%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CSR012+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 07:06:32 AM UTC 2026
% Result : Theorem 12.85s 2.10s
% Output : CNFRefutation 12.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 18
% Syntax : Number of formulae : 136 ( 40 unt; 0 def)
% Number of atoms : 473 ( 201 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 478 ( 141 ~; 288 |; 37 &)
% ( 10 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-4 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-3 aty)
% Number of variables : 234 ( 16 sgn 76 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(stoppedin_defn,axiom,
! [Time1,Fluent,Time2] :
( stoppedIn(Time1,Fluent,Time2)
<=> ? [Event,Time] :
( terminates(Event,Fluent,Time)
& less(Time,Time2)
& less(Time1,Time)
& happens(Event,Time) ) ),
file('theBenchmark.p',stoppedin_defn) ).
fof(change_holding,axiom,
! [Event,Time,Fluent,Fluent2,Offset] :
( ( ~ stoppedIn(Time,Fluent,plus(Time,Offset))
& trajectory(Fluent,Time,Fluent2,Offset)
& less(n0,Offset)
& initiates(Event,Fluent,Time)
& happens(Event,Time) )
=> holdsAt(Fluent2,plus(Time,Offset)) ),
file('theBenchmark.p',change_holding) ).
fof(initiates_all_defn,axiom,
! [Event,Fluent,Time] :
( initiates(Event,Fluent,Time)
<=> ( ? [Height] :
( Fluent = waterLevel(Height)
& Event = overflow
& holdsAt(waterLevel(Height),Time) )
| ? [Height] :
( Fluent = waterLevel(Height)
& Event = tapOff
& holdsAt(waterLevel(Height),Time) )
| ( Fluent = spilling
& Event = overflow )
| ( Fluent = filling
& Event = tapOn ) ) ),
file('theBenchmark.p',initiates_all_defn) ).
fof(releases_all_defn,axiom,
! [Event,Fluent,Time] :
( releases(Event,Fluent,Time)
<=> ? [Height] :
( Fluent = waterLevel(Height)
& Event = tapOn ) ),
file('theBenchmark.p',releases_all_defn) ).
fof(happens_all_defn,axiom,
! [Event,Time] :
( happens(Event,Time)
<=> ( ( Event = overflow
& holdsAt(filling,Time)
& holdsAt(waterLevel(n3),Time) )
| ( Time = n0
& Event = tapOn ) ) ),
file('theBenchmark.p',happens_all_defn) ).
fof(change_of_waterLevel,axiom,
! [Height1,Time,Height2,Offset] :
( ( Height2 = plus(Height1,Offset)
& holdsAt(waterLevel(Height1),Time) )
=> trajectory(filling,Time,waterLevel(Height2),Offset) ),
file('theBenchmark.p',change_of_waterLevel) ).
fof(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(less_property,axiom,
! [X,Y] :
( less(X,Y)
<=> ( Y != X
& ~ less(Y,X) ) ),
file('theBenchmark.p',less_property) ).
fof(waterLevel_1,conjecture,
holdsAt(waterLevel(n1),n1),
file('theBenchmark.p',waterLevel_1) ).
fof(waterLevel_1_neg,negated_conjecture,
~ holdsAt(waterLevel(n1),n1),
inference(assume_negation,[status(cth)],[waterLevel_1]) ).
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(sK2(Time1,Fluent,Time2),Fluent,sK0(Time1,Fluent,Time2))
& less(sK0(Time1,Fluent,Time2),Time2)
& less(Time1,sK0(Time1,Fluent,Time2))
& happens(sK2(Time1,Fluent,Time2),sK0(Time1,Fluent,Time2)) )
| ~ stoppedIn(Time1,Fluent,Time2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK0]),skolemize(X0,sK2(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(sK2(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(sK2(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_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]) ).
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(sK1(Event,Fluent,Time)) = Fluent
& tapOn = Event )
| ~ releases(Event,Fluent,Time) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1(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(sK1(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(sK1(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(sK1(A,C,D)) = C
| waterLevel(B) != C
| tapOn != A ),
inference(resolve,[status(thm)],[c_58,c_57]) ).
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(n1),n1),
inference(clausify,[status(thm)],[waterLevel_1_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_94,plain,
( ~ less_or_equal(A,n2)
| less(A,n3) ),
inference(clausify,[status(thm)],[less3]) ).
cnf(c_95,plain,
( less_or_equal(A,n2)
| ~ less(A,n3) ),
inference(clausify,[status(thm)],[less3]) ).
cnf(c_96,plain,
( ~ less_or_equal(A,n1)
| less(A,n2) ),
inference(clausify,[status(thm)],[less2]) ).
cnf(c_97,plain,
( less_or_equal(A,n1)
| ~ less(A,n2) ),
inference(clausify,[status(thm)],[less2]) ).
cnf(c_98,plain,
( ~ less_or_equal(A,n0)
| less(A,n1) ),
inference(clausify,[status(thm)],[less1]) ).
cnf(c_99,plain,
( less_or_equal(A,n0)
| ~ less(A,n1) ),
inference(clausify,[status(thm)],[less1]) ).
cnf(c_100,plain,
~ less(A,n0),
inference(clausify,[status(thm)],[less0]) ).
cnf(c_101,plain,
( B != A
| less_or_equal(A,B) ),
inference(clausify,[status(thm)],[less_or_equal]) ).
cnf(c_102,plain,
( ~ less(A,B)
| less_or_equal(A,B) ),
inference(clausify,[status(thm)],[less_or_equal]) ).
cnf(c_103,plain,
( B = A
| less(A,B)
| ~ less_or_equal(A,B) ),
inference(clausify,[status(thm)],[less_or_equal]) ).
cnf(c_104,plain,
plus(A,B) = plus(B,A),
inference(clausify,[status(thm)],[symmetry_of_plus]) ).
fof(plus0_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_128,plain,
( n0 != B
| tapOn != A
| happens(A,B) ),
inference(clausify,[status(thm)],[happens_all_defn]) ).
cnf(c_142,plain,
( filling != B
| tapOn != A
| initiates(A,B,C) ),
inference(clausify,[status(thm)],[initiates_all_defn]) ).
cnf(c_180,plain,
~ less(A,A),
inference(factor,[status(thm)],[c_81]) ).
cnf(c_181,plain,
( waterLevel(sK1(tapOn,B,C)) = B
| waterLevel(A) != B ),
inference(xxres,[status(thm)],[c_60]) ).
cnf(c_2006,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_2006]) ).
cnf(c_2007,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_2007]) ).
cnf(c_194,plain,
less_or_equal(A,A),
inference(xxres,[status(thm)],[c_101]) ).
cnf(c_203,plain,
( n0 != A
| happens(tapOn,A) ),
inference(xxres,[status(thm)],[c_128]) ).
cnf(c_213,plain,
( filling != A
| initiates(tapOn,A,B) ),
inference(xxres,[status(thm)],[c_142]) ).
cnf(c_223,plain,
waterLevel(sK1(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_2008,plain,
n1 != n0,
inference(resolve,[status(thm)],[c_224,c_80]) ).
cnf(c_234,plain,
n0 != n1,
inference(copy,[status(thm)],[c_2008]) ).
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_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_2009,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_2009]) ).
cnf(c_2010,plain,
n0 = plus(n0,n0),
inference(copy,[status(thm)],[c_116]) ).
cnf(c_2011,plain,
happens(tapOn,plus(n0,n0)),
inference(resolve,[status(thm)],[c_203,c_2010]) ).
cnf(c_416,plain,
happens(tapOn,n0),
inference(paramod,[status(thm)],[c_116,c_2011]) ).
cnf(c_454,plain,
initiates(tapOn,filling,A),
inference(xxres,[status(thm)],[c_213]) ).
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_499,plain,
sK1(tapOn,waterLevel(A),B) = A,
inference(resolve,[status(thm)],[c_223,c_118]) ).
cnf(c_507,plain,
( ~ less(A,n1)
| n0 = A
| n1 = A ),
inference(resolve,[status(thm)],[c_327,c_81]) ).
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_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_895,plain,
( n1 = A
| less(A,n1)
| n2 = A
| n3 = A
| less(n3,A) ),
inference(resolve,[status(thm)],[c_584,c_103]) ).
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_2012,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_2013,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_2012]) ).
cnf(c_2014,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_2013]) ).
cnf(c_2015,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_2014]) ).
cnf(c_2016,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_2015]) ).
cnf(c_2017,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_2016]) ).
cnf(c_2018,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_2017]) ).
cnf(c_2019,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_2018]) ).
cnf(c_2020,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_2019]) ).
cnf(c_2021,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_2020]) ).
cnf(c_2022,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_2021]) ).
cnf(c_2023,plain,
( n0 = n1
| n2 = n0
| n1 != A
| less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(A),n1) ),
inference(resolve,[status(thm)],[c_304,c_2022]) ).
cnf(c_2024,plain,
( n0 = n1
| n1 != A
| less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(A),n1) ),
inference(resolve,[status(thm)],[c_270,c_2023]) ).
cnf(c_1531,plain,
( n1 != A
| less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(A),n1) ),
inference(resolve,[status(thm)],[c_234,c_2024]) ).
cnf(c_2025,plain,
A = sK1(tapOn,waterLevel(A),B),
inference(copy,[status(thm)],[c_499]) ).
cnf(c_2026,plain,
( less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(sK1(tapOn,waterLevel(n1),A)),n1) ),
inference(resolve,[status(thm)],[c_1531,c_2025]) ).
cnf(c_2027,plain,
( less(sK0(n0,filling,n1),n1)
| holdsAt(waterLevel(n1),n1) ),
inference(paramod,[status(thm)],[c_499,c_2026]) ).
cnf(c_1557,negated_conjecture,
less(sK0(n0,filling,n1),n1),
inference(resolve,[status(thm)],[c_72,c_2027]) ).
cnf(c_2028,plain,
( n0 = sK0(n0,filling,n1)
| n1 = sK0(n0,filling,n1) ),
inference(resolve,[status(thm)],[c_1557,c_507]) ).
cnf(c_2029,plain,
( n0 = sK0(n0,filling,n1)
| sK0(n0,filling,n1) = n1 ),
inference(copy,[status(thm)],[c_2028]) ).
cnf(c_1606,plain,
( sK0(n0,filling,n1) = n0
| sK0(n0,filling,n1) = n1 ),
inference(copy,[status(thm)],[c_2029]) ).
cnf(c_2030,plain,
n1 != sK0(n0,filling,n1),
inference(resolve,[status(thm)],[c_1557,c_80]) ).
cnf(c_1610,plain,
sK0(n0,filling,n1) != n1,
inference(copy,[status(thm)],[c_2030]) ).
cnf(c_1611,plain,
sK0(n0,filling,n1) = n0,
inference(resolve,[status(thm)],[c_1610,c_1606]) ).
cnf(c_2031,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_2032,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_2031]) ).
cnf(c_2033,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_2032]) ).
cnf(c_2034,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_2033]) ).
cnf(c_2035,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_2034]) ).
cnf(c_2036,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| plus(n0,n1) != A
| less(n0,n0)
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_1611,c_2035]) ).
cnf(c_2037,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| plus(n1,n0) != A
| less(n0,n0)
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_104,c_2036]) ).
cnf(c_2038,plain,
( n1 = n0
| n2 = n0
| n3 = n0
| less(n3,n0)
| n1 != A
| less(n0,n0)
| holdsAt(waterLevel(A),n1) ),
inference(paramod,[status(thm)],[c_115,c_2037]) ).
cnf(c_2039,plain,
( n0 = n1
| n2 = n0
| n3 = n0
| less(n3,n0)
| n1 != A
| less(n0,n0)
| holdsAt(waterLevel(A),n1) ),
inference(copy,[status(thm)],[c_2038]) ).
cnf(c_2040,plain,
( n0 = n1
| n2 = n0
| n3 = n0
| less(n3,n0)
| n1 != A
| holdsAt(waterLevel(A),n1) ),
inference(resolve,[status(thm)],[c_180,c_2039]) ).
cnf(c_2041,plain,
( n0 = n1
| n2 = n0
| n3 = n0
| n1 != A
| holdsAt(waterLevel(A),n1) ),
inference(resolve,[status(thm)],[c_100,c_2040]) ).
cnf(c_2042,plain,
( n0 = n1
| n2 = n0
| n1 != A
| holdsAt(waterLevel(A),n1) ),
inference(resolve,[status(thm)],[c_304,c_2041]) ).
cnf(c_2043,plain,
( n0 = n1
| n1 != A
| holdsAt(waterLevel(A),n1) ),
inference(resolve,[status(thm)],[c_270,c_2042]) ).
cnf(c_1995,plain,
( n1 != A
| holdsAt(waterLevel(A),n1) ),
inference(resolve,[status(thm)],[c_234,c_2043]) ).
cnf(c_2044,plain,
A = sK1(tapOn,waterLevel(A),B),
inference(copy,[status(thm)],[c_499]) ).
cnf(c_2045,plain,
holdsAt(waterLevel(sK1(tapOn,waterLevel(n1),A)),n1),
inference(resolve,[status(thm)],[c_1995,c_2044]) ).
cnf(c_2046,plain,
holdsAt(waterLevel(n1),n1),
inference(paramod,[status(thm)],[c_499,c_2045]) ).
cnf(c_2005,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_72,c_2046]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CSR012+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n010.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 23:56:18 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 340447 was started by sandbox2 on n010,
% 0.08/0.36 % Sat Sep 26 23:56:18 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.38
% 0.08/0.38 % From the command line: assign(max_seconds, 300).
% 12.85/2.10
% 12.85/2.10 % given #500 (T,wt=9): 654 n1 = A | less(A,n4) | -less(A,n1). [resolve(641,a,81,b)].
% 12.85/2.10
% 12.85/2.10 % given #1000 (T,wt=12): 1800 holdsAt(filling,n2) | happens(f3(n0,n2,spilling),f4(n0,n2,spilling)). [resolve(1160,c,894,d),unit_del(c,307),unit_del(d,308),unit_del(e,274),unit_del(f,237)].
% 12.85/2.10
% 12.85/2.10 % SZS status Theorem for theBenchmark
% 12.85/2.10
% 12.85/2.10 % Proof 1 at 1.15 (+ 0.54) seconds.
% 12.85/2.10 % Length of proof is 85.
% 12.85/2.10 % Level of proof is 14.
% 12.85/2.10 % Maximum clause weight is 35.000.
% 12.85/2.10 % Given clauses 1030.
% 12.85/2.10
% 12.85/2.10 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------