%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : CSR007+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 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 : Fri Sep 25 01:09:52 PM UTC 2026
% Result : Theorem 239.22s 37.15s
% Output : CNFRefutation 239.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 30
% Syntax : Number of formulae : 258 ( 60 unt; 3 def)
% Number of atoms : 783 ( 274 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 831 ( 328 ~; 380 |; 102 &)
% ( 15 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 2 prp; 0-4 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-3 aty)
% Number of variables : 449 ( 0 sgn 431 !; 18 ?; 174 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( stoppedIn(X0,X1,X2)
<=> ? [X3,X4] :
( terminates(X3,X1,X4)
& less(X4,X2)
& less(X0,X4)
& happens(X3,X4) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+0.ax',stoppedin_defn) ).
fof(f3,axiom,
! [X0,X1,X2,X3,X4] :
( ( ~ stoppedIn(X1,X2,plus(X1,X4))
& trajectory(X2,X1,X3,X4)
& less(n0,X4)
& initiates(X0,X2,X1)
& happens(X0,X1) )
=> holdsAt(X3,plus(X1,X4)) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+0.ax',change_holding) ).
fof(f9,axiom,
! [X0,X1,X2] :
( ( initiates(X0,X2,X1)
& happens(X0,X1) )
=> holdsAt(X2,plus(X1,n1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+0.ax',happens_holds) ).
fof(f10,axiom,
! [X0,X1,X2] :
( ( terminates(X0,X2,X1)
& happens(X0,X1) )
=> ~ holdsAt(X2,plus(X1,n1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+0.ax',happens_terminates_not_holds) ).
fof(f13,axiom,
! [X0,X1,X2] :
( initiates(X0,X1,X2)
<=> ( ? [X3] :
( X1 = waterLevel(X3)
& X0 = overflow
& holdsAt(waterLevel(X3),X2) )
| ? [X3] :
( X1 = waterLevel(X3)
& X0 = tapOff
& holdsAt(waterLevel(X3),X2) )
| ( X1 = spilling
& X0 = overflow )
| ( X1 = filling
& X0 = tapOn ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax',initiates_all_defn) ).
fof(f14,axiom,
! [X0,X1,X2] :
( terminates(X0,X1,X2)
<=> ( ( X1 = filling
& X0 = overflow )
| ( X1 = filling
& X0 = tapOff ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax',terminates_all_defn) ).
fof(f15,axiom,
! [X0,X1,X2] :
( releases(X0,X1,X2)
<=> ? [X3] :
( X1 = waterLevel(X3)
& X0 = tapOn ) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax',releases_all_defn) ).
fof(f16,axiom,
! [X0,X1] :
( happens(X0,X1)
<=> ( ( X0 = overflow
& holdsAt(filling,X1)
& holdsAt(waterLevel(n3),X1) )
| ( X1 = n0
& X0 = tapOn ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax',happens_all_defn) ).
fof(f17,axiom,
! [X0,X1,X2,X3] :
( ( X2 = plus(X0,X3)
& holdsAt(waterLevel(X0),X1) )
=> trajectory(filling,X1,waterLevel(X2),X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax',change_of_waterLevel) ).
fof(f18,axiom,
! [X0,X1,X2] :
( ( holdsAt(waterLevel(X2),X0)
& holdsAt(waterLevel(X1),X0) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax',same_waterLevel) ).
fof(f19,axiom,
tapOff != tapOn,
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax',tapOff_not_tapOn) ).
fof(f21,axiom,
overflow != tapOn,
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax',overflow_not_tapOn) ).
fof(f25,axiom,
! [X0,X1] :
( waterLevel(X0) = waterLevel(X1)
<=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax',distinct_waterLevels) ).
fof(f27,axiom,
plus(n0,n1) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus0_1) ).
fof(f28,axiom,
plus(n0,n2) = n2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus0_2) ).
fof(f30,axiom,
plus(n1,n1) = n2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus1_1) ).
fof(f36,axiom,
! [X0,X1] : plus(X0,X1) = plus(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_plus) ).
fof(f37,axiom,
! [X0,X1] :
( less_or_equal(X0,X1)
<=> ( X0 = X1
| less(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal) ).
fof(f38,axiom,
~ ? [X0] : less(X0,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less0) ).
fof(f39,axiom,
! [X0] :
( less(X0,n1)
<=> less_or_equal(X0,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less1) ).
fof(f40,axiom,
! [X0] :
( less(X0,n2)
<=> less_or_equal(X0,n1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less2) ).
fof(f41,axiom,
! [X0] :
( less(X0,n3)
<=> less_or_equal(X0,n2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less3) ).
fof(f48,axiom,
! [X0,X1] :
( less(X0,X1)
<=> ( X1 != X0
& ~ less(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_property) ).
fof(f49,axiom,
holdsAt(waterLevel(n0),n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',waterLevel_0) ).
fof(f55,conjecture,
~ holdsAt(waterLevel(n3),n2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',waterlevel_not_3) ).
fof(f56,negated_conjecture,
~ ~ holdsAt(waterLevel(n3),n2),
inference(negated_conjecture,[status(cth)],[f55]) ).
fof(f57,plain,
! [X0,X1,X2] :
( initiates(X0,X1,X2)
<=> ( ? [X4] :
( waterLevel(X4) = X1
& X0 = overflow
& holdsAt(waterLevel(X4),X2) )
| ? [X3] :
( X1 = waterLevel(X3)
& X0 = tapOff
& holdsAt(waterLevel(X3),X2) )
| ( X1 = spilling
& X0 = overflow )
| ( X1 = filling
& X0 = tapOn ) ) ),
inference(rectify,[],[f13]) ).
fof(f58,plain,
holdsAt(waterLevel(n3),n2),
inference(flattening,[],[f56]) ).
fof(f60,plain,
! [X0,X1,X2] :
( stoppedIn(X0,X1,X2)
=> ? [X3,X4] :
( terminates(X3,X1,X4)
& less(X4,X2)
& less(X0,X4)
& happens(X3,X4) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ stoppedIn(X0,X1,X2)
| ? [X3,X4] :
( terminates(X3,X1,X4)
& less(X4,X2)
& less(X0,X4)
& happens(X3,X4) ) ),
inference(ennf_transformation,[],[f60]) ).
fof(f64,plain,
! [X0,X1,X2,X3,X4] :
( stoppedIn(X1,X2,plus(X1,X4))
| ~ trajectory(X2,X1,X3,X4)
| ~ less(n0,X4)
| ~ initiates(X0,X2,X1)
| ~ happens(X0,X1)
| holdsAt(X3,plus(X1,X4)) ),
inference(ennf_transformation,[],[f3]) ).
fof(f65,plain,
! [X0,X1,X2,X3,X4] :
( stoppedIn(X1,X2,plus(X1,X4))
| ~ trajectory(X2,X1,X3,X4)
| ~ less(n0,X4)
| ~ initiates(X0,X2,X1)
| ~ happens(X0,X1)
| holdsAt(X3,plus(X1,X4)) ),
inference(flattening,[],[f64]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ~ initiates(X0,X2,X1)
| ~ happens(X0,X1)
| holdsAt(X2,plus(X1,n1)) ),
inference(ennf_transformation,[],[f9]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ~ initiates(X0,X2,X1)
| ~ happens(X0,X1)
| holdsAt(X2,plus(X1,n1)) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ~ terminates(X0,X2,X1)
| ~ happens(X0,X1)
| ~ holdsAt(X2,plus(X1,n1)) ),
inference(ennf_transformation,[],[f10]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ~ terminates(X0,X2,X1)
| ~ happens(X0,X1)
| ~ holdsAt(X2,plus(X1,n1)) ),
inference(flattening,[],[f76]) ).
fof(f82,plain,
! [X0,X1,X2,X3] :
( plus(X0,X3) != X2
| ~ holdsAt(waterLevel(X0),X1)
| trajectory(filling,X1,waterLevel(X2),X3) ),
inference(ennf_transformation,[],[f17]) ).
fof(f83,plain,
! [X0,X1,X2,X3] :
( plus(X0,X3) != X2
| ~ holdsAt(waterLevel(X0),X1)
| trajectory(filling,X1,waterLevel(X2),X3) ),
inference(flattening,[],[f82]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ~ holdsAt(waterLevel(X2),X0)
| ~ holdsAt(waterLevel(X1),X0)
| X1 = X2 ),
inference(ennf_transformation,[],[f18]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ~ holdsAt(waterLevel(X2),X0)
| ~ holdsAt(waterLevel(X1),X0)
| X1 = X2 ),
inference(flattening,[],[f84]) ).
fof(f86,plain,
! [X0] : ~ less(X0,n0),
inference(ennf_transformation,[],[f38]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ~ stoppedIn(X0,X1,X2)
| ( terminates(sK2(X0,X1,X2),X1,sK3(X0,X1,X2))
& less(sK3(X0,X1,X2),X2)
& less(X0,sK3(X0,X1,X2))
& happens(sK2(X0,X1,X2),sK3(X0,X1,X2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X3,sK2(X0,X1,X2)),skolemize(X4,sK3(X0,X1,X2))],[f63]) ).
fof(f101,plain,
! [X0,X1,X2] :
( ( ~ initiates(X0,X1,X2)
| sP0(X2,X0,X1)
| sP1(X2,X0,X1)
| ( X1 = spilling
& X0 = overflow )
| ( X1 = filling
& X0 = tapOn ) )
& ( ( ~ sP0(X2,X0,X1)
& ~ sP1(X2,X0,X1)
& ( spilling != X1
| overflow != X0 )
& ( filling != X1
| tapOn != X0 ) )
| initiates(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f89]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ( ~ initiates(X0,X1,X2)
| sP0(X2,X0,X1)
| sP1(X2,X0,X1)
| ( X1 = spilling
& X0 = overflow )
| ( X1 = filling
& X0 = tapOn ) )
& ( ( ~ sP0(X2,X0,X1)
& ~ sP1(X2,X0,X1)
& ( spilling != X1
| overflow != X0 )
& ( filling != X1
| tapOn != X0 ) )
| initiates(X0,X1,X2) ) ),
inference(flattening,[],[f101]) ).
fof(f103,plain,
! [X0,X1,X2] :
( ( ~ terminates(X0,X1,X2)
| ( X1 = filling
& X0 = overflow )
| ( X1 = filling
& X0 = tapOff ) )
& ( ( ( filling != X1
| overflow != X0 )
& ( filling != X1
| tapOff != X0 ) )
| terminates(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f104,plain,
! [X0,X1,X2] :
( ( ~ terminates(X0,X1,X2)
| ( X1 = filling
& X0 = overflow )
| ( X1 = filling
& X0 = tapOff ) )
& ( ( ( filling != X1
| overflow != X0 )
& ( filling != X1
| tapOff != X0 ) )
| terminates(X0,X1,X2) ) ),
inference(flattening,[],[f103]) ).
fof(f105,plain,
! [X0,X1,X2] :
( ( ~ releases(X0,X1,X2)
| ? [X3] :
( X1 = waterLevel(X3)
& X0 = tapOn ) )
& ( ! [X3] :
( waterLevel(X3) != X1
| tapOn != X0 )
| releases(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f106,plain,
! [X0,X1,X2] :
( ( ~ releases(X0,X1,X2)
| ? [X4] :
( waterLevel(X4) = X1
& X0 = tapOn ) )
& ( ! [X3] :
( waterLevel(X3) != X1
| tapOn != X0 )
| releases(X0,X1,X2) ) ),
inference(rectify,[],[f105]) ).
fof(f107,plain,
! [X0,X1,X2] :
( ( ~ releases(X0,X1,X2)
| ( waterLevel(sK10(X0,X1)) = X1
& X0 = tapOn ) )
& ( ! [X3] :
( waterLevel(X3) != X1
| tapOn != X0 )
| releases(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X4,sK10(X0,X1))],[f106]) ).
fof(f108,plain,
! [X0,X1] :
( ( ~ happens(X0,X1)
| ( X0 = overflow
& holdsAt(filling,X1)
& holdsAt(waterLevel(n3),X1) )
| ( X1 = n0
& X0 = tapOn ) )
& ( ( ( overflow != X0
| ~ holdsAt(filling,X1)
| ~ holdsAt(waterLevel(n3),X1) )
& ( n0 != X1
| tapOn != X0 ) )
| happens(X0,X1) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f109,plain,
! [X0,X1] :
( ( ~ happens(X0,X1)
| ( X0 = overflow
& holdsAt(filling,X1)
& holdsAt(waterLevel(n3),X1) )
| ( X1 = n0
& X0 = tapOn ) )
& ( ( ( overflow != X0
| ~ holdsAt(filling,X1)
| ~ holdsAt(waterLevel(n3),X1) )
& ( n0 != X1
| tapOn != X0 ) )
| happens(X0,X1) ) ),
inference(flattening,[],[f108]) ).
fof(f110,plain,
! [X0,X1] :
( ( waterLevel(X0) != waterLevel(X1)
| X0 = X1 )
& ( X0 != X1
| waterLevel(X0) = waterLevel(X1) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f111,plain,
! [X0,X1] :
( ( ~ less_or_equal(X0,X1)
| X0 = X1
| less(X0,X1) )
& ( ( X0 != X1
& ~ less(X0,X1) )
| less_or_equal(X0,X1) ) ),
inference(nnf_transformation,[],[f37]) ).
fof(f112,plain,
! [X0,X1] :
( ( ~ less_or_equal(X0,X1)
| X0 = X1
| less(X0,X1) )
& ( ( X0 != X1
& ~ less(X0,X1) )
| less_or_equal(X0,X1) ) ),
inference(flattening,[],[f111]) ).
fof(f113,plain,
! [X0] :
( ( ~ less(X0,n1)
| less_or_equal(X0,n0) )
& ( ~ less_or_equal(X0,n0)
| less(X0,n1) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f114,plain,
! [X0] :
( ( ~ less(X0,n2)
| less_or_equal(X0,n1) )
& ( ~ less_or_equal(X0,n1)
| less(X0,n2) ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f115,plain,
! [X0] :
( ( ~ less(X0,n3)
| less_or_equal(X0,n2) )
& ( ~ less_or_equal(X0,n2)
| less(X0,n3) ) ),
inference(nnf_transformation,[],[f41]) ).
fof(f122,plain,
! [X0,X1] :
( ( ~ less(X0,X1)
| ( X1 != X0
& ~ less(X1,X0) ) )
& ( X0 = X1
| less(X1,X0)
| less(X0,X1) ) ),
inference(nnf_transformation,[],[f48]) ).
fof(f123,plain,
! [X0,X1] :
( ( ~ less(X0,X1)
| ( X1 != X0
& ~ less(X1,X0) ) )
& ( X0 = X1
| less(X1,X0)
| less(X0,X1) ) ),
inference(flattening,[],[f122]) ).
fof(f124,plain,
! [X2,X0,X1] :
( ~ stoppedIn(X0,X1,X2)
| terminates(sK2(X0,X1,X2),X1,sK3(X0,X1,X2)) ),
inference(cnf_transformation,[],[f90]) ).
fof(f125,plain,
! [X2,X0,X1] :
( ~ stoppedIn(X0,X1,X2)
| less(sK3(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f90]) ).
fof(f126,plain,
! [X2,X0,X1] :
( ~ stoppedIn(X0,X1,X2)
| less(X0,sK3(X0,X1,X2)) ),
inference(cnf_transformation,[],[f90]) ).
fof(f127,plain,
! [X2,X0,X1] :
( ~ stoppedIn(X0,X1,X2)
| happens(sK2(X0,X1,X2),sK3(X0,X1,X2)) ),
inference(cnf_transformation,[],[f90]) ).
fof(f128,plain,
! [X2,X3,X0,X1,X4] :
( stoppedIn(X1,X2,plus(X1,X4))
| ~ trajectory(X2,X1,X3,X4)
| ~ less(n0,X4)
| ~ initiates(X0,X2,X1)
| ~ happens(X0,X1)
| holdsAt(X3,plus(X1,X4)) ),
inference(cnf_transformation,[],[f65]) ).
fof(f137,plain,
! [X2,X0,X1] :
( ~ initiates(X0,X2,X1)
| ~ happens(X0,X1)
| holdsAt(X2,plus(X1,n1)) ),
inference(cnf_transformation,[],[f75]) ).
fof(f138,plain,
! [X2,X0,X1] :
( ~ terminates(X0,X2,X1)
| ~ happens(X0,X1)
| ~ holdsAt(X2,plus(X1,n1)) ),
inference(cnf_transformation,[],[f77]) ).
fof(f154,plain,
! [X2,X0,X1] :
( ~ sP0(X2,X0,X1)
| initiates(X0,X1,X2) ),
inference(cnf_transformation,[],[f102]) ).
fof(f157,plain,
! [X2,X0,X1] :
( filling != X1
| tapOn != X0
| initiates(X0,X1,X2) ),
inference(cnf_transformation,[],[f102]) ).
fof(f161,plain,
! [X2,X0,X1] :
( ~ terminates(X0,X1,X2)
| overflow = X0
| tapOff = X0 ),
inference(cnf_transformation,[],[f104]) ).
fof(f162,plain,
! [X2,X0,X1] :
( filling != X1
| overflow != X0
| terminates(X0,X1,X2) ),
inference(cnf_transformation,[],[f104]) ).
fof(f164,plain,
! [X2,X0,X1] :
( ~ releases(X0,X1,X2)
| waterLevel(sK10(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f107]) ).
fof(f166,plain,
! [X2,X3,X0,X1] :
( waterLevel(X3) != X1
| tapOn != X0
| releases(X0,X1,X2) ),
inference(cnf_transformation,[],[f107]) ).
fof(f170,plain,
! [X0,X1] :
( ~ happens(X0,X1)
| overflow = X0
| tapOn = X0 ),
inference(cnf_transformation,[],[f109]) ).
fof(f172,plain,
! [X0,X1] :
( ~ happens(X0,X1)
| holdsAt(waterLevel(n3),X1)
| tapOn = X0 ),
inference(cnf_transformation,[],[f109]) ).
fof(f174,plain,
! [X0,X1] :
( n0 != X1
| tapOn != X0
| happens(X0,X1) ),
inference(cnf_transformation,[],[f109]) ).
fof(f175,plain,
! [X2,X3,X0,X1] :
( plus(X0,X3) != X2
| ~ holdsAt(waterLevel(X0),X1)
| trajectory(filling,X1,waterLevel(X2),X3) ),
inference(cnf_transformation,[],[f83]) ).
fof(f176,plain,
! [X2,X0,X1] :
( ~ holdsAt(waterLevel(X2),X0)
| ~ holdsAt(waterLevel(X1),X0)
| X1 = X2 ),
inference(cnf_transformation,[],[f85]) ).
fof(f177,plain,
tapOn != tapOff,
inference(cnf_transformation,[],[f19]) ).
fof(f179,plain,
tapOn != overflow,
inference(cnf_transformation,[],[f21]) ).
fof(f183,plain,
! [X0,X1] :
( waterLevel(X0) != waterLevel(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f110]) ).
fof(f186,plain,
n1 = plus(n0,n1),
inference(cnf_transformation,[],[f27]) ).
fof(f187,plain,
n2 = plus(n0,n2),
inference(cnf_transformation,[],[f28]) ).
fof(f189,plain,
n2 = plus(n1,n1),
inference(cnf_transformation,[],[f30]) ).
fof(f195,plain,
! [X0,X1] : plus(X0,X1) = plus(X1,X0),
inference(cnf_transformation,[],[f36]) ).
fof(f196,plain,
! [X0,X1] :
( ~ less_or_equal(X0,X1)
| X0 = X1
| less(X0,X1) ),
inference(cnf_transformation,[],[f112]) ).
fof(f197,plain,
! [X0,X1] :
( X0 != X1
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f112]) ).
fof(f198,plain,
! [X0,X1] :
( ~ less(X0,X1)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f112]) ).
fof(f199,plain,
! [X0] : ~ less(X0,n0),
inference(cnf_transformation,[],[f86]) ).
fof(f200,plain,
! [X0] :
( ~ less(X0,n1)
| less_or_equal(X0,n0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f201,plain,
! [X0] :
( ~ less_or_equal(X0,n0)
| less(X0,n1) ),
inference(cnf_transformation,[],[f113]) ).
fof(f202,plain,
! [X0] :
( ~ less(X0,n2)
| less_or_equal(X0,n1) ),
inference(cnf_transformation,[],[f114]) ).
fof(f203,plain,
! [X0] :
( ~ less_or_equal(X0,n1)
| less(X0,n2) ),
inference(cnf_transformation,[],[f114]) ).
fof(f205,plain,
! [X0] :
( ~ less_or_equal(X0,n2)
| less(X0,n3) ),
inference(cnf_transformation,[],[f115]) ).
fof(f218,plain,
! [X0,X1] :
( ~ less(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f123]) ).
fof(f219,plain,
! [X0,X1] :
( ~ less(X0,X1)
| ~ less(X1,X0) ),
inference(cnf_transformation,[],[f123]) ).
fof(f220,plain,
! [X0,X1] :
( X0 = X1
| less(X1,X0)
| less(X0,X1) ),
inference(cnf_transformation,[],[f123]) ).
fof(f221,plain,
holdsAt(waterLevel(n0),n0),
inference(cnf_transformation,[],[f49]) ).
fof(f227,plain,
holdsAt(waterLevel(n3),n2),
inference(cnf_transformation,[],[f58]) ).
fof(f232,plain,
! [X2,X1] :
( filling != X1
| initiates(tapOn,X1,X2) ),
inference(equality_resolution,[],[f157]) ).
fof(f233,plain,
! [X2] : initiates(tapOn,filling,X2),
inference(equality_resolution,[],[f232]) ).
fof(f238,plain,
! [X2,X1] :
( filling != X1
| terminates(overflow,X1,X2) ),
inference(equality_resolution,[],[f162]) ).
fof(f239,plain,
! [X2] : terminates(overflow,filling,X2),
inference(equality_resolution,[],[f238]) ).
fof(f240,plain,
! [X2,X3,X1] :
( waterLevel(X3) != X1
| releases(tapOn,X1,X2) ),
inference(equality_resolution,[],[f166]) ).
fof(f241,plain,
! [X2,X3] : releases(tapOn,waterLevel(X3),X2),
inference(equality_resolution,[],[f240]) ).
fof(f242,plain,
! [X1] :
( n0 != X1
| happens(tapOn,X1) ),
inference(equality_resolution,[],[f174]) ).
fof(f243,plain,
happens(tapOn,n0),
inference(equality_resolution,[],[f242]) ).
fof(f245,plain,
! [X3,X0,X1] :
( ~ holdsAt(waterLevel(X0),X1)
| trajectory(filling,X1,waterLevel(plus(X0,X3)),X3) ),
inference(equality_resolution,[],[f175]) ).
fof(f247,plain,
! [X1] : less_or_equal(X1,X1),
inference(equality_resolution,[],[f197]) ).
fof(f248,plain,
! [X1] : ~ less(X1,X1),
inference(equality_resolution,[],[f218]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( happens(sK2(X0,X1,X2),sK3(X0,X1,X2))
| ~ stoppedIn(X0,X1,X2) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( less(X0,sK3(X0,X1,X2))
| ~ stoppedIn(X0,X1,X2) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( less(sK3(X0,X1,X2),X2)
| ~ stoppedIn(X0,X1,X2) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( terminates(sK2(X0,X1,X2),X1,sK3(X0,X1,X2))
| ~ stoppedIn(X0,X1,X2) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( holdsAt(X2,plus(X1,X3))
| stoppedIn(X1,X0,plus(X1,X3))
| ~ less(n0,X3)
| ~ happens(X4,X1)
| ~ initiates(X4,X0,X1)
| ~ trajectory(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( holdsAt(X1,plus(X2,n1))
| ~ happens(X0,X2)
| ~ initiates(X0,X1,X2) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ happens(X2,X1)
| ~ terminates(X2,X0,X1)
| ~ holdsAt(X0,plus(X1,n1)) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_75,plain,
! [X0: $i] : initiates(tapOn,filling,X0),
inference(cnf_transformation,[],[f233]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i] :
( initiates(X1,X2,X0)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_84,plain,
! [X0: $i] : terminates(overflow,filling,X0),
inference(cnf_transformation,[],[f239]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = overflow )
| ( X0 = tapOff )
| ~ terminates(X0,X1,X2) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] : releases(tapOn,waterLevel(X0),X1),
inference(cnf_transformation,[],[f241]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( waterLevel(sK10(X0,X1)) = X1 )
| ~ releases(X0,X1,X2) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_92,plain,
happens(tapOn,n0),
inference(cnf_transformation,[],[f243]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( holdsAt(waterLevel(n3),X1)
| ( X0 = tapOn )
| ~ happens(X0,X1) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] :
( ( X0 = tapOn )
| ( X0 = overflow )
| ~ happens(X0,X1) ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i] :
( trajectory(filling,X1,waterLevel(plus(X0,X2)),X2)
| ~ holdsAt(waterLevel(X0),X1) ),
inference(cnf_transformation,[],[f245]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ holdsAt(waterLevel(X2),X1)
| ~ holdsAt(waterLevel(X0),X1) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_102,plain,
tapOff != tapOn,
inference(cnf_transformation,[],[f177]) ).
tcf(c_104,plain,
overflow != tapOn,
inference(cnf_transformation,[],[f179]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( waterLevel(X0) != waterLevel(X1) ) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_110,plain,
plus(n0,n1) = n1,
inference(cnf_transformation,[],[f186]) ).
tcf(c_111,plain,
plus(n0,n2) = n2,
inference(cnf_transformation,[],[f187]) ).
tcf(c_113,plain,
plus(n1,n1) = n2,
inference(cnf_transformation,[],[f189]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i] : plus(X0,X1) = plus(X1,X0),
inference(cnf_transformation,[],[f195]) ).
tcf(c_120,plain,
! [X0: $i,X1: $i] :
( less_or_equal(X0,X1)
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f198]) ).
tcf(c_121,plain,
! [X0: $i] : less_or_equal(X0,X0),
inference(cnf_transformation,[],[f247]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i] :
( less(X0,X1)
| ( X0 = X1 )
| ~ less_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f196]) ).
tcf(c_123,plain,
! [X0: $i] : ~ less(X0,n0),
inference(cnf_transformation,[],[f199]) ).
tcf(c_124,plain,
! [X0: $i] :
( less(X0,n1)
| ~ less_or_equal(X0,n0) ),
inference(cnf_transformation,[],[f201]) ).
tcf(c_125,plain,
! [X0: $i] :
( less_or_equal(X0,n0)
| ~ less(X0,n1) ),
inference(cnf_transformation,[],[f200]) ).
tcf(c_126,plain,
! [X0: $i] :
( less(X0,n2)
| ~ less_or_equal(X0,n1) ),
inference(cnf_transformation,[],[f203]) ).
tcf(c_127,plain,
! [X0: $i] :
( less_or_equal(X0,n1)
| ~ less(X0,n2) ),
inference(cnf_transformation,[],[f202]) ).
tcf(c_128,plain,
! [X0: $i] :
( less(X0,n3)
| ~ less_or_equal(X0,n2) ),
inference(cnf_transformation,[],[f205]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i] :
( less(X1,X0)
| less(X0,X1)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f220]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i] :
( ~ less(X1,X0)
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_144,plain,
! [X0: $i] : ~ less(X0,X0),
inference(cnf_transformation,[],[f248]) ).
tcf(c_145,plain,
holdsAt(waterLevel(n0),n0),
inference(cnf_transformation,[],[f221]) ).
tcf(c_151,negated_conjecture,
holdsAt(waterLevel(n3),n2),
inference(cnf_transformation,[],[f227]) ).
tcf(c_152,plain,
less_or_equal(n1,n1),
inference(instantiation,[status(thm)],[c_121]) ).
tcf(c_153,plain,
~ less(n1,n1),
inference(instantiation,[status(thm)],[c_144]) ).
tcf(c_177,plain,
( less(n1,n2)
| ~ less_or_equal(n1,n1) ),
inference(instantiation,[status(thm)],[c_126]) ).
tcf(c_186,plain,
( less(n1,n1)
| ( n1 = n1 ) ),
inference(instantiation,[status(thm)],[c_142]) ).
tcf(c_240,plain,
! [X0: $i] :
( less(X0,n3)
| ~ less_or_equal(X0,n2) ),
inference(prop_impl_just,[status(thm)],[c_128]) ).
tcf(c_276,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( waterLevel(sK10(X0,X1)) = X1 )
| ~ releases(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_91]) ).
tcf(c_282,plain,
! [X0: $i,X1: $i,X2: $i] :
( trajectory(filling,X1,waterLevel(plus(X0,X2)),X2)
| ~ holdsAt(waterLevel(X0),X1) ),
inference(prop_impl_just,[status(thm)],[c_100]) ).
tcf(c_304,plain,
! [X0: $i,X1: $i] :
( less_or_equal(X0,X1)
| ~ less(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_120]) ).
tcf(c_1018,plain,
plus(n1,n0) = n1,
inference(demodulation,[status(thm)],[c_110,c_119]) ).
tcf(c_1315,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( holdsAt(X5,plus(X1,X6))
| stoppedIn(X1,X0,plus(X1,X6))
| ~ less(n0,X6)
| ~ happens(X7,X1)
| ~ holdsAt(waterLevel(X3),X2)
| ~ initiates(X7,X0,X1)
| ( X4 != X6 )
| ( X1 != X2 )
| ( X0 != filling )
| ( waterLevel(plus(X3,X4)) != X5 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_282]) ).
tcf(c_1316,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( stoppedIn(X1,filling,plus(X1,X3))
| holdsAt(waterLevel(plus(X0,X3)),plus(X1,X3))
| ~ less(n0,X3)
| ~ happens(X2,X1)
| ~ initiates(X2,filling,X1)
| ~ holdsAt(waterLevel(X0),X1) ),
inference(unflattening,[status(thm)],[c_1315]) ).
tcf(c_1368,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( waterLevel(sK10(X0,X2)) = X2 )
| ( X3 != X4 )
| ( X0 != tapOn )
| ( waterLevel(X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_276,c_89]) ).
tcf(c_1369,plain,
! [X0: $i] : waterLevel(sK10(tapOn,waterLevel(X0))) = waterLevel(X0),
inference(unflattening,[status(thm)],[c_1368]) ).
tcf(c_2753,plain,
! [X0: $i,X1: $i,X2: $i] :
( less(X1,n3)
| ~ less(X0,X2)
| ( X2 != n2 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_304,c_240]) ).
tcf(c_2754,plain,
! [X0: $i] :
( less(X0,n3)
| ~ less(X0,n2) ),
inference(unflattening,[status(thm)],[c_2753]) ).
tcf(c_2755,plain,
( less(n1,n3)
| ~ less(n1,n2) ),
inference(instantiation,[status(thm)],[c_2754]) ).
tcf(c_9975,definition,
iPr_def_10 = waterLevel(n3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_9976,negated_conjecture,
holdsAt(iPr_def_10,n2),
inference(demodulation,[status(thm)],[c_151,c_9975]) ).
tcf(c_9982,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( less(X0,X2)
| ~ less(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_9985,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( holdsAt(X0,X2)
| ~ holdsAt(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_11655,plain,
! [X0: $i] :
( ( X0 = n3 )
| ( waterLevel(X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_9975,c_108]) ).
tcf(c_11682,plain,
waterLevel(sK10(tapOn,iPr_def_10)) = iPr_def_10,
inference(superposition,[status(thm)],[c_9975,c_1369]) ).
tcf(c_11773,plain,
sK10(tapOn,iPr_def_10) = n3,
inference(superposition,[status(thm)],[c_11682,c_11655]) ).
tcf(c_11781,plain,
waterLevel(n3) = iPr_def_10,
inference(demodulation,[status(thm)],[c_11682,c_11773]) ).
tcf(c_12970,plain,
! [X0: $i,X1: $i,X2: $i] :
( less(X0,X2)
| ~ less(X1,n3)
| ( X2 != n3 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_9982]) ).
tcf(c_12971,plain,
( less(n1,n1)
| ~ less(n1,n3)
| ( n1 != n3 )
| ( n1 != n1 ) ),
inference(instantiation,[status(thm)],[c_12970]) ).
tcf(c_16030,plain,
! [X0: $i,X1: $i] :
( ( X0 = n3 )
| ~ holdsAt(waterLevel(n3),X1)
| ~ holdsAt(waterLevel(X0),X1) ),
inference(instantiation,[status(thm)],[c_101]) ).
tcf(c_51447,plain,
! [X0: $i,X1: $i] :
( ( X0 = n3 )
| ~ holdsAt(waterLevel(n3),plus(X1,n1))
| ~ holdsAt(waterLevel(X0),plus(X1,n1)) ),
inference(instantiation,[status(thm)],[c_16030]) ).
tcf(c_51449,plain,
( ( n1 = n3 )
| ~ holdsAt(waterLevel(n3),plus(n1,n1))
| ~ holdsAt(waterLevel(n1),plus(n1,n1)) ),
inference(instantiation,[status(thm)],[c_51447]) ).
tcf(c_143434,plain,
! [X0: $i,X1: $i] :
( holdsAt(X0,X1)
| ~ holdsAt(iPr_def_10,n2)
| ( X1 != n2 )
| ( X0 != iPr_def_10 ) ),
inference(instantiation,[status(thm)],[c_9985]) ).
tcf(c_143558,plain,
! [X0: $i] :
( holdsAt(X0,plus(n1,n1))
| ~ holdsAt(iPr_def_10,n2)
| ( X0 != iPr_def_10 )
| ( plus(n1,n1) != n2 ) ),
inference(instantiation,[status(thm)],[c_143434]) ).
tcf(c_144195,plain,
( holdsAt(waterLevel(n3),plus(n1,n1))
| ~ holdsAt(iPr_def_10,n2)
| ( waterLevel(n3) != iPr_def_10 )
| ( plus(n1,n1) != n2 ) ),
inference(instantiation,[status(thm)],[c_143558]) ).
tcf(c_365427,plain,
! [X0: $i] :
( holdsAt(filling,plus(X0,n1))
| ~ happens(tapOn,X0) ),
inference(superposition,[status(thm)],[c_75,c_62]) ).
tcf(c_365552,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(X0,X1,X2) = overflow )
| ( sK2(X0,X1,X2) = tapOff )
| ~ stoppedIn(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_52,c_85]) ).
tcf(c_365599,plain,
! [X0: $i,X1: $i] :
( holdsAt(iPr_def_10,X1)
| ( X0 = tapOn )
| ~ happens(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_94,c_9975]) ).
tcf(c_365653,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(X0,X1,X2) = tapOn )
| ( sK2(X0,X1,X2) = overflow )
| ~ stoppedIn(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_49,c_96]) ).
tcf(c_365765,plain,
! [X0: $i,X1: $i] :
( ( X0 = n3 )
| ~ holdsAt(iPr_def_10,X1)
| ~ holdsAt(waterLevel(X0),X1) ),
inference(superposition,[status(thm)],[c_9975,c_101]) ).
tcf(c_365821,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ happens(X2,X1)
| ~ terminates(X2,X0,X1)
| ~ holdsAt(X0,plus(n1,X1)) ),
inference(superposition,[status(thm)],[c_119,c_63]) ).
tcf(c_365877,plain,
less(n0,n1),
inference(superposition,[status(thm)],[c_121,c_124]) ).
tcf(c_365882,plain,
! [X0: $i,X1: $i] :
( less_or_equal(sK3(X0,X1,n1),n0)
| ~ stoppedIn(X0,X1,n1) ),
inference(superposition,[status(thm)],[c_51,c_125]) ).
tcf(c_365896,plain,
! [X0: $i,X1: $i] :
( less_or_equal(sK3(X0,X1,n2),n1)
| ~ stoppedIn(X0,X1,n2) ),
inference(superposition,[status(thm)],[c_51,c_127]) ).
tcf(c_365903,plain,
less(n2,n3),
inference(superposition,[status(thm)],[c_121,c_128]) ).
tcf(c_365912,plain,
less_or_equal(n0,n1),
inference(superposition,[status(thm)],[c_365877,c_120]) ).
tcf(c_365955,plain,
less(n0,n2),
inference(superposition,[status(thm)],[c_365912,c_126]) ).
tcf(c_366030,plain,
! [X0: $i] :
( less_or_equal(X0,n0)
| less(n1,X0)
| ( X0 = n1 ) ),
inference(superposition,[status(thm)],[c_142,c_125]) ).
tcf(c_366197,plain,
! [X0: $i,X1: $i,X2: $i] :
( stoppedIn(X1,filling,plus(X1,X2))
| holdsAt(waterLevel(plus(X0,X2)),plus(X1,X2))
| ~ less(n0,X2)
| ~ happens(tapOn,X1)
| ~ holdsAt(waterLevel(X0),X1) ),
inference(superposition,[status(thm)],[c_75,c_1316]) ).
tcf(c_366460,plain,
! [X0: $i] :
( holdsAt(filling,plus(n1,X0))
| ~ happens(tapOn,X0) ),
inference(superposition,[status(thm)],[c_119,c_365427]) ).
tcf(c_368900,plain,
! [X0: $i,X1: $i] :
( ~ holdsAt(X1,n1)
| ~ happens(X0,n0)
| ~ terminates(X0,X1,n0) ),
inference(superposition,[status(thm)],[c_1018,c_365821]) ).
tcf(c_369413,plain,
! [X0: $i,X1: $i] :
( less(sK3(X0,X1,n1),n0)
| ( sK3(X0,X1,n1) = n0 )
| ~ stoppedIn(X0,X1,n1) ),
inference(superposition,[status(thm)],[c_365882,c_122]) ).
tcf(c_369417,plain,
! [X0: $i,X1: $i] :
( ( sK3(X0,X1,n1) = n0 )
| ~ stoppedIn(X0,X1,n1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_369413,c_123]) ).
tcf(c_369432,plain,
! [X0: $i,X1: $i] :
( less(sK3(X0,X1,n2),n1)
| ( sK3(X0,X1,n2) = n1 )
| ~ stoppedIn(X0,X1,n2) ),
inference(superposition,[status(thm)],[c_365896,c_122]) ).
tcf(c_369697,plain,
! [X0: $i] :
( less(n1,X0)
| less(X0,n0)
| ( X0 = n1 )
| ( X0 = n0 ) ),
inference(superposition,[status(thm)],[c_366030,c_122]) ).
tcf(c_369702,plain,
! [X0: $i] :
( less(n1,X0)
| ( X0 = n1 )
| ( X0 = n0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_369697,c_123]) ).
tcf(c_370716,plain,
! [X0: $i,X1: $i,X2: $i] :
( stoppedIn(X1,filling,plus(X2,X1))
| holdsAt(waterLevel(plus(X0,X2)),plus(X1,X2))
| ~ less(n0,X2)
| ~ happens(tapOn,X1)
| ~ holdsAt(waterLevel(X0),X1) ),
inference(superposition,[status(thm)],[c_119,c_366197]) ).
tcf(c_370733,plain,
! [X0: $i] :
( stoppedIn(n0,filling,plus(n0,n2))
| holdsAt(waterLevel(plus(X0,n2)),n2)
| ~ less(n0,n2)
| ~ happens(tapOn,n0)
| ~ holdsAt(waterLevel(X0),n0) ),
inference(superposition,[status(thm)],[c_111,c_366197]) ).
tcf(c_370782,plain,
! [X0: $i] :
( stoppedIn(n0,filling,n2)
| holdsAt(waterLevel(plus(X0,n2)),n2)
| ~ less(n0,n2)
| ~ happens(tapOn,n0)
| ~ holdsAt(waterLevel(X0),n0) ),
inference(light_normalisation,[status(thm)],[c_370733,c_111]) ).
tcf(c_370783,plain,
! [X0: $i] :
( stoppedIn(n0,filling,n2)
| holdsAt(waterLevel(plus(X0,n2)),n2)
| ~ holdsAt(waterLevel(X0),n0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_370782,c_365955,c_92]) ).
tcf(c_372387,plain,
( holdsAt(filling,n1)
| ~ happens(tapOn,n0) ),
inference(superposition,[status(thm)],[c_1018,c_366460]) ).
tcf(c_372394,plain,
holdsAt(filling,n1),
inference(forward_subsumption_resolution,[status(thm)],[c_372387,c_92]) ).
tcf(c_381525,plain,
( ~ holdsAt(filling,n1)
| ~ happens(overflow,n0) ),
inference(superposition,[status(thm)],[c_84,c_368900]) ).
tcf(c_381526,plain,
~ happens(overflow,n0),
inference(forward_subsumption_resolution,[status(thm)],[c_381525,c_372394]) ).
tcf(c_383085,plain,
! [X0: $i,X1: $i] :
( ( sK3(X0,X1,n2) = n1 )
| ~ stoppedIn(X0,X1,n2)
| ~ less(n1,sK3(X0,X1,n2)) ),
inference(superposition,[status(thm)],[c_369432,c_143]) ).
tcf(c_388683,plain,
! [X0: $i,X1: $i,X2: $i] :
( stoppedIn(X1,filling,plus(X2,X1))
| holdsAt(waterLevel(plus(X0,X2)),plus(X2,X1))
| ~ less(n0,X2)
| ~ happens(tapOn,X1)
| ~ holdsAt(waterLevel(X0),X1) ),
inference(superposition,[status(thm)],[c_119,c_370716]) ).
tcf(c_390638,plain,
! [X0: $i] :
( stoppedIn(n0,filling,n2)
| ( plus(X0,n2) = n3 )
| ~ holdsAt(iPr_def_10,n2)
| ~ holdsAt(waterLevel(X0),n0) ),
inference(superposition,[status(thm)],[c_370783,c_365765]) ).
tcf(c_390652,plain,
! [X0: $i] :
( stoppedIn(n0,filling,n2)
| ( plus(X0,n2) = n3 )
| ~ holdsAt(waterLevel(X0),n0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_390638,c_9976]) ).
tcf(c_419138,plain,
! [X0: $i,X1: $i] :
( ( sK3(X0,X1,n2) = n1 )
| ( sK3(X0,X1,n2) = n0 )
| ~ stoppedIn(X0,X1,n2) ),
inference(superposition,[status(thm)],[c_369702,c_383085]) ).
tcf(c_431811,plain,
! [X0: $i] :
( stoppedIn(n0,filling,plus(n1,n0))
| holdsAt(waterLevel(plus(X0,n1)),n1)
| ~ less(n0,n1)
| ~ happens(tapOn,n0)
| ~ holdsAt(waterLevel(X0),n0) ),
inference(superposition,[status(thm)],[c_1018,c_388683]) ).
tcf(c_431854,plain,
! [X0: $i] :
( stoppedIn(n0,filling,n1)
| holdsAt(waterLevel(plus(X0,n1)),n1)
| ~ less(n0,n1)
| ~ happens(tapOn,n0)
| ~ holdsAt(waterLevel(X0),n0) ),
inference(light_normalisation,[status(thm)],[c_431811,c_1018]) ).
tcf(c_431855,plain,
! [X0: $i] :
( stoppedIn(n0,filling,n1)
| holdsAt(waterLevel(plus(X0,n1)),n1)
| ~ holdsAt(waterLevel(X0),n0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_431854,c_365877,c_92]) ).
tcf(c_452520,plain,
( stoppedIn(n0,filling,n2)
| ( plus(n0,n2) = n3 ) ),
inference(superposition,[status(thm)],[c_145,c_390652]) ).
tcf(c_452527,plain,
( stoppedIn(n0,filling,n2)
| ( n3 = n2 ) ),
inference(light_normalisation,[status(thm)],[c_452520,c_111]) ).
tcf(c_452543,plain,
( ( n3 = n2 )
| ( sK2(n0,filling,n2) = tapOn )
| ( sK2(n0,filling,n2) = overflow ) ),
inference(superposition,[status(thm)],[c_452527,c_365653]) ).
tcf(c_452545,plain,
( ( n3 = n2 )
| ( sK2(n0,filling,n2) = overflow )
| ( sK2(n0,filling,n2) = tapOff ) ),
inference(superposition,[status(thm)],[c_452527,c_365552]) ).
tcf(c_454804,plain,
! [X0: $i] :
( stoppedIn(n0,filling,n1)
| holdsAt(waterLevel(plus(n1,X0)),n1)
| ~ holdsAt(waterLevel(X0),n0) ),
inference(superposition,[status(thm)],[c_119,c_431855]) ).
tcf(c_457308,plain,
( holdsAt(waterLevel(n1),n1)
| stoppedIn(n0,filling,n1)
| ~ holdsAt(waterLevel(n0),n0) ),
inference(superposition,[status(thm)],[c_1018,c_454804]) ).
tcf(c_457330,plain,
( holdsAt(waterLevel(n1),n1)
| stoppedIn(n0,filling,n1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_457308,c_145]) ).
tcf(c_457734,plain,
( holdsAt(waterLevel(n1),n1)
| ( sK3(n0,filling,n1) = n0 ) ),
inference(superposition,[status(thm)],[c_457330,c_369417]) ).
tcf(c_457829,plain,
( ( n1 = n3 )
| ( sK3(n0,filling,n1) = n0 )
| ~ holdsAt(iPr_def_10,n1) ),
inference(superposition,[status(thm)],[c_457734,c_365765]) ).
tcf(c_458342,plain,
( ~ holdsAt(iPr_def_10,n1)
| ( sK3(n0,filling,n1) = n0 ) ),
inference(global_subsumption_just,[status(thm)],[c_457829,c_152,c_153,c_177,c_186,c_2755,c_12971,c_457829]) ).
tcf(c_458343,plain,
( ( sK3(n0,filling,n1) = n0 )
| ~ holdsAt(iPr_def_10,n1) ),
inference(renaming,[status(thm)],[c_458342]) ).
tcf(c_502626,plain,
( ( n3 = n2 )
| ( tapOff = tapOn )
| ( sK2(n0,filling,n2) = overflow ) ),
inference(superposition,[status(thm)],[c_452545,c_452543]) ).
tcf(c_502628,plain,
( ( n3 = n2 )
| ( sK2(n0,filling,n2) = overflow ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_502626,c_102]) ).
tcf(c_502787,plain,
( happens(overflow,sK3(n0,filling,n2))
| ( n3 = n2 )
| ~ stoppedIn(n0,filling,n2) ),
inference(superposition,[status(thm)],[c_502628,c_49]) ).
tcf(c_502791,plain,
( happens(overflow,sK3(n0,filling,n2))
| ( n3 = n2 ) ),
inference(global_subsumption_just,[status(thm)],[c_502787,c_452527,c_502787]) ).
tcf(c_502802,plain,
( holdsAt(iPr_def_10,sK3(n0,filling,n2))
| ( n3 = n2 )
| ( overflow = tapOn ) ),
inference(superposition,[status(thm)],[c_502791,c_365599]) ).
tcf(c_502822,plain,
( holdsAt(iPr_def_10,sK3(n0,filling,n2))
| ( n3 = n2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_502802,c_104]) ).
tcf(c_534582,plain,
( ( n3 = n2 )
| ( sK3(n0,filling,n2) = n1 )
| ( sK3(n0,filling,n2) = n0 ) ),
inference(superposition,[status(thm)],[c_452527,c_419138]) ).
tcf(c_534977,plain,
( happens(overflow,n0)
| ( n3 = n2 )
| ( sK3(n0,filling,n2) = n1 ) ),
inference(superposition,[status(thm)],[c_534582,c_502791]) ).
tcf(c_534978,plain,
( ( n3 = n2 )
| ( sK3(n0,filling,n2) = n1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_534977,c_381526]) ).
tcf(c_535056,plain,
( holdsAt(iPr_def_10,n1)
| ( n3 = n2 ) ),
inference(superposition,[status(thm)],[c_534978,c_502822]) ).
tcf(c_535057,plain,
( happens(overflow,n1)
| ( n3 = n2 ) ),
inference(superposition,[status(thm)],[c_534978,c_502791]) ).
tcf(c_535406,plain,
( ( n3 = n2 )
| ( sK3(n0,filling,n1) = n0 ) ),
inference(superposition,[status(thm)],[c_535056,c_458343]) ).
tcf(c_536423,plain,
( less(n0,n0)
| ( n3 = n2 )
| ~ stoppedIn(n0,filling,n1) ),
inference(superposition,[status(thm)],[c_535406,c_50]) ).
tcf(c_536464,plain,
( ( n3 = n2 )
| ~ stoppedIn(n0,filling,n1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_536423,c_123]) ).
fof(f87,definition,
! [X2,X0,X1] :
( sP0(X2,X0,X1)
<=> ? [X4] :
( waterLevel(X4) = X1
& X0 = overflow
& holdsAt(waterLevel(X4),X2) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f88,definition,
! [X2,X0,X1] :
( sP1(X2,X0,X1)
<=> ? [X3] :
( X1 = waterLevel(X3)
& X0 = tapOff
& holdsAt(waterLevel(X3),X2) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f89,plain,
! [X0,X1,X2] :
( initiates(X0,X1,X2)
<=> ( sP0(X2,X0,X1)
| sP1(X2,X0,X1)
| ( X1 = spilling
& X0 = overflow )
| ( X1 = filling
& X0 = tapOn ) ) ),
inference(definition_folding,[],[f57,f88,f87]) ).
fof(f98,plain,
! [X2,X0,X1] :
( ( ~ sP0(X2,X0,X1)
| ? [X4] :
( waterLevel(X4) = X1
& X0 = overflow
& holdsAt(waterLevel(X4),X2) ) )
& ( ! [X4] :
( waterLevel(X4) != X1
| overflow != X0
| ~ holdsAt(waterLevel(X4),X2) )
| sP0(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f87]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ( ~ sP0(X0,X1,X2)
| ? [X4] :
( waterLevel(X4) = X2
& overflow = X1
& holdsAt(waterLevel(X4),X0) ) )
& ( ! [X3] :
( waterLevel(X3) != X2
| overflow != X1
| ~ holdsAt(waterLevel(X3),X0) )
| sP0(X0,X1,X2) ) ),
inference(rectify,[],[f98]) ).
fof(f100,plain,
! [X0,X1,X2] :
( ( ~ sP0(X0,X1,X2)
| ( waterLevel(sK9(X0,X1,X2)) = X2
& overflow = X1
& holdsAt(waterLevel(sK9(X0,X1,X2)),X0) ) )
& ( ! [X3] :
( waterLevel(X3) != X2
| overflow != X1
| ~ holdsAt(waterLevel(X3),X0) )
| sP0(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X4,sK9(X0,X1,X2))],[f99]) ).
fof(f149,plain,
! [X2,X3,X0,X1] :
( waterLevel(X3) != X2
| overflow != X1
| ~ holdsAt(waterLevel(X3),X0)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f100]) ).
fof(f230,plain,
! [X2,X3,X0] :
( waterLevel(X3) != X2
| ~ holdsAt(waterLevel(X3),X0)
| sP0(X0,overflow,X2) ),
inference(equality_resolution,[],[f149]) ).
fof(f231,plain,
! [X3,X0] :
( ~ holdsAt(waterLevel(X3),X0)
| sP0(X0,overflow,waterLevel(X3)) ),
inference(equality_resolution,[],[f230]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( sP0(X1,overflow,waterLevel(X0))
| ~ holdsAt(waterLevel(X0),X1) ),
inference(cnf_transformation,[],[f231]) ).
tcf(c_11966,plain,
! [X0: $i,X1: $i] :
( initiates(overflow,waterLevel(X0),X1)
| ~ holdsAt(waterLevel(X0),X1) ),
inference(superposition,[status(thm)],[c_71,c_78]) ).
tcf(c_13435,plain,
! [X0: $i,X1: $i] :
( holdsAt(waterLevel(X0),plus(X1,n1))
| ~ happens(overflow,X1)
| ~ holdsAt(waterLevel(X0),X1) ),
inference(superposition,[status(thm)],[c_11966,c_62]) ).
tcf(c_13440,plain,
( holdsAt(waterLevel(n1),plus(n1,n1))
| ~ happens(overflow,n1)
| ~ holdsAt(waterLevel(n1),n1) ),
inference(instantiation,[status(thm)],[c_13435]) ).
tcf(c_536481,plain,
n3 = n2,
inference(global_subsumption_just,[status(thm)],[c_536464,c_152,c_153,c_113,c_177,c_186,c_2755,c_9976,c_11781,c_12971,c_13440,c_51449,c_144195,c_457330,c_535057,c_536464]) ).
tcf(c_536970,plain,
less(n3,n3),
inference(demodulation,[status(thm)],[c_365903,c_536481]) ).
tcf(c_536983,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_536970,c_144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CSR007+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n007.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Fri Sep 25 08:03:54 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.44
% 0.10/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.44
% 0.10/0.44 % Detected problem language: tptp
% 0.10/0.45 % Proving...
% 239.22/37.15 % SZS status Started for theBenchmark.p
% 239.22/37.15 % SZS status Theorem for theBenchmark.p
% 239.22/37.15
% 239.22/37.15 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 239.22/37.15
% 239.22/37.15 % ------ iProver source info
% 239.22/37.15
% 239.22/37.15 % git: date: 2026-07-19 20:42:38 +0200
% 239.22/37.15 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 239.22/37.15 % git: non_committed_changes: false
% 239.22/37.15
% 239.22/37.15 % ------ Parsing...
% 239.22/37.15 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 239.22/37.15
% 239.22/37.15 % ------ Preprocessing... sup_sim: 2 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 239.22/37.15
% 239.22/37.15 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 239.22/37.15
% 239.22/37.15 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 239.22/37.15 % ------ Proving...
% 239.22/37.15 % ------ Problem Properties
% 239.22/37.15
% 239.22/37.15 %
% 239.22/37.15 % clauses 100
% 239.22/37.15 % conjectures 1
% 239.22/37.15 % EPR 53
% 239.22/37.15 % Horn 77
% 239.22/37.15 % unary 34
% 239.22/37.15 % binary 37
% 239.22/37.15 % lits 209
% 239.22/37.15 % lits eq 49
% 239.22/37.15 % fd_pure 0
% 239.22/37.15 % fd_pseudo 0
% 239.22/37.15 % fd_cond 14
% 239.22/37.15 % fd_pseudo_cond 4
% 239.22/37.15 % AC symbols 0
% 239.22/37.15
% 239.22/37.15 % ------ Schedule dynamic 5 is on
% 239.22/37.15
% 239.22/37.15 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 239.22/37.15
% 239.22/37.15
% 239.22/37.15 % ------
% 239.22/37.15 % Current options:
% 239.22/37.15 % ------
% 239.22/37.15
% 239.22/37.15
% 239.22/37.15 %
% 239.22/37.15
% 239.22/37.15 % ------ Proving...
% 239.22/37.15 % Proof_search_loop: time out after: 8691 full_loop iterations
% 239.22/37.15
% 239.22/37.15 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 239.22/37.15
% 239.22/37.15
% 239.22/37.15 % ------
% 239.22/37.15 % Current options:
% 239.22/37.15 % ------
% 239.22/37.15
% 239.22/37.15
% 239.22/37.15 %
% 239.22/37.15
% 239.22/37.15 % ------ Proving...
% 239.22/37.15 % Proof_search_loop: time out after: 8487 full_loop iterations
% 239.22/37.15
% 239.22/37.15 % ------ Option_1: Negative Selections Time Limit: 35.
% 239.22/37.15
% 239.22/37.15
% 239.22/37.15 % ------
% 239.22/37.15 % Current options:
% 239.22/37.15 % ------
% 239.22/37.15
% 239.22/37.15
% 239.22/37.15 %
% 239.22/37.15
% 239.22/37.15 % ------ Proving...
% 239.22/37.15 %
% 239.22/37.15
% 239.22/37.15 % SZS status Theorem for theBenchmark.p
% 239.22/37.15
% 239.22/37.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 239.22/37.17
% 239.22/37.17
%------------------------------------------------------------------------------