%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CSR013+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 : n012.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 20.94s 3.32s
% Output : CNFRefutation 20.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 22
% Syntax : Number of formulae : 159 ( 45 unt; 0 def)
% Number of atoms : 442 ( 109 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 446 ( 163 ~; 230 |; 39 &)
% ( 9 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-3 aty)
% Number of variables : 203 ( 9 sgn 65 !; 10 ?)
% 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(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(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(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(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(nothing_terminates_filling_2,conjecture,
~ ? [Event] :
( terminates(Event,filling,n2)
& happens(Event,n2) ),
file('theBenchmark.p',nothing_terminates_filling_2) ).
fof(nothing_terminates_filling_2_neg,negated_conjecture,
~ ~ ? [Event] :
( terminates(Event,filling,n2)
& happens(Event,n2) ),
inference(assume_negation,[status(cth)],[nothing_terminates_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_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]) ).
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]) ).
fof(nnf_36,plain,
? [Event] :
( terminates(Event,filling,n2)
& happens(Event,n2) ),
inference(fof_nnf,[status(thm)],[nothing_terminates_filling_2_neg]) ).
fof(sk_nothing_terminates_filling_2_neg,plain,
( terminates(sK2,filling,n2)
& happens(sK2,n2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(Event,sK2)],[nnf_36]) ).
cnf(c_73,negated_conjecture,
happens(sK2,n2),
inference(split_conjunct,[status(thm)],[sk_nothing_terminates_filling_2_neg]) ).
fof(waterLevel_0,axiom,
holdsAt(waterLevel(n0),n0),
file('theBenchmark.p',waterLevel_0) ).
cnf(c_79,plain,
holdsAt(waterLevel(n0),n0),
inference(clausify,[status(thm)],[waterLevel_0]) ).
cnf(c_80,plain,
( B = A
| less(B,A)
| less(A,B) ),
inference(clausify,[status(thm)],[less_property]) ).
cnf(c_81,plain,
( B != A
| ~ less(A,B) ),
inference(clausify,[status(thm)],[less_property]) ).
cnf(c_82,plain,
( ~ less(B,A)
| ~ less(A,B) ),
inference(clausify,[status(thm)],[less_property]) ).
cnf(c_95,plain,
( ~ less_or_equal(A,n2)
| less(A,n3) ),
inference(clausify,[status(thm)],[less3]) ).
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,n1)
| ~ less(A,n2) ),
inference(clausify,[status(thm)],[less2]) ).
cnf(c_99,plain,
( ~ less_or_equal(A,n0)
| less(A,n1) ),
inference(clausify,[status(thm)],[less1]) ).
cnf(c_100,plain,
( less_or_equal(A,n0)
| ~ less(A,n1) ),
inference(clausify,[status(thm)],[less1]) ).
cnf(c_101,plain,
~ less(A,n0),
inference(clausify,[status(thm)],[less0]) ).
cnf(c_102,plain,
( B != A
| less_or_equal(A,B) ),
inference(clausify,[status(thm)],[less_or_equal]) ).
cnf(c_103,plain,
( ~ less(A,B)
| less_or_equal(A,B) ),
inference(clausify,[status(thm)],[less_or_equal]) ).
cnf(c_104,plain,
( B = A
| less(A,B)
| ~ less_or_equal(A,B) ),
inference(clausify,[status(thm)],[less_or_equal]) ).
cnf(c_105,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_112,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_114,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_115,plain,
plus(n0,n1) = n1,
inference(clausify,[status(thm)],[plus0_1]) ).
cnf(c_116,plain,
plus(n1,n0) = n1,
inference(paramod,[status(thm)],[c_105,c_115]) ).
fof(plus0_0,axiom,
plus(n0,n0) = n0,
file('theBenchmark.p',plus0_0) ).
cnf(c_117,plain,
plus(n0,n0) = n0,
inference(clausify,[status(thm)],[plus0_0]) ).
cnf(c_127,plain,
( C = A
| ~ holdsAt(waterLevel(C),B)
| ~ holdsAt(waterLevel(A),B) ),
inference(clausify,[status(thm)],[same_waterLevel]) ).
cnf(c_128,plain,
( overflow != A
| ~ holdsAt(filling,B)
| ~ holdsAt(waterLevel(n3),B)
| happens(A,B) ),
inference(clausify,[status(thm)],[happens_all_defn]) ).
cnf(c_129,plain,
( n0 != B
| tapOn != A
| happens(A,B) ),
inference(clausify,[status(thm)],[happens_all_defn]) ).
cnf(c_131,plain,
( holdsAt(filling,B)
| n0 = B
| ~ happens(A,B) ),
inference(clausify,[status(thm)],[happens_all_defn]) ).
cnf(c_132,plain,
( holdsAt(waterLevel(n3),B)
| n0 = B
| ~ happens(A,B) ),
inference(clausify,[status(thm)],[happens_all_defn]) ).
cnf(c_136,plain,
( filling != B
| overflow != A
| terminates(A,B,C) ),
inference(clausify,[status(thm)],[terminates_all_defn]) ).
cnf(c_143,plain,
( filling != B
| tapOn != A
| initiates(A,B,C) ),
inference(clausify,[status(thm)],[initiates_all_defn]) ).
cnf(c_164,plain,
( ~ holdsAt(C,plus(B,n1))
| ~ terminates(A,C,B)
| ~ happens(A,B) ),
inference(clausify,[status(thm)],[happens_terminates_not_holds]) ).
cnf(c_165,plain,
( holdsAt(C,plus(B,n1))
| ~ initiates(A,C,B)
| ~ happens(A,B) ),
inference(clausify,[status(thm)],[happens_holds]) ).
cnf(c_17055,plain,
( A = n2
| less(n2,A)
| less_or_equal(A,n1) ),
inference(resolve,[status(thm)],[c_98,c_80]) ).
cnf(c_235,plain,
( n2 = A
| less(n2,A)
| less_or_equal(A,n1) ),
inference(copy,[status(thm)],[c_17055]) ).
cnf(c_17056,plain,
( A = n1
| less(n1,A)
| less_or_equal(A,n0) ),
inference(resolve,[status(thm)],[c_100,c_80]) ).
cnf(c_236,plain,
( n1 = A
| less(n1,A)
| less_or_equal(A,n0) ),
inference(copy,[status(thm)],[c_17056]) ).
cnf(c_238,plain,
less_or_equal(A,A),
inference(xxres,[status(thm)],[c_102]) ).
cnf(c_276,plain,
( ~ holdsAt(waterLevel(n0),B)
| less(sK0(B,filling,plus(B,n2)),plus(B,n2))
| holdsAt(waterLevel(n2),plus(B,n2))
| ~ less(n0,n2)
| ~ initiates(A,filling,B)
| ~ happens(A,B) ),
inference(resolve,[status(thm)],[c_114,c_66]) ).
cnf(c_277,plain,
( ~ holdsAt(waterLevel(n0),B)
| less(B,sK0(B,filling,plus(B,n2)))
| holdsAt(waterLevel(n2),plus(B,n2))
| ~ less(n0,n2)
| ~ initiates(A,filling,B)
| ~ happens(A,B) ),
inference(resolve,[status(thm)],[c_114,c_65]) ).
cnf(c_278,plain,
( ~ holdsAt(waterLevel(n0),B)
| happens(sK1(B,filling,plus(B,n2)),sK0(B,filling,plus(B,n2)))
| holdsAt(waterLevel(n2),plus(B,n2))
| ~ less(n0,n2)
| ~ initiates(A,filling,B)
| ~ happens(A,B) ),
inference(resolve,[status(thm)],[c_114,c_64]) ).
cnf(c_280,plain,
( ~ holdsAt(filling,A)
| ~ holdsAt(waterLevel(n3),A)
| happens(overflow,A) ),
inference(xxres,[status(thm)],[c_128]) ).
cnf(c_281,plain,
( n0 != A
| happens(tapOn,A) ),
inference(xxres,[status(thm)],[c_129]) ).
cnf(c_17057,negated_conjecture,
( holdsAt(filling,n2)
| n0 = n2 ),
inference(resolve,[status(thm)],[c_131,c_73]) ).
cnf(c_284,negated_conjecture,
( holdsAt(filling,n2)
| n2 = n0 ),
inference(copy,[status(thm)],[c_17057]) ).
cnf(c_17058,negated_conjecture,
( holdsAt(waterLevel(n3),n2)
| n0 = n2 ),
inference(resolve,[status(thm)],[c_132,c_73]) ).
cnf(c_285,negated_conjecture,
( holdsAt(waterLevel(n3),n2)
| n2 = n0 ),
inference(copy,[status(thm)],[c_17058]) ).
cnf(c_289,plain,
( filling != A
| terminates(overflow,A,B) ),
inference(xxres,[status(thm)],[c_136]) ).
cnf(c_302,plain,
( filling != A
| initiates(tapOn,A,B) ),
inference(xxres,[status(thm)],[c_143]) ).
cnf(c_333,plain,
less(n0,n1),
inference(resolve,[status(thm)],[c_238,c_99]) ).
cnf(c_335,plain,
less(n2,n3),
inference(resolve,[status(thm)],[c_238,c_95]) ).
cnf(c_350,plain,
less_or_equal(n0,n1),
inference(resolve,[status(thm)],[c_333,c_103]) ).
cnf(c_17059,plain,
n1 != n0,
inference(resolve,[status(thm)],[c_333,c_81]) ).
cnf(c_351,plain,
n0 != n1,
inference(copy,[status(thm)],[c_17059]) ).
cnf(c_17060,plain,
n3 != n2,
inference(resolve,[status(thm)],[c_335,c_81]) ).
cnf(c_389,plain,
n2 != n3,
inference(copy,[status(thm)],[c_17060]) ).
cnf(c_513,plain,
less(n0,n2),
inference(resolve,[status(thm)],[c_350,c_97]) ).
cnf(c_514,plain,
( ~ holdsAt(waterLevel(n0),B)
| happens(sK1(B,filling,plus(B,n2)),sK0(B,filling,plus(B,n2)))
| holdsAt(waterLevel(n2),plus(B,n2))
| ~ initiates(A,filling,B)
| ~ happens(A,B) ),
inference(resolve,[status(thm)],[c_513,c_278]) ).
cnf(c_515,plain,
( ~ holdsAt(waterLevel(n0),B)
| less(B,sK0(B,filling,plus(B,n2)))
| holdsAt(waterLevel(n2),plus(B,n2))
| ~ initiates(A,filling,B)
| ~ happens(A,B) ),
inference(resolve,[status(thm)],[c_513,c_277]) ).
cnf(c_516,plain,
( ~ holdsAt(waterLevel(n0),B)
| less(sK0(B,filling,plus(B,n2)),plus(B,n2))
| holdsAt(waterLevel(n2),plus(B,n2))
| ~ initiates(A,filling,B)
| ~ happens(A,B) ),
inference(resolve,[status(thm)],[c_513,c_276]) ).
cnf(c_543,plain,
n2 != n0,
inference(resolve,[status(thm)],[c_513,c_81]) ).
cnf(c_552,negated_conjecture,
holdsAt(waterLevel(n3),n2),
inference(resolve,[status(thm)],[c_543,c_285]) ).
cnf(c_553,negated_conjecture,
holdsAt(filling,n2),
inference(resolve,[status(thm)],[c_543,c_284]) ).
cnf(c_17061,plain,
n0 = plus(n0,n0),
inference(copy,[status(thm)],[c_117]) ).
cnf(c_17062,plain,
happens(tapOn,plus(n0,n0)),
inference(resolve,[status(thm)],[c_281,c_17061]) ).
cnf(c_1535,plain,
happens(tapOn,n0),
inference(paramod,[status(thm)],[c_117,c_17062]) ).
cnf(c_17063,plain,
( holdsAt(A,plus(n0,n1))
| ~ initiates(tapOn,A,n0) ),
inference(resolve,[status(thm)],[c_1535,c_165]) ).
cnf(c_17064,plain,
( holdsAt(A,plus(n1,n0))
| ~ initiates(tapOn,A,n0) ),
inference(paramod,[status(thm)],[c_105,c_17063]) ).
cnf(c_1584,plain,
( holdsAt(A,n1)
| ~ initiates(tapOn,A,n0) ),
inference(paramod,[status(thm)],[c_116,c_17064]) ).
cnf(c_1592,plain,
terminates(overflow,filling,A),
inference(xxres,[status(thm)],[c_289]) ).
cnf(c_1597,plain,
( ~ holdsAt(filling,plus(A,n1))
| ~ happens(overflow,A) ),
inference(resolve,[status(thm)],[c_1592,c_164]) ).
cnf(c_1714,plain,
initiates(tapOn,filling,A),
inference(xxres,[status(thm)],[c_302]) ).
cnf(c_1797,plain,
holdsAt(filling,n1),
inference(resolve,[status(thm)],[c_1584,c_1714]) ).
cnf(c_1851,plain,
( n1 = A
| less(A,n1)
| n2 = A
| less(n2,A) ),
inference(resolve,[status(thm)],[c_235,c_104]) ).
cnf(c_17065,plain,
( n0 = A
| less(A,n0)
| n1 = A
| less(n1,A) ),
inference(resolve,[status(thm)],[c_236,c_104]) ).
cnf(c_1852,plain,
( n0 = A
| n1 = A
| less(n1,A) ),
inference(resolve,[status(thm)],[c_101,c_17065]) ).
cnf(c_1870,plain,
( n3 = A
| ~ holdsAt(waterLevel(A),n2) ),
inference(resolve,[status(thm)],[c_552,c_127]) ).
cnf(c_1901,plain,
( ~ less(A,n1)
| n0 = A
| n1 = A ),
inference(resolve,[status(thm)],[c_1852,c_82]) ).
cnf(c_3388,plain,
( ~ holdsAt(waterLevel(n3),n1)
| happens(overflow,n1) ),
inference(resolve,[status(thm)],[c_280,c_1797]) ).
cnf(c_17066,plain,
( n0 = A
| n1 = A
| n1 = A
| n2 = A
| less(n2,A) ),
inference(resolve,[status(thm)],[c_1851,c_1901]) ).
cnf(c_6411,plain,
( n0 = A
| n1 = A
| n2 = A
| less(n2,A) ),
inference(copy,[status(thm)],[c_17066]) ).
cnf(c_6723,plain,
( ~ less(A,n2)
| n0 = A
| n1 = A
| n2 = A ),
inference(resolve,[status(thm)],[c_6411,c_82]) ).
cnf(c_17067,plain,
( ~ holdsAt(waterLevel(n0),n0)
| happens(sK1(n0,filling,plus(n0,n2)),sK0(n0,filling,plus(n0,n2)))
| holdsAt(waterLevel(n2),plus(n0,n2))
| ~ initiates(tapOn,filling,n0) ),
inference(resolve,[status(thm)],[c_514,c_1535]) ).
cnf(c_17068,plain,
( ~ holdsAt(waterLevel(n0),n0)
| happens(sK1(n0,filling,plus(n0,n2)),sK0(n0,filling,plus(n0,n2)))
| holdsAt(waterLevel(n2),n2)
| ~ initiates(tapOn,filling,n0) ),
inference(paramod,[status(thm)],[c_114,c_17067]) ).
cnf(c_17069,plain,
( ~ holdsAt(waterLevel(n0),n0)
| happens(sK1(n0,filling,n2),sK0(n0,filling,plus(n0,n2)))
| holdsAt(waterLevel(n2),n2)
| ~ initiates(tapOn,filling,n0) ),
inference(paramod,[status(thm)],[c_114,c_17068]) ).
cnf(c_17070,plain,
( ~ holdsAt(waterLevel(n0),n0)
| happens(sK1(n0,filling,n2),sK0(n0,filling,n2))
| holdsAt(waterLevel(n2),n2)
| ~ initiates(tapOn,filling,n0) ),
inference(paramod,[status(thm)],[c_114,c_17069]) ).
cnf(c_17071,plain,
( ~ holdsAt(waterLevel(n0),n0)
| happens(sK1(n0,filling,n2),sK0(n0,filling,n2))
| holdsAt(waterLevel(n2),n2) ),
inference(resolve,[status(thm)],[c_1714,c_17070]) ).
cnf(c_16645,plain,
( happens(sK1(n0,filling,n2),sK0(n0,filling,n2))
| holdsAt(waterLevel(n2),n2) ),
inference(resolve,[status(thm)],[c_79,c_17071]) ).
cnf(c_17072,plain,
( ~ holdsAt(waterLevel(n0),n0)
| less(n0,sK0(n0,filling,plus(n0,n2)))
| holdsAt(waterLevel(n2),plus(n0,n2))
| ~ initiates(tapOn,filling,n0) ),
inference(resolve,[status(thm)],[c_515,c_1535]) ).
cnf(c_17073,plain,
( ~ holdsAt(waterLevel(n0),n0)
| less(n0,sK0(n0,filling,plus(n0,n2)))
| holdsAt(waterLevel(n2),n2)
| ~ initiates(tapOn,filling,n0) ),
inference(paramod,[status(thm)],[c_114,c_17072]) ).
cnf(c_17074,plain,
( ~ holdsAt(waterLevel(n0),n0)
| less(n0,sK0(n0,filling,n2))
| holdsAt(waterLevel(n2),n2)
| ~ initiates(tapOn,filling,n0) ),
inference(paramod,[status(thm)],[c_114,c_17073]) ).
cnf(c_17075,plain,
( ~ holdsAt(waterLevel(n0),n0)
| less(n0,sK0(n0,filling,n2))
| holdsAt(waterLevel(n2),n2) ),
inference(resolve,[status(thm)],[c_1714,c_17074]) ).
cnf(c_16692,plain,
( less(n0,sK0(n0,filling,n2))
| holdsAt(waterLevel(n2),n2) ),
inference(resolve,[status(thm)],[c_79,c_17075]) ).
cnf(c_17076,plain,
( n3 = n2
| less(n0,sK0(n0,filling,n2)) ),
inference(resolve,[status(thm)],[c_16692,c_1870]) ).
cnf(c_17077,plain,
( n2 = n3
| less(n0,sK0(n0,filling,n2)) ),
inference(copy,[status(thm)],[c_17076]) ).
cnf(c_16697,plain,
less(n0,sK0(n0,filling,n2)),
inference(resolve,[status(thm)],[c_389,c_17077]) ).
cnf(c_16703,plain,
sK0(n0,filling,n2) != n0,
inference(resolve,[status(thm)],[c_16697,c_81]) ).
cnf(c_17078,plain,
( ~ holdsAt(waterLevel(n0),n0)
| less(sK0(n0,filling,plus(n0,n2)),plus(n0,n2))
| holdsAt(waterLevel(n2),plus(n0,n2))
| ~ initiates(tapOn,filling,n0) ),
inference(resolve,[status(thm)],[c_516,c_1535]) ).
cnf(c_17079,plain,
( ~ holdsAt(waterLevel(n0),n0)
| less(sK0(n0,filling,plus(n0,n2)),plus(n0,n2))
| holdsAt(waterLevel(n2),n2)
| ~ initiates(tapOn,filling,n0) ),
inference(paramod,[status(thm)],[c_114,c_17078]) ).
cnf(c_17080,plain,
( ~ holdsAt(waterLevel(n0),n0)
| less(sK0(n0,filling,n2),plus(n0,n2))
| holdsAt(waterLevel(n2),n2)
| ~ initiates(tapOn,filling,n0) ),
inference(paramod,[status(thm)],[c_114,c_17079]) ).
cnf(c_17081,plain,
( ~ holdsAt(waterLevel(n0),n0)
| less(sK0(n0,filling,n2),n2)
| holdsAt(waterLevel(n2),n2)
| ~ initiates(tapOn,filling,n0) ),
inference(paramod,[status(thm)],[c_114,c_17080]) ).
cnf(c_17082,plain,
( ~ holdsAt(waterLevel(n0),n0)
| less(sK0(n0,filling,n2),n2)
| holdsAt(waterLevel(n2),n2) ),
inference(resolve,[status(thm)],[c_1714,c_17081]) ).
cnf(c_16708,plain,
( less(sK0(n0,filling,n2),n2)
| holdsAt(waterLevel(n2),n2) ),
inference(resolve,[status(thm)],[c_79,c_17082]) ).
cnf(c_17083,plain,
( n3 = n2
| less(sK0(n0,filling,n2),n2) ),
inference(resolve,[status(thm)],[c_16708,c_1870]) ).
cnf(c_17084,plain,
( n2 = n3
| less(sK0(n0,filling,n2),n2) ),
inference(copy,[status(thm)],[c_17083]) ).
cnf(c_16712,plain,
less(sK0(n0,filling,n2),n2),
inference(resolve,[status(thm)],[c_389,c_17084]) ).
cnf(c_17085,plain,
( n0 = sK0(n0,filling,n2)
| n1 = sK0(n0,filling,n2)
| n2 = sK0(n0,filling,n2) ),
inference(resolve,[status(thm)],[c_16712,c_6723]) ).
cnf(c_17086,plain,
( n0 = sK0(n0,filling,n2)
| n1 = sK0(n0,filling,n2)
| sK0(n0,filling,n2) = n2 ),
inference(copy,[status(thm)],[c_17085]) ).
cnf(c_17087,plain,
( n0 = sK0(n0,filling,n2)
| sK0(n0,filling,n2) = n1
| sK0(n0,filling,n2) = n2 ),
inference(copy,[status(thm)],[c_17086]) ).
cnf(c_17088,plain,
( sK0(n0,filling,n2) = n0
| sK0(n0,filling,n2) = n1
| sK0(n0,filling,n2) = n2 ),
inference(copy,[status(thm)],[c_17087]) ).
cnf(c_16718,plain,
( sK0(n0,filling,n2) = n1
| sK0(n0,filling,n2) = n2 ),
inference(resolve,[status(thm)],[c_16703,c_17088]) ).
cnf(c_17089,plain,
n2 != sK0(n0,filling,n2),
inference(resolve,[status(thm)],[c_16712,c_81]) ).
cnf(c_16773,plain,
sK0(n0,filling,n2) != n2,
inference(copy,[status(thm)],[c_17089]) ).
cnf(c_16788,plain,
sK0(n0,filling,n2) = n1,
inference(resolve,[status(thm)],[c_16773,c_16718]) ).
cnf(c_16789,plain,
( happens(sK1(n0,filling,n2),n1)
| holdsAt(waterLevel(n2),n2) ),
inference(paramod,[status(thm)],[c_16788,c_16645]) ).
cnf(c_17090,plain,
( holdsAt(waterLevel(n3),n1)
| n0 = n1
| holdsAt(waterLevel(n2),n2) ),
inference(resolve,[status(thm)],[c_16789,c_132]) ).
cnf(c_16842,plain,
( holdsAt(waterLevel(n3),n1)
| holdsAt(waterLevel(n2),n2) ),
inference(resolve,[status(thm)],[c_351,c_17090]) ).
cnf(c_17091,plain,
( n3 = n2
| holdsAt(waterLevel(n3),n1) ),
inference(resolve,[status(thm)],[c_16842,c_1870]) ).
cnf(c_17092,plain,
( n2 = n3
| holdsAt(waterLevel(n3),n1) ),
inference(copy,[status(thm)],[c_17091]) ).
cnf(c_16854,plain,
holdsAt(waterLevel(n3),n1),
inference(resolve,[status(thm)],[c_389,c_17092]) ).
cnf(c_16855,plain,
happens(overflow,n1),
inference(resolve,[status(thm)],[c_16854,c_3388]) ).
cnf(c_17093,plain,
~ holdsAt(filling,plus(n1,n1)),
inference(resolve,[status(thm)],[c_16855,c_1597]) ).
cnf(c_17094,plain,
~ holdsAt(filling,n2),
inference(paramod,[status(thm)],[c_112,c_17093]) ).
cnf(c_17054,plain,
$false,
inference(resolve,[status(thm)],[c_553,c_17094]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : CSR013+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Sat Sep 26 23:55:35 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.29 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.29 % Process 1785628 was started by sandbox2 on n012,
% 0.03/0.29 % Sat Sep 26 23:55:35 2026
% 0.03/0.29 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.03/0.30
% 0.03/0.30 % From the command line: assign(max_seconds, 300).
% 20.94/3.32
% 20.94/3.32 % Assigning unary symbol waterLevel kb_weight 0 and highest precedence (37).
% 20.94/3.32
% 20.94/3.32 % given #500 (W,wt=14): 3110 less(n2,A) | n2 = A | less_or_equal(A,n5). [resolve(2927,c,103,b)].
% 20.94/3.32
% 20.94/3.32 % given #1000 (W,wt=16): 8406 less(f2(n1,filling,n3),n7). [back_unit_del(8363),unit_del(a,8394)].
% 20.94/3.32
% 20.94/3.32 % given #1500 (T,wt=20): 12064 -holdsAt(waterLevel(A),f2(n0,filling,n4)) | n3 = A. [resolve(12025,a,127,b)].
% 20.94/3.32
% 20.94/3.32 % SZS status Theorem for theBenchmark
% 20.94/3.32
% 20.94/3.32 % Proof 1 at 2.07 (+ 0.79) seconds.
% 20.94/3.32 % Length of proof is 108.
% 20.94/3.32 % Level of proof is 17.
% 20.94/3.32 % Maximum clause weight is 53.000.
% 20.94/3.32 % Given clauses 1978.
% 20.94/3.32
% 20.94/3.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------