%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CSR009+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 : n007.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 31.49s 4.54s
% Output : CNFRefutation 31.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 59
% Number of leaves : 28
% Syntax : Number of formulae : 296 ( 76 unt; 0 def)
% Number of atoms : 901 ( 292 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 889 ( 284 ~; 517 |; 68 &)
% ( 13 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-4 aty)
% Number of functors : 20 ( 20 usr; 11 con; 0-3 aty)
% Number of variables : 424 ( 13 sgn 139 !; 17 ?)
% 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(startedin_defn,axiom,
! [Time1,Time2,Fluent] :
( startedIn(Time1,Fluent,Time2)
<=> ? [Event,Time] :
( initiates(Event,Fluent,Time)
& less(Time,Time2)
& less(Time1,Time)
& happens(Event,Time) ) ),
file('theBenchmark.p',startedin_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_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(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(filling_2,conjecture,
holdsAt(filling,n2),
file('theBenchmark.p',filling_2) ).
fof(filling_2_neg,negated_conjecture,
~ holdsAt(filling,n2),
inference(assume_negation,[status(cth)],[filling_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_37,plain,
( ~ terminates(D,B,E)
| ~ less(E,C)
| ~ less(A,E)
| ~ happens(D,E)
| stoppedIn(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_stoppedin_defn]) ).
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]) ).
fof(nnf_2,plain,
! [Time1,Time2,Fluent] :
( ( ! [Event,Time] :
( ~ initiates(Event,Fluent,Time)
| ~ less(Time,Time2)
| ~ less(Time1,Time)
| ~ happens(Event,Time) )
| startedIn(Time1,Fluent,Time2) )
& ( ? [X0,X1] :
( initiates(X0,Fluent,X1)
& less(X1,Time2)
& less(Time1,X1)
& happens(X0,X1) )
| ~ startedIn(Time1,Fluent,Time2) ) ),
inference(fof_nnf,[status(thm)],[startedin_defn]) ).
fof(sk_startedin_defn_sk,plain,
! [Time1,Time2,Fluent] :
( ( ! [Event,Time] :
( ~ initiates(Event,Fluent,Time)
| ~ less(Time,Time2)
| ~ less(Time1,Time)
| ~ happens(Event,Time) )
| startedIn(Time1,Fluent,Time2) )
& ( ( initiates(sK6(Time1,Time2,Fluent),Fluent,sK2(Time1,Time2,Fluent))
& less(sK2(Time1,Time2,Fluent),Time2)
& less(Time1,sK2(Time1,Time2,Fluent))
& happens(sK6(Time1,Time2,Fluent),sK2(Time1,Time2,Fluent)) )
| ~ startedIn(Time1,Fluent,Time2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK2]),skolemize(X0,sK6(Time1,Time2,Fluent)),skolemize(X1,sK2(Time1,Time2,Fluent))],[nnf_2]) ).
fof(sk_startedin_defn,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ~ initiates(VAR_3,VAR_1,VAR_4)
| ~ less(VAR_4,VAR_2)
| ~ less(VAR_0,VAR_4)
| ~ happens(VAR_3,VAR_4)
| startedIn(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1,VAR_2] :
( initiates(sK6(VAR_0,VAR_2,VAR_1),VAR_1,sK2(VAR_0,VAR_2,VAR_1))
| ~ startedIn(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1,VAR_2] :
( less(sK2(VAR_0,VAR_2,VAR_1),VAR_2)
| ~ startedIn(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1,VAR_2] :
( less(VAR_0,sK2(VAR_0,VAR_2,VAR_1))
| ~ startedIn(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1,VAR_2] :
( happens(sK6(VAR_0,VAR_2,VAR_1),sK2(VAR_0,VAR_2,VAR_1))
| ~ startedIn(VAR_0,VAR_1,VAR_2) ) ),
inference(cnf_transformation,[status(thm)],[sk_startedin_defn_sk]) ).
cnf(c_44,plain,
( ~ initiates(D,B,E)
| ~ less(E,C)
| ~ less(A,E)
| ~ happens(D,E)
| startedIn(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_startedin_defn]) ).
cnf(c_46,plain,
( less(sK2(A,C,B),C)
| ~ startedIn(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_startedin_defn]) ).
cnf(c_47,plain,
( less(A,sK2(A,C,B))
| ~ startedIn(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_startedin_defn]) ).
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]) ).
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(sK3(Fluent,Time),Fluent,Time)
& happens(sK3(Fluent,Time),Time) )
| releasedAt(Fluent,Time) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(Event,sK3(Fluent,Time))],[nnf_8]) ).
fof(sk_keep_not_released,plain,
( ! [VAR_0,VAR_1] :
( ~ releasedAt(VAR_0,plus(VAR_1,n1))
| releases(sK3(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(sK3(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(sK3(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(sK4(Event,Fluent,Time)) = Fluent
& tapOn = Event )
| ~ releases(Event,Fluent,Time) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X0,sK4(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(sK4(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(sK4(A,B,C)) = B
| ~ releases(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_releases_all_defn]) ).
cnf(c_61,plain,
( ~ releasedAt(A,plus(B,n1))
| releasedAt(A,B)
| waterLevel(sK4(sK3(A,B),A,B)) = A ),
inference(resolve,[status(thm)],[c_57,c_55]) ).
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_68,plain,
( happens(sK1(C,E,D),sK0(C,E,D))
| ~ terminates(A,E,B)
| ~ less(B,D)
| ~ less(C,B)
| ~ happens(A,B) ),
inference(resolve,[status(thm)],[c_37,c_41]) ).
cnf(c_69,plain,
( less(C,sK0(C,E,D))
| ~ terminates(A,E,B)
| ~ less(B,D)
| ~ less(C,B)
| ~ happens(A,B) ),
inference(resolve,[status(thm)],[c_37,c_40]) ).
cnf(c_70,plain,
( less(sK0(C,E,D),D)
| ~ terminates(A,E,B)
| ~ less(B,D)
| ~ less(C,B)
| ~ happens(A,B) ),
inference(resolve,[status(thm)],[c_37,c_39]) ).
cnf(c_72,negated_conjecture,
~ holdsAt(filling,n2),
inference(clausify,[status(thm)],[filling_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_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_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_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_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_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_141,plain,
( spilling != B
| overflow != A
| 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_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(sK5(Fluent,Time),Fluent,Time)
& happens(sK5(Fluent,Time),Time) )
| releasedAt(Fluent,plus(Time,n1))
| ~ holdsAt(Fluent,Time) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(Event,sK5(Fluent,Time))],[nnf_5]) ).
fof(sk_keep_holding,plain,
( ! [VAR_0,VAR_1] :
( holdsAt(VAR_0,plus(VAR_1,n1))
| terminates(sK5(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(sK5(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(sK5(A,B),B)
| releasedAt(A,plus(B,n1))
| ~ holdsAt(A,B) ),
inference(split_conjunct,[status(thm)],[sk_keep_holding]) ).
cnf(c_173,plain,
( ~ initiates(D,C,E)
| ~ less(E,B)
| ~ less(A,E)
| ~ happens(D,E)
| less(sK2(A,B,C),B) ),
inference(resolve,[status(thm)],[c_46,c_44]) ).
cnf(c_174,plain,
( ~ initiates(D,C,E)
| ~ less(E,B)
| ~ less(A,E)
| ~ happens(D,E)
| less(A,sK2(A,B,C)) ),
inference(resolve,[status(thm)],[c_47,c_44]) ).
cnf(c_180,plain,
~ less(A,A),
inference(factor,[status(thm)],[c_81]) ).
cnf(c_7530,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_7530]) ).
cnf(c_7531,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_7531]) ).
cnf(c_7532,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_7532]) ).
cnf(c_7533,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_7533]) ).
cnf(c_194,plain,
less_or_equal(A,A),
inference(xxres,[status(thm)],[c_101]) ).
cnf(c_195,plain,
( A = B
| less(B,A)
| less_or_equal(A,B) ),
inference(resolve,[status(thm)],[c_102,c_79]) ).
cnf(c_200,plain,
( ~ releasedAt(A,n2)
| releasedAt(A,n1)
| waterLevel(sK4(sK3(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_211,plain,
( spilling != A
| initiates(overflow,A,B) ),
inference(xxres,[status(thm)],[c_141]) ).
cnf(c_213,plain,
( filling != A
| initiates(tapOn,A,B) ),
inference(xxres,[status(thm)],[c_142]) ).
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_7534,plain,
n1 != n0,
inference(resolve,[status(thm)],[c_224,c_80]) ).
cnf(c_234,plain,
n0 != n1,
inference(copy,[status(thm)],[c_7534]) ).
cnf(c_235,plain,
less_or_equal(n1,n2),
inference(resolve,[status(thm)],[c_225,c_102]) ).
cnf(c_236,plain,
~ less(n2,n1),
inference(resolve,[status(thm)],[c_225,c_81]) ).
cnf(c_237,plain,
n2 != n1,
inference(resolve,[status(thm)],[c_225,c_80]) ).
cnf(c_260,plain,
less(n1,n3),
inference(resolve,[status(thm)],[c_235,c_94]) ).
cnf(c_272,plain,
less_or_equal(n1,n3),
inference(resolve,[status(thm)],[c_260,c_102]) ).
cnf(c_273,plain,
~ less(n3,n1),
inference(resolve,[status(thm)],[c_260,c_81]) ).
cnf(c_274,plain,
n3 != n1,
inference(resolve,[status(thm)],[c_260,c_80]) ).
cnf(c_295,plain,
( n4 = A
| less(A,n4)
| n5 = A
| less(n5,A) ),
inference(resolve,[status(thm)],[c_188,c_103]) ).
cnf(c_296,plain,
less(n1,n4),
inference(resolve,[status(thm)],[c_272,c_92]) ).
cnf(c_305,plain,
( n2 = A
| less(A,n2)
| n3 = A
| less(n3,A) ),
inference(resolve,[status(thm)],[c_190,c_103]) ).
cnf(c_306,plain,
less_or_equal(n1,n4),
inference(resolve,[status(thm)],[c_296,c_102]) ).
cnf(c_308,plain,
n4 != n1,
inference(resolve,[status(thm)],[c_296,c_80]) ).
cnf(c_318,plain,
( n1 = A
| less(A,n1)
| n2 = A
| less(n2,A) ),
inference(resolve,[status(thm)],[c_191,c_103]) ).
cnf(c_326,plain,
less(n1,n5),
inference(resolve,[status(thm)],[c_306,c_90]) ).
cnf(c_7535,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_7535]) ).
cnf(c_341,plain,
~ less(n5,n1),
inference(resolve,[status(thm)],[c_326,c_81]) ).
cnf(c_342,plain,
n5 != n1,
inference(resolve,[status(thm)],[c_326,c_80]) ).
cnf(c_7536,plain,
( less(A,n3)
| A = n2
| less(n2,A) ),
inference(resolve,[status(thm)],[c_195,c_94]) ).
cnf(c_347,plain,
( less(A,n3)
| n2 = A
| less(n2,A) ),
inference(copy,[status(thm)],[c_7536]) ).
cnf(c_7537,plain,
n0 = plus(n0,n0),
inference(copy,[status(thm)],[c_116]) ).
cnf(c_7538,plain,
happens(tapOn,plus(n0,n0)),
inference(resolve,[status(thm)],[c_203,c_7537]) ).
cnf(c_416,plain,
happens(tapOn,n0),
inference(paramod,[status(thm)],[c_116,c_7538]) ).
cnf(c_426,plain,
terminates(overflow,filling,A),
inference(xxres,[status(thm)],[c_205]) ).
cnf(c_430,plain,
( less(sK0(B,filling,C),C)
| ~ less(A,C)
| ~ less(B,A)
| ~ happens(overflow,A) ),
inference(resolve,[status(thm)],[c_426,c_70]) ).
cnf(c_431,plain,
( less(B,sK0(B,filling,C))
| ~ less(A,C)
| ~ less(B,A)
| ~ happens(overflow,A) ),
inference(resolve,[status(thm)],[c_426,c_69]) ).
cnf(c_432,plain,
( happens(sK1(B,filling,C),sK0(B,filling,C))
| ~ less(A,C)
| ~ less(B,A)
| ~ happens(overflow,A) ),
inference(resolve,[status(thm)],[c_426,c_68]) ).
cnf(c_445,plain,
initiates(overflow,spilling,A),
inference(xxres,[status(thm)],[c_211]) ).
cnf(c_447,plain,
( ~ less(C,B)
| ~ less(A,C)
| ~ happens(overflow,C)
| less(A,sK2(A,B,spilling)) ),
inference(resolve,[status(thm)],[c_445,c_174]) ).
cnf(c_448,plain,
( ~ less(C,B)
| ~ less(A,C)
| ~ happens(overflow,C)
| less(sK2(A,B,spilling),B) ),
inference(resolve,[status(thm)],[c_445,c_173]) ).
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_484,plain,
( ~ releasedAt(filling,plus(n1,A))
| ~ happens(tapOn,A) ),
inference(paramod,[status(thm)],[c_104,c_460]) ).
cnf(c_7539,plain,
holdsAt(filling,plus(n0,n1)),
inference(resolve,[status(thm)],[c_459,c_416]) ).
cnf(c_7540,plain,
holdsAt(filling,plus(n1,n0)),
inference(paramod,[status(thm)],[c_104,c_7539]) ).
cnf(c_489,plain,
holdsAt(filling,n1),
inference(paramod,[status(thm)],[c_115,c_7540]) ).
cnf(c_7541,plain,
( holdsAt(filling,plus(n1,n1))
| happens(sK5(filling,n1),n1)
| releasedAt(filling,plus(n1,n1)) ),
inference(resolve,[status(thm)],[c_489,c_171]) ).
cnf(c_7542,plain,
( holdsAt(filling,plus(n1,n1))
| happens(sK5(filling,n1),n1)
| releasedAt(filling,n2) ),
inference(paramod,[status(thm)],[c_111,c_7541]) ).
cnf(c_7543,plain,
( holdsAt(filling,n2)
| happens(sK5(filling,n1),n1)
| releasedAt(filling,n2) ),
inference(paramod,[status(thm)],[c_111,c_7542]) ).
cnf(c_490,negated_conjecture,
( happens(sK5(filling,n1),n1)
| releasedAt(filling,n2) ),
inference(resolve,[status(thm)],[c_72,c_7543]) ).
cnf(c_7544,plain,
( releasedAt(filling,n1)
| waterLevel(sK4(sK3(filling,n1),filling,n1)) = filling
| happens(sK5(filling,n1),n1) ),
inference(resolve,[status(thm)],[c_490,c_200]) ).
cnf(c_504,plain,
( releasedAt(filling,n1)
| happens(sK5(filling,n1),n1) ),
inference(resolve,[status(thm)],[c_122,c_7544]) ).
cnf(c_7545,plain,
( ~ releasedAt(filling,n1)
| ~ happens(tapOn,n0) ),
inference(paramod,[status(thm)],[c_115,c_484]) ).
cnf(c_512,plain,
~ releasedAt(filling,n1),
inference(resolve,[status(thm)],[c_416,c_7545]) ).
cnf(c_513,plain,
happens(sK5(filling,n1),n1),
inference(resolve,[status(thm)],[c_512,c_504]) ).
cnf(c_7546,plain,
( holdsAt(waterLevel(n3),n1)
| n0 = n1 ),
inference(resolve,[status(thm)],[c_513,c_131]) ).
cnf(c_516,plain,
holdsAt(waterLevel(n3),n1),
inference(resolve,[status(thm)],[c_234,c_7546]) ).
cnf(c_7547,plain,
( overflow = sK5(filling,n1)
| n0 = n1 ),
inference(resolve,[status(thm)],[c_513,c_129]) ).
cnf(c_7548,plain,
( sK5(filling,n1) = overflow
| n0 = n1 ),
inference(copy,[status(thm)],[c_7547]) ).
cnf(c_517,plain,
sK5(filling,n1) = overflow,
inference(resolve,[status(thm)],[c_234,c_7548]) ).
cnf(c_518,plain,
happens(overflow,n1),
inference(paramod,[status(thm)],[c_517,c_513]) ).
cnf(c_529,plain,
( n3 = A
| ~ holdsAt(waterLevel(A),n1) ),
inference(resolve,[status(thm)],[c_516,c_126]) ).
cnf(c_536,plain,
( ~ less(A,n1)
| n0 = A
| n1 = A ),
inference(resolve,[status(thm)],[c_327,c_81]) ).
cnf(c_607,plain,
( less_or_equal(A,n3)
| n4 = A
| n5 = A
| less(n5,A) ),
inference(resolve,[status(thm)],[c_295,c_93]) ).
cnf(c_618,plain,
( ~ less(n2,A)
| n2 = A
| n3 = A
| less(n3,A) ),
inference(resolve,[status(thm)],[c_305,c_81]) ).
cnf(c_7549,plain,
( n0 = A
| n1 = A
| n1 = A
| n2 = A
| less(n2,A) ),
inference(resolve,[status(thm)],[c_318,c_536]) ).
cnf(c_621,plain,
( n0 = A
| n1 = A
| n2 = A
| less(n2,A) ),
inference(copy,[status(thm)],[c_7549]) ).
cnf(c_678,plain,
( less(sK0(A,filling,B),B)
| ~ less(n1,B)
| ~ less(A,n1) ),
inference(resolve,[status(thm)],[c_430,c_518]) ).
cnf(c_681,plain,
( less(A,sK0(A,filling,B))
| ~ less(n1,B)
| ~ less(A,n1) ),
inference(resolve,[status(thm)],[c_431,c_518]) ).
cnf(c_684,plain,
( happens(sK1(A,filling,B),sK0(A,filling,B))
| ~ less(n1,B)
| ~ less(A,n1) ),
inference(resolve,[status(thm)],[c_432,c_518]) ).
cnf(c_693,plain,
( ~ less(n1,B)
| ~ less(A,n1)
| less(A,sK2(A,B,spilling)) ),
inference(resolve,[status(thm)],[c_447,c_518]) ).
cnf(c_709,plain,
( ~ less(n1,B)
| ~ less(A,n1)
| less(sK2(A,B,spilling),B) ),
inference(resolve,[status(thm)],[c_448,c_518]) ).
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_754,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_1008,plain,
( n3 = A
| less(A,n3)
| n4 = A
| n5 = A
| less(n5,A) ),
inference(resolve,[status(thm)],[c_607,c_103]) ).
cnf(c_7550,plain,
( n2 = A
| n3 = A
| less(n3,A)
| n0 = A
| n1 = A
| n2 = A ),
inference(resolve,[status(thm)],[c_621,c_618]) ).
cnf(c_1011,plain,
( n3 = A
| less(n3,A)
| n0 = A
| n1 = A
| n2 = A ),
inference(copy,[status(thm)],[c_7550]) ).
cnf(c_1013,plain,
( ~ less(A,n2)
| n0 = A
| n1 = A
| n2 = A ),
inference(resolve,[status(thm)],[c_621,c_81]) ).
cnf(c_1015,plain,
( less(sK0(n0,filling,A),A)
| ~ less(n1,A) ),
inference(resolve,[status(thm)],[c_678,c_224]) ).
cnf(c_7551,plain,
( n2 = n1
| less(n2,n1)
| less(sK0(n0,filling,n3),n3) ),
inference(resolve,[status(thm)],[c_1015,c_347]) ).
cnf(c_7552,plain,
( n2 = n1
| less(sK0(n0,filling,n3),n3) ),
inference(resolve,[status(thm)],[c_236,c_7551]) ).
cnf(c_1048,plain,
less(sK0(n0,filling,n3),n3),
inference(resolve,[status(thm)],[c_237,c_7552]) ).
cnf(c_1125,plain,
( less(n0,sK0(n0,filling,A))
| ~ less(n1,A) ),
inference(resolve,[status(thm)],[c_681,c_224]) ).
cnf(c_1170,plain,
~ less(n3,sK0(n0,filling,n3)),
inference(resolve,[status(thm)],[c_1048,c_81]) ).
cnf(c_7553,plain,
n3 != sK0(n0,filling,n3),
inference(resolve,[status(thm)],[c_1048,c_80]) ).
cnf(c_1171,plain,
sK0(n0,filling,n3) != n3,
inference(copy,[status(thm)],[c_7553]) ).
cnf(c_1200,plain,
( happens(sK1(n0,filling,A),sK0(n0,filling,A))
| ~ less(n1,A) ),
inference(resolve,[status(thm)],[c_684,c_224]) ).
cnf(c_1251,plain,
( ~ less(n1,A)
| less(n0,sK2(n0,A,spilling)) ),
inference(resolve,[status(thm)],[c_693,c_224]) ).
cnf(c_7554,plain,
( n2 = n1
| n3 = n1
| less(n3,n1)
| ~ less(A,n1)
| less(A,sK2(A,n2,spilling)) ),
inference(resolve,[status(thm)],[c_693,c_305]) ).
cnf(c_7555,plain,
( n2 = n1
| n3 = n1
| ~ less(A,n1)
| less(A,sK2(A,n2,spilling)) ),
inference(resolve,[status(thm)],[c_273,c_7554]) ).
cnf(c_7556,plain,
( n2 = n1
| ~ less(A,n1)
| less(A,sK2(A,n2,spilling)) ),
inference(resolve,[status(thm)],[c_274,c_7555]) ).
cnf(c_1269,plain,
( ~ less(A,n1)
| less(A,sK2(A,n2,spilling)) ),
inference(resolve,[status(thm)],[c_237,c_7556]) ).
cnf(c_1279,plain,
( ~ less(n1,A)
| less(sK2(n0,A,spilling),A) ),
inference(resolve,[status(thm)],[c_709,c_224]) ).
cnf(c_1345,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_1352,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_754,c_78]) ).
cnf(c_7557,plain,
( n2 = n1
| less(n2,n1)
| less(n0,sK0(n0,filling,n3)) ),
inference(resolve,[status(thm)],[c_1125,c_347]) ).
cnf(c_7558,plain,
( n2 = n1
| less(n0,sK0(n0,filling,n3)) ),
inference(resolve,[status(thm)],[c_236,c_7557]) ).
cnf(c_1574,plain,
less(n0,sK0(n0,filling,n3)),
inference(resolve,[status(thm)],[c_237,c_7558]) ).
cnf(c_1598,plain,
sK0(n0,filling,n3) != n0,
inference(resolve,[status(thm)],[c_1574,c_80]) ).
cnf(c_7559,plain,
( n2 = n1
| n3 = n1
| less(n3,n1)
| less(n0,sK2(n0,n2,spilling)) ),
inference(resolve,[status(thm)],[c_1251,c_305]) ).
cnf(c_7560,plain,
( n2 = n1
| n3 = n1
| less(n0,sK2(n0,n2,spilling)) ),
inference(resolve,[status(thm)],[c_273,c_7559]) ).
cnf(c_7561,plain,
( n2 = n1
| less(n0,sK2(n0,n2,spilling)) ),
inference(resolve,[status(thm)],[c_274,c_7560]) ).
cnf(c_1640,plain,
less(n0,sK2(n0,n2,spilling)),
inference(resolve,[status(thm)],[c_237,c_7561]) ).
cnf(c_1657,plain,
sK2(n0,n2,spilling) != n0,
inference(resolve,[status(thm)],[c_1640,c_80]) ).
cnf(c_7562,plain,
( A = n1
| less(n1,A)
| less(A,sK2(A,n2,spilling)) ),
inference(resolve,[status(thm)],[c_1269,c_79]) ).
cnf(c_1685,plain,
( n1 = A
| less(n1,A)
| less(A,sK2(A,n2,spilling)) ),
inference(copy,[status(thm)],[c_7562]) ).
cnf(c_7563,plain,
( n2 = n1
| n3 = n1
| less(n3,n1)
| less(sK2(n0,n2,spilling),n2) ),
inference(resolve,[status(thm)],[c_1279,c_305]) ).
cnf(c_7564,plain,
( n2 = n1
| n3 = n1
| less(sK2(n0,n2,spilling),n2) ),
inference(resolve,[status(thm)],[c_273,c_7563]) ).
cnf(c_7565,plain,
( n2 = n1
| less(sK2(n0,n2,spilling),n2) ),
inference(resolve,[status(thm)],[c_274,c_7564]) ).
cnf(c_1702,plain,
less(sK2(n0,n2,spilling),n2),
inference(resolve,[status(thm)],[c_237,c_7565]) ).
cnf(c_7566,plain,
n2 != sK2(n0,n2,spilling),
inference(resolve,[status(thm)],[c_1702,c_80]) ).
cnf(c_1849,plain,
sK2(n0,n2,spilling) != n2,
inference(copy,[status(thm)],[c_7566]) ).
cnf(c_7567,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_1011,c_1170]) ).
cnf(c_7568,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_7567]) ).
cnf(c_7569,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_7568]) ).
cnf(c_7570,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_7569]) ).
cnf(c_7571,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_7570]) ).
cnf(c_7572,plain,
( sK0(n0,filling,n3) = n3
| sK0(n0,filling,n3) = n1
| sK0(n0,filling,n3) = n2 ),
inference(resolve,[status(thm)],[c_1598,c_7571]) ).
cnf(c_1859,plain,
( sK0(n0,filling,n3) = n1
| sK0(n0,filling,n3) = n2 ),
inference(resolve,[status(thm)],[c_1171,c_7572]) ).
cnf(c_7573,plain,
( n0 = sK2(n0,n2,spilling)
| n1 = sK2(n0,n2,spilling)
| n2 = sK2(n0,n2,spilling) ),
inference(resolve,[status(thm)],[c_1013,c_1702]) ).
cnf(c_7574,plain,
( n0 = sK2(n0,n2,spilling)
| n1 = sK2(n0,n2,spilling)
| sK2(n0,n2,spilling) = n2 ),
inference(copy,[status(thm)],[c_7573]) ).
cnf(c_7575,plain,
( n0 = sK2(n0,n2,spilling)
| sK2(n0,n2,spilling) = n1
| sK2(n0,n2,spilling) = n2 ),
inference(copy,[status(thm)],[c_7574]) ).
cnf(c_7576,plain,
( sK2(n0,n2,spilling) = n0
| sK2(n0,n2,spilling) = n1
| sK2(n0,n2,spilling) = n2 ),
inference(copy,[status(thm)],[c_7575]) ).
cnf(c_7577,plain,
( sK2(n0,n2,spilling) = n0
| sK2(n0,n2,spilling) = n1 ),
inference(resolve,[status(thm)],[c_1849,c_7576]) ).
cnf(c_1885,plain,
sK2(n0,n2,spilling) = n1,
inference(resolve,[status(thm)],[c_1657,c_7577]) ).
cnf(c_7578,plain,
( n3 = n1
| n4 = n1
| n5 = n1
| less(n5,n1)
| happens(sK1(n0,filling,n3),sK0(n0,filling,n3)) ),
inference(resolve,[status(thm)],[c_1200,c_1008]) ).
cnf(c_7579,plain,
( n3 = n1
| n4 = n1
| n5 = n1
| happens(sK1(n0,filling,n3),sK0(n0,filling,n3)) ),
inference(resolve,[status(thm)],[c_341,c_7578]) ).
cnf(c_7580,plain,
( n3 = n1
| n4 = n1
| happens(sK1(n0,filling,n3),sK0(n0,filling,n3)) ),
inference(resolve,[status(thm)],[c_342,c_7579]) ).
cnf(c_7581,plain,
( n3 = n1
| happens(sK1(n0,filling,n3),sK0(n0,filling,n3)) ),
inference(resolve,[status(thm)],[c_308,c_7580]) ).
cnf(c_2489,plain,
happens(sK1(n0,filling,n3),sK0(n0,filling,n3)),
inference(resolve,[status(thm)],[c_274,c_7581]) ).
cnf(c_7582,plain,
( holdsAt(filling,sK0(n0,filling,n3))
| n0 = sK0(n0,filling,n3) ),
inference(resolve,[status(thm)],[c_2489,c_130]) ).
cnf(c_7583,plain,
( holdsAt(filling,sK0(n0,filling,n3))
| sK0(n0,filling,n3) = n0 ),
inference(copy,[status(thm)],[c_7582]) ).
cnf(c_2564,plain,
holdsAt(filling,sK0(n0,filling,n3)),
inference(resolve,[status(thm)],[c_1598,c_7583]) ).
cnf(c_7584,plain,
( holdsAt(filling,n2)
| sK0(n0,filling,n3) = n1 ),
inference(paramod,[status(thm)],[c_1859,c_2564]) ).
cnf(c_4279,negated_conjecture,
sK0(n0,filling,n3) = n1,
inference(resolve,[status(thm)],[c_72,c_7584]) ).
cnf(c_7585,plain,
( n1 = n0
| less(n1,n0)
| plus(n0,sK2(n0,n2,spilling)) != A
| less(sK0(n0,filling,plus(n0,sK2(n0,n2,spilling))),plus(n0,sK2(n0,n2,spilling)))
| holdsAt(waterLevel(A),plus(n0,sK2(n0,n2,spilling))) ),
inference(resolve,[status(thm)],[c_1345,c_1685]) ).
cnf(c_7586,plain,
( n1 = n0
| less(n1,n0)
| plus(n0,sK2(n0,n2,spilling)) != A
| less(sK0(n0,filling,plus(n0,sK2(n0,n2,spilling))),plus(n0,sK2(n0,n2,spilling)))
| holdsAt(waterLevel(A),plus(n0,n1)) ),
inference(paramod,[status(thm)],[c_1885,c_7585]) ).
cnf(c_7587,plain,
( n1 = n0
| less(n1,n0)
| plus(n0,sK2(n0,n2,spilling)) != A
| less(sK0(n0,filling,plus(n0,sK2(n0,n2,spilling))),plus(n0,sK2(n0,n2,spilling)))
| holdsAt(waterLevel(A),plus(n1,n0)) ),
inference(paramod,[status(thm)],[c_104,c_7586]) ).
cnf(c_7588,plain,
( n1 = n0
| less(n1,n0)
| plus(n0,sK2(n0,n2,spilling)) != A
| less(sK0(n0,filling,plus(n0,sK2(n0,n2,spilling))),plus(n0,sK2(n0,n2,spilling)))
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_115,c_7587]) ).
cnf(c_7589,plain,
( n1 = n0
| less(n1,n0)
| plus(n0,sK2(n0,n2,spilling)) != A
| less(sK0(n0,filling,plus(n0,n1)),plus(n0,sK2(n0,n2,spilling)))
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_1885,c_7588]) ).
cnf(c_7590,plain,
( n1 = n0
| less(n1,n0)
| plus(n0,sK2(n0,n2,spilling)) != A
| less(sK0(n0,filling,plus(n1,n0)),plus(n0,sK2(n0,n2,spilling)))
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_104,c_7589]) ).
cnf(c_7591,plain,
( n1 = n0
| less(n1,n0)
| plus(n0,sK2(n0,n2,spilling)) != A
| less(sK0(n0,filling,n1),plus(n0,sK2(n0,n2,spilling)))
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_115,c_7590]) ).
cnf(c_7592,plain,
( n1 = n0
| less(n1,n0)
| plus(n0,sK2(n0,n2,spilling)) != A
| less(sK0(n0,filling,n1),plus(n0,n1))
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_1885,c_7591]) ).
cnf(c_7593,plain,
( n1 = n0
| less(n1,n0)
| plus(n0,sK2(n0,n2,spilling)) != A
| less(sK0(n0,filling,n1),plus(n1,n0))
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_104,c_7592]) ).
cnf(c_7594,plain,
( n1 = n0
| less(n1,n0)
| plus(n0,sK2(n0,n2,spilling)) != A
| less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_115,c_7593]) ).
cnf(c_7595,plain,
( n1 = n0
| less(n1,n0)
| plus(n0,n1) != A
| less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_1885,c_7594]) ).
cnf(c_7596,plain,
( n1 = n0
| less(n1,n0)
| plus(n1,n0) != A
| less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_104,c_7595]) ).
cnf(c_7597,plain,
( n1 = n0
| less(n1,n0)
| n1 != A
| less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_115,c_7596]) ).
cnf(c_7598,plain,
( n0 = n1
| less(n1,n0)
| n1 != A
| less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(A),n1) ),
inference(copy,[status(thm)],[c_7597]) ).
cnf(c_7599,plain,
( n0 = n1
| n1 != A
| less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(A),n1) ),
inference(resolve,[status(thm)],[c_100,c_7598]) ).
cnf(c_4748,plain,
( n1 != A
| less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(A),n1) ),
inference(resolve,[status(thm)],[c_234,c_7599]) ).
cnf(c_7600,plain,
( n1 = n0
| less(n1,n0)
| plus(n0,sK2(n0,n2,spilling)) != A
| less(n0,sK0(n0,filling,plus(n0,sK2(n0,n2,spilling))))
| holdsAt(waterLevel(A),plus(n0,sK2(n0,n2,spilling))) ),
inference(resolve,[status(thm)],[c_1352,c_1685]) ).
cnf(c_7601,plain,
( n1 = n0
| less(n1,n0)
| plus(n0,sK2(n0,n2,spilling)) != A
| less(n0,sK0(n0,filling,plus(n0,sK2(n0,n2,spilling))))
| holdsAt(waterLevel(A),plus(n0,n1)) ),
inference(paramod,[status(thm)],[c_1885,c_7600]) ).
cnf(c_7602,plain,
( n1 = n0
| less(n1,n0)
| plus(n0,sK2(n0,n2,spilling)) != A
| less(n0,sK0(n0,filling,plus(n0,sK2(n0,n2,spilling))))
| holdsAt(waterLevel(A),plus(n1,n0)) ),
inference(paramod,[status(thm)],[c_104,c_7601]) ).
cnf(c_7603,plain,
( n1 = n0
| less(n1,n0)
| plus(n0,sK2(n0,n2,spilling)) != A
| less(n0,sK0(n0,filling,plus(n0,sK2(n0,n2,spilling))))
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_115,c_7602]) ).
cnf(c_7604,plain,
( n1 = n0
| less(n1,n0)
| plus(n0,sK2(n0,n2,spilling)) != A
| less(n0,sK0(n0,filling,plus(n0,n1)))
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_1885,c_7603]) ).
cnf(c_7605,plain,
( n1 = n0
| less(n1,n0)
| plus(n0,sK2(n0,n2,spilling)) != A
| less(n0,sK0(n0,filling,plus(n1,n0)))
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_104,c_7604]) ).
cnf(c_7606,plain,
( n1 = n0
| less(n1,n0)
| plus(n0,sK2(n0,n2,spilling)) != A
| less(n0,sK0(n0,filling,n1))
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_115,c_7605]) ).
cnf(c_7607,plain,
( n1 = n0
| less(n1,n0)
| plus(n0,n1) != A
| less(n0,sK0(n0,filling,n1))
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_1885,c_7606]) ).
cnf(c_7608,plain,
( n1 = n0
| less(n1,n0)
| plus(n1,n0) != A
| less(n0,sK0(n0,filling,n1))
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_104,c_7607]) ).
cnf(c_7609,plain,
( n1 = n0
| less(n1,n0)
| n1 != A
| less(n0,sK0(n0,filling,n1))
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_115,c_7608]) ).
cnf(c_7610,plain,
( n0 = n1
| less(n1,n0)
| n1 != A
| less(n0,sK0(n0,filling,n1))
| holdsAt(waterLevel(A),n1) ),
inference(copy,[status(thm)],[c_7609]) ).
cnf(c_7611,plain,
( n0 = n1
| n1 != A
| less(n0,sK0(n0,filling,n1))
| holdsAt(waterLevel(A),n1) ),
inference(resolve,[status(thm)],[c_100,c_7610]) ).
cnf(c_4807,plain,
( n1 != A
| less(n0,sK0(n0,filling,n1))
| holdsAt(waterLevel(A),n1) ),
inference(resolve,[status(thm)],[c_234,c_7611]) ).
cnf(c_7612,plain,
n1 = sK0(n0,filling,n3),
inference(copy,[status(thm)],[c_4279]) ).
cnf(c_7613,plain,
( less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(sK0(n0,filling,n3)),n1) ),
inference(resolve,[status(thm)],[c_4748,c_7612]) ).
cnf(c_7282,plain,
( less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(n1),n1) ),
inference(paramod,[status(thm)],[c_4279,c_7613]) ).
cnf(c_7614,plain,
( n3 = n1
| less(sK0(n0,filling,n1),n1) ),
inference(resolve,[status(thm)],[c_7282,c_529]) ).
cnf(c_7283,plain,
less(sK0(n0,filling,n1),n1),
inference(resolve,[status(thm)],[c_274,c_7614]) ).
cnf(c_7615,plain,
( n0 = sK0(n0,filling,n1)
| n1 = sK0(n0,filling,n1) ),
inference(resolve,[status(thm)],[c_7283,c_536]) ).
cnf(c_7616,plain,
( n0 = sK0(n0,filling,n1)
| sK0(n0,filling,n1) = n1 ),
inference(copy,[status(thm)],[c_7615]) ).
cnf(c_7520,plain,
( sK0(n0,filling,n1) = n0
| sK0(n0,filling,n1) = n1 ),
inference(copy,[status(thm)],[c_7616]) ).
cnf(c_7617,plain,
n1 != sK0(n0,filling,n1),
inference(resolve,[status(thm)],[c_7283,c_80]) ).
cnf(c_7524,plain,
sK0(n0,filling,n1) != n1,
inference(copy,[status(thm)],[c_7617]) ).
cnf(c_7525,plain,
sK0(n0,filling,n1) = n0,
inference(resolve,[status(thm)],[c_7524,c_7520]) ).
cnf(c_7618,plain,
( n1 != A
| less(n0,n0)
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_7525,c_4807]) ).
cnf(c_7527,plain,
( n1 != A
| holdsAt(waterLevel(A),n1) ),
inference(resolve,[status(thm)],[c_180,c_7618]) ).
cnf(c_7619,plain,
n1 = sK0(n0,filling,n3),
inference(copy,[status(thm)],[c_4279]) ).
cnf(c_7620,plain,
holdsAt(waterLevel(sK0(n0,filling,n3)),n1),
inference(resolve,[status(thm)],[c_7527,c_7619]) ).
cnf(c_7528,plain,
holdsAt(waterLevel(n1),n1),
inference(paramod,[status(thm)],[c_4279,c_7620]) ).
cnf(c_7621,plain,
n3 = n1,
inference(resolve,[status(thm)],[c_7528,c_529]) ).
cnf(c_7529,plain,
$false,
inference(resolve,[status(thm)],[c_274,c_7621]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CSR009+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.38 % Computer : n007.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sat Sep 26 23:53:25 UTC 2026
% 0.09/0.39 % CPUTime :
% 0.09/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.39 % Process 786180 was started by sandbox on n007,
% 0.09/0.39 % Sat Sep 26 23:53:25 2026
% 0.09/0.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.40
% 0.09/0.40 % From the command line: assign(max_seconds, 300).
% 31.49/4.54
% 31.49/4.54 % given #500 (T,wt=9): 670 less(n6,A) | n6 = A | -less(n8,A). [resolve(626,c,81,b)].
% 31.49/4.54
% 31.49/4.54 % given #1000 (T,wt=6): 1656 less_or_equal(n0,f4(n0,n2,spilling)). [resolve(1640,a,102,b)].
% 31.49/4.54
% 31.49/4.54 % given #1500 (T,wt=11): 2618 happens(f5(filling,f2(n0,filling,n5)),f2(n0,filling,n5)). [resolve(2615,a,171,a),rewrite([104(7),104(26)]),unit_del(a,2522),unit_del(c,2523)].
% 31.49/4.54
% 31.49/4.54 % given #2000 (T,wt=9): 5164 holdsAt(spilling,plus(n1,f4(n0,n5,waterLevel(n3)))). [resolve(5161,a,450,a),rewrite([104(8)])].
% 31.49/4.54
% 31.49/4.54 % given #2500 (T,wt=13): 2078 less(f4(n0,A,waterLevel(n3)),A) | n1 = A | less(A,n6). [resolve(1471,b,801,a)].
% 31.49/4.54
% 31.49/4.54 % SZS status Theorem for theBenchmark
% 31.49/4.54
% 31.49/4.54 % Proof 1 at 2.76 (+ 0.98) seconds.
% 31.49/4.54 % Length of proof is 184.
% 31.49/4.54 % Level of proof is 23.
% 31.49/4.54 % Maximum clause weight is 35.000.
% 31.49/4.54 % Given clauses 2525.
% 31.49/4.54
% 31.49/4.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------