%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CSR008+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 : n010.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 8.14s 13.52s
% Output : CNFRefutation 8.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 29
% Syntax : Number of formulae : 271 ( 71 unt; 0 def)
% Number of atoms : 905 ( 361 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 876 ( 242 ~; 560 |; 54 &)
% ( 12 <=>; 8 =>; 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 : 17 ( 17 usr; 10 con; 0-3 aty)
% Number of variables : 379 ( 27 sgn 113 !; 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(same_waterLevel,axiom,
! [Time,Height1,Height2] :
( ( holdsAt(waterLevel(Height2),Time)
& holdsAt(waterLevel(Height1),Time) )
=> Height1 = Height2 ),
file('theBenchmark.p',same_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(less_property,axiom,
! [X,Y] :
( less(X,Y)
<=> ( Y != X
& ~ less(Y,X) ) ),
file('theBenchmark.p',less_property) ).
fof(waterLevel_2,conjecture,
holdsAt(waterLevel(n2),n2),
file('theBenchmark.p',waterLevel_2) ).
fof(waterLevel_2_neg,negated_conjecture,
~ holdsAt(waterLevel(n2),n2),
inference(assume_negation,[status(cth)],[waterLevel_2]) ).
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(n2),n2),
inference(clausify,[status(thm)],[waterLevel_2_neg]) ).
fof(waterLevel_0,axiom,
holdsAt(waterLevel(n0),n0),
file('theBenchmark.p',waterLevel_0) ).
cnf(c_78,plain,
holdsAt(waterLevel(n0),n0),
inference(clausify,[status(thm)],[waterLevel_0]) ).
cnf(c_79,plain,
( B = A
| less(B,A)
| less(A,B) ),
inference(clausify,[status(thm)],[less_property]) ).
cnf(c_80,plain,
( B != A
| ~ less(A,B) ),
inference(clausify,[status(thm)],[less_property]) ).
cnf(c_81,plain,
( ~ less(B,A)
| ~ less(A,B) ),
inference(clausify,[status(thm)],[less_property]) ).
cnf(c_92,plain,
( ~ less_or_equal(A,n3)
| less(A,n4) ),
inference(clausify,[status(thm)],[less4]) ).
cnf(c_93,plain,
( less_or_equal(A,n3)
| ~ less(A,n4) ),
inference(clausify,[status(thm)],[less4]) ).
cnf(c_94,plain,
( ~ less_or_equal(A,n2)
| less(A,n3) ),
inference(clausify,[status(thm)],[less3]) ).
cnf(c_95,plain,
( less_or_equal(A,n2)
| ~ less(A,n3) ),
inference(clausify,[status(thm)],[less3]) ).
cnf(c_96,plain,
( ~ less_or_equal(A,n1)
| less(A,n2) ),
inference(clausify,[status(thm)],[less2]) ).
cnf(c_97,plain,
( less_or_equal(A,n1)
| ~ less(A,n2) ),
inference(clausify,[status(thm)],[less2]) ).
cnf(c_98,plain,
( ~ less_or_equal(A,n0)
| less(A,n1) ),
inference(clausify,[status(thm)],[less1]) ).
cnf(c_99,plain,
( less_or_equal(A,n0)
| ~ less(A,n1) ),
inference(clausify,[status(thm)],[less1]) ).
cnf(c_100,plain,
~ less(A,n0),
inference(clausify,[status(thm)],[less0]) ).
cnf(c_101,plain,
( B != A
| less_or_equal(A,B) ),
inference(clausify,[status(thm)],[less_or_equal]) ).
cnf(c_102,plain,
( ~ less(A,B)
| less_or_equal(A,B) ),
inference(clausify,[status(thm)],[less_or_equal]) ).
cnf(c_103,plain,
( B = A
| less(A,B)
| ~ less_or_equal(A,B) ),
inference(clausify,[status(thm)],[less_or_equal]) ).
cnf(c_104,plain,
plus(A,B) = plus(B,A),
inference(clausify,[status(thm)],[symmetry_of_plus]) ).
fof(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_2,axiom,
plus(n0,n2) = n2,
file('theBenchmark.p',plus0_2) ).
cnf(c_113,plain,
plus(n0,n2) = n2,
inference(clausify,[status(thm)],[plus0_2]) ).
fof(plus0_1,axiom,
plus(n0,n1) = n1,
file('theBenchmark.p',plus0_1) ).
cnf(c_114,plain,
plus(n0,n1) = n1,
inference(clausify,[status(thm)],[plus0_1]) ).
cnf(c_115,plain,
plus(n1,n0) = n1,
inference(paramod,[status(thm)],[c_104,c_114]) ).
fof(plus0_0,axiom,
plus(n0,n0) = n0,
file('theBenchmark.p',plus0_0) ).
cnf(c_116,plain,
plus(n0,n0) = n0,
inference(clausify,[status(thm)],[plus0_0]) ).
cnf(c_118,plain,
( A = B
| waterLevel(A) != waterLevel(B) ),
inference(clausify,[status(thm)],[distinct_waterLevels]) ).
cnf(c_122,plain,
waterLevel(A) != filling,
inference(clausify,[status(thm)],[filling_not_waterLevel]) ).
cnf(c_126,plain,
( C = A
| ~ holdsAt(waterLevel(C),B)
| ~ holdsAt(waterLevel(A),B) ),
inference(clausify,[status(thm)],[same_waterLevel]) ).
cnf(c_128,plain,
( n0 != B
| tapOn != A
| happens(A,B) ),
inference(clausify,[status(thm)],[happens_all_defn]) ).
cnf(c_129,plain,
( overflow = A
| 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_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]) ).
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_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_180,plain,
~ less(A,A),
inference(factor,[status(thm)],[c_81]) ).
cnf(c_181,plain,
( waterLevel(sK3(tapOn,B,C)) = B
| waterLevel(A) != B ),
inference(xxres,[status(thm)],[c_60]) ).
cnf(c_2581,plain,
( A = n4
| less(n4,A)
| less_or_equal(A,n3) ),
inference(resolve,[status(thm)],[c_93,c_79]) ).
cnf(c_189,plain,
( n4 = A
| less(n4,A)
| less_or_equal(A,n3) ),
inference(copy,[status(thm)],[c_2581]) ).
cnf(c_2582,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_2582]) ).
cnf(c_2583,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_2583]) ).
cnf(c_2584,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_2584]) ).
cnf(c_194,plain,
less_or_equal(A,A),
inference(xxres,[status(thm)],[c_101]) ).
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_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_225,plain,
less(n1,n2),
inference(resolve,[status(thm)],[c_194,c_96]) ).
cnf(c_233,plain,
less_or_equal(n0,n1),
inference(resolve,[status(thm)],[c_224,c_102]) ).
cnf(c_2585,plain,
n1 != n0,
inference(resolve,[status(thm)],[c_224,c_80]) ).
cnf(c_234,plain,
n0 != n1,
inference(copy,[status(thm)],[c_2585]) ).
cnf(c_235,plain,
less_or_equal(n1,n2),
inference(resolve,[status(thm)],[c_225,c_102]) ).
cnf(c_259,plain,
less(n0,n2),
inference(resolve,[status(thm)],[c_233,c_96]) ).
cnf(c_260,plain,
less(n1,n3),
inference(resolve,[status(thm)],[c_235,c_94]) ).
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_274,plain,
n3 != n1,
inference(resolve,[status(thm)],[c_260,c_80]) ).
cnf(c_294,plain,
less(n0,n3),
inference(resolve,[status(thm)],[c_269,c_94]) ).
cnf(c_300,plain,
( n3 = A
| less(A,n3)
| n4 = A
| less(n4,A) ),
inference(resolve,[status(thm)],[c_189,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_2586,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_2586]) ).
cnf(c_339,plain,
n4 != n0,
inference(resolve,[status(thm)],[c_325,c_80]) ).
cnf(c_2587,plain,
n0 = plus(n0,n0),
inference(copy,[status(thm)],[c_116]) ).
cnf(c_2588,plain,
happens(tapOn,plus(n0,n0)),
inference(resolve,[status(thm)],[c_203,c_2587]) ).
cnf(c_416,plain,
happens(tapOn,n0),
inference(paramod,[status(thm)],[c_116,c_2588]) ).
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_484,plain,
( ~ releasedAt(filling,plus(n1,A))
| ~ happens(tapOn,A) ),
inference(paramod,[status(thm)],[c_104,c_460]) ).
cnf(c_2589,plain,
holdsAt(filling,plus(n0,n1)),
inference(resolve,[status(thm)],[c_459,c_416]) ).
cnf(c_2590,plain,
holdsAt(filling,plus(n1,n0)),
inference(paramod,[status(thm)],[c_104,c_2589]) ).
cnf(c_489,plain,
holdsAt(filling,n1),
inference(paramod,[status(thm)],[c_115,c_2590]) ).
cnf(c_2591,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_2592,plain,
( holdsAt(filling,plus(n1,n1))
| happens(sK4(filling,n1),n1)
| releasedAt(filling,n2) ),
inference(paramod,[status(thm)],[c_111,c_2591]) ).
cnf(c_490,plain,
( holdsAt(filling,n2)
| happens(sK4(filling,n1),n1)
| releasedAt(filling,n2) ),
inference(paramod,[status(thm)],[c_111,c_2592]) ).
cnf(c_499,plain,
sK3(tapOn,waterLevel(A),B) = A,
inference(resolve,[status(thm)],[c_223,c_118]) ).
cnf(c_2593,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_2593]) ).
cnf(c_507,plain,
( ~ less(A,n1)
| n0 = A
| n1 = A ),
inference(resolve,[status(thm)],[c_327,c_81]) ).
cnf(c_579,plain,
( less_or_equal(A,n2)
| n3 = A
| n4 = A
| less(n4,A) ),
inference(resolve,[status(thm)],[c_300,c_95]) ).
cnf(c_584,plain,
( less_or_equal(A,n1)
| n2 = A
| n3 = A
| less(n3,A) ),
inference(resolve,[status(thm)],[c_305,c_97]) ).
cnf(c_2594,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_2594]) ).
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_2595,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_2596,plain,
( releasedAt(filling,n1)
| holdsAt(filling,n2)
| happens(sK4(filling,n1),n1) ),
inference(resolve,[status(thm)],[c_122,c_2595]) ).
cnf(c_804,plain,
( holdsAt(filling,n2)
| happens(sK4(filling,n1),n1) ),
inference(resolve,[status(thm)],[c_505,c_2596]) ).
cnf(c_2597,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_2597]) ).
cnf(c_815,plain,
( n3 = A
| ~ holdsAt(waterLevel(A),n1)
| holdsAt(filling,n2) ),
inference(resolve,[status(thm)],[c_807,c_126]) ).
cnf(c_894,plain,
( n2 = A
| less(A,n2)
| n3 = A
| n4 = A
| less(n4,A) ),
inference(resolve,[status(thm)],[c_579,c_103]) ).
cnf(c_895,plain,
( n1 = A
| less(A,n1)
| n2 = A
| n3 = A
| less(n3,A) ),
inference(resolve,[status(thm)],[c_584,c_103]) ).
cnf(c_898,plain,
( ~ less(A,n2)
| n0 = A
| n1 = A
| n2 = A ),
inference(resolve,[status(thm)],[c_589,c_81]) ).
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_2598,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| plus(n0,n1) != A
| less(sK0(n0,filling,plus(n0,n1)),plus(n0,n1))
| holdsAt(waterLevel(A),plus(n0,n1)) ),
inference(resolve,[status(thm)],[c_900,c_895]) ).
cnf(c_2599,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| plus(n0,n1) != A
| less(sK0(n0,filling,plus(n0,n1)),plus(n0,n1))
| holdsAt(waterLevel(A),plus(n1,n0)) ),
inference(paramod,[status(thm)],[c_104,c_2598]) ).
cnf(c_2600,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| plus(n0,n1) != A
| less(sK0(n0,filling,plus(n0,n1)),plus(n0,n1))
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_115,c_2599]) ).
cnf(c_2601,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| plus(n0,n1) != A
| less(sK0(n0,filling,plus(n1,n0)),plus(n0,n1))
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_104,c_2600]) ).
cnf(c_2602,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| plus(n0,n1) != A
| less(sK0(n0,filling,n1),plus(n0,n1))
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_115,c_2601]) ).
cnf(c_2603,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| plus(n0,n1) != A
| less(sK0(n0,filling,n1),plus(n1,n0))
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_104,c_2602]) ).
cnf(c_2604,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| plus(n0,n1) != A
| less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_115,c_2603]) ).
cnf(c_2605,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| plus(n1,n0) != A
| less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_104,c_2604]) ).
cnf(c_2606,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| n1 != A
| less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_115,c_2605]) ).
cnf(c_2607,plain,
( n0 = n1
| n2 = n0
| n3 = n0
| less(n3,n0)
| n1 != A
| less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(A),n1) ),
inference(copy,[status(thm)],[c_2606]) ).
cnf(c_2608,plain,
( n0 = n1
| n2 = n0
| n3 = n0
| n1 != A
| less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(A),n1) ),
inference(resolve,[status(thm)],[c_100,c_2607]) ).
cnf(c_2609,plain,
( n0 = n1
| n2 = n0
| n1 != A
| less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(A),n1) ),
inference(resolve,[status(thm)],[c_304,c_2608]) ).
cnf(c_2610,plain,
( n0 = n1
| n1 != A
| less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(A),n1) ),
inference(resolve,[status(thm)],[c_270,c_2609]) ).
cnf(c_1531,plain,
( n1 != A
| less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(A),n1) ),
inference(resolve,[status(thm)],[c_234,c_2610]) ).
cnf(c_2611,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| less(n4,n0)
| plus(n0,n2) != A
| less(sK0(n0,filling,plus(n0,n2)),plus(n0,n2))
| holdsAt(waterLevel(A),plus(n0,n2)) ),
inference(resolve,[status(thm)],[c_900,c_894]) ).
cnf(c_2612,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| less(n4,n0)
| plus(n0,n2) != A
| less(sK0(n0,filling,plus(n0,n2)),plus(n0,n2))
| holdsAt(waterLevel(A),n2) ),
inference(paramod,[status(thm)],[c_113,c_2611]) ).
cnf(c_2613,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| less(n4,n0)
| plus(n0,n2) != A
| less(sK0(n0,filling,n2),plus(n0,n2))
| holdsAt(waterLevel(A),n2) ),
inference(paramod,[status(thm)],[c_113,c_2612]) ).
cnf(c_2614,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| less(n4,n0)
| plus(n0,n2) != A
| less(sK0(n0,filling,n2),n2)
| holdsAt(waterLevel(A),n2) ),
inference(paramod,[status(thm)],[c_113,c_2613]) ).
cnf(c_2615,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| less(n4,n0)
| n2 != A
| less(sK0(n0,filling,n2),n2)
| holdsAt(waterLevel(A),n2) ),
inference(paramod,[status(thm)],[c_113,c_2614]) ).
cnf(c_2616,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| n2 != A
| less(sK0(n0,filling,n2),n2)
| holdsAt(waterLevel(A),n2) ),
inference(resolve,[status(thm)],[c_100,c_2615]) ).
cnf(c_2617,plain,
( n2 = n0
| n3 = n0
| n2 != A
| less(sK0(n0,filling,n2),n2)
| holdsAt(waterLevel(A),n2) ),
inference(resolve,[status(thm)],[c_339,c_2616]) ).
cnf(c_2618,plain,
( n2 = n0
| n2 != A
| less(sK0(n0,filling,n2),n2)
| holdsAt(waterLevel(A),n2) ),
inference(resolve,[status(thm)],[c_304,c_2617]) ).
cnf(c_1532,plain,
( n2 != A
| less(sK0(n0,filling,n2),n2)
| holdsAt(waterLevel(A),n2) ),
inference(resolve,[status(thm)],[c_270,c_2618]) ).
cnf(c_2619,plain,
A = sK3(tapOn,waterLevel(A),B),
inference(copy,[status(thm)],[c_499]) ).
cnf(c_2620,plain,
( less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(sK3(tapOn,waterLevel(n1),A)),n1) ),
inference(resolve,[status(thm)],[c_1531,c_2619]) ).
cnf(c_1557,plain,
( less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(n1),n1) ),
inference(paramod,[status(thm)],[c_499,c_2620]) ).
cnf(c_2621,plain,
( n3 = n1
| holdsAt(filling,n2)
| less(sK0(n0,filling,n1),n1) ),
inference(resolve,[status(thm)],[c_1557,c_815]) ).
cnf(c_1559,plain,
( holdsAt(filling,n2)
| less(sK0(n0,filling,n1),n1) ),
inference(resolve,[status(thm)],[c_274,c_2621]) ).
cnf(c_2622,plain,
A = sK3(tapOn,waterLevel(A),B),
inference(copy,[status(thm)],[c_499]) ).
cnf(c_2623,plain,
( less(sK0(n0,filling,n2),n2)
| holdsAt(waterLevel(sK3(tapOn,waterLevel(n2),A)),n2) ),
inference(resolve,[status(thm)],[c_1532,c_2622]) ).
cnf(c_2624,plain,
( less(sK0(n0,filling,n2),n2)
| holdsAt(waterLevel(n2),n2) ),
inference(paramod,[status(thm)],[c_499,c_2623]) ).
cnf(c_1568,negated_conjecture,
less(sK0(n0,filling,n2),n2),
inference(resolve,[status(thm)],[c_72,c_2624]) ).
cnf(c_2625,plain,
( n0 = sK0(n0,filling,n2)
| n1 = sK0(n0,filling,n2)
| n2 = sK0(n0,filling,n2) ),
inference(resolve,[status(thm)],[c_1568,c_898]) ).
cnf(c_2626,plain,
( n0 = sK0(n0,filling,n2)
| n1 = sK0(n0,filling,n2)
| sK0(n0,filling,n2) = n2 ),
inference(copy,[status(thm)],[c_2625]) ).
cnf(c_2627,plain,
( n0 = sK0(n0,filling,n2)
| sK0(n0,filling,n2) = n1
| sK0(n0,filling,n2) = n2 ),
inference(copy,[status(thm)],[c_2626]) ).
cnf(c_1569,plain,
( sK0(n0,filling,n2) = n0
| sK0(n0,filling,n2) = n1
| sK0(n0,filling,n2) = n2 ),
inference(copy,[status(thm)],[c_2627]) ).
cnf(c_2628,plain,
n2 != sK0(n0,filling,n2),
inference(resolve,[status(thm)],[c_1568,c_80]) ).
cnf(c_1581,plain,
sK0(n0,filling,n2) != n2,
inference(copy,[status(thm)],[c_2628]) ).
cnf(c_1590,plain,
( sK0(n0,filling,n2) = n0
| sK0(n0,filling,n2) = n1 ),
inference(resolve,[status(thm)],[c_1581,c_1569]) ).
cnf(c_2629,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| plus(n0,n1) != A
| less(n0,sK0(n0,filling,plus(n0,n1)))
| holdsAt(waterLevel(A),plus(n0,n1)) ),
inference(resolve,[status(thm)],[c_924,c_895]) ).
cnf(c_2630,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| plus(n0,n1) != A
| less(n0,sK0(n0,filling,plus(n0,n1)))
| holdsAt(waterLevel(A),plus(n1,n0)) ),
inference(paramod,[status(thm)],[c_104,c_2629]) ).
cnf(c_2631,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| plus(n0,n1) != A
| less(n0,sK0(n0,filling,plus(n0,n1)))
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_115,c_2630]) ).
cnf(c_2632,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| plus(n0,n1) != A
| less(n0,sK0(n0,filling,plus(n1,n0)))
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_104,c_2631]) ).
cnf(c_2633,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| plus(n0,n1) != A
| less(n0,sK0(n0,filling,n1))
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_115,c_2632]) ).
cnf(c_2634,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| plus(n1,n0) != A
| less(n0,sK0(n0,filling,n1))
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_104,c_2633]) ).
cnf(c_2635,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| n1 != A
| less(n0,sK0(n0,filling,n1))
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_115,c_2634]) ).
cnf(c_2636,plain,
( n0 = n1
| n2 = n0
| n3 = n0
| less(n3,n0)
| n1 != A
| less(n0,sK0(n0,filling,n1))
| holdsAt(waterLevel(A),n1) ),
inference(copy,[status(thm)],[c_2635]) ).
cnf(c_2637,plain,
( n0 = n1
| n2 = n0
| n3 = n0
| n1 != A
| less(n0,sK0(n0,filling,n1))
| holdsAt(waterLevel(A),n1) ),
inference(resolve,[status(thm)],[c_100,c_2636]) ).
cnf(c_2638,plain,
( n0 = n1
| n2 = n0
| n1 != A
| less(n0,sK0(n0,filling,n1))
| holdsAt(waterLevel(A),n1) ),
inference(resolve,[status(thm)],[c_304,c_2637]) ).
cnf(c_2639,plain,
( n0 = n1
| n1 != A
| less(n0,sK0(n0,filling,n1))
| holdsAt(waterLevel(A),n1) ),
inference(resolve,[status(thm)],[c_270,c_2638]) ).
cnf(c_1901,plain,
( n1 != A
| less(n0,sK0(n0,filling,n1))
| holdsAt(waterLevel(A),n1) ),
inference(resolve,[status(thm)],[c_234,c_2639]) ).
cnf(c_2640,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| less(n4,n0)
| plus(n0,n2) != A
| less(n0,sK0(n0,filling,plus(n0,n2)))
| holdsAt(waterLevel(A),plus(n0,n2)) ),
inference(resolve,[status(thm)],[c_924,c_894]) ).
cnf(c_2641,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| less(n4,n0)
| plus(n0,n2) != A
| less(n0,sK0(n0,filling,plus(n0,n2)))
| holdsAt(waterLevel(A),n2) ),
inference(paramod,[status(thm)],[c_113,c_2640]) ).
cnf(c_2642,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| less(n4,n0)
| plus(n0,n2) != A
| less(n0,sK0(n0,filling,n2))
| holdsAt(waterLevel(A),n2) ),
inference(paramod,[status(thm)],[c_113,c_2641]) ).
cnf(c_2643,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| less(n4,n0)
| n2 != A
| less(n0,sK0(n0,filling,n2))
| holdsAt(waterLevel(A),n2) ),
inference(paramod,[status(thm)],[c_113,c_2642]) ).
cnf(c_2644,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| n2 != A
| less(n0,sK0(n0,filling,n2))
| holdsAt(waterLevel(A),n2) ),
inference(resolve,[status(thm)],[c_100,c_2643]) ).
cnf(c_2645,plain,
( n2 = n0
| n3 = n0
| n2 != A
| less(n0,sK0(n0,filling,n2))
| holdsAt(waterLevel(A),n2) ),
inference(resolve,[status(thm)],[c_339,c_2644]) ).
cnf(c_2646,plain,
( n2 = n0
| n2 != A
| less(n0,sK0(n0,filling,n2))
| holdsAt(waterLevel(A),n2) ),
inference(resolve,[status(thm)],[c_304,c_2645]) ).
cnf(c_1902,plain,
( n2 != A
| less(n0,sK0(n0,filling,n2))
| holdsAt(waterLevel(A),n2) ),
inference(resolve,[status(thm)],[c_270,c_2646]) ).
cnf(c_2647,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| less(n4,n0)
| plus(n0,n2) != A
| happens(sK1(n0,filling,plus(n0,n2)),sK0(n0,filling,plus(n0,n2)))
| holdsAt(waterLevel(A),plus(n0,n2)) ),
inference(resolve,[status(thm)],[c_925,c_894]) ).
cnf(c_2648,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| less(n4,n0)
| plus(n0,n2) != A
| happens(sK1(n0,filling,plus(n0,n2)),sK0(n0,filling,plus(n0,n2)))
| holdsAt(waterLevel(A),n2) ),
inference(paramod,[status(thm)],[c_113,c_2647]) ).
cnf(c_2649,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| less(n4,n0)
| plus(n0,n2) != A
| happens(sK1(n0,filling,n2),sK0(n0,filling,plus(n0,n2)))
| holdsAt(waterLevel(A),n2) ),
inference(paramod,[status(thm)],[c_113,c_2648]) ).
cnf(c_2650,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| less(n4,n0)
| plus(n0,n2) != A
| happens(sK1(n0,filling,n2),sK0(n0,filling,n2))
| holdsAt(waterLevel(A),n2) ),
inference(paramod,[status(thm)],[c_113,c_2649]) ).
cnf(c_2651,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| less(n4,n0)
| n2 != A
| happens(sK1(n0,filling,n2),sK0(n0,filling,n2))
| holdsAt(waterLevel(A),n2) ),
inference(paramod,[status(thm)],[c_113,c_2650]) ).
cnf(c_2652,plain,
( n2 = n0
| n3 = n0
| n4 = n0
| n2 != A
| happens(sK1(n0,filling,n2),sK0(n0,filling,n2))
| holdsAt(waterLevel(A),n2) ),
inference(resolve,[status(thm)],[c_100,c_2651]) ).
cnf(c_2653,plain,
( n2 = n0
| n3 = n0
| n2 != A
| happens(sK1(n0,filling,n2),sK0(n0,filling,n2))
| holdsAt(waterLevel(A),n2) ),
inference(resolve,[status(thm)],[c_339,c_2652]) ).
cnf(c_2654,plain,
( n2 = n0
| n2 != A
| happens(sK1(n0,filling,n2),sK0(n0,filling,n2))
| holdsAt(waterLevel(A),n2) ),
inference(resolve,[status(thm)],[c_304,c_2653]) ).
cnf(c_1940,plain,
( n2 != A
| happens(sK1(n0,filling,n2),sK0(n0,filling,n2))
| holdsAt(waterLevel(A),n2) ),
inference(resolve,[status(thm)],[c_270,c_2654]) ).
cnf(c_2655,plain,
A = sK3(tapOn,waterLevel(A),B),
inference(copy,[status(thm)],[c_499]) ).
cnf(c_2656,plain,
( less(n0,sK0(n0,filling,n1))
| holdsAt(waterLevel(sK3(tapOn,waterLevel(n1),A)),n1) ),
inference(resolve,[status(thm)],[c_1901,c_2655]) ).
cnf(c_1956,plain,
( less(n0,sK0(n0,filling,n1))
| holdsAt(waterLevel(n1),n1) ),
inference(paramod,[status(thm)],[c_499,c_2656]) ).
cnf(c_2657,plain,
( n3 = n1
| holdsAt(filling,n2)
| less(n0,sK0(n0,filling,n1)) ),
inference(resolve,[status(thm)],[c_1956,c_815]) ).
cnf(c_1959,plain,
( holdsAt(filling,n2)
| less(n0,sK0(n0,filling,n1)) ),
inference(resolve,[status(thm)],[c_274,c_2657]) ).
cnf(c_2658,plain,
A = sK3(tapOn,waterLevel(A),B),
inference(copy,[status(thm)],[c_499]) ).
cnf(c_2659,plain,
( less(n0,sK0(n0,filling,n2))
| holdsAt(waterLevel(sK3(tapOn,waterLevel(n2),A)),n2) ),
inference(resolve,[status(thm)],[c_1902,c_2658]) ).
cnf(c_2660,plain,
( less(n0,sK0(n0,filling,n2))
| holdsAt(waterLevel(n2),n2) ),
inference(paramod,[status(thm)],[c_499,c_2659]) ).
cnf(c_1970,negated_conjecture,
less(n0,sK0(n0,filling,n2)),
inference(resolve,[status(thm)],[c_72,c_2660]) ).
cnf(c_2661,plain,
( less(n0,n0)
| sK0(n0,filling,n2) = n1 ),
inference(paramod,[status(thm)],[c_1590,c_1970]) ).
cnf(c_1977,plain,
sK0(n0,filling,n2) = n1,
inference(resolve,[status(thm)],[c_180,c_2661]) ).
cnf(c_1978,plain,
( n2 != A
| happens(sK1(n0,filling,n2),n1)
| holdsAt(waterLevel(A),n2) ),
inference(paramod,[status(thm)],[c_1977,c_1940]) ).
cnf(c_2662,plain,
A = sK3(tapOn,waterLevel(A),B),
inference(copy,[status(thm)],[c_499]) ).
cnf(c_2663,plain,
( happens(sK1(n0,filling,n2),n1)
| holdsAt(waterLevel(sK3(tapOn,waterLevel(n2),A)),n2) ),
inference(resolve,[status(thm)],[c_1978,c_2662]) ).
cnf(c_2664,plain,
( happens(sK1(n0,filling,n2),n1)
| holdsAt(waterLevel(n2),n2) ),
inference(paramod,[status(thm)],[c_499,c_2663]) ).
cnf(c_1992,negated_conjecture,
happens(sK1(n0,filling,n2),n1),
inference(resolve,[status(thm)],[c_72,c_2664]) ).
cnf(c_2665,plain,
( overflow = sK1(n0,filling,n2)
| n0 = n1 ),
inference(resolve,[status(thm)],[c_1992,c_129]) ).
cnf(c_2666,plain,
( sK1(n0,filling,n2) = overflow
| n0 = n1 ),
inference(copy,[status(thm)],[c_2665]) ).
cnf(c_1996,plain,
sK1(n0,filling,n2) = overflow,
inference(resolve,[status(thm)],[c_234,c_2666]) ).
cnf(c_1997,negated_conjecture,
happens(overflow,n1),
inference(paramod,[status(thm)],[c_1996,c_1992]) ).
cnf(c_2667,plain,
~ holdsAt(filling,plus(n1,n1)),
inference(resolve,[status(thm)],[c_1997,c_427]) ).
cnf(c_2023,plain,
~ holdsAt(filling,n2),
inference(paramod,[status(thm)],[c_111,c_2667]) ).
cnf(c_2037,plain,
less(n0,sK0(n0,filling,n1)),
inference(resolve,[status(thm)],[c_2023,c_1959]) ).
cnf(c_2133,plain,
less(sK0(n0,filling,n1),n1),
inference(resolve,[status(thm)],[c_2023,c_1559]) ).
cnf(c_2569,plain,
sK0(n0,filling,n1) != n0,
inference(resolve,[status(thm)],[c_2037,c_80]) ).
cnf(c_2668,plain,
( n0 = sK0(n0,filling,n1)
| n1 = sK0(n0,filling,n1) ),
inference(resolve,[status(thm)],[c_2133,c_507]) ).
cnf(c_2669,plain,
( n0 = sK0(n0,filling,n1)
| sK0(n0,filling,n1) = n1 ),
inference(copy,[status(thm)],[c_2668]) ).
cnf(c_2670,plain,
( sK0(n0,filling,n1) = n0
| sK0(n0,filling,n1) = n1 ),
inference(copy,[status(thm)],[c_2669]) ).
cnf(c_2578,plain,
sK0(n0,filling,n1) = n1,
inference(resolve,[status(thm)],[c_2569,c_2670]) ).
cnf(c_2671,plain,
n1 != sK0(n0,filling,n1),
inference(resolve,[status(thm)],[c_2133,c_80]) ).
cnf(c_2672,plain,
n1 != n1,
inference(paramod,[status(thm)],[c_2578,c_2671]) ).
cnf(c_2580,plain,
$false,
inference(copy,[status(thm)],[c_2672]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CSR008+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/10.98 % Computer : n010.cluster.edu
% 0.07/10.98 % Model : x86_64 x86_64
% 0.07/10.98 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/10.98 % Memory : 8046.5625MB
% 0.07/10.98 % OS : Linux 6.8.0-71-generic
% 0.07/10.98 % CPULimit : 300
% 0.07/10.98 % WCLimit : 300
% 0.07/10.98 % DateTime : Sat Sep 26 23:55:01 UTC 2026
% 0.07/10.98 % CPUTime :
% 0.07/10.98 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/10.98 % Process 335673 was started by sandbox on n010,
% 0.07/10.98 % Sat Sep 26 23:55:01 2026
% 0.07/10.98 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/10.99
% 0.07/10.99 % From the command line: assign(max_seconds, 300).
% 8.14/13.52
% 8.14/13.52 % given #500 (T,wt=9): 654 n1 = A | less(A,n4) | -less(A,n1). [resolve(641,a,81,b)].
% 8.14/13.52
% 8.14/13.52 % given #1000 (T,wt=13): 1744 f2(n0,filling,n2) = n1 | holdsAt(filling,n2) | -holdsAt(waterLevel(n0),n2). [para(1660(b,1),978(b,1)),flip(d),unit_del(d,1594)].
% 8.14/13.52
% 8.14/13.52 % SZS status Theorem for theBenchmark
% 8.14/13.52
% 8.14/13.52 % Proof 1 at 0.81 (+ 0.33) seconds.
% 8.14/13.52 % Length of proof is 161.
% 8.14/13.52 % Level of proof is 24.
% 8.14/13.52 % Maximum clause weight is 38.000.
% 8.14/13.52 % Given clauses 1088.
% 8.14/13.52
% 8.14/13.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------