%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CSR014+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 : n015.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 0.79s 0.56s
% Output : CNFRefutation 0.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 58 ( 25 unt; 0 def)
% Number of atoms : 141 ( 59 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 132 ( 49 ~; 56 |; 22 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-3 aty)
% Number of variables : 84 ( 6 sgn 42 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
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_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(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(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(filling_3_l1,conjecture,
~ releasedAt(filling,n3),
file('theBenchmark.p',filling_3_l1) ).
fof(filling_3_l1_neg,negated_conjecture,
~ ~ releasedAt(filling,n3),
inference(assume_negation,[status(cth)],[filling_3_l1]) ).
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(sK0(Fluent,Time),Fluent,Time)
& happens(sK0(Fluent,Time),Time) )
| releasedAt(Fluent,Time) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Event,sK0(Fluent,Time))],[nnf_8]) ).
fof(sk_keep_not_released,plain,
( ! [VAR_0,VAR_1] :
( ~ releasedAt(VAR_0,plus(VAR_1,n1))
| releases(sK0(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(sK0(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(sK0(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(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_56,plain,
( tapOn = A
| ~ releases(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_releases_all_defn]) ).
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_61,plain,
( ~ releasedAt(A,plus(B,n1))
| releasedAt(A,B)
| waterLevel(sK1(sK0(A,B),A,B)) = A ),
inference(resolve,[status(thm)],[c_57,c_55]) ).
cnf(c_62,plain,
( ~ releasedAt(A,plus(B,n1))
| releasedAt(A,B)
| tapOn = sK0(A,B) ),
inference(resolve,[status(thm)],[c_56,c_55]) ).
cnf(c_63,plain,
( ~ releasedAt(A,plus(B,n1))
| releasedAt(A,B)
| sK0(A,B) = tapOn ),
inference(copy,[status(thm)],[c_62]) ).
cnf(c_72,negated_conjecture,
releasedAt(filling,n3),
inference(clausify,[status(thm)],[filling_3_l1_neg]) ).
cnf(c_104,plain,
plus(A,B) = plus(B,A),
inference(clausify,[status(thm)],[symmetry_of_plus]) ).
fof(plus1_2,axiom,
plus(n1,n2) = n3,
file('theBenchmark.p',plus1_2) ).
cnf(c_110,plain,
plus(n1,n2) = n3,
inference(clausify,[status(thm)],[plus1_2]) ).
fof(plus1_1,axiom,
plus(n1,n1) = n2,
file('theBenchmark.p',plus1_1) ).
cnf(c_111,plain,
plus(n1,n1) = n2,
inference(clausify,[status(thm)],[plus1_1]) ).
fof(plus0_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_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_162,plain,
( ~ releasedAt(C,plus(B,n1))
| ~ initiates(A,C,B)
| ~ happens(A,B) ),
inference(clausify,[status(thm)],[happens_not_released]) ).
cnf(c_198,plain,
( ~ releasedAt(A,plus(n1,B))
| releasedAt(A,B)
| waterLevel(sK1(sK0(A,B),A,B)) = A ),
inference(paramod,[status(thm)],[c_104,c_61]) ).
cnf(c_200,plain,
( ~ releasedAt(A,n2)
| releasedAt(A,n1)
| waterLevel(sK1(sK0(A,n1),A,n1)) = A ),
inference(paramod,[status(thm)],[c_111,c_61]) ).
cnf(c_201,plain,
( ~ releasedAt(A,n2)
| releasedAt(A,n1)
| sK0(A,n1) = tapOn ),
inference(paramod,[status(thm)],[c_111,c_63]) ).
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_379,plain,
( ~ releasedAt(A,n3)
| releasedAt(A,n2)
| waterLevel(sK1(sK0(A,n2),A,n2)) = A ),
inference(paramod,[status(thm)],[c_110,c_198]) ).
cnf(c_612,plain,
n0 = plus(n0,n0),
inference(copy,[status(thm)],[c_116]) ).
cnf(c_613,plain,
happens(tapOn,plus(n0,n0)),
inference(resolve,[status(thm)],[c_203,c_612]) ).
cnf(c_418,plain,
happens(tapOn,n0),
inference(paramod,[status(thm)],[c_116,c_613]) ).
cnf(c_456,plain,
initiates(tapOn,filling,A),
inference(xxres,[status(thm)],[c_213]) ).
cnf(c_462,plain,
( ~ releasedAt(filling,plus(A,n1))
| ~ happens(tapOn,A) ),
inference(resolve,[status(thm)],[c_456,c_162]) ).
cnf(c_483,plain,
( ~ releasedAt(filling,plus(n1,A))
| ~ happens(tapOn,A) ),
inference(paramod,[status(thm)],[c_104,c_462]) ).
cnf(c_614,plain,
( ~ releasedAt(filling,n1)
| ~ happens(tapOn,n0) ),
inference(paramod,[status(thm)],[c_115,c_483]) ).
cnf(c_512,plain,
~ releasedAt(filling,n1),
inference(resolve,[status(thm)],[c_418,c_614]) ).
cnf(c_615,negated_conjecture,
( releasedAt(filling,n2)
| waterLevel(sK1(sK0(filling,n2),filling,n2)) = filling ),
inference(resolve,[status(thm)],[c_379,c_72]) ).
cnf(c_605,negated_conjecture,
releasedAt(filling,n2),
inference(resolve,[status(thm)],[c_122,c_615]) ).
cnf(c_616,plain,
( releasedAt(filling,n1)
| sK0(filling,n1) = tapOn ),
inference(resolve,[status(thm)],[c_605,c_201]) ).
cnf(c_610,plain,
sK0(filling,n1) = tapOn,
inference(resolve,[status(thm)],[c_512,c_616]) ).
cnf(c_617,plain,
( releasedAt(filling,n1)
| waterLevel(sK1(sK0(filling,n1),filling,n1)) = filling ),
inference(resolve,[status(thm)],[c_605,c_200]) ).
cnf(c_618,plain,
( releasedAt(filling,n1)
| waterLevel(sK1(tapOn,filling,n1)) = filling ),
inference(paramod,[status(thm)],[c_610,c_617]) ).
cnf(c_619,plain,
releasedAt(filling,n1),
inference(resolve,[status(thm)],[c_122,c_618]) ).
cnf(c_611,plain,
$false,
inference(resolve,[status(thm)],[c_512,c_619]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CSR014+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 23:59:14 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1070152 was started by sandbox2 on n015,
% 0.09/0.37 % Sat Sep 26 23:59:14 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.79/0.56
% 0.79/0.56 % SZS status Theorem for theBenchmark
% 0.79/0.56
% 0.79/0.56 % Proof 1 at 0.12 (+ 0.04) seconds.
% 0.79/0.56 % Length of proof is 39.
% 0.79/0.56 % Level of proof is 8.
% 0.79/0.56 % Maximum clause weight is 17.000.
% 0.79/0.56 % Given clauses 441.
% 0.79/0.56
% 0.79/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------