_269,plain,
less_or_equal(n0,n2),
inference(resolve,[status(thm)],[c_259,c_102]) ).
cnf(c_270,plain,
n2 != n0,
inference(resolve,[status(thm)],[c_259,c_80]) ).
cnf(c_294,plain,
less(n0,n3),
inference(resolve,[status(thm)],[c_269,c_94]) ).
cnf(c_295,plain,
( n4 = A
| less(A,n4)
| n5 = A
| less(n5,A) ),
inference(resolve,[status(thm)],[c_188,c_103]) ).
cnf(c_303,plain,
less_or_equal(n0,n3),
inference(resolve,[status(thm)],[c_294,c_102]) ).
cnf(c_304,plain,
n3 != n0,
inference(resolve,[status(thm)],[c_294,c_80]) ).
cnf(c_305,plain,
( n2 = A
| less(A,n2)
| n3 = A
| less(n3,A) ),
inference(resolve,[status(thm)],[c_190,c_103]) ).
cnf(c_318,plain,
( n1 = A
| less(A,n1)
| n2 = A
| less(n2,A) ),
inference(resolve,[status(thm)],[c_191,c_103]) ).
cnf(c_325,plain,
less(n0,n4),
inference(resolve,[status(thm)],[c_303,c_92]) ).
cnf(c_2093,plain,
( n0 = A
| less(A,n0)
| n1 = A
| less(n1,A) ),
inference(resolve,[status(thm)],[c_192,c_103]) ).
cnf(c_327,plain,
( n0 = A
| n1 = A
| less(n1,A) ),
inference(resolve,[status(thm)],[c_100,c_2093]) ).
cnf(c_338,plain,
less_or_equal(n0,n4),
inference(resolve,[status(thm)],[c_325,c_102]) ).
cnf(c_339,plain,
n4 != n0,
inference(resolve,[status(thm)],[c_325,c_80]) ).
cnf(c_363,plain,
less(n0,n5),
inference(resolve,[status(thm)],[c_338,c_90]) ).
cnf(c_369,plain,
n5 != n0,
inference(resolve,[status(thm)],[c_363,c_80]) ).
cnf(c_377,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_2094,plain,
n0 = plus(n0,n0),
inference(copy,[status(thm)],[c_116]) ).
cnf(c_2095,plain,
happens(tapOn,plus(n0,n0)),
inference(resolve,[status(thm)],[c_203,c_2094]) ).
cnf(c_416,plain,
happens(tapOn,n0),
inference(paramod,[status(thm)],[c_116,c_2095]) ).
cnf(c_426,plain,
terminates(overflow,filling,A),
inference(xxres,[status(thm)],[c_205]) ).
cnf(c_427,plain,
( ~ holdsAt(filling,plus(A,n1))
| ~ happens(overflow,A) ),
inference(resolve,[status(thm)],[c_426,c_163]) ).
cnf(c_454,plain,
initiates(tapOn,filling,A),
inference(xxres,[status(thm)],[c_213]) ).
cnf(c_459,plain,
( holdsAt(filling,plus(A,n1))
| ~ happens(tapOn,A) ),
inference(resolve,[status(thm)],[c_454,c_164]) ).
cnf(c_460,plain,
( ~ releasedAt(filling,plus(A,n1))
| ~ happens(tapOn,A) ),
inference(resolve,[status(thm)],[c_454,c_162]) ).
cnf(c_462,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_454,c_66]) ).
cnf(c_463,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_454,c_65]) ).
cnf(c_464,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_454,c_64]) ).
cnf(c_482,plain,
( ~ releasedAt(A,n3)
| happens(sK2(A,n2),n2)
| releasedAt(A,n2) ),
inference(paramod,[status(thm)],[c_110,c_215]) ).
cnf(c_484,plain,
( ~ releasedAt(filling,plus(n1,A))
| ~ happens(tapOn,A) ),
inference(paramod,[status(thm)],[c_104,c_460]) ).
cnf(c_2096,plain,
holdsAt(filling,plus(n0,n1)),
inference(resolve,[status(thm)],[c_459,c_416]) ).
cnf(c_2097,plain,
holdsAt(filling,plus(n1,n0)),
inference(paramod,[status(thm)],[c_104,c_2096]) ).
cnf(c_489,plain,
holdsAt(filling,n1),
inference(paramod,[status(thm)],[c_115,c_2097]) ).
cnf(c_2098,plain,
( holdsAt(filling,plus(n1,n1))
| happens(sK4(filling,n1),n1)
| releasedAt(filling,plus(n1,n1)) ),
inference(resolve,[status(thm)],[c_489,c_171]) ).
cnf(c_2099,plain,
( holdsAt(filling,plus(n1,n1))
| happens(sK4(filling,n1),n1)
| releasedAt(filling,n2) ),
inference(paramod,[status(thm)],[c_111,c_2098]) ).
cnf(c_490,plain,
( holdsAt(filling,n2)
| happens(sK4(filling,n1),n1)
| releasedAt(filling,n2) ),
inference(paramod,[status(thm)],[c_111,c_2099]) ).
cnf(c_499,plain,
sK3(tapOn,waterLevel(A),B) = A,
inference(resolve,[status(thm)],[c_223,c_118]) ).
cnf(c_2100,plain,
( ~ releasedAt(filling,n1)
| ~ happens(tapOn,n0) ),
inference(paramod,[status(thm)],[c_115,c_484]) ).
cnf(c_505,plain,
~ releasedAt(filling,n1),
inference(resolve,[status(thm)],[c_416,c_2100]) ).
cnf(c_507,plain,
( ~ less(A,n1)
| n0 = A
| n1 = A ),
inference(resolve,[status(thm)],[c_327,c_81]) ).
cnf(c_574,plain,
( less_or_equal(A,n3)
| n4 = A
| n5 = A
| less(n5,A) ),
inference(resolve,[status(thm)],[c_295,c_93]) ).
cnf(c_585,plain,
( ~ less(n2,A)
| n2 = A
| n3 = A
| less(n3,A) ),
inference(resolve,[status(thm)],[c_305,c_81]) ).
cnf(c_2101,plain,
( n0 = A
| n1 = A
| n1 = A
| n2 = A
| less(n2,A) ),
inference(resolve,[status(thm)],[c_318,c_507]) ).
cnf(c_589,plain,
( n0 = A
| n1 = A
| n2 = A
| less(n2,A) ),
inference(copy,[status(thm)],[c_2101]) ).
cnf(c_753,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_462,c_416]) ).
cnf(c_756,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_463,c_416]) ).
cnf(c_758,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_464,c_416]) ).
cnf(c_2102,plain,
( releasedAt(filling,n1)
| waterLevel(sK3(sK2(filling,n1),filling,n1)) = filling
| holdsAt(filling,n2)
| happens(sK4(filling,n1),n1) ),
inference(resolve,[status(thm)],[c_490,c_200]) ).
cnf(c_2103,plain,
( releasedAt(filling,n1)
| holdsAt(filling,n2)
| happens(sK4(filling,n1),n1) ),
inference(resolve,[status(thm)],[c_122,c_2102]) ).
cnf(c_804,plain,
( holdsAt(filling,n2)
| happens(sK4(filling,n1),n1) ),
inference(resolve,[status(thm)],[c_505,c_2103]) ).
cnf(c_2104,plain,
( holdsAt(waterLevel(n3),n1)
| n0 = n1
| holdsAt(filling,n2) ),
inference(resolve,[status(thm)],[c_804,c_131]) ).
cnf(c_807,plain,
( holdsAt(waterLevel(n3),n1)
| holdsAt(filling,n2) ),
inference(resolve,[status(thm)],[c_234,c_2104]) ).
cnf(c_813,plain,
( waterLevel(n3) != B
| overflow != A
| initiates(A,B,n1)
| holdsAt(filling,n2) ),
inference(resolve,[status(thm)],[c_807,c_139]) ).
cnf(c_2105,plain,
( overflow != A
| ~ holdsAt(filling,n1)
| happens(A,n1)
| holdsAt(filling,n2) ),
inference(resolve,[status(thm)],[c_807,c_127]) ).
cnf(c_814,plain,
( overflow != A
| happens(A,n1)
| holdsAt(filling,n2) ),
inference(resolve,[status(thm)],[c_489,c_2105]) ).
cnf(c_2106,plain,
A = sK3(tapOn,waterLevel(A),B),
inference(copy,[status(thm)],[c_499]) ).
cnf(c_2107,plain,
( happens(sK3(tapOn,waterLevel(overflow),A),n1)
| holdsAt(filling,n2) ),
inference(resolve,[status(thm)],[c_814,c_2106]) ).
cnf(c_841,plain,
( happens(overflow,n1)
| holdsAt(filling,n2) ),
inference(paramod,[status(thm)],[c_499,c_2107]) ).
cnf(c_893,plain,
( n3 = A
| less(A,n3)
| n4 = A
| n5 = A
| less(n5,A) ),
inference(resolve,[status(thm)],[c_574,c_103]) ).
cnf(c_2108,plain,
( n2 = A
| n3 = A
| less(n3,A)
| n0 = A
| n1 = A
| n2 = A ),
inference(resolve,[status(thm)],[c_589,c_585]) ).
cnf(c_896,plain,
( n3 = A
| less(n3,A)
| n0 = A
| n1 = A
| n2 = A ),
inference(copy,[status(thm)],[c_2108]) ).
cnf(c_900,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_753,c_78]) ).
cnf(c_924,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_756,c_78]) ).
cnf(c_925,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_758,c_78]) ).
cnf(c_2109,plain,
A = sK3(tapOn,waterLevel(A),B),
inference(copy,[status(thm)],[c_499]) ).
cnf(c_2110,plain,
( waterLevel(n3) != B
| initiates(sK3(tapOn,waterLevel(overflow),A),B,n1)
| holdsAt(filling,n2) ),
inference(resolve,[status(thm)],[c_813,c_2109]) ).
cnf(c_960,plain,
( waterLevel(n3) != A
| initiates(overflow,A,n1)
| holdsAt(filling,n2) ),
inference(paramod,[status(thm)],[c_499,c_2110]) ).
cnf(c_2111,plain,
A = sK3(tapOn,waterLevel(A),B),
inference(copy,[status(thm)],[c_499]) ).
cnf(c_2112,plain,
( initiates(overflow,sK3(tapOn,waterLevel(waterLevel(n3)),A),n1)
| holdsAt(filling,n2) ),
inference(resolve,[status(thm)],[c_960,c_2111]) ).
cnf(c_962,plain,
( initiates(overflow,waterLevel(n3),n1)
| holdsAt(filling,n2) ),
inference(paramod,[status(thm)],[c_499,c_2112]) ).
cnf(c_2113,plain,
( holdsAt(waterLevel(n3),plus(n1,n1))
| ~ happens(overflow,n1)
| holdsAt(filling,n2) ),
inference(resolve,[status(thm)],[c_962,c_164]) ).
cnf(c_967,plain,
( holdsAt(waterLevel(n3),n2)
| ~ happens(overflow,n1)
| holdsAt(filling,n2) ),
inference(paramod,[status(thm)],[c_111,c_2113]) ).
cnf(c_2114,plain,
( ~ releasedAt(waterLevel(n3),plus(n1,n1))
| ~ happens(overflow,n1)
| holdsAt(filling,n2) ),
inference(resolve,[status(thm)],[c_962,c_162]) ).
cnf(c_968,plain,
( ~ releasedAt(waterLevel(n3),n2)
| ~ happens(overflow,n1)
| holdsAt(filling,n2) ),
inference(paramod,[status(thm)],[c_111,c_2114]) ).
cnf(c_2115,plain,
( holdsAt(filling,n2)
| holdsAt(waterLevel(n3),n2)
| holdsAt(filling,n2) ),
inference(resolve,[status(thm)],[c_967,c_841]) ).
cnf(c_973,plain,
( holdsAt(waterLevel(n3),n2)
| holdsAt(filling,n2) ),
inference(copy,[status(thm)],[c_2115]) ).
cnf(c_2116,plain,
( holdsAt(waterLevel(n3),plus(n2,n1))
| terminates(sK4(waterLevel(n3),n2),waterLevel(n3),n2)
| releasedAt(waterLevel(n3),plus(n2,n1))
| holdsAt(filling,n2) ),
inference(resolve,[status(thm)],[c_973,c_170]) ).
cnf(c_2117,plain,
( holdsAt(waterLevel(n3),plus(n2,n1))
| terminates(sK4(waterLevel(n3),n2),waterLevel(n3),n2)
| releasedAt(waterLevel(n3),plus(n1,n2))
| holdsAt(filling,n2) ),
inference(paramod,[status(thm)],[c_104,c_2116]) ).
cnf(c_2118,plain,
( holdsAt(waterLevel(n3),plus(n2,n1))
| terminates(sK4(waterLevel(n3),n2),waterLevel(n3),n2)
| releasedAt(waterLevel(n3),n3)
| holdsAt(filling,n2) ),
inference(paramod,[status(thm)],[c_110,c_2117]) ).
cnf(c_2119,plain,
( holdsAt(waterLevel(n3),plus(n1,n2))
| terminates(sK4(waterLevel(n3),n2),waterLevel(n3),n2)
| releasedAt(waterLevel(n3),n3)
| holdsAt(filling,n2) ),
inference(paramod,[status(thm)],[c_104,c_2118]) ).
cnf(c_2120,plain,
( holdsAt(waterLevel(n3),n3)
| terminates(sK4(waterLevel(n3),n2),waterLevel(n3),n2)
| releasedAt(waterLevel(n3),n3)
| holdsAt(filling,n2) ),
inference(paramod,[status(thm)],[c_110,c_2119]) ).
cnf(c_975,negated_conjecture,
( terminates(sK4(waterLevel(n3),n2),waterLevel(n3),n2)
| releasedAt(waterLevel(n3),n3)
| holdsAt(filling,n2) ),
inference(resolve,[status(thm)],[c_72,c_2120]) ).
cnf(c_2121,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_900,c_893]) ).
cnf(c_2122,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_2121]) ).
cnf(c_2123,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_2122]) ).
cnf(c_2124,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_2123]) ).
cnf(c_2125,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_2124]) ).
cnf(c_2126,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_2125]) ).
cnf(c_2127,plain,
( n3 = n0
| n4 = n0
| n3 != A
| less(sK0(n0,filling,n3),n3)
| holdsAt(waterLevel(A),n3) ),
inference(resolve,[status(thm)],[c_369,c_2126]) ).
cnf(c_2128,plain,
( n3 = n0
| n3 != A
| less(sK0(n0,filling,n3),n3)
| holdsAt(waterLevel(A),n3) ),
inference(resolve,[status(thm)],[c_339,c_2127]) ).
cnf(c_1541,plain,
( n3 != A
| less(sK0(n0,filling,n3),n3)
| holdsAt(waterLevel(A),n3) ),
inference(resolve,[status(thm)],[c_304,c_2128]) ).
cnf(c_2129,plain,
A = sK3(tapOn,waterLevel(A),B),
inference(copy,[status(thm)],[c_499]) ).
cnf(c_2130,plain,
( less(sK0(n0,filling,n3),n3)
| holdsAt(waterLevel(sK3(tapOn,waterLevel(n3),A)),n3) ),
inference(resolve,[status(thm)],[c_1541,c_2129]) ).
cnf(c_2131,plain,
( less(sK0(n0,filling,n3),n3)
| holdsAt(waterLevel(n3),n3) ),
inference(paramod,[status(thm)],[c_499,c_2130]) ).
cnf(c_1578,negated_conjecture,
less(sK0(n0,filling,n3),n3),
inference(resolve,[status(thm)],[c_72,c_2131]) ).
cnf(c_1588,plain,
~ less(n3,sK0(n0,filling,n3)),
inference(resolve,[status(thm)],[c_1578,c_81]) ).
cnf(c_2132,plain,
n3 != sK0(n0,filling,n3),
inference(resolve,[status(thm)],[c_1578,c_80]) ).
cnf(c_1589,plain,
sK0(n0,filling,n3) != n3,
inference(copy,[status(thm)],[c_2132]) ).
cnf(c_2133,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_1588,c_896]) ).
cnf(c_2134,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_2133]) ).
cnf(c_2135,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_2134]) ).
cnf(c_2136,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_2135]) ).
cnf(c_2137,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_2136]) ).
cnf(c_1598,plain,
( sK0(n0,filling,n3) = n0
| sK0(n0,filling,n3) = n1
| sK0(n0,filling,n3) = n2 ),
inference(resolve,[status(thm)],[c_1589,c_2137]) ).
cnf(c_2138,plain,
( filling = waterLevel(n3)
| releasedAt(waterLevel(n3),n3)
| holdsAt(filling,n2) ),
inference(resolve,[status(thm)],[c_975,c_137]) ).
cnf(c_2139,plain,
( waterLevel(n3) = filling
| releasedAt(waterLevel(n3),n3)
| holdsAt(filling,n2) ),
inference(copy,[status(thm)],[c_2138]) ).
cnf(c_1681,plain,
( releasedAt(waterLevel(n3),n3)
| holdsAt(filling,n2) ),
inference(resolve,[status(thm)],[c_122,c_2139]) ).
cnf(c_1684,plain,
( happens(sK2(waterLevel(n3),n2),n2)
| releasedAt(waterLevel(n3),n2)
| holdsAt(filling,n2) ),
inference(resolve,[status(thm)],[c_1681,c_482]) ).
cnf(c_2140,plain,
( ~ happens(overflow,n1)
| holdsAt(filling,n2)
| happens(sK2(waterLevel(n3),n2),n2)
| holdsAt(filling,n2) ),
inference(resolve,[status(thm)],[c_1684,c_968]) ).
cnf(c_1689,plain,
( ~ happens(overflow,n1)
| happens(sK2(waterLevel(n3),n2),n2)
| holdsAt(filling,n2) ),
inference(copy,[status(thm)],[c_2140]) ).
cnf(c_2141,plain,
( holdsAt(filling,n2)
| happens(sK2(waterLevel(n3),n2),n2)
| holdsAt(filling,n2) ),
inference(resolve,[status(thm)],[c_1689,c_841]) ).
cnf(c_1691,plain,
( happens(sK2(waterLevel(n3),n2),n2)
| holdsAt(filling,n2) ),
inference(copy,[status(thm)],[c_2141]) ).
cnf(c_2142,plain,
( holdsAt(filling,n2)
| n0 = n2
| holdsAt(filling,n2) ),
inference(resolve,[status(thm)],[c_1691,c_130]) ).
cnf(c_2143,plain,
( holdsAt(filling,n2)
| n2 = n0
| holdsAt(filling,n2) ),
inference(copy,[status(thm)],[c_2142]) ).
cnf(c_2144,plain,
( n2 = n0
| holdsAt(filling,n2) ),
inference(copy,[status(thm)],[c_2143]) ).
cnf(c_1693,plain,
holdsAt(filling,n2),
inference(resolve,[status(thm)],[c_270,c_2144]) ).
cnf(c_2145,plain,
( holdsAt(filling,plus(n2,n1))
| happens(sK4(filling,n2),n2)
| releasedAt(filling,plus(n2,n1)) ),
inference(resolve,[status(thm)],[c_1693,c_171]) ).
cnf(c_2146,plain,
( holdsAt(filling,plus(n2,n1))
| happens(sK4(filling,n2),n2)
| releasedAt(filling,plus(n1,n2)) ),
inference(paramod,[status(thm)],[c_104,c_2145]) ).
cnf(c_2147,plain,
( holdsAt(filling,plus(n2,n1))
| happens(sK4(filling,n2),n2)
| releasedAt(filling,n3) ),
inference(paramod,[status(thm)],[c_110,c_2146]) ).
cnf(c_2148,plain,
( holdsAt(filling,plus(n1,n2))
| happens(sK4(filling,n2),n2)
| releasedAt(filling,n3) ),
inference(paramod,[status(thm)],[c_104,c_2147]) ).
cnf(c_1696,plain,
( holdsAt(filling,n3)
| happens(sK4(filling,n2),n2)
| releasedAt(filling,n3) ),
inference(paramod,[status(thm)],[c_110,c_2148]) ).
cnf(c_2149,plain,
( releasedAt(filling,n2)
| waterLevel(sK3(sK2(filling,n2),filling,n2)) = filling
| holdsAt(filling,n3)
| happens(sK4(filling,n2),n2) ),
inference(resolve,[status(thm)],[c_1696,c_377]) ).
cnf(c_1703,plain,
( releasedAt(filling,n2)
| holdsAt(filling,n3)
| happens(sK4(filling,n2),n2) ),
inference(resolve,[status(thm)],[c_122,c_2149]) ).
cnf(c_2150,plain,
( releasedAt(filling,n1)
| waterLevel(sK3(sK2(filling,n1),filling,n1)) = filling
| holdsAt(filling,n3)
| happens(sK4(filling,n2),n2) ),
inference(resolve,[status(thm)],[c_1703,c_200]) ).
cnf(c_2151,plain,
( releasedAt(filling,n1)
| holdsAt(filling,n3)
| happens(sK4(filling,n2),n2) ),
inference(resolve,[status(thm)],[c_122,c_2150]) ).
cnf(c_1713,plain,
( holdsAt(filling,n3)
| happens(sK4(filling,n2),n2) ),
inference(resolve,[status(thm)],[c_505,c_2151]) ).
cnf(c_2152,plain,
( holdsAt(waterLevel(n3),n2)
| n0 = n2
| holdsAt(filling,n3) ),
inference(resolve,[status(thm)],[c_1713,c_131]) ).
cnf(c_2153,plain,
( holdsAt(waterLevel(n3),n2)
| n2 = n0
| holdsAt(filling,n3) ),
inference(copy,[status(thm)],[c_2152]) ).
cnf(c_1716,plain,
( holdsAt(waterLevel(n3),n2)
| holdsAt(filling,n3) ),
inference(resolve,[status(thm)],[c_270,c_2153]) ).
cnf(c_1727,plain,
( waterLevel(n3) != B
| overflow != A
| initiates(A,B,n2)
| holdsAt(filling,n3) ),
inference(resolve,[status(thm)],[c_1716,c_139]) ).
cnf(c_2154,plain,
( overflow != A
| ~ holdsAt(filling,n2)
| happens(A,n2)
| holdsAt(filling,n3) ),
inference(resolve,[status(thm)],[c_1716,c_127]) ).
cnf(c_1728,plain,
( overflow != A
| happens(A,n2)
| holdsAt(filling,n3) ),
inference(resolve,[status(thm)],[c_1693,c_2154]) ).
cnf(c_2155,plain,
A = sK3(tapOn,waterLevel(A),B),
inference(copy,[status(thm)],[c_499]) ).
cnf(c_2156,plain,
( happens(sK3(tapOn,waterLevel(overflow),A),n2)
| holdsAt(filling,n3) ),
inference(resolve,[status(thm)],[c_1728,c_2155]) ).
cnf(c_1734,plain,
( happens(overflow,n2)
| holdsAt(filling,n3) ),
inference(paramod,[status(thm)],[c_499,c_2156]) ).
cnf(c_2157,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_924,c_893]) ).
cnf(c_2158,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_2157]) ).
cnf(c_2159,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_2158]) ).
cnf(c_2160,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_2159]) ).
cnf(c_2161,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_2160]) ).
cnf(c_2162,plain,
( n3 = n0
| n4 = n0
| n3 != A
| less(n0,sK0(n0,filling,n3))
| holdsAt(waterLevel(A),n3) ),
inference(resolve,[status(thm)],[c_369,c_2161]) ).
cnf(c_2163,plain,
( n3 = n0
| n3 != A
| less(n0,sK0(n0,filling,n3))
| holdsAt(waterLevel(A),n3) ),
inference(resolve,[status(thm)],[c_339,c_2162]) ).
cnf(c_1775,plain,
( n3 != A
| less(n0,sK0(n0,filling,n3))
| holdsAt(waterLevel(A),n3) ),
inference(resolve,[status(thm)],[c_304,c_2163]) ).
cnf(c_2164,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_925,c_893]) ).
cnf(c_2165,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_2164]) ).
cnf(c_2166,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_2165]) ).
cnf(c_2167,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_2166]) ).
cnf(c_2168,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_2167]) ).
cnf(c_2169,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_2168]) ).
cnf(c_2170,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_369,c_2169]) ).
cnf(c_2171,plain,
( n3 = n0
| n3 != A
| happens(sK1(n0,filling,n3),sK0(n0,filling,n3))
| holdsAt(waterLevel(A),n3) ),
inference(resolve,[status(thm)],[c_339,c_2170]) ).
cnf(c_1798,plain,
( n3 != A
| happens(sK1(n0,filling,n3),sK0(n0,filling,n3))
| holdsAt(waterLevel(A),n3) ),
inference(resolve,[status(thm)],[c_304,c_2171]) ).
cnf(c_2172,plain,
A = sK3(tapOn,waterLevel(A),B),
inference(copy,[status(thm)],[c_499]) ).
cnf(c_2173,plain,
( less(n0,sK0(n0,filling,n3))
| holdsAt(waterLevel(sK3(tapOn,waterLevel(n3),A)),n3) ),
inference(resolve,[status(thm)],[c_1775,c_2172]) ).
cnf(c_2174,plain,
( less(n0,sK0(n0,filling,n3))
| holdsAt(waterLevel(n3),n3) ),
inference(paramod,[status(thm)],[c_499,c_2173]) ).
cnf(c_1824,negated_conjecture,
less(n0,sK0(n0,filling,n3)),
inference(resolve,[status(thm)],[c_72,c_2174]) ).
cnf(c_1830,plain,
sK0(n0,filling,n3) != n0,
inference(resolve,[status(thm)],[c_1824,c_80]) ).
cnf(c_1831,plain,
( sK0(n0,filling,n3) = n1
| sK0(n0,filling,n3) = n2 ),
inference(resolve,[status(thm)],[c_1830,c_1598]) ).
cnf(c_2175,plain,
A = sK3(tapOn,waterLevel(A),B),
inference(copy,[status(thm)],[c_499]) ).
cnf(c_2176,plain,
( waterLevel(n3) != B
| initiates(sK3(tapOn,waterLevel(overflow),A),B,n2)
| holdsAt(filling,n3) ),
inference(resolve,[status(thm)],[c_1727,c_2175]) ).
cnf(c_1842,plain,
( waterLevel(n3) != A
| initiates(overflow,A,n2)
| holdsAt(filling,n3) ),
inference(paramod,[status(thm)],[c_499,c_2176]) ).
cnf(c_2177,plain,
A = sK3(tapOn,waterLevel(A),B),
inference(copy,[status(thm)],[c_499]) ).
cnf(c_2178,plain,
( initiates(overflow,sK3(tapOn,waterLevel(waterLevel(n3)),A),n2)
| holdsAt(filling,n3) ),
inference(resolve,[status(thm)],[c_1842,c_2177]) ).
cnf(c_1844,plain,
( initiates(overflow,waterLevel(n3),n2)
| holdsAt(filling,n3) ),
inference(paramod,[status(thm)],[c_499,c_2178]) ).
cnf(c_2179,plain,
( holdsAt(waterLevel(n3),plus(n2,n1))
| ~ happens(overflow,n2)
| holdsAt(filling,n3) ),
inference(resolve,[status(thm)],[c_1844,c_164]) ).
cnf(c_2180,plain,
( holdsAt(waterLevel(n3),plus(n1,n2))
| ~ happens(overflow,n2)
| holdsAt(filling,n3) ),
inference(paramod,[status(thm)],[c_104,c_2179]) ).
cnf(c_2181,plain,
( holdsAt(waterLevel(n3),n3)
| ~ happens(overflow,n2)
| holdsAt(filling,n3) ),
inference(paramod,[status(thm)],[c_110,c_2180]) ).
cnf(c_1858,negated_conjecture,
( ~ happens(overflow,n2)
| holdsAt(filling,n3) ),
inference(resolve,[status(thm)],[c_72,c_2181]) ).
cnf(c_2182,plain,
( holdsAt(filling,n3)
| holdsAt(filling,n3) ),
inference(resolve,[status(thm)],[c_1858,c_1734]) ).
cnf(c_1863,plain,
holdsAt(filling,n3),
inference(copy,[status(thm)],[c_2182]) ).
cnf(c_2183,plain,
A = sK3(tapOn,waterLevel(A),B),
inference(copy,[status(thm)],[c_499]) ).
cnf(c_2184,plain,
( happens(sK1(n0,filling,n3),sK0(n0,filling,n3))
| holdsAt(waterLevel(sK3(tapOn,waterLevel(n3),A)),n3) ),
inference(resolve,[status(thm)],[c_1798,c_2183]) ).
cnf(c_2185,plain,
( happens(sK1(n0,filling,n3),sK0(n0,filling,n3))
| holdsAt(waterLevel(n3),n3) ),
inference(paramod,[status(thm)],[c_499,c_2184]) ).
cnf(c_2039,negated_conjecture,
happens(sK1(n0,filling,n3),sK0(n0,filling,n3)),
inference(resolve,[status(thm)],[c_72,c_2185]) ).
cnf(c_2186,plain,
( overflow = sK1(n0,filling,n3)
| n0 = sK0(n0,filling,n3) ),
inference(resolve,[status(thm)],[c_2039,c_129]) ).
cnf(c_2187,plain,
( overflow = sK1(n0,filling,n3)
| sK0(n0,filling,n3) = n0 ),
inference(copy,[status(thm)],[c_2186]) ).
cnf(c_2188,plain,
( sK1(n0,filling,n3) = overflow
| sK0(n0,filling,n3) = n0 ),
inference(copy,[status(thm)],[c_2187]) ).
cnf(c_2045,plain,
sK1(n0,filling,n3) = overflow,
inference(resolve,[status(thm)],[c_1830,c_2188]) ).
cnf(c_2047,negated_conjecture,
happens(overflow,sK0(n0,filling,n3)),
inference(paramod,[status(thm)],[c_2045,c_2039]) ).
cnf(c_2189,plain,
~ holdsAt(filling,plus(sK0(n0,filling,n3),n1)),
inference(resolve,[status(thm)],[c_2047,c_427]) ).
cnf(c_2059,plain,
~ holdsAt(filling,plus(n1,sK0(n0,filling,n3))),
inference(paramod,[status(thm)],[c_104,c_2189]) ).
cnf(c_2190,plain,
( ~ holdsAt(filling,plus(n1,n2))
| sK0(n0,filling,n3) = n1 ),
inference(paramod,[status(thm)],[c_1831,c_2059]) ).
cnf(c_2191,plain,
( ~ holdsAt(filling,n3)
| sK0(n0,filling,n3) = n1 ),
inference(paramod,[status(thm)],[c_110,c_2190]) ).
cnf(c_2074,plain,
sK0(n0,filling,n3) = n1,
inference(resolve,[status(thm)],[c_1863,c_2191]) ).
cnf(c_2192,plain,
~ holdsAt(filling,plus(n1,n1)),
inference(paramod,[status(thm)],[c_2074,c_2059]) ).
cnf(c_2193,plain,
~ holdsAt(filling,n2),
inference(paramod,[status(thm)],[c_111,c_2192]) ).
cnf(c_2087,plain,
$false,
inference(resolve,[status(thm)],[c_1693,c_2193]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : CSR006+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n017.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sat Sep 26 23:50:04 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 1949103 was started by sandbox on n017,
% 0.18/0.43 % Sat Sep 26 23:50:04 2026
% 0.18/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 17.83/2.75
% 17.83/2.75 % given #500 (T,wt=9): 654 n1 = A | less(A,n4) | -less(A,n1). [resolve(641,a,81,b)].
% 17.83/2.75
% 17.83/2.75 % given #1000 (T,wt=12): 1689 holdsAt(filling,n2) | happens(f8(waterLevel(n3),n2),n2) | -happens(overflow,n1). [resolve(1684,b,968,c),merge(c)].
% 17.83/2.75
% 17.83/2.75 % SZS status Theorem for theBenchmark
% 17.83/2.75
% 17.83/2.75 % Proof 1 at 1.57 (+ 0.68) seconds.
% 17.83/2.75 % Length of proof is 185.
% 17.83/2.75 % Level of proof is 30.
% 17.83/2.75 % Maximum clause weight is 38.000.
% 17.83/2.75 % Given clauses 1354.
% 17.83/2.75
% 17.83/2.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
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