%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : CSR011+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 46.88s 8.38s
% Output : CNFRefutation 46.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 37
% Syntax : Number of formulae : 563 ( 84 unt; 2 def)
% Number of atoms : 1749 ( 405 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 2008 ( 822 ~;1040 |; 123 &)
% ( 13 <=>; 10 =>; 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 : 13 ( 11 usr; 1 prp; 0-4 aty)
% Number of functors : 18 ( 18 usr; 9 con; 0-3 aty)
% Number of variables : 780 ( 0 sgn 754 !; 26 ?; 428 :)
% 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(f5,axiom,
! [X0,X1] :
( ( ~ ? [X2] :
( terminates(X2,X0,X1)
& happens(X2,X1) )
& ~ releasedAt(X0,plus(X1,n1))
& holdsAt(X0,X1) )
=> holdsAt(X0,plus(X1,n1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+0.ax',keep_holding) ).
fof(f6,axiom,
! [X0,X1] :
( ( ~ ? [X2] :
( initiates(X2,X0,X1)
& happens(X2,X1) )
& ~ releasedAt(X0,plus(X1,n1))
& ~ holdsAt(X0,X1) )
=> ~ holdsAt(X0,plus(X1,n1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+0.ax',keep_not_holding) ).
fof(f7,axiom,
! [X0,X1] :
( ( ~ ? [X2] :
( ( terminates(X2,X0,X1)
| initiates(X2,X0,X1) )
& happens(X2,X1) )
& releasedAt(X0,X1) )
=> releasedAt(X0,plus(X1,n1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+0.ax',keep_released) ).
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(f12,axiom,
! [X0,X1,X2] :
( ( ( terminates(X0,X2,X1)
| initiates(X0,X2,X1) )
& happens(X0,X1) )
=> ~ releasedAt(X2,plus(X1,n1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+0.ax',happens_not_released) ).
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(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(f20,axiom,
tapOff != overflow,
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax',tapOff_not_overflow) ).
fof(f21,axiom,
overflow != tapOn,
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax',overflow_not_tapOn) ).
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(f31,axiom,
plus(n1,n2) = n3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus1_2) ).
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(f50,axiom,
~ holdsAt(filling,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_filling_0) ).
fof(f55,conjecture,
~ stoppedIn(n0,filling,n3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_stopped_filling_0_3) ).
fof(f56,negated_conjecture,
~ ~ stoppedIn(n0,filling,n3),
inference(negated_conjecture,[status(cth)],[f55]) ).
fof(f57,plain,
stoppedIn(n0,filling,n3),
inference(flattening,[],[f56]) ).
fof(f58,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(f59,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(f60,plain,
! [X0] : ~ less(X0,n0),
inference(ennf_transformation,[],[f38]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ~ holdsAt(waterLevel(X2),X0)
| ~ holdsAt(waterLevel(X1),X0)
| X1 = X2 ),
inference(ennf_transformation,[],[f18]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ~ holdsAt(waterLevel(X2),X0)
| ~ holdsAt(waterLevel(X1),X0)
| X1 = X2 ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ( ~ terminates(X0,X2,X1)
& ~ initiates(X0,X2,X1) )
| ~ happens(X0,X1)
| ~ releasedAt(X2,plus(X1,n1)) ),
inference(ennf_transformation,[],[f12]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ( ~ terminates(X0,X2,X1)
& ~ initiates(X0,X2,X1) )
| ~ happens(X0,X1)
| ~ releasedAt(X2,plus(X1,n1)) ),
inference(flattening,[],[f63]) ).
fof(f65,plain,
! [X0,X1] :
( ? [X2] :
( ( terminates(X2,X0,X1)
| initiates(X2,X0,X1) )
& happens(X2,X1) )
| ~ releasedAt(X0,X1)
| releasedAt(X0,plus(X1,n1)) ),
inference(ennf_transformation,[],[f7]) ).
fof(f66,plain,
! [X0,X1] :
( ? [X2] :
( ( terminates(X2,X0,X1)
| initiates(X2,X0,X1) )
& happens(X2,X1) )
| ~ releasedAt(X0,X1)
| releasedAt(X0,plus(X1,n1)) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( ? [X2] :
( initiates(X2,X0,X1)
& happens(X2,X1) )
| releasedAt(X0,plus(X1,n1))
| holdsAt(X0,X1)
| ~ holdsAt(X0,plus(X1,n1)) ),
inference(ennf_transformation,[],[f6]) ).
fof(f68,plain,
! [X0,X1] :
( ? [X2] :
( initiates(X2,X0,X1)
& happens(X2,X1) )
| releasedAt(X0,plus(X1,n1))
| holdsAt(X0,X1)
| ~ holdsAt(X0,plus(X1,n1)) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( ? [X2] :
( terminates(X2,X0,X1)
& happens(X2,X1) )
| releasedAt(X0,plus(X1,n1))
| ~ holdsAt(X0,X1)
| holdsAt(X0,plus(X1,n1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f70,plain,
! [X0,X1] :
( ? [X2] :
( terminates(X2,X0,X1)
& happens(X2,X1) )
| releasedAt(X0,plus(X1,n1))
| ~ holdsAt(X0,X1)
| holdsAt(X0,plus(X1,n1)) ),
inference(flattening,[],[f69]) ).
fof(f71,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(f72,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,[],[f71]) ).
fof(f73,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,[],[f59]) ).
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(f78,plain,
! [X0,X1,X2,X3] :
( plus(X0,X3) != X2
| ~ holdsAt(waterLevel(X0),X1)
| trajectory(filling,X1,waterLevel(X2),X3) ),
inference(ennf_transformation,[],[f17]) ).
fof(f79,plain,
! [X0,X1,X2,X3] :
( plus(X0,X3) != X2
| ~ holdsAt(waterLevel(X0),X1)
| trajectory(filling,X1,waterLevel(X2),X3) ),
inference(flattening,[],[f78]) ).
fof(f84,plain,
! [X2,X0,X1] :
( ( ~ sP1(X2,X0,X1)
| ? [X3] :
( X1 = waterLevel(X3)
& X0 = tapOff
& holdsAt(waterLevel(X3),X2) ) )
& ( ! [X3] :
( waterLevel(X3) != X1
| tapOff != X0
| ~ holdsAt(waterLevel(X3),X2) )
| sP1(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f81]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ( ~ sP1(X0,X1,X2)
| ? [X4] :
( waterLevel(X4) = X2
& tapOff = X1
& holdsAt(waterLevel(X4),X0) ) )
& ( ! [X3] :
( waterLevel(X3) != X2
| tapOff != X1
| ~ holdsAt(waterLevel(X3),X0) )
| sP1(X0,X1,X2) ) ),
inference(rectify,[],[f84]) ).
fof(f86,plain,
! [X0,X1,X2] :
( ( ~ sP1(X0,X1,X2)
| ( waterLevel(sK2(X0,X1,X2)) = X2
& tapOff = X1
& holdsAt(waterLevel(sK2(X0,X1,X2)),X0) ) )
& ( ! [X3] :
( waterLevel(X3) != X2
| tapOff != X1
| ~ holdsAt(waterLevel(X3),X0) )
| sP1(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X4,sK2(X0,X1,X2))],[f85]) ).
fof(f90,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,[],[f82]) ).
fof(f91,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,[],[f90]) ).
fof(f92,plain,
! [X0,X1] :
( ( ( terminates(sK4(X0,X1),X0,X1)
| initiates(sK4(X0,X1),X0,X1) )
& happens(sK4(X0,X1),X1) )
| ~ releasedAt(X0,X1)
| releasedAt(X0,plus(X1,n1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f66]) ).
fof(f93,plain,
! [X0,X1] :
( ( initiates(sK5(X0,X1),X0,X1)
& happens(sK5(X0,X1),X1) )
| releasedAt(X0,plus(X1,n1))
| holdsAt(X0,X1)
| ~ holdsAt(X0,plus(X1,n1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f68]) ).
fof(f94,plain,
! [X0,X1] :
( ( terminates(sK6(X0,X1),X0,X1)
& happens(sK6(X0,X1),X1) )
| releasedAt(X0,plus(X1,n1))
| ~ holdsAt(X0,X1)
| holdsAt(X0,plus(X1,n1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f70]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ~ stoppedIn(X0,X1,X2)
| ( terminates(sK7(X0,X1,X2),X1,sK8(X0,X1,X2))
& less(sK8(X0,X1,X2),X2)
& less(X0,sK8(X0,X1,X2))
& happens(sK7(X0,X1,X2),sK8(X0,X1,X2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X3,sK7(X0,X1,X2)),skolemize(X4,sK8(X0,X1,X2))],[f73]) ).
fof(f96,plain,
! [X0] :
( ( ~ less(X0,n3)
| less_or_equal(X0,n2) )
& ( ~ less_or_equal(X0,n2)
| less(X0,n3) ) ),
inference(nnf_transformation,[],[f41]) ).
fof(f97,plain,
! [X0,X1] :
( ( ~ less(X0,X1)
| ( X1 != X0
& ~ less(X1,X0) ) )
& ( X0 = X1
| less(X1,X0)
| less(X0,X1) ) ),
inference(nnf_transformation,[],[f48]) ).
fof(f98,plain,
! [X0,X1] :
( ( ~ less(X0,X1)
| ( X1 != X0
& ~ less(X1,X0) ) )
& ( X0 = X1
| less(X1,X0)
| less(X0,X1) ) ),
inference(flattening,[],[f97]) ).
fof(f99,plain,
! [X0] :
( ( ~ less(X0,n1)
| less_or_equal(X0,n0) )
& ( ~ less_or_equal(X0,n0)
| less(X0,n1) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f100,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(f101,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,[],[f100]) ).
fof(f102,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(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(flattening,[],[f102]) ).
fof(f104,plain,
! [X0] :
( ( ~ less(X0,n2)
| less_or_equal(X0,n1) )
& ( ~ less_or_equal(X0,n1)
| less(X0,n2) ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f105,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(f106,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,[],[f105]) ).
fof(f107,plain,
holdsAt(waterLevel(n0),n0),
inference(cnf_transformation,[],[f49]) ).
fof(f108,plain,
~ holdsAt(filling,n0),
inference(cnf_transformation,[],[f50]) ).
fof(f113,plain,
stoppedIn(n0,filling,n3),
inference(cnf_transformation,[],[f57]) ).
fof(f114,plain,
! [X0] : ~ less(X0,n0),
inference(cnf_transformation,[],[f60]) ).
fof(f115,plain,
n1 = plus(n0,n1),
inference(cnf_transformation,[],[f27]) ).
fof(f120,plain,
! [X2,X0,X1] :
( ~ holdsAt(waterLevel(X2),X0)
| ~ holdsAt(waterLevel(X1),X0)
| X1 = X2 ),
inference(cnf_transformation,[],[f62]) ).
fof(f123,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1,X2)
| waterLevel(sK2(X0,X1,X2)) = X2 ),
inference(cnf_transformation,[],[f86]) ).
fof(f126,plain,
! [X2,X3,X0,X1] :
( waterLevel(X3) != X2
| tapOff != X1
| ~ holdsAt(waterLevel(X3),X0)
| sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f86]) ).
fof(f135,plain,
! [X2,X0,X1] :
( ~ sP0(X2,X0,X1)
| initiates(X0,X1,X2) ),
inference(cnf_transformation,[],[f91]) ).
fof(f136,plain,
! [X2,X0,X1] :
( ~ sP1(X2,X0,X1)
| initiates(X0,X1,X2) ),
inference(cnf_transformation,[],[f91]) ).
fof(f137,plain,
! [X2,X0,X1] :
( spilling != X1
| overflow != X0
| initiates(X0,X1,X2) ),
inference(cnf_transformation,[],[f91]) ).
fof(f138,plain,
! [X2,X0,X1] :
( filling != X1
| tapOn != X0
| initiates(X0,X1,X2) ),
inference(cnf_transformation,[],[f91]) ).
fof(f139,plain,
! [X2,X0,X1] :
( ~ terminates(X0,X2,X1)
| ~ happens(X0,X1)
| ~ releasedAt(X2,plus(X1,n1)) ),
inference(cnf_transformation,[],[f64]) ).
fof(f140,plain,
! [X2,X0,X1] :
( ~ initiates(X0,X2,X1)
| ~ happens(X0,X1)
| ~ releasedAt(X2,plus(X1,n1)) ),
inference(cnf_transformation,[],[f64]) ).
fof(f142,plain,
! [X0,X1] :
( happens(sK4(X0,X1),X1)
| ~ releasedAt(X0,X1)
| releasedAt(X0,plus(X1,n1)) ),
inference(cnf_transformation,[],[f92]) ).
fof(f144,plain,
! [X0,X1] :
( happens(sK5(X0,X1),X1)
| releasedAt(X0,plus(X1,n1))
| holdsAt(X0,X1)
| ~ holdsAt(X0,plus(X1,n1)) ),
inference(cnf_transformation,[],[f93]) ).
fof(f146,plain,
! [X0,X1] :
( happens(sK6(X0,X1),X1)
| releasedAt(X0,plus(X1,n1))
| ~ holdsAt(X0,X1)
| holdsAt(X0,plus(X1,n1)) ),
inference(cnf_transformation,[],[f94]) ).
fof(f147,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,[],[f72]) ).
fof(f148,plain,
! [X2,X0,X1] :
( ~ stoppedIn(X0,X1,X2)
| terminates(sK7(X0,X1,X2),X1,sK8(X0,X1,X2)) ),
inference(cnf_transformation,[],[f95]) ).
fof(f149,plain,
! [X2,X0,X1] :
( ~ stoppedIn(X0,X1,X2)
| less(sK8(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f95]) ).
fof(f150,plain,
! [X2,X0,X1] :
( ~ stoppedIn(X0,X1,X2)
| less(X0,sK8(X0,X1,X2)) ),
inference(cnf_transformation,[],[f95]) ).
fof(f151,plain,
! [X2,X0,X1] :
( ~ stoppedIn(X0,X1,X2)
| happens(sK7(X0,X1,X2),sK8(X0,X1,X2)) ),
inference(cnf_transformation,[],[f95]) ).
fof(f152,plain,
! [X0] :
( ~ less(X0,n3)
| less_or_equal(X0,n2) ),
inference(cnf_transformation,[],[f96]) ).
fof(f153,plain,
! [X0] :
( ~ less_or_equal(X0,n2)
| less(X0,n3) ),
inference(cnf_transformation,[],[f96]) ).
fof(f154,plain,
n3 = plus(n1,n2),
inference(cnf_transformation,[],[f31]) ).
fof(f156,plain,
! [X0,X1] :
( ~ less(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f98]) ).
fof(f157,plain,
! [X0,X1] :
( ~ less(X0,X1)
| ~ less(X1,X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f158,plain,
! [X0,X1] :
( X0 = X1
| less(X1,X0)
| less(X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f159,plain,
! [X0,X1] : plus(X0,X1) = plus(X1,X0),
inference(cnf_transformation,[],[f36]) ).
fof(f160,plain,
! [X0] :
( ~ less(X0,n1)
| less_or_equal(X0,n0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f161,plain,
! [X0] :
( ~ less_or_equal(X0,n0)
| less(X0,n1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f162,plain,
tapOn != overflow,
inference(cnf_transformation,[],[f21]) ).
fof(f163,plain,
tapOn != tapOff,
inference(cnf_transformation,[],[f19]) ).
fof(f164,plain,
! [X0,X1] :
( ~ happens(X0,X1)
| overflow = X0
| n0 = X1 ),
inference(cnf_transformation,[],[f101]) ).
fof(f165,plain,
! [X0,X1] :
( ~ happens(X0,X1)
| holdsAt(filling,X1)
| n0 = X1 ),
inference(cnf_transformation,[],[f101]) ).
fof(f166,plain,
! [X0,X1] :
( ~ happens(X0,X1)
| holdsAt(waterLevel(n3),X1)
| n0 = X1 ),
inference(cnf_transformation,[],[f101]) ).
fof(f167,plain,
! [X0,X1] :
( ~ happens(X0,X1)
| overflow = X0
| tapOn = X0 ),
inference(cnf_transformation,[],[f101]) ).
fof(f168,plain,
! [X0,X1] :
( ~ happens(X0,X1)
| holdsAt(filling,X1)
| tapOn = X0 ),
inference(cnf_transformation,[],[f101]) ).
fof(f169,plain,
! [X0,X1] :
( ~ happens(X0,X1)
| holdsAt(waterLevel(n3),X1)
| tapOn = X0 ),
inference(cnf_transformation,[],[f101]) ).
fof(f170,plain,
! [X0,X1] :
( overflow != X0
| ~ holdsAt(filling,X1)
| ~ holdsAt(waterLevel(n3),X1)
| happens(X0,X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f171,plain,
! [X0,X1] :
( n0 != X1
| tapOn != X0
| happens(X0,X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f172,plain,
overflow != tapOff,
inference(cnf_transformation,[],[f20]) ).
fof(f176,plain,
! [X2,X0,X1] :
( ~ terminates(X0,X1,X2)
| overflow = X0
| tapOff = X0 ),
inference(cnf_transformation,[],[f103]) ).
fof(f177,plain,
! [X2,X0,X1] :
( filling != X1
| overflow != X0
| terminates(X0,X1,X2) ),
inference(cnf_transformation,[],[f103]) ).
fof(f178,plain,
! [X2,X0,X1] :
( filling != X1
| tapOff != X0
| terminates(X0,X1,X2) ),
inference(cnf_transformation,[],[f103]) ).
fof(f179,plain,
! [X2,X0,X1] :
( ~ initiates(X0,X2,X1)
| ~ happens(X0,X1)
| holdsAt(X2,plus(X1,n1)) ),
inference(cnf_transformation,[],[f75]) ).
fof(f180,plain,
! [X2,X0,X1] :
( ~ terminates(X0,X2,X1)
| ~ happens(X0,X1)
| ~ holdsAt(X2,plus(X1,n1)) ),
inference(cnf_transformation,[],[f77]) ).
fof(f181,plain,
! [X2,X3,X0,X1] :
( plus(X0,X3) != X2
| ~ holdsAt(waterLevel(X0),X1)
| trajectory(filling,X1,waterLevel(X2),X3) ),
inference(cnf_transformation,[],[f79]) ).
fof(f182,plain,
! [X0] :
( ~ less(X0,n2)
| less_or_equal(X0,n1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f183,plain,
! [X0] :
( ~ less_or_equal(X0,n1)
| less(X0,n2) ),
inference(cnf_transformation,[],[f104]) ).
fof(f184,plain,
n2 = plus(n1,n1),
inference(cnf_transformation,[],[f30]) ).
fof(f185,plain,
n2 = plus(n0,n2),
inference(cnf_transformation,[],[f28]) ).
fof(f186,plain,
! [X0,X1] :
( ~ less_or_equal(X0,X1)
| X0 = X1
| less(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
fof(f187,plain,
! [X0,X1] :
( X0 != X1
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
fof(f188,plain,
! [X0,X1] :
( ~ less(X0,X1)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
fof(f190,plain,
! [X2,X3,X0] :
( waterLevel(X3) != X2
| ~ holdsAt(waterLevel(X3),X0)
| sP1(X0,tapOff,X2) ),
inference(equality_resolution,[],[f126]) ).
fof(f191,plain,
! [X3,X0] :
( ~ holdsAt(waterLevel(X3),X0)
| sP1(X0,tapOff,waterLevel(X3)) ),
inference(equality_resolution,[],[f190]) ).
fof(f194,plain,
! [X2,X1] :
( filling != X1
| initiates(tapOn,X1,X2) ),
inference(equality_resolution,[],[f138]) ).
fof(f195,plain,
! [X2] : initiates(tapOn,filling,X2),
inference(equality_resolution,[],[f194]) ).
fof(f196,plain,
! [X2,X1] :
( spilling != X1
| initiates(overflow,X1,X2) ),
inference(equality_resolution,[],[f137]) ).
fof(f197,plain,
! [X2] : initiates(overflow,spilling,X2),
inference(equality_resolution,[],[f196]) ).
fof(f198,plain,
! [X1] : ~ less(X1,X1),
inference(equality_resolution,[],[f156]) ).
fof(f199,plain,
! [X1] :
( n0 != X1
| happens(tapOn,X1) ),
inference(equality_resolution,[],[f171]) ).
fof(f200,plain,
happens(tapOn,n0),
inference(equality_resolution,[],[f199]) ).
fof(f201,plain,
! [X1] :
( ~ holdsAt(filling,X1)
| ~ holdsAt(waterLevel(n3),X1)
| happens(overflow,X1) ),
inference(equality_resolution,[],[f170]) ).
fof(f202,plain,
! [X2,X1] :
( filling != X1
| terminates(tapOff,X1,X2) ),
inference(equality_resolution,[],[f178]) ).
fof(f203,plain,
! [X2] : terminates(tapOff,filling,X2),
inference(equality_resolution,[],[f202]) ).
fof(f204,plain,
! [X2,X1] :
( filling != X1
| terminates(overflow,X1,X2) ),
inference(equality_resolution,[],[f177]) ).
fof(f205,plain,
! [X2] : terminates(overflow,filling,X2),
inference(equality_resolution,[],[f204]) ).
fof(f206,plain,
! [X3,X0,X1] :
( ~ holdsAt(waterLevel(X0),X1)
| trajectory(filling,X1,waterLevel(plus(X0,X3)),X3) ),
inference(equality_resolution,[],[f181]) ).
fof(f207,plain,
! [X1] : less_or_equal(X1,X1),
inference(equality_resolution,[],[f187]) ).
tcf(c_49,plain,
holdsAt(waterLevel(n0),n0),
inference(cnf_transformation,[],[f107]) ).
tcf(c_50,plain,
~ holdsAt(filling,n0),
inference(cnf_transformation,[],[f108]) ).
tcf(c_55,negated_conjecture,
stoppedIn(n0,filling,n3),
inference(cnf_transformation,[],[f113]) ).
tcf(c_56,plain,
! [X0: $i] : ~ less(X0,n0),
inference(cnf_transformation,[],[f114]) ).
tcf(c_57,plain,
plus(n0,n1) = n1,
inference(cnf_transformation,[],[f115]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ holdsAt(waterLevel(X2),X1)
| ~ holdsAt(waterLevel(X0),X1) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( sP1(X1,tapOff,waterLevel(X0))
| ~ holdsAt(waterLevel(X0),X1) ),
inference(cnf_transformation,[],[f191]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( waterLevel(sK2(X0,X1,X2)) = X2 )
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_72,plain,
! [X0: $i] : initiates(tapOn,filling,X0),
inference(cnf_transformation,[],[f195]) ).
tcf(c_73,plain,
! [X0: $i] : initiates(overflow,spilling,X0),
inference(cnf_transformation,[],[f197]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( initiates(X1,X2,X0)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i] :
( initiates(X1,X2,X0)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ happens(X2,X1)
| ~ initiates(X2,X0,X1)
| ~ releasedAt(X0,plus(X1,n1)) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ happens(X2,X1)
| ~ terminates(X2,X0,X1)
| ~ releasedAt(X0,plus(X1,n1)) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] :
( releasedAt(X0,plus(X1,n1))
| happens(sK4(X0,X1),X1)
| ~ releasedAt(X0,X1) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( holdsAt(X0,X1)
| releasedAt(X0,plus(X1,n1))
| happens(sK5(X0,X1),X1)
| ~ holdsAt(X0,plus(X1,n1)) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] :
( releasedAt(X0,plus(X1,n1))
| holdsAt(X0,plus(X1,n1))
| happens(sK6(X0,X1),X1)
| ~ holdsAt(X0,X1) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_88,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,[],[f147]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i] :
( happens(sK7(X0,X1,X2),sK8(X0,X1,X2))
| ~ stoppedIn(X0,X1,X2) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i] :
( less(X0,sK8(X0,X1,X2))
| ~ stoppedIn(X0,X1,X2) ),
inference(cnf_transformation,[],[f150]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] :
( less(sK8(X0,X1,X2),X2)
| ~ stoppedIn(X0,X1,X2) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i,X2: $i] :
( terminates(sK7(X0,X1,X2),X1,sK8(X0,X1,X2))
| ~ stoppedIn(X0,X1,X2) ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_93,plain,
! [X0: $i] :
( less(X0,n3)
| ~ less_or_equal(X0,n2) ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_94,plain,
! [X0: $i] :
( less_or_equal(X0,n2)
| ~ less(X0,n3) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_95,plain,
plus(n1,n2) = n3,
inference(cnf_transformation,[],[f154]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i] :
( less(X1,X0)
| less(X0,X1)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( ~ less(X1,X0)
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_99,plain,
! [X0: $i] : ~ less(X0,X0),
inference(cnf_transformation,[],[f198]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i] : plus(X0,X1) = plus(X1,X0),
inference(cnf_transformation,[],[f159]) ).
tcf(c_101,plain,
! [X0: $i] :
( less(X0,n1)
| ~ less_or_equal(X0,n0) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_102,plain,
! [X0: $i] :
( less_or_equal(X0,n0)
| ~ less(X0,n1) ),
inference(cnf_transformation,[],[f160]) ).
tcf(c_103,plain,
overflow != tapOn,
inference(cnf_transformation,[],[f162]) ).
tcf(c_104,plain,
tapOff != tapOn,
inference(cnf_transformation,[],[f163]) ).
tcf(c_105,plain,
happens(tapOn,n0),
inference(cnf_transformation,[],[f200]) ).
tcf(c_106,plain,
! [X0: $i] :
( happens(overflow,X0)
| ~ holdsAt(filling,X0)
| ~ holdsAt(waterLevel(n3),X0) ),
inference(cnf_transformation,[],[f201]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i] :
( holdsAt(waterLevel(n3),X1)
| ( X0 = tapOn )
| ~ happens(X0,X1) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i] :
( holdsAt(filling,X1)
| ( X0 = tapOn )
| ~ happens(X0,X1) ),
inference(cnf_transformation,[],[f168]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] :
( ( X0 = tapOn )
| ( X0 = overflow )
| ~ happens(X0,X1) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i] :
( holdsAt(waterLevel(n3),X1)
| ( X1 = n0 )
| ~ happens(X0,X1) ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i] :
( holdsAt(filling,X1)
| ( X1 = n0 )
| ~ happens(X0,X1) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i] :
( ( X1 = n0 )
| ( X0 = overflow )
| ~ happens(X0,X1) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_113,plain,
tapOff != overflow,
inference(cnf_transformation,[],[f172]) ).
tcf(c_114,plain,
! [X0: $i] : terminates(tapOff,filling,X0),
inference(cnf_transformation,[],[f203]) ).
tcf(c_115,plain,
! [X0: $i] : terminates(overflow,filling,X0),
inference(cnf_transformation,[],[f205]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = overflow )
| ( X0 = tapOff )
| ~ terminates(X0,X1,X2) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_120,plain,
! [X0: $i,X1: $i,X2: $i] :
( holdsAt(X1,plus(X2,n1))
| ~ happens(X0,X2)
| ~ initiates(X0,X1,X2) ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_121,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ happens(X2,X1)
| ~ terminates(X2,X0,X1)
| ~ holdsAt(X0,plus(X1,n1)) ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i,X2: $i] :
( trajectory(filling,X1,waterLevel(plus(X0,X2)),X2)
| ~ holdsAt(waterLevel(X0),X1) ),
inference(cnf_transformation,[],[f206]) ).
tcf(c_123,plain,
! [X0: $i] :
( less(X0,n2)
| ~ less_or_equal(X0,n1) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_124,plain,
! [X0: $i] :
( less_or_equal(X0,n1)
| ~ less(X0,n2) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_125,plain,
plus(n1,n1) = n2,
inference(cnf_transformation,[],[f184]) ).
tcf(c_126,plain,
plus(n0,n2) = n2,
inference(cnf_transformation,[],[f185]) ).
tcf(c_127,plain,
! [X0: $i,X1: $i] :
( less_or_equal(X0,X1)
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f188]) ).
tcf(c_128,plain,
! [X0: $i] : less_or_equal(X0,X0),
inference(cnf_transformation,[],[f207]) ).
tcf(c_129,plain,
! [X0: $i,X1: $i] :
( less(X0,X1)
| ( X0 = X1 )
| ~ less_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_130,plain,
less_or_equal(n1,n1),
inference(instantiation,[status(thm)],[c_128]) ).
tcf(c_133,plain,
~ less(n1,n1),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_140,plain,
( less(n1,n2)
| ~ less_or_equal(n1,n1) ),
inference(instantiation,[status(thm)],[c_123]) ).
tcf(c_150,plain,
( less(n1,n1)
| ( n1 = n1 ) ),
inference(instantiation,[status(thm)],[c_97]) ).
tcf(c_162,plain,
( happens(overflow,n1)
| ~ holdsAt(filling,n1)
| ~ holdsAt(waterLevel(n3),n1) ),
inference(instantiation,[status(thm)],[c_106]) ).
tcf(c_190,plain,
! [X0: $i] :
( ~ less(X0,n3)
| less_or_equal(X0,n2) ),
inference(prop_impl_just,[status(thm)],[c_94]) ).
tcf(c_191,plain,
! [X0: $i] :
( less_or_equal(X0,n2)
| ~ less(X0,n3) ),
inference(renaming,[status(thm)],[c_190]) ).
tcf(c_192,plain,
! [X0: $i] :
( less(X0,n3)
| ~ less_or_equal(X0,n2) ),
inference(prop_impl_just,[status(thm)],[c_93]) ).
tcf(c_194,plain,
! [X0: $i] :
( ~ less(X0,n1)
| less_or_equal(X0,n0) ),
inference(prop_impl_just,[status(thm)],[c_102]) ).
tcf(c_195,plain,
! [X0: $i] :
( less_or_equal(X0,n0)
| ~ less(X0,n1) ),
inference(renaming,[status(thm)],[c_194]) ).
tcf(c_196,plain,
! [X0: $i] :
( less(X0,n1)
| ~ less_or_equal(X0,n0) ),
inference(prop_impl_just,[status(thm)],[c_101]) ).
tcf(c_198,plain,
! [X0: $i] :
( ~ less(X0,n2)
| less_or_equal(X0,n1) ),
inference(prop_impl_just,[status(thm)],[c_124]) ).
tcf(c_199,plain,
! [X0: $i] :
( less_or_equal(X0,n1)
| ~ less(X0,n2) ),
inference(renaming,[status(thm)],[c_198]) ).
tcf(c_200,plain,
! [X0: $i] :
( less(X0,n2)
| ~ less_or_equal(X0,n1) ),
inference(prop_impl_just,[status(thm)],[c_123]) ).
tcf(c_208,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_122]) ).
tcf(c_230,plain,
! [X0: $i,X1: $i,X2: $i] :
( less(sK8(X0,X1,X2),X2)
| ~ stoppedIn(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_91]) ).
tcf(c_236,plain,
! [X0: $i,X1: $i] :
( less_or_equal(X0,X1)
| ~ less(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_127]) ).
tcf(c_763,plain,
plus(n1,n0) = n1,
inference(demodulation,[status(thm)],[c_57,c_100]) ).
tcf(c_1036,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_88,c_208]) ).
tcf(c_1037,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_1036]) ).
tcf(c_1068,plain,
! [X0: $i,X1: $i,X2: $i] :
( less(sK8(X0,X1,X2),X2)
| ( X2 != n3 )
| ( X1 != filling )
| ( X0 != n0 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_230]) ).
tcf(c_1069,plain,
less(sK8(n0,filling,n3),n3),
inference(unflattening,[status(thm)],[c_1068]) ).
tcf(c_1203,plain,
! [X0: $i,X1: $i] :
( less(X1,n1)
| ~ less(X0,n3)
| ( n0 != n2 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_191,c_196]) ).
tcf(c_1204,plain,
! [X0: $i] :
( less(X0,n1)
| ~ less(X0,n3)
| ( n0 != n2 ) ),
inference(unflattening,[status(thm)],[c_1203]) ).
tcf(c_1205,plain,
( less(n1,n1)
| ~ less(n1,n3)
| ( n0 != n2 ) ),
inference(instantiation,[status(thm)],[c_1204]) ).
tcf(c_1250,plain,
! [X0: $i,X1: $i,X2: $i] :
( less(X1,X2)
| ( X1 = X2 )
| ~ less(X0,n3)
| ( X2 != n2 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_191,c_129]) ).
tcf(c_1251,plain,
! [X0: $i] :
( less(X0,n2)
| ( X0 = n2 )
| ~ less(X0,n3) ),
inference(unflattening,[status(thm)],[c_1250]) ).
tcf(c_1262,plain,
! [X0: $i,X1: $i,X2: $i] :
( less(X0,n3)
| ~ less(X1,X2)
| ( X2 != n2 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_192,c_236]) ).
tcf(c_1263,plain,
! [X0: $i] :
( less(X0,n3)
| ~ less(X0,n2) ),
inference(unflattening,[status(thm)],[c_1262]) ).
tcf(c_1264,plain,
( less(n1,n3)
| ~ less(n1,n2) ),
inference(instantiation,[status(thm)],[c_1263]) ).
tcf(c_1271,plain,
! [X0: $i,X1: $i] :
( less(X0,n3)
| ( X1 != n2 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_192,c_128]) ).
tcf(c_1272,plain,
less(n2,n3),
inference(unflattening,[status(thm)],[c_1271]) ).
tcf(c_1287,plain,
! [X0: $i,X1: $i] :
( less(X0,n1)
| ~ less(X1,n2)
| ( n0 != n1 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_196,c_199]) ).
tcf(c_1288,plain,
! [X0: $i] :
( less(X0,n1)
| ~ less(X0,n2)
| ( n0 != n1 ) ),
inference(unflattening,[status(thm)],[c_1287]) ).
tcf(c_1289,plain,
( less(n1,n1)
| ~ less(n1,n2)
| ( n0 != n1 ) ),
inference(instantiation,[status(thm)],[c_1288]) ).
tcf(c_1290,plain,
n0 != n1,
inference(global_subsumption_just,[status(thm)],[c_1288,c_130,c_133,c_140,c_1289]) ).
tcf(c_1295,plain,
! [X0: $i,X1: $i,X2: $i] :
( less(X1,X2)
| ( X1 = X2 )
| ~ less(X0,n1)
| ( X2 != n0 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_195,c_129]) ).
tcf(c_1296,plain,
! [X0: $i] :
( less(X0,n0)
| ( X0 = n0 )
| ~ less(X0,n1) ),
inference(unflattening,[status(thm)],[c_1295]) ).
tcf(c_1297,plain,
! [X0: $i] :
( ~ less(X0,n1)
| ( X0 = n0 ) ),
inference(global_subsumption_just,[status(thm)],[c_1296,c_56,c_1296]) ).
tcf(c_1298,plain,
! [X0: $i] :
( ( X0 = n0 )
| ~ less(X0,n1) ),
inference(renaming,[status(thm)],[c_1297]) ).
tcf(c_1307,plain,
! [X0: $i,X1: $i] :
( less(X0,n1)
| ( X1 != n0 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_196,c_128]) ).
tcf(c_1308,plain,
less(n0,n1),
inference(unflattening,[status(thm)],[c_1307]) ).
tcf(c_1312,plain,
! [X0: $i,X1: $i,X2: $i] :
( less(X1,X2)
| ( X1 = X2 )
| ~ less(X0,n2)
| ( X2 != n1 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_199,c_129]) ).
tcf(c_1313,plain,
! [X0: $i] :
( less(X0,n1)
| ( X0 = n1 )
| ~ less(X0,n2) ),
inference(unflattening,[status(thm)],[c_1312]) ).
tcf(c_1324,plain,
! [X0: $i,X1: $i,X2: $i] :
( less(X0,n2)
| ~ less(X1,X2)
| ( X2 != n1 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_200,c_236]) ).
tcf(c_1325,plain,
! [X0: $i] :
( less(X0,n2)
| ~ less(X0,n1) ),
inference(unflattening,[status(thm)],[c_1324]) ).
tcf(c_2033,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ happens(X3,X1)
| ~ releasedAt(X2,plus(X1,n1))
| ( X3 != tapOn )
| ( X2 != filling )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_72,c_80]) ).
tcf(c_2034,plain,
! [X0: $i] :
( ~ happens(tapOn,X0)
| ~ releasedAt(filling,plus(X0,n1)) ),
inference(unflattening,[status(thm)],[c_2033]) ).
tcf(c_2077,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ happens(X3,X1)
| ~ releasedAt(X2,plus(X1,n1))
| ( X3 != overflow )
| ( X2 != spilling )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_73,c_80]) ).
tcf(c_2078,plain,
! [X0: $i] :
( ~ happens(overflow,X0)
| ~ releasedAt(spilling,plus(X0,n1)) ),
inference(unflattening,[status(thm)],[c_2077]) ).
tcf(c_3678,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_3680,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3682,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( holdsAt(X0,X2)
| ~ holdsAt(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3685,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( less(X0,X2)
| ~ less(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3690,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( happens(X0,X2)
| ~ happens(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_5021,plain,
less(n0,n2),
inference(superposition,[status(thm)],[c_1308,c_1325]) ).
tcf(c_5069,plain,
! [X0: $i,X1: $i] :
( initiates(tapOff,waterLevel(X0),X1)
| ~ holdsAt(waterLevel(X0),X1) ),
inference(superposition,[status(thm)],[c_64,c_74]) ).
tcf(c_5216,plain,
! [X0: $i,X1: $i] :
( ( sK8(X0,X1,n1) = n0 )
| ~ stoppedIn(X0,X1,n1) ),
inference(superposition,[status(thm)],[c_91,c_1298]) ).
tcf(c_5300,plain,
! [X0: $i] :
( less(n2,X0)
| less(X0,n1)
| ( X0 = n2 )
| ( X0 = n1 ) ),
inference(superposition,[status(thm)],[c_97,c_1313]) ).
tcf(c_5455,plain,
! [X0: $i,X1: $i] :
( ( waterLevel(sK2(X1,tapOff,waterLevel(X0))) = waterLevel(X0) )
| ~ holdsAt(waterLevel(X0),X1) ),
inference(superposition,[status(thm)],[c_64,c_67]) ).
tcf(c_5483,plain,
n0 != n2,
inference(global_subsumption_just,[status(thm)],[c_1204,c_130,c_133,c_140,c_1205,c_1264]) ).
tcf(c_5551,plain,
! [X0: $i,X1: $i,X2: $i] :
( stoppedIn(X1,filling,plus(X1,X2))
| holdsAt(waterLevel(plus(X0,X2)),plus(X1,X2))
| ~ happens(tapOn,X1)
| ~ less(n0,X2)
| ~ holdsAt(waterLevel(X0),X1) ),
inference(superposition,[status(thm)],[c_72,c_1037]) ).
tcf(c_5598,plain,
! [X0: $i,X1: $i] :
( releasedAt(X0,plus(n1,X1))
| happens(sK4(X0,X1),X1)
| ~ releasedAt(X0,X1) ),
inference(superposition,[status(thm)],[c_100,c_82]) ).
tcf(c_5600,plain,
! [X0: $i] :
( releasedAt(X0,n2)
| happens(sK4(X0,n1),n1)
| ~ releasedAt(X0,n1) ),
inference(superposition,[status(thm)],[c_125,c_82]) ).
tcf(c_5689,plain,
! [X0: $i] :
( releasedAt(X0,n2)
| holdsAt(waterLevel(n3),n1)
| ( n0 = n1 )
| ~ releasedAt(X0,n1) ),
inference(superposition,[status(thm)],[c_5600,c_110]) ).
tcf(c_5698,plain,
! [X0: $i] :
( releasedAt(X0,n2)
| holdsAt(waterLevel(n3),n1)
| ~ releasedAt(X0,n1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5689,c_1290]) ).
tcf(c_5737,plain,
! [X0: $i] :
( happens(overflow,n1)
| releasedAt(X0,n2)
| ~ holdsAt(filling,n1)
| ~ releasedAt(X0,n1) ),
inference(superposition,[status(thm)],[c_5698,c_106]) ).
tcf(c_5785,plain,
~ less(n2,n2),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_5801,plain,
! [X0: $i,X1: $i,X2: $i] :
( stoppedIn(X1,filling,plus(X2,X1))
| holdsAt(waterLevel(plus(X0,X2)),plus(X1,X2))
| ~ happens(tapOn,X1)
| ~ less(n0,X2)
| ~ holdsAt(waterLevel(X0),X1) ),
inference(superposition,[status(thm)],[c_100,c_5551]) ).
tcf(c_5809,plain,
! [X0: $i,X1: $i,X2: $i] :
( stoppedIn(X1,filling,plus(X1,X2))
| holdsAt(waterLevel(plus(X2,X0)),plus(X1,X2))
| ~ happens(tapOn,X1)
| ~ less(n0,X2)
| ~ holdsAt(waterLevel(X0),X1) ),
inference(superposition,[status(thm)],[c_100,c_5551]) ).
tcf(c_5820,plain,
! [X0: $i] :
( stoppedIn(n0,filling,plus(n0,n2))
| holdsAt(waterLevel(plus(X0,n2)),n2)
| ~ happens(tapOn,n0)
| ~ less(n0,n2)
| ~ holdsAt(waterLevel(X0),n0) ),
inference(superposition,[status(thm)],[c_126,c_5551]) ).
tcf(c_5824,plain,
! [X0: $i] :
( stoppedIn(n0,filling,n2)
| holdsAt(waterLevel(plus(X0,n2)),n2)
| ~ happens(tapOn,n0)
| ~ less(n0,n2)
| ~ holdsAt(waterLevel(X0),n0) ),
inference(light_normalisation,[status(thm)],[c_5820,c_126]) ).
tcf(c_5825,plain,
! [X0: $i] :
( stoppedIn(n0,filling,n2)
| holdsAt(waterLevel(plus(X0,n2)),n2)
| ~ holdsAt(waterLevel(X0),n0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5824,c_105,c_5021]) ).
tcf(c_5900,plain,
( ( n0 = n0 )
| ~ less(n0,n1) ),
inference(instantiation,[status(thm)],[c_1298]) ).
tcf(c_5906,plain,
( holdsAt(filling,n0)
| ( tapOn = tapOn )
| ~ happens(tapOn,n0) ),
inference(instantiation,[status(thm)],[c_108]) ).
tcf(c_5915,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(X0,X1,X2) = tapOn )
| ( sK7(X0,X1,X2) = overflow )
| ~ stoppedIn(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_89,c_109]) ).
tcf(c_5949,plain,
! [X0: $i] :
( holdsAt(filling,plus(X0,n1))
| ~ happens(tapOn,X0) ),
inference(superposition,[status(thm)],[c_72,c_120]) ).
tcf(c_5950,plain,
! [X0: $i] :
( holdsAt(spilling,plus(X0,n1))
| ~ happens(overflow,X0) ),
inference(superposition,[status(thm)],[c_73,c_120]) ).
tcf(c_5952,plain,
! [X0: $i,X1: $i] :
( holdsAt(waterLevel(X0),plus(X1,n1))
| ~ happens(tapOff,X1)
| ~ holdsAt(waterLevel(X0),X1) ),
inference(superposition,[status(thm)],[c_5069,c_120]) ).
tcf(c_5976,plain,
! [X0: $i,X1: $i,X2: $i] :
( happens(sK4(X1,X2),X2)
| ~ happens(X0,X2)
| ~ releasedAt(X1,X2)
| ~ initiates(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_82,c_80]) ).
tcf(c_5977,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ happens(X2,X1)
| ~ initiates(X2,X0,X1)
| ~ releasedAt(X0,plus(n1,X1)) ),
inference(superposition,[status(thm)],[c_100,c_80]) ).
tcf(c_5979,plain,
! [X0: $i,X1: $i] :
( ~ happens(X0,n1)
| ~ releasedAt(X1,n2)
| ~ initiates(X0,X1,n1) ),
inference(superposition,[status(thm)],[c_125,c_80]) ).
tcf(c_5999,plain,
! [X0: $i,X1: $i,X2: $i] :
( happens(sK4(X1,X2),X2)
| ~ happens(X0,X2)
| ~ releasedAt(X1,X2)
| ~ terminates(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_82,c_81]) ).
tcf(c_6000,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ happens(X2,X1)
| ~ terminates(X2,X0,X1)
| ~ releasedAt(X0,plus(n1,X1)) ),
inference(superposition,[status(thm)],[c_100,c_81]) ).
tcf(c_6002,plain,
! [X0: $i,X1: $i] :
( ~ happens(X0,n1)
| ~ releasedAt(X1,n2)
| ~ terminates(X0,X1,n1) ),
inference(superposition,[status(thm)],[c_125,c_81]) ).
tcf(c_6024,plain,
! [X0: $i] :
( holdsAt(filling,plus(n1,X0))
| ~ happens(tapOn,X0) ),
inference(superposition,[status(thm)],[c_100,c_5949]) ).
tcf(c_6061,plain,
( holdsAt(filling,n1)
| ~ happens(tapOn,n0) ),
inference(superposition,[status(thm)],[c_763,c_6024]) ).
tcf(c_6062,plain,
holdsAt(filling,n1),
inference(forward_subsumption_resolution,[status(thm)],[c_6061,c_105]) ).
tcf(c_6153,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(X0,X1,X2) = overflow )
| ( sK7(X0,X1,X2) = tapOff )
| ~ stoppedIn(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_92,c_116]) ).
tcf(c_6168,plain,
! [X0: $i,X1: $i] :
( ~ happens(tapOn,X1)
| ~ happens(X0,X1)
| ~ terminates(X0,filling,X1) ),
inference(superposition,[status(thm)],[c_5949,c_121]) ).
tcf(c_6173,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ happens(X2,X1)
| ~ terminates(X2,X0,X1)
| ~ holdsAt(X0,plus(n1,X1)) ),
inference(superposition,[status(thm)],[c_100,c_121]) ).
tcf(c_6175,plain,
! [X0: $i,X1: $i] :
( ~ happens(X0,n1)
| ~ holdsAt(X1,n2)
| ~ terminates(X0,X1,n1) ),
inference(superposition,[status(thm)],[c_125,c_121]) ).
tcf(c_6288,plain,
( ~ happens(overflow,n1)
| ~ releasedAt(filling,n2) ),
inference(superposition,[status(thm)],[c_115,c_6002]) ).
tcf(c_6325,plain,
! [X0: $i] :
( ~ happens(tapOn,X0)
| ~ happens(overflow,X0) ),
inference(superposition,[status(thm)],[c_115,c_6168]) ).
tcf(c_6333,plain,
( ~ happens(tapOn,n1)
| ~ happens(overflow,n1) ),
inference(instantiation,[status(thm)],[c_6325]) ).
tcf(c_6406,plain,
! [X0: $i] :
( holdsAt(filling,X0)
| releasedAt(filling,plus(X0,n1))
| happens(sK5(filling,X0),X0)
| ~ happens(tapOn,X0) ),
inference(superposition,[status(thm)],[c_5949,c_84]) ).
tcf(c_6408,plain,
! [X0: $i] :
( holdsAt(spilling,X0)
| releasedAt(spilling,plus(X0,n1))
| happens(sK5(spilling,X0),X0)
| ~ happens(overflow,X0) ),
inference(superposition,[status(thm)],[c_5950,c_84]) ).
tcf(c_6413,plain,
! [X0: $i] :
( holdsAt(X0,n1)
| happens(sK5(X0,n1),n1)
| releasedAt(X0,plus(n1,n1))
| ~ holdsAt(X0,n2) ),
inference(superposition,[status(thm)],[c_125,c_84]) ).
tcf(c_6414,plain,
! [X0: $i] :
( releasedAt(X0,n2)
| holdsAt(X0,n1)
| happens(sK5(X0,n1),n1)
| ~ holdsAt(X0,n2) ),
inference(light_normalisation,[status(thm)],[c_6413,c_125]) ).
tcf(c_6474,plain,
! [X0: $i,X1: $i] :
( releasedAt(X0,plus(n1,X1))
| holdsAt(X0,plus(X1,n1))
| happens(sK6(X0,X1),X1)
| ~ holdsAt(X0,X1) ),
inference(superposition,[status(thm)],[c_100,c_86]) ).
tcf(c_6476,plain,
! [X0: $i] :
( releasedAt(X0,n2)
| happens(sK6(X0,n1),n1)
| holdsAt(X0,plus(n1,n1))
| ~ holdsAt(X0,n1) ),
inference(superposition,[status(thm)],[c_125,c_86]) ).
tcf(c_6485,plain,
! [X0: $i] :
( releasedAt(X0,n2)
| holdsAt(X0,n2)
| happens(sK6(X0,n1),n1)
| ~ holdsAt(X0,n1) ),
inference(light_normalisation,[status(thm)],[c_6476,c_125]) ).
tcf(c_6717,plain,
! [X0: $i] :
( less(n2,X0)
| ( X0 = n2 )
| ( X0 = n1 )
| ( X0 = n0 ) ),
inference(superposition,[status(thm)],[c_5300,c_1298]) ).
tcf(c_6763,plain,
! [X0: $i,X1: $i,X2: $i] :
( less(X0,X2)
| ~ less(X1,n3)
| ( X2 != n3 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_3685]) ).
tcf(c_6764,plain,
( less(n1,n1)
| ~ less(n1,n3)
| ( n1 != n1 )
| ( n1 != n3 ) ),
inference(instantiation,[status(thm)],[c_6763]) ).
tcf(c_6779,plain,
! [X0: $i] :
( releasedAt(X0,n3)
| happens(sK4(X0,n2),n2)
| ~ releasedAt(X0,n2) ),
inference(superposition,[status(thm)],[c_95,c_5598]) ).
tcf(c_6824,plain,
! [X0: $i,X1: $i] :
( happens(X0,X1)
| ~ happens(tapOn,n0)
| ( X1 != n0 )
| ( X0 != tapOn ) ),
inference(instantiation,[status(thm)],[c_3690]) ).
tcf(c_6839,plain,
! [X0: $i] :
( releasedAt(X0,n3)
| holdsAt(waterLevel(n3),n2)
| ( n0 = n2 )
| ~ releasedAt(X0,n2) ),
inference(superposition,[status(thm)],[c_6779,c_110]) ).
tcf(c_6842,plain,
! [X0: $i] :
( holdsAt(filling,n2)
| releasedAt(X0,n3)
| ( n0 = n2 )
| ~ releasedAt(X0,n2) ),
inference(superposition,[status(thm)],[c_6779,c_111]) ).
tcf(c_6844,plain,
! [X0: $i] :
( holdsAt(filling,n2)
| releasedAt(X0,n3)
| ~ releasedAt(X0,n2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6842,c_5483]) ).
tcf(c_6848,plain,
! [X0: $i] :
( releasedAt(X0,n3)
| holdsAt(waterLevel(n3),n2)
| ~ releasedAt(X0,n2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6839,c_5483]) ).
tcf(c_6900,plain,
! [X0: $i] :
( releasedAt(X0,n3)
| holdsAt(waterLevel(n3),n2)
| holdsAt(waterLevel(n3),n1)
| ~ releasedAt(X0,n1) ),
inference(superposition,[status(thm)],[c_5698,c_6848]) ).
tcf(c_7281,plain,
! [X0: $i,X1: $i] :
( stoppedIn(n0,filling,n2)
| ( plus(X0,n2) = X1 )
| ~ holdsAt(waterLevel(X1),n2)
| ~ holdsAt(waterLevel(X0),n0) ),
inference(superposition,[status(thm)],[c_5825,c_61]) ).
tcf(c_7453,plain,
! [X0: $i] :
( holdsAt(waterLevel(X0),n2)
| ~ happens(tapOff,n1)
| ~ holdsAt(waterLevel(X0),n1) ),
inference(superposition,[status(thm)],[c_125,c_5952]) ).
tcf(c_7553,plain,
! [X0: $i,X1: $i] :
( ~ happens(X0,n2)
| ~ releasedAt(X1,n3)
| ~ initiates(X0,X1,n2) ),
inference(superposition,[status(thm)],[c_95,c_5977]) ).
tcf(c_7638,plain,
( ~ happens(tapOn,n2)
| ~ releasedAt(filling,n3) ),
inference(superposition,[status(thm)],[c_72,c_7553]) ).
tcf(c_7642,plain,
! [X0: $i] :
( ~ happens(tapOff,n2)
| ~ releasedAt(waterLevel(X0),n3)
| ~ holdsAt(waterLevel(X0),n2) ),
inference(superposition,[status(thm)],[c_5069,c_7553]) ).
tcf(c_7837,plain,
! [X0: $i,X1: $i] :
( happens(sK6(X1,n1),n1)
| holdsAt(X1,plus(n1,n1))
| ~ happens(X0,n1)
| ~ holdsAt(X1,n1)
| ~ terminates(X0,X1,n1) ),
inference(superposition,[status(thm)],[c_86,c_6000]) ).
tcf(c_7842,plain,
! [X0: $i,X1: $i] :
( ~ happens(X0,n2)
| ~ releasedAt(X1,n3)
| ~ terminates(X0,X1,n2) ),
inference(superposition,[status(thm)],[c_95,c_6000]) ).
tcf(c_7863,plain,
! [X0: $i,X1: $i] :
( holdsAt(X1,n2)
| happens(sK6(X1,n1),n1)
| ~ happens(X0,n1)
| ~ holdsAt(X1,n1)
| ~ terminates(X0,X1,n1) ),
inference(light_normalisation,[status(thm)],[c_7837,c_125]) ).
tcf(c_7938,plain,
( ~ happens(tapOff,n2)
| ~ releasedAt(filling,n3) ),
inference(superposition,[status(thm)],[c_114,c_7842]) ).
tcf(c_8062,plain,
! [X0: $i,X1: $i] :
( ~ happens(X0,n2)
| ~ holdsAt(X1,n3)
| ~ terminates(X0,X1,n2) ),
inference(superposition,[status(thm)],[c_95,c_6173]) ).
tcf(c_8066,plain,
! [X0: $i,X1: $i] :
( ~ happens(X0,n0)
| ~ holdsAt(X1,n1)
| ~ terminates(X0,X1,n0) ),
inference(superposition,[status(thm)],[c_763,c_6173]) ).
tcf(c_8130,plain,
( ~ happens(tapOff,n2)
| ~ holdsAt(filling,n3) ),
inference(superposition,[status(thm)],[c_114,c_8062]) ).
tcf(c_8173,plain,
( ~ happens(overflow,n0)
| ~ holdsAt(filling,n1) ),
inference(superposition,[status(thm)],[c_115,c_8066]) ).
tcf(c_8174,plain,
~ happens(overflow,n0),
inference(forward_subsumption_resolution,[status(thm)],[c_8173,c_6062]) ).
tcf(c_8199,plain,
! [X0: $i] :
( releasedAt(X0,n2)
| holdsAt(X0,n1)
| holdsAt(waterLevel(n3),n1)
| ( n0 = n1 )
| ~ holdsAt(X0,n2) ),
inference(superposition,[status(thm)],[c_6414,c_110]) ).
tcf(c_8204,plain,
! [X0: $i] :
( releasedAt(X0,n2)
| holdsAt(X0,n1)
| holdsAt(waterLevel(n3),n1)
| ~ holdsAt(X0,n2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8199,c_1290]) ).
tcf(c_8242,plain,
! [X0: $i] :
( happens(overflow,n1)
| releasedAt(X0,n2)
| holdsAt(X0,n1)
| ~ holdsAt(filling,n1)
| ~ holdsAt(X0,n2) ),
inference(superposition,[status(thm)],[c_8204,c_106]) ).
tcf(c_8247,plain,
! [X0: $i] :
( happens(overflow,n1)
| releasedAt(X0,n2)
| holdsAt(X0,n1)
| ~ holdsAt(X0,n2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8242,c_6062]) ).
tcf(c_8591,plain,
! [X0: $i] :
( releasedAt(X0,n2)
| holdsAt(X0,n2)
| holdsAt(waterLevel(n3),n1)
| ( n0 = n1 )
| ~ holdsAt(X0,n1) ),
inference(superposition,[status(thm)],[c_6485,c_110]) ).
tcf(c_8596,plain,
! [X0: $i] :
( releasedAt(X0,n2)
| holdsAt(X0,n2)
| holdsAt(waterLevel(n3),n1)
| ~ holdsAt(X0,n1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8591,c_1290]) ).
tcf(c_8639,plain,
! [X0: $i] :
( holdsAt(filling,n2)
| releasedAt(X0,n3)
| holdsAt(X0,n2)
| holdsAt(waterLevel(n3),n1)
| ~ holdsAt(X0,n1) ),
inference(superposition,[status(thm)],[c_8596,c_6844]) ).
tcf(c_8644,plain,
! [X0: $i] :
( happens(overflow,n1)
| releasedAt(X0,n2)
| holdsAt(X0,n2)
| ~ holdsAt(filling,n1)
| ~ holdsAt(X0,n1) ),
inference(superposition,[status(thm)],[c_8596,c_106]) ).
tcf(c_8649,plain,
! [X0: $i] :
( happens(overflow,n1)
| releasedAt(X0,n2)
| holdsAt(X0,n2)
| ~ holdsAt(X0,n1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8644,c_6062]) ).
tcf(c_8719,plain,
! [X0: $i] :
( happens(tapOn,X0)
| ~ happens(tapOn,n0)
| ( tapOn != tapOn )
| ( X0 != n0 ) ),
inference(instantiation,[status(thm)],[c_6824]) ).
tcf(c_8762,plain,
( happens(overflow,n1)
| releasedAt(filling,n2)
| holdsAt(filling,n2) ),
inference(superposition,[status(thm)],[c_6062,c_8649]) ).
tcf(c_8807,plain,
! [X0: $i,X1: $i] :
( ( X0 = n3 )
| ~ holdsAt(waterLevel(n3),X1)
| ~ holdsAt(waterLevel(X0),X1) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_8808,plain,
( ( n1 = n3 )
| ~ holdsAt(waterLevel(n1),n1)
| ~ holdsAt(waterLevel(n3),n1) ),
inference(instantiation,[status(thm)],[c_8807]) ).
tcf(c_8825,plain,
( happens(overflow,n1)
| releasedAt(filling,n3)
| holdsAt(filling,n2) ),
inference(superposition,[status(thm)],[c_8762,c_6844]) ).
tcf(c_8980,plain,
! [X0: $i] :
( ( X0 = n2 )
| ( X0 = n1 )
| ( X0 = n0 )
| ~ less(X0,n2) ),
inference(superposition,[status(thm)],[c_6717,c_98]) ).
tcf(c_9219,plain,
( less(n2,n2)
| ( n2 = n2 )
| ~ less(n2,n3) ),
inference(instantiation,[status(thm)],[c_1251]) ).
tcf(c_9545,plain,
! [X0: $i] :
( stoppedIn(n0,filling,n1)
| holdsAt(waterLevel(plus(X0,n1)),plus(n0,n1))
| ~ happens(tapOn,n0)
| ~ less(n0,n1)
| ~ holdsAt(waterLevel(X0),n0) ),
inference(superposition,[status(thm)],[c_763,c_5801]) ).
tcf(c_9602,plain,
! [X0: $i] :
( stoppedIn(n0,filling,n1)
| holdsAt(waterLevel(plus(X0,n1)),plus(n0,n1))
| ~ holdsAt(waterLevel(X0),n0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9545,c_105,c_1308]) ).
tcf(c_10251,plain,
! [X0: $i] :
( stoppedIn(n1,filling,plus(n1,n1))
| holdsAt(waterLevel(plus(n1,X0)),n2)
| ~ happens(tapOn,n1)
| ~ less(n0,n1)
| ~ holdsAt(waterLevel(X0),n1) ),
inference(superposition,[status(thm)],[c_125,c_5809]) ).
tcf(c_10264,plain,
! [X0: $i] :
( stoppedIn(n1,filling,n2)
| holdsAt(waterLevel(plus(n1,X0)),n2)
| ~ happens(tapOn,n1)
| ~ less(n0,n1)
| ~ holdsAt(waterLevel(X0),n1) ),
inference(light_normalisation,[status(thm)],[c_10251,c_125]) ).
tcf(c_10265,plain,
! [X0: $i] :
( stoppedIn(n1,filling,n2)
| holdsAt(waterLevel(plus(n1,X0)),n2)
| ~ happens(tapOn,n1)
| ~ holdsAt(waterLevel(X0),n1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10264,c_1308]) ).
tcf(c_10346,plain,
( sP1(sK8(n0,filling,n3),tapOff,waterLevel(n3))
| ~ holdsAt(waterLevel(n3),sK8(n0,filling,n3)) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_10349,plain,
! [X0: $i,X1: $i] :
( holdsAt(X0,X1)
| ~ holdsAt(waterLevel(n3),sK8(n0,filling,n3))
| ( X1 != sK8(n0,filling,n3) )
| ( X0 != waterLevel(n3) ) ),
inference(instantiation,[status(thm)],[c_3682]) ).
tcf(c_10926,plain,
! [X0: $i] :
( ~ less(X0,n2)
| ( X0 = n0 )
| ( X0 = n1 ) ),
inference(global_subsumption_just,[status(thm)],[c_8980,c_56,c_1296,c_1313]) ).
tcf(c_10927,plain,
! [X0: $i] :
( ( X0 = n1 )
| ( X0 = n0 )
| ~ less(X0,n2) ),
inference(renaming,[status(thm)],[c_10926]) ).
tcf(c_10934,plain,
! [X0: $i,X1: $i] :
( ( sK8(X0,X1,n2) = n1 )
| ( sK8(X0,X1,n2) = n0 )
| ~ stoppedIn(X0,X1,n2) ),
inference(superposition,[status(thm)],[c_91,c_10927]) ).
tcf(c_12103,plain,
! [X0: $i] :
( holdsAt(filling,X0)
| ~ happens(tapOn,X0)
| happens(sK5(filling,X0),X0) ),
inference(global_subsumption_just,[status(thm)],[c_6406,c_2034,c_6406]) ).
tcf(c_12104,plain,
! [X0: $i] :
( holdsAt(filling,X0)
| happens(sK5(filling,X0),X0)
| ~ happens(tapOn,X0) ),
inference(renaming,[status(thm)],[c_12103]) ).
tcf(c_12115,plain,
! [X0: $i] :
( holdsAt(filling,X0)
| ( X0 = n0 )
| ~ happens(tapOn,X0) ),
inference(superposition,[status(thm)],[c_12104,c_111]) ).
tcf(c_12325,plain,
! [X0: $i] :
( holdsAt(spilling,X0)
| ~ happens(overflow,X0)
| happens(sK5(spilling,X0),X0) ),
inference(global_subsumption_just,[status(thm)],[c_6408,c_2078,c_6408]) ).
tcf(c_12326,plain,
! [X0: $i] :
( holdsAt(spilling,X0)
| happens(sK5(spilling,X0),X0)
| ~ happens(overflow,X0) ),
inference(renaming,[status(thm)],[c_12325]) ).
tcf(c_12334,plain,
! [X0: $i] :
( holdsAt(spilling,X0)
| holdsAt(waterLevel(n3),X0)
| ( X0 = n0 )
| ~ happens(overflow,X0) ),
inference(superposition,[status(thm)],[c_12326,c_110]) ).
tcf(c_12397,plain,
! [X0: $i] :
( holdsAt(spilling,X0)
| holdsAt(waterLevel(n3),X0)
| ~ happens(overflow,X0) ),
inference(global_subsumption_just,[status(thm)],[c_12334,c_105,c_50,c_5906,c_6325,c_8719,c_12334]) ).
tcf(c_12406,plain,
! [X0: $i] :
( holdsAt(spilling,X0)
| ( waterLevel(sK2(X0,tapOff,waterLevel(n3))) = waterLevel(n3) )
| ~ happens(overflow,X0) ),
inference(superposition,[status(thm)],[c_12397,c_5455]) ).
tcf(c_13143,plain,
( happens(tapOn,sK8(n0,filling,n3))
| ~ happens(tapOn,n0)
| ( tapOn != tapOn )
| ( sK8(n0,filling,n3) != n0 ) ),
inference(instantiation,[status(thm)],[c_8719]) ).
tcf(c_14803,plain,
( holdsAt(filling,n2)
| holdsAt(waterLevel(n3),n1)
| ~ happens(tapOff,n2)
| ~ holdsAt(filling,n1) ),
inference(superposition,[status(thm)],[c_8639,c_7938]) ).
tcf(c_14829,plain,
( holdsAt(filling,n2)
| holdsAt(waterLevel(n3),n1)
| ~ happens(tapOff,n2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14803,c_6062]) ).
tcf(c_14992,plain,
( holdsAt(filling,n2)
| holdsAt(waterLevel(n3),n2)
| ~ happens(tapOff,n2)
| ~ happens(tapOff,n1) ),
inference(superposition,[status(thm)],[c_14829,c_7453]) ).
tcf(c_15639,plain,
! [X0: $i] :
( stoppedIn(n0,filling,n1)
| holdsAt(waterLevel(plus(X0,n1)),n1)
| ~ holdsAt(waterLevel(X0),n0) ),
inference(demodulation,[status(thm)],[c_9602,c_100,c_763]) ).
tcf(c_15649,plain,
! [X0: $i] :
( stoppedIn(n0,filling,n1)
| holdsAt(waterLevel(plus(n1,X0)),n1)
| ~ holdsAt(waterLevel(X0),n0) ),
inference(superposition,[status(thm)],[c_100,c_15639]) ).
tcf(c_15766,plain,
( stoppedIn(n0,filling,n1)
| holdsAt(waterLevel(n1),n1)
| ~ holdsAt(waterLevel(n0),n0) ),
inference(superposition,[status(thm)],[c_763,c_15649]) ).
tcf(c_15782,plain,
( stoppedIn(n0,filling,n1)
| holdsAt(waterLevel(n1),n1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15766,c_49]) ).
tcf(c_15974,plain,
( holdsAt(waterLevel(n1),n1)
| ( sK8(n0,filling,n1) = n0 ) ),
inference(superposition,[status(thm)],[c_15782,c_5216]) ).
tcf(c_15986,plain,
! [X0: $i] :
( ( X0 = n1 )
| ( sK8(n0,filling,n1) = n0 )
| ~ holdsAt(waterLevel(X0),n1) ),
inference(superposition,[status(thm)],[c_15974,c_61]) ).
tcf(c_16194,plain,
! [X0: $i,X1: $i] :
( ( X1 = sK8(n0,filling,n3) )
| ( X1 != X0 )
| ( sK8(n0,filling,n3) != X0 ) ),
inference(instantiation,[status(thm)],[c_3680]) ).
tcf(c_16195,plain,
( ( n1 = sK8(n0,filling,n3) )
| ( n1 != n1 )
| ( sK8(n0,filling,n3) != n1 ) ),
inference(instantiation,[status(thm)],[c_16194]) ).
tcf(c_18447,plain,
! [X0: $i] :
( happens(sK4(filling,X0),X0)
| ~ happens(tapOn,X0)
| ~ releasedAt(filling,X0) ),
inference(superposition,[status(thm)],[c_72,c_5976]) ).
tcf(c_18476,plain,
! [X0: $i] :
( holdsAt(waterLevel(n3),X0)
| ( X0 = n0 )
| ~ happens(tapOn,X0)
| ~ releasedAt(filling,X0) ),
inference(superposition,[status(thm)],[c_18447,c_110]) ).
tcf(c_18641,plain,
! [X0: $i] :
( ~ releasedAt(filling,X0)
| ~ happens(tapOn,X0)
| ( X0 = n0 ) ),
inference(global_subsumption_just,[status(thm)],[c_18476,c_106,c_6325,c_12115,c_18476]) ).
tcf(c_18642,plain,
! [X0: $i] :
( ( X0 = n0 )
| ~ happens(tapOn,X0)
| ~ releasedAt(filling,X0) ),
inference(renaming,[status(thm)],[c_18641]) ).
tcf(c_18661,plain,
( holdsAt(filling,n2)
| holdsAt(waterLevel(n3),n1)
| ( n0 = n2 )
| ~ happens(tapOn,n2)
| ~ holdsAt(filling,n1) ),
inference(superposition,[status(thm)],[c_8596,c_18642]) ).
tcf(c_18696,plain,
( holdsAt(filling,n2)
| holdsAt(waterLevel(n3),n1)
| ~ happens(tapOn,n2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18661,c_5483,c_6062]) ).
tcf(c_18815,plain,
( holdsAt(filling,n2)
| holdsAt(waterLevel(n3),n2)
| ~ happens(tapOn,n2)
| ~ happens(tapOff,n1) ),
inference(superposition,[status(thm)],[c_18696,c_7453]) ).
tcf(c_19585,plain,
( ( waterLevel(sK2(sK8(n0,filling,n3),tapOff,waterLevel(n3))) = waterLevel(n3) )
| ~ sP1(sK8(n0,filling,n3),tapOff,waterLevel(n3)) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_19807,plain,
( holdsAt(waterLevel(n3),sK8(n0,filling,n3))
| ( overflow = tapOn )
| ~ happens(overflow,sK8(n0,filling,n3)) ),
inference(instantiation,[status(thm)],[c_107]) ).
tcf(c_20251,plain,
! [X0: $i] :
( happens(sK4(filling,X0),X0)
| ~ happens(overflow,X0)
| ~ releasedAt(filling,X0) ),
inference(superposition,[status(thm)],[c_115,c_5999]) ).
tcf(c_20347,plain,
! [X0: $i] :
( holdsAt(waterLevel(n3),X0)
| ( X0 = n0 )
| ~ happens(overflow,X0)
| ~ releasedAt(filling,X0) ),
inference(superposition,[status(thm)],[c_20251,c_110]) ).
tcf(c_20587,plain,
~ less(n0,n0),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_20765,plain,
! [X0: $i] :
( holdsAt(waterLevel(n3),X0)
| ~ releasedAt(filling,X0)
| ~ happens(overflow,X0) ),
inference(global_subsumption_just,[status(thm)],[c_20347,c_105,c_50,c_5906,c_6325,c_8719,c_20347]) ).
tcf(c_20766,plain,
! [X0: $i] :
( holdsAt(waterLevel(n3),X0)
| ~ happens(overflow,X0)
| ~ releasedAt(filling,X0) ),
inference(renaming,[status(thm)],[c_20765]) ).
tcf(c_20802,plain,
( happens(overflow,n1)
| releasedAt(waterLevel(n3),n2)
| holdsAt(waterLevel(n3),n1)
| ~ happens(overflow,n2)
| ~ releasedAt(filling,n2) ),
inference(superposition,[status(thm)],[c_20766,c_8247]) ).
tcf(c_22567,plain,
! [X0: $i] :
( holdsAt(waterLevel(n3),X0)
| ~ holdsAt(waterLevel(n3),sK8(n0,filling,n3))
| ( X0 != sK8(n0,filling,n3) )
| ( waterLevel(n3) != waterLevel(n3) ) ),
inference(instantiation,[status(thm)],[c_10349]) ).
tcf(c_22568,plain,
waterLevel(n3) = waterLevel(n3),
inference(instantiation,[status(thm)],[c_3678]) ).
tcf(c_22569,plain,
( holdsAt(waterLevel(n3),n1)
| ~ holdsAt(waterLevel(n3),sK8(n0,filling,n3))
| ( n1 != sK8(n0,filling,n3) )
| ( waterLevel(n3) != waterLevel(n3) ) ),
inference(instantiation,[status(thm)],[c_22567]) ).
tcf(c_26903,plain,
( ( sK8(n0,filling,n3) = n0 )
| ~ less(sK8(n0,filling,n3),n1) ),
inference(instantiation,[status(thm)],[c_1298]) ).
tcf(c_27331,plain,
( less(sK8(n0,filling,n3),n1)
| ( sK8(n0,filling,n3) = n1 )
| ~ less(sK8(n0,filling,n3),n2) ),
inference(instantiation,[status(thm)],[c_1313]) ).
tcf(c_28048,plain,
( ( sK7(n0,filling,n3) = tapOn )
| ( sK7(n0,filling,n3) = overflow ) ),
inference(superposition,[status(thm)],[c_55,c_5915]) ).
tcf(c_28176,plain,
( terminates(tapOn,filling,sK8(n0,filling,n3))
| ( sK7(n0,filling,n3) = overflow )
| ~ stoppedIn(n0,filling,n3) ),
inference(superposition,[status(thm)],[c_28048,c_92]) ).
tcf(c_28182,plain,
( terminates(tapOn,filling,sK8(n0,filling,n3))
| ( sK7(n0,filling,n3) = overflow ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28176,c_55]) ).
tcf(c_28205,plain,
( ( overflow = tapOn )
| ( tapOff = tapOn )
| ( sK7(n0,filling,n3) = overflow ) ),
inference(superposition,[status(thm)],[c_28182,c_116]) ).
tcf(c_28210,plain,
sK7(n0,filling,n3) = overflow,
inference(forward_subsumption_resolution,[status(thm)],[c_28205,c_103,c_104]) ).
tcf(c_28222,plain,
( happens(overflow,sK8(n0,filling,n3))
| ~ stoppedIn(n0,filling,n3) ),
inference(superposition,[status(thm)],[c_28210,c_89]) ).
tcf(c_28223,plain,
happens(overflow,sK8(n0,filling,n3)),
inference(forward_subsumption_resolution,[status(thm)],[c_28222,c_55]) ).
tcf(c_28232,plain,
( holdsAt(spilling,sK8(n0,filling,n3))
| ( waterLevel(sK2(sK8(n0,filling,n3),tapOff,waterLevel(n3))) = waterLevel(n3) ) ),
inference(superposition,[status(thm)],[c_28223,c_12406]) ).
tcf(c_28236,plain,
~ happens(tapOn,sK8(n0,filling,n3)),
inference(superposition,[status(thm)],[c_28223,c_6325]) ).
tcf(c_28249,plain,
waterLevel(sK2(sK8(n0,filling,n3),tapOff,waterLevel(n3))) = waterLevel(n3),
inference(global_subsumption_just,[status(thm)],[c_28232,c_103,c_10346,c_19585,c_19807,c_28223]) ).
tcf(c_28269,plain,
( ( sK8(n0,filling,n1) = n0 )
| ( sK2(sK8(n0,filling,n3),tapOff,waterLevel(n3)) = n1 )
| ~ holdsAt(waterLevel(n3),n1) ),
inference(superposition,[status(thm)],[c_28249,c_15986]) ).
tcf(c_31046,plain,
( ( sK8(n0,filling,n1) = n0 )
| ~ holdsAt(waterLevel(n3),n1) ),
inference(global_subsumption_just,[status(thm)],[c_28269,c_130,c_133,c_140,c_150,c_1264,c_6764,c_8808,c_15974]) ).
tcf(c_31064,plain,
! [X0: $i] :
( releasedAt(X0,n2)
| holdsAt(X0,n1)
| ( sK8(n0,filling,n1) = n0 )
| ~ holdsAt(X0,n2) ),
inference(superposition,[status(thm)],[c_8204,c_31046]) ).
tcf(c_31144,plain,
! [X0: $i] :
( releasedAt(X0,n3)
| happens(sK6(X0,n2),n2)
| holdsAt(X0,plus(n2,n1))
| ~ holdsAt(X0,n2) ),
inference(superposition,[status(thm)],[c_95,c_6474]) ).
tcf(c_31332,plain,
! [X0: $i] :
( releasedAt(X0,n3)
| holdsAt(X0,n3)
| happens(sK6(X0,n2),n2)
| ~ holdsAt(X0,n2) ),
inference(demodulation,[status(thm)],[c_31144,c_95,c_100]) ).
tcf(c_31346,plain,
! [X0: $i] :
( releasedAt(X0,n3)
| holdsAt(X0,n3)
| holdsAt(waterLevel(n3),n2)
| ( n0 = n2 )
| ~ holdsAt(X0,n2) ),
inference(superposition,[status(thm)],[c_31332,c_110]) ).
tcf(c_31356,plain,
! [X0: $i] :
( releasedAt(X0,n3)
| holdsAt(X0,n3)
| holdsAt(waterLevel(n3),n2)
| ~ holdsAt(X0,n2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31346,c_5483]) ).
tcf(c_31498,plain,
( holdsAt(filling,n3)
| holdsAt(waterLevel(n3),n2)
| ~ happens(tapOff,n2)
| ~ holdsAt(filling,n2) ),
inference(superposition,[status(thm)],[c_31356,c_7938]) ).
tcf(c_33642,plain,
! [X0: $i] :
( happens(overflow,n1)
| stoppedIn(n1,filling,n2)
| releasedAt(waterLevel(plus(n1,X0)),n2)
| holdsAt(waterLevel(plus(n1,X0)),n1)
| ~ happens(tapOn,n1)
| ~ holdsAt(waterLevel(X0),n1) ),
inference(superposition,[status(thm)],[c_10265,c_8247]) ).
tcf(c_34225,plain,
( releasedAt(waterLevel(n3),n2)
| holdsAt(waterLevel(n3),n1)
| ( sK8(n0,filling,n1) = n0 )
| ~ happens(overflow,n2)
| ~ releasedAt(filling,n2) ),
inference(superposition,[status(thm)],[c_20766,c_31064]) ).
tcf(c_34251,plain,
! [X0: $i] :
( stoppedIn(n1,filling,n2)
| releasedAt(waterLevel(plus(n1,X0)),n2)
| holdsAt(waterLevel(plus(n1,X0)),n1)
| ( sK8(n0,filling,n1) = n0 )
| ~ happens(tapOn,n1)
| ~ holdsAt(waterLevel(X0),n1) ),
inference(superposition,[status(thm)],[c_10265,c_31064]) ).
tcf(c_41481,plain,
! [X0: $i] :
( stoppedIn(n0,filling,n2)
| ( plus(n0,n2) = X0 )
| ~ holdsAt(waterLevel(X0),n2) ),
inference(superposition,[status(thm)],[c_49,c_7281]) ).
tcf(c_41490,plain,
! [X0: $i] :
( stoppedIn(n0,filling,n2)
| ( X0 = n2 )
| ~ holdsAt(waterLevel(X0),n2) ),
inference(light_normalisation,[status(thm)],[c_41481,c_126]) ).
tcf(c_48575,plain,
( less(sK8(n0,filling,n3),n2)
| ( sK8(n0,filling,n3) = n2 )
| ~ less(sK8(n0,filling,n3),n3) ),
inference(instantiation,[status(thm)],[c_1251]) ).
tcf(c_51770,plain,
( holdsAt(waterLevel(n3),n2)
| ~ holdsAt(waterLevel(n3),sK8(n0,filling,n3))
| ( n2 != sK8(n0,filling,n3) )
| ( waterLevel(n3) != waterLevel(n3) ) ),
inference(instantiation,[status(thm)],[c_22567]) ).
tcf(c_55405,plain,
! [X0: $i,X1: $i] :
( initiates(tapOff,waterLevel(X0),X1)
| ~ holdsAt(waterLevel(X0),X1) ),
inference(superposition,[status(thm)],[c_64,c_74]) ).
tcf(c_55901,plain,
! [X0: $i,X1: $i] :
( releasedAt(X0,plus(n1,X1))
| happens(sK4(X0,X1),X1)
| ~ releasedAt(X0,X1) ),
inference(superposition,[status(thm)],[c_100,c_82]) ).
tcf(c_55903,plain,
! [X0: $i] :
( releasedAt(X0,n2)
| happens(sK4(X0,n1),n1)
| ~ releasedAt(X0,n1) ),
inference(superposition,[status(thm)],[c_125,c_82]) ).
tcf(c_56013,plain,
n0 != n2,
inference(global_subsumption_just,[status(thm)],[c_1204,c_130,c_133,c_140,c_1205,c_1264]) ).
tcf(c_56051,plain,
! [X0: $i] :
( holdsAt(filling,plus(X0,n1))
| ~ happens(tapOn,X0) ),
inference(superposition,[status(thm)],[c_72,c_120]) ).
tcf(c_56072,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ happens(X2,X1)
| ~ initiates(X2,X0,X1)
| ~ releasedAt(X0,plus(n1,X1)) ),
inference(superposition,[status(thm)],[c_100,c_80]) ).
tcf(c_56153,plain,
! [X0: $i] :
( holdsAt(filling,plus(n1,X0))
| ~ happens(tapOn,X0) ),
inference(superposition,[status(thm)],[c_100,c_56051]) ).
tcf(c_56192,plain,
( holdsAt(filling,n1)
| ~ happens(tapOn,n0) ),
inference(superposition,[status(thm)],[c_763,c_56153]) ).
tcf(c_56193,plain,
holdsAt(filling,n1),
inference(forward_subsumption_resolution,[status(thm)],[c_56192,c_105]) ).
tcf(c_56307,plain,
! [X0: $i] :
( holdsAt(X0,n1)
| happens(sK5(X0,n1),n1)
| releasedAt(X0,plus(n1,n1))
| ~ holdsAt(X0,n2) ),
inference(superposition,[status(thm)],[c_125,c_84]) ).
tcf(c_56308,plain,
! [X0: $i] :
( releasedAt(X0,n2)
| holdsAt(X0,n1)
| happens(sK5(X0,n1),n1)
| ~ holdsAt(X0,n2) ),
inference(light_normalisation,[status(thm)],[c_56307,c_125]) ).
tcf(c_56458,plain,
! [X0: $i] :
( releasedAt(X0,n2)
| holdsAt(waterLevel(n3),n1)
| ( n0 = n1 )
| ~ releasedAt(X0,n1) ),
inference(superposition,[status(thm)],[c_55903,c_110]) ).
tcf(c_56463,plain,
! [X0: $i] :
( releasedAt(X0,n2)
| holdsAt(waterLevel(n3),n1)
| ~ releasedAt(X0,n1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_56458,c_1290]) ).
tcf(c_57164,plain,
! [X0: $i] :
( releasedAt(X0,n3)
| happens(sK4(X0,n2),n2)
| ~ releasedAt(X0,n2) ),
inference(superposition,[status(thm)],[c_95,c_55901]) ).
tcf(c_57218,plain,
! [X0: $i] :
( releasedAt(X0,n3)
| holdsAt(waterLevel(n3),n2)
| ( n0 = n2 )
| ~ releasedAt(X0,n2) ),
inference(superposition,[status(thm)],[c_57164,c_110]) ).
tcf(c_57227,plain,
! [X0: $i] :
( releasedAt(X0,n3)
| holdsAt(waterLevel(n3),n2)
| ~ releasedAt(X0,n2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_57218,c_56013]) ).
tcf(c_57264,plain,
! [X0: $i] :
( releasedAt(X0,n3)
| holdsAt(waterLevel(n3),n2)
| holdsAt(waterLevel(n3),n1)
| ~ releasedAt(X0,n1) ),
inference(superposition,[status(thm)],[c_56463,c_57227]) ).
tcf(c_57823,plain,
! [X0: $i,X1: $i] :
( ~ happens(X0,n2)
| ~ releasedAt(X1,n3)
| ~ initiates(X0,X1,n2) ),
inference(superposition,[status(thm)],[c_95,c_56072]) ).
tcf(c_57925,plain,
! [X0: $i] :
( ~ happens(tapOff,n2)
| ~ releasedAt(waterLevel(X0),n3)
| ~ holdsAt(waterLevel(X0),n2) ),
inference(superposition,[status(thm)],[c_55405,c_57823]) ).
tcf(c_58403,plain,
! [X0: $i] :
( releasedAt(X0,n2)
| holdsAt(X0,n1)
| ( n0 = n1 )
| ( sK5(X0,n1) = overflow )
| ~ holdsAt(X0,n2) ),
inference(superposition,[status(thm)],[c_56308,c_112]) ).
tcf(c_58404,plain,
! [X0: $i] :
( releasedAt(X0,n2)
| holdsAt(X0,n1)
| holdsAt(waterLevel(n3),n1)
| ( n0 = n1 )
| ~ holdsAt(X0,n2) ),
inference(superposition,[status(thm)],[c_56308,c_110]) ).
tcf(c_58409,plain,
! [X0: $i] :
( releasedAt(X0,n2)
| holdsAt(X0,n1)
| holdsAt(waterLevel(n3),n1)
| ~ holdsAt(X0,n2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_58404,c_1290]) ).
tcf(c_58419,plain,
! [X0: $i] :
( releasedAt(X0,n2)
| holdsAt(X0,n1)
| ( sK5(X0,n1) = overflow )
| ~ holdsAt(X0,n2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_58403,c_1290]) ).
tcf(c_58444,plain,
! [X0: $i] :
( happens(overflow,n1)
| releasedAt(X0,n2)
| holdsAt(X0,n1)
| ~ holdsAt(filling,n1)
| ~ holdsAt(X0,n2) ),
inference(superposition,[status(thm)],[c_58409,c_106]) ).
tcf(c_58454,plain,
! [X0: $i] :
( happens(overflow,n1)
| releasedAt(X0,n2)
| holdsAt(X0,n1)
| ~ holdsAt(X0,n2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_58444,c_56193]) ).
tcf(c_66048,plain,
( releasedAt(waterLevel(n3),n2)
| ~ happens(overflow,n2)
| ~ releasedAt(filling,n2) ),
inference(global_subsumption_just,[status(thm)],[c_34225,c_162,c_6062,c_6288,c_20802]) ).
tcf(c_73616,plain,
! [X0: $i] :
( ( X0 = sK8(n0,filling,n3) )
| ( X0 != n2 )
| ( sK8(n0,filling,n3) != n2 ) ),
inference(instantiation,[status(thm)],[c_16194]) ).
tcf(c_81064,plain,
! [X0: $i,X1: $i] :
( ~ terminates(X0,X1,n1)
| ~ holdsAt(X1,n1)
| ~ happens(X0,n1)
| happens(sK6(X1,n1),n1) ),
inference(global_subsumption_just,[status(thm)],[c_7863,c_6175,c_7863]) ).
tcf(c_81065,plain,
! [X0: $i,X1: $i] :
( happens(sK6(X1,n1),n1)
| ~ happens(X0,n1)
| ~ holdsAt(X1,n1)
| ~ terminates(X0,X1,n1) ),
inference(renaming,[status(thm)],[c_81064]) ).
tcf(c_81078,plain,
( happens(sK6(filling,n1),n1)
| ~ happens(overflow,n1)
| ~ holdsAt(filling,n1) ),
inference(superposition,[status(thm)],[c_115,c_81065]) ).
tcf(c_81079,plain,
( happens(sK6(filling,n1),n1)
| ~ happens(overflow,n1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_81078,c_6062]) ).
tcf(c_81098,plain,
( holdsAt(waterLevel(n3),n1)
| ( n0 = n1 )
| ~ happens(overflow,n1) ),
inference(superposition,[status(thm)],[c_81079,c_110]) ).
tcf(c_81103,plain,
( holdsAt(waterLevel(n3),n1)
| ~ happens(overflow,n1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_81098,c_1290]) ).
tcf(c_108864,plain,
( ( n2 = sK8(n0,filling,n3) )
| ( n2 != n2 )
| ( sK8(n0,filling,n3) != n2 ) ),
inference(instantiation,[status(thm)],[c_73616]) ).
tcf(c_112414,plain,
! [X0: $i] :
( stoppedIn(n1,filling,n2)
| releasedAt(waterLevel(plus(n1,X0)),n2)
| holdsAt(waterLevel(plus(n1,X0)),n1)
| ~ holdsAt(waterLevel(X0),n1)
| ~ happens(tapOn,n1) ),
inference(global_subsumption_just,[status(thm)],[c_34251,c_6333,c_33642]) ).
tcf(c_112415,plain,
! [X0: $i] :
( stoppedIn(n1,filling,n2)
| releasedAt(waterLevel(plus(n1,X0)),n2)
| holdsAt(waterLevel(plus(n1,X0)),n1)
| ~ happens(tapOn,n1)
| ~ holdsAt(waterLevel(X0),n1) ),
inference(renaming,[status(thm)],[c_112414]) ).
tcf(c_112430,plain,
( stoppedIn(n1,filling,n2)
| releasedAt(waterLevel(n1),n2)
| holdsAt(waterLevel(plus(n1,n0)),n1)
| ~ happens(tapOn,n1)
| ~ holdsAt(waterLevel(n0),n1) ),
inference(superposition,[status(thm)],[c_763,c_112415]) ).
tcf(c_112433,plain,
( stoppedIn(n1,filling,n2)
| releasedAt(waterLevel(n1),n2)
| holdsAt(waterLevel(n1),n1)
| ~ happens(tapOn,n1)
| ~ holdsAt(waterLevel(n0),n1) ),
inference(light_normalisation,[status(thm)],[c_112430,c_763]) ).
tcf(c_120315,plain,
! [X0: $i,X1: $i] :
( ( n0 = X0 )
| ( n0 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_3680]) ).
tcf(c_120564,plain,
! [X0: $i,X1: $i,X2: $i] :
( less(X0,X1)
| ~ less(n0,X2)
| ( X1 != X2 )
| ( X0 != n0 ) ),
inference(instantiation,[status(thm)],[c_3685]) ).
tcf(c_120934,plain,
! [X0: $i] :
( ( n0 = X0 )
| ( n0 != n0 )
| ( X0 != n0 ) ),
inference(instantiation,[status(thm)],[c_120315]) ).
tcf(c_121537,plain,
! [X0: $i] :
( less(n0,sK8(n0,filling,X0))
| ~ stoppedIn(n0,filling,X0) ),
inference(instantiation,[status(thm)],[c_90]) ).
tcf(c_121538,plain,
( less(n0,sK8(n0,filling,n1))
| ~ stoppedIn(n0,filling,n1) ),
inference(instantiation,[status(thm)],[c_121537]) ).
tcf(c_121657,plain,
! [X0: $i,X1: $i] :
( less(n0,X0)
| ~ less(n0,X1)
| ( n0 != n0 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_120564]) ).
tcf(c_123879,plain,
! [X0: $i] :
( ( tapOff = tapOn )
| ( tapOff = overflow )
| ~ happens(tapOff,X0) ),
inference(instantiation,[status(thm)],[c_109]) ).
tcf(c_124491,plain,
! [X0: $i] :
( less(n0,n0)
| ~ less(n0,X0)
| ( n0 != n0 )
| ( n0 != X0 ) ),
inference(instantiation,[status(thm)],[c_121657]) ).
tcf(c_137103,plain,
( ( n0 = sK8(n0,filling,n1) )
| ( n0 != n0 )
| ( sK8(n0,filling,n1) != n0 ) ),
inference(instantiation,[status(thm)],[c_120934]) ).
tcf(c_142008,plain,
( less(n0,n0)
| ~ less(n0,sK8(n0,filling,n1))
| ( n0 != n0 )
| ( n0 != sK8(n0,filling,n1) ) ),
inference(instantiation,[status(thm)],[c_124491]) ).
tcf(c_143065,plain,
holdsAt(waterLevel(n1),n1),
inference(global_subsumption_just,[status(thm)],[c_112433,c_1308,c_5900,c_15782,c_15974,c_20587,c_121538,c_137103,c_142008]) ).
fof(f80,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(f81,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(f82,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,[],[f58,f81,f80]) ).
fof(f87,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,[],[f80]) ).
fof(f88,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,[],[f87]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ( ~ sP0(X0,X1,X2)
| ( waterLevel(sK3(X0,X1,X2)) = X2
& overflow = X1
& holdsAt(waterLevel(sK3(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,[sK3]),skolemize(X4,sK3(X0,X1,X2))],[f88]) ).
fof(f127,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| waterLevel(sK3(X0,X1,X2)) = X2 ),
inference(cnf_transformation,[],[f89]) ).
fof(f129,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| holdsAt(waterLevel(sK3(X0,X1,X2)),X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f130,plain,
! [X2,X3,X0,X1] :
( waterLevel(X3) != X2
| overflow != X1
| ~ holdsAt(waterLevel(X3),X0)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f89]) ).
fof(f192,plain,
! [X2,X3,X0] :
( waterLevel(X3) != X2
| ~ holdsAt(waterLevel(X3),X0)
| sP0(X0,overflow,X2) ),
inference(equality_resolution,[],[f130]) ).
fof(f193,plain,
! [X3,X0] :
( ~ holdsAt(waterLevel(X3),X0)
| sP0(X0,overflow,waterLevel(X3)) ),
inference(equality_resolution,[],[f192]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( sP0(X1,overflow,waterLevel(X0))
| ~ holdsAt(waterLevel(X0),X1) ),
inference(cnf_transformation,[],[f193]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( holdsAt(waterLevel(sK3(X0,X1,X2)),X0)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( waterLevel(sK3(X0,X1,X2)) = X2 )
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_5077,plain,
! [X0: $i,X1: $i] :
( initiates(overflow,waterLevel(X0),X1)
| ~ holdsAt(waterLevel(X0),X1) ),
inference(superposition,[status(thm)],[c_68,c_75]) ).
tcf(c_5561,plain,
! [X0: $i,X1: $i] :
( ( waterLevel(sK3(X1,overflow,waterLevel(X0))) = waterLevel(X0) )
| ~ holdsAt(waterLevel(X0),X1) ),
inference(superposition,[status(thm)],[c_68,c_71]) ).
tcf(c_5951,plain,
! [X0: $i,X1: $i] :
( holdsAt(waterLevel(X0),plus(X1,n1))
| ~ happens(overflow,X1)
| ~ holdsAt(waterLevel(X0),X1) ),
inference(superposition,[status(thm)],[c_5077,c_120]) ).
tcf(c_6254,plain,
! [X0: $i] :
( ~ happens(overflow,n1)
| ~ releasedAt(waterLevel(X0),n2)
| ~ holdsAt(waterLevel(X0),n1) ),
inference(superposition,[status(thm)],[c_5077,c_5979]) ).
tcf(c_7365,plain,
! [X0: $i] :
( holdsAt(waterLevel(X0),n2)
| ~ happens(overflow,n1)
| ~ holdsAt(waterLevel(X0),n1) ),
inference(superposition,[status(thm)],[c_125,c_5951]) ).
tcf(c_7396,plain,
( holdsAt(waterLevel(n1),n2)
| ~ happens(overflow,n1)
| ~ holdsAt(waterLevel(n1),n1) ),
inference(instantiation,[status(thm)],[c_7365]) ).
tcf(c_7424,plain,
! [X0: $i] :
( releasedAt(X0,n2)
| holdsAt(waterLevel(n3),n2)
| ~ happens(overflow,n1)
| ~ releasedAt(X0,n1) ),
inference(superposition,[status(thm)],[c_5698,c_7365]) ).
tcf(c_7641,plain,
! [X0: $i] :
( ~ happens(overflow,n2)
| ~ releasedAt(waterLevel(X0),n3)
| ~ holdsAt(waterLevel(X0),n2) ),
inference(superposition,[status(thm)],[c_5077,c_7553]) ).
tcf(c_9047,plain,
! [X0: $i] :
( releasedAt(X0,n3)
| holdsAt(waterLevel(n3),n2)
| ~ releasedAt(X0,n1) ),
inference(global_subsumption_just,[status(thm)],[c_6900,c_5737,c_6062,c_6848,c_7424]) ).
tcf(c_9061,plain,
! [X0: $i] :
( happens(overflow,n1)
| releasedAt(X0,n3)
| releasedAt(waterLevel(n3),n2)
| holdsAt(waterLevel(n3),n1)
| ~ releasedAt(X0,n1) ),
inference(superposition,[status(thm)],[c_9047,c_8247]) ).
tcf(c_9311,plain,
! [X0: $i] :
( releasedAt(X0,n2)
| holdsAt(waterLevel(n3),n2)
| ~ releasedAt(X0,n1) ),
inference(global_subsumption_just,[status(thm)],[c_7424,c_5737,c_6062,c_7424]) ).
tcf(c_14993,plain,
( holdsAt(filling,n2)
| holdsAt(waterLevel(n3),n2)
| ~ happens(overflow,n1)
| ~ happens(tapOff,n2) ),
inference(superposition,[status(thm)],[c_14829,c_7365]) ).
tcf(c_15045,plain,
( holdsAt(filling,n2)
| holdsAt(waterLevel(n3),n2)
| ~ happens(tapOff,n2) ),
inference(global_subsumption_just,[status(thm)],[c_14992,c_7938,c_8825,c_14993]) ).
tcf(c_18816,plain,
( holdsAt(filling,n2)
| holdsAt(waterLevel(n3),n2)
| ~ happens(tapOn,n2)
| ~ happens(overflow,n1) ),
inference(superposition,[status(thm)],[c_18696,c_7365]) ).
tcf(c_19060,plain,
( holdsAt(filling,n2)
| holdsAt(waterLevel(n3),n2)
| ~ happens(tapOn,n2) ),
inference(global_subsumption_just,[status(thm)],[c_18815,c_7638,c_8825,c_18816]) ).
tcf(c_28288,plain,
( holdsAt(waterLevel(sK2(sK8(n0,filling,n3),tapOff,waterLevel(n3))),n2)
| ~ happens(overflow,n1)
| ~ holdsAt(waterLevel(n3),n1) ),
inference(superposition,[status(thm)],[c_28249,c_7365]) ).
tcf(c_28293,plain,
( ~ happens(overflow,n1)
| ~ holdsAt(waterLevel(n3),n1)
| ~ releasedAt(waterLevel(sK2(sK8(n0,filling,n3),tapOff,waterLevel(n3))),n2) ),
inference(superposition,[status(thm)],[c_28249,c_6254]) ).
tcf(c_28332,plain,
( holdsAt(waterLevel(n3),n2)
| ~ happens(overflow,n1)
| ~ holdsAt(waterLevel(n3),n1) ),
inference(light_normalisation,[status(thm)],[c_28288,c_28249]) ).
tcf(c_28351,plain,
( ~ happens(overflow,n1)
| ~ releasedAt(waterLevel(n3),n2)
| ~ holdsAt(waterLevel(n3),n1) ),
inference(light_normalisation,[status(thm)],[c_28293,c_28249]) ).
tcf(c_29034,plain,
( holdsAt(waterLevel(n3),n2)
| ~ holdsAt(waterLevel(n3),n1) ),
inference(global_subsumption_just,[status(thm)],[c_28332,c_162,c_6062,c_28332]) ).
tcf(c_29051,plain,
! [X0: $i] :
( releasedAt(X0,n2)
| holdsAt(X0,n2)
| holdsAt(waterLevel(n3),n2)
| ~ holdsAt(X0,n1) ),
inference(superposition,[status(thm)],[c_8596,c_29034]) ).
tcf(c_29062,plain,
( ~ holdsAt(waterLevel(n3),n1)
| ~ releasedAt(waterLevel(n3),n2) ),
inference(global_subsumption_just,[status(thm)],[c_28351,c_162,c_6062,c_28351]) ).
tcf(c_29063,plain,
( ~ releasedAt(waterLevel(n3),n2)
| ~ holdsAt(waterLevel(n3),n1) ),
inference(renaming,[status(thm)],[c_29062]) ).
tcf(c_29079,plain,
! [X0: $i] :
( releasedAt(X0,n2)
| holdsAt(X0,n2)
| ~ holdsAt(X0,n1)
| ~ releasedAt(waterLevel(n3),n2) ),
inference(superposition,[status(thm)],[c_8596,c_29063]) ).
tcf(c_29080,plain,
! [X0: $i] :
( releasedAt(X0,n2)
| holdsAt(X0,n1)
| ~ holdsAt(X0,n2)
| ~ releasedAt(waterLevel(n3),n2) ),
inference(superposition,[status(thm)],[c_8204,c_29063]) ).
tcf(c_32196,plain,
( ~ happens(tapOff,n2)
| holdsAt(waterLevel(n3),n2) ),
inference(global_subsumption_just,[status(thm)],[c_31498,c_8130,c_15045,c_31498]) ).
tcf(c_32197,plain,
( holdsAt(waterLevel(n3),n2)
| ~ happens(tapOff,n2) ),
inference(renaming,[status(thm)],[c_32196]) ).
tcf(c_32229,plain,
( ~ happens(tapOff,n2)
| ~ releasedAt(waterLevel(n3),n3) ),
inference(superposition,[status(thm)],[c_32197,c_7642]) ).
tcf(c_41525,plain,
! [X0: $i,X1: $i] :
( stoppedIn(n0,filling,n2)
| ( sK3(n2,X0,X1) = n2 )
| ~ sP0(n2,X0,X1) ),
inference(superposition,[status(thm)],[c_69,c_41490]) ).
tcf(c_42229,plain,
! [X0: $i] :
( stoppedIn(n0,filling,n2)
| ( sK3(n2,overflow,waterLevel(X0)) = n2 )
| ~ holdsAt(waterLevel(X0),n2) ),
inference(superposition,[status(thm)],[c_68,c_41525]) ).
tcf(c_42559,plain,
! [X0: $i] :
( releasedAt(X0,n2)
| holdsAt(X0,n2)
| stoppedIn(n0,filling,n2)
| ( sK3(n2,overflow,waterLevel(n3)) = n2 )
| ~ holdsAt(X0,n1) ),
inference(superposition,[status(thm)],[c_29051,c_42229]) ).
tcf(c_46600,plain,
! [X0: $i] :
( happens(overflow,n1)
| releasedAt(X0,n3)
| releasedAt(waterLevel(n3),n2)
| ~ releasedAt(X0,n1) ),
inference(global_subsumption_just,[status(thm)],[c_9061,c_162,c_6062,c_9061]) ).
tcf(c_55413,plain,
! [X0: $i,X1: $i] :
( initiates(overflow,waterLevel(X0),X1)
| ~ holdsAt(waterLevel(X0),X1) ),
inference(superposition,[status(thm)],[c_68,c_75]) ).
tcf(c_56053,plain,
! [X0: $i,X1: $i] :
( holdsAt(waterLevel(X0),plus(X1,n1))
| ~ happens(overflow,X1)
| ~ holdsAt(waterLevel(X0),X1) ),
inference(superposition,[status(thm)],[c_55413,c_120]) ).
tcf(c_57394,plain,
! [X0: $i,X1: $i] :
( holdsAt(waterLevel(X0),plus(n1,X1))
| ~ happens(overflow,X1)
| ~ holdsAt(waterLevel(X0),X1) ),
inference(superposition,[status(thm)],[c_100,c_56053]) ).
tcf(c_57396,plain,
! [X0: $i] :
( holdsAt(waterLevel(X0),n2)
| ~ happens(overflow,n1)
| ~ holdsAt(waterLevel(X0),n1) ),
inference(superposition,[status(thm)],[c_125,c_56053]) ).
tcf(c_57444,plain,
! [X0: $i] :
( releasedAt(X0,n2)
| holdsAt(waterLevel(n3),n2)
| ~ happens(overflow,n1)
| ~ releasedAt(X0,n1) ),
inference(superposition,[status(thm)],[c_56463,c_57396]) ).
tcf(c_57863,plain,
! [X0: $i] :
( releasedAt(X0,n3)
| holdsAt(waterLevel(n3),n2)
| ~ releasedAt(X0,n1) ),
inference(global_subsumption_just,[status(thm)],[c_57264,c_9047]) ).
tcf(c_58161,plain,
! [X0: $i] :
( releasedAt(X0,n2)
| holdsAt(waterLevel(n3),n2)
| ~ releasedAt(X0,n1) ),
inference(global_subsumption_just,[status(thm)],[c_57444,c_9311]) ).
tcf(c_58237,plain,
! [X0: $i] :
( releasedAt(X0,n2)
| ~ happens(tapOff,n2)
| ~ releasedAt(X0,n1)
| ~ releasedAt(waterLevel(n3),n3) ),
inference(superposition,[status(thm)],[c_58161,c_57925]) ).
tcf(c_58683,plain,
! [X0: $i] :
( holdsAt(waterLevel(X0),n3)
| ~ happens(overflow,n2)
| ~ holdsAt(waterLevel(X0),n2) ),
inference(superposition,[status(thm)],[c_95,c_57394]) ).
tcf(c_58721,plain,
! [X0: $i] :
( releasedAt(X0,n2)
| holdsAt(waterLevel(n3),n3)
| ~ happens(overflow,n2)
| ~ releasedAt(X0,n1) ),
inference(superposition,[status(thm)],[c_58161,c_58683]) ).
tcf(c_59041,plain,
! [X0: $i] :
( releasedAt(X0,n3)
| holdsAt(waterLevel(n3),n2)
| holdsAt(waterLevel(n3),n3)
| ~ happens(overflow,n2)
| ~ releasedAt(X0,n1) ),
inference(superposition,[status(thm)],[c_58721,c_57227]) ).
tcf(c_59298,plain,
( ~ releasedAt(waterLevel(n3),n3)
| ~ happens(tapOff,n2) ),
inference(global_subsumption_just,[status(thm)],[c_58237,c_32229]) ).
tcf(c_59299,plain,
( ~ happens(tapOff,n2)
| ~ releasedAt(waterLevel(n3),n3) ),
inference(renaming,[status(thm)],[c_59298]) ).
tcf(c_59305,plain,
( holdsAt(waterLevel(n3),n2)
| ~ happens(tapOff,n2)
| ~ releasedAt(waterLevel(n3),n1) ),
inference(superposition,[status(thm)],[c_57863,c_59299]) ).
tcf(c_59318,plain,
( holdsAt(waterLevel(n3),n2)
| ~ happens(tapOff,n2) ),
inference(global_subsumption_just,[status(thm)],[c_59305,c_32197]) ).
tcf(c_60032,plain,
( releasedAt(waterLevel(n3),n2)
| holdsAt(waterLevel(n3),n1)
| ( sK5(waterLevel(n3),n1) = overflow )
| ~ happens(tapOff,n2) ),
inference(superposition,[status(thm)],[c_59318,c_58419]) ).
tcf(c_65209,plain,
! [X0: $i] :
( releasedAt(X0,n2)
| holdsAt(X0,n2)
| stoppedIn(n0,filling,n2)
| holdsAt(waterLevel(n3),n2)
| ( sK3(n2,overflow,waterLevel(n3)) = n2 )
| ~ holdsAt(X0,n1)
| ~ holdsAt(waterLevel(n3),n1) ),
inference(superposition,[status(thm)],[c_42559,c_29079]) ).
tcf(c_66069,plain,
! [X0: $i] :
( releasedAt(X0,n2)
| holdsAt(X0,n1)
| ~ happens(overflow,n2)
| ~ releasedAt(filling,n2)
| ~ holdsAt(X0,n2) ),
inference(superposition,[status(thm)],[c_66048,c_29080]) ).
tcf(c_66234,plain,
! [X0: $i] :
( releasedAt(X0,n2)
| holdsAt(X0,n1)
| ~ holdsAt(X0,n2)
| ~ releasedAt(filling,n2) ),
inference(global_subsumption_just,[status(thm)],[c_66069,c_162,c_6062,c_6288,c_8204]) ).
tcf(c_66235,plain,
! [X0: $i] :
( releasedAt(X0,n2)
| holdsAt(X0,n1)
| ~ releasedAt(filling,n2)
| ~ holdsAt(X0,n2) ),
inference(renaming,[status(thm)],[c_66234]) ).
tcf(c_66265,plain,
( holdsAt(filling,n2)
| releasedAt(waterLevel(n3),n2)
| holdsAt(waterLevel(n3),n1)
| ~ happens(tapOn,n2)
| ~ releasedAt(filling,n2) ),
inference(superposition,[status(thm)],[c_19060,c_66235]) ).
tcf(c_81154,plain,
( ~ happens(overflow,n1)
| ~ releasedAt(waterLevel(n3),n2) ),
inference(superposition,[status(thm)],[c_81103,c_6254]) ).
tcf(c_109782,plain,
holdsAt(waterLevel(n3),n2),
inference(global_subsumption_just,[status(thm)],[c_59041,c_105,c_133,c_50,c_103,c_150,c_1069,c_1272,c_5785,c_5906,c_9219,c_13143,c_16195,c_19807,c_22569,c_22568,c_26903,c_27331,c_28223,c_28236,c_29034,c_48575,c_51770,c_108864]) ).
tcf(c_109790,plain,
! [X0: $i] :
( ( X0 = n3 )
| ~ holdsAt(waterLevel(X0),n2) ),
inference(superposition,[status(thm)],[c_109782,c_61]) ).
tcf(c_109800,plain,
( happens(overflow,n1)
| releasedAt(waterLevel(n3),n2)
| holdsAt(waterLevel(n3),n1) ),
inference(superposition,[status(thm)],[c_109782,c_58454]) ).
tcf(c_109844,plain,
( ( n1 = n3 )
| ~ holdsAt(waterLevel(n1),n2) ),
inference(instantiation,[status(thm)],[c_109790]) ).
tcf(c_110057,plain,
( releasedAt(waterLevel(n3),n2)
| holdsAt(waterLevel(n3),n1) ),
inference(global_subsumption_just,[status(thm)],[c_60032,c_81103,c_109800]) ).
tcf(c_111518,plain,
holdsAt(waterLevel(n3),n2),
inference(global_subsumption_just,[status(thm)],[c_65209,c_109782]) ).
tcf(c_111574,plain,
( stoppedIn(n0,filling,n2)
| ( n3 = n2 ) ),
inference(superposition,[status(thm)],[c_111518,c_41490]) ).
tcf(c_111590,plain,
( ~ happens(overflow,n2)
| ~ releasedAt(waterLevel(n3),n3) ),
inference(superposition,[status(thm)],[c_111518,c_7641]) ).
tcf(c_112198,plain,
( ( n3 = n2 )
| ( sK7(n0,filling,n2) = overflow )
| ( sK7(n0,filling,n2) = tapOff ) ),
inference(superposition,[status(thm)],[c_111574,c_6153]) ).
tcf(c_112202,plain,
( ( n3 = n2 )
| ( sK8(n0,filling,n2) = n1 )
| ( sK8(n0,filling,n2) = n0 ) ),
inference(superposition,[status(thm)],[c_111574,c_10934]) ).
tcf(c_112341,plain,
( happens(overflow,n1)
| releasedAt(waterLevel(n3),n2)
| ~ happens(overflow,n2)
| ~ releasedAt(waterLevel(n3),n1) ),
inference(superposition,[status(thm)],[c_46600,c_111590]) ).
tcf(c_140098,plain,
( happens(overflow,n1)
| releasedAt(waterLevel(n3),n2) ),
inference(global_subsumption_just,[status(thm)],[c_112341,c_162,c_6062,c_110057]) ).
tcf(c_142070,plain,
releasedAt(waterLevel(n3),n2),
inference(global_subsumption_just,[status(thm)],[c_66265,c_130,c_133,c_140,c_150,c_1264,c_1308,c_5900,c_6764,c_7396,c_15782,c_15974,c_20587,c_109844,c_121538,c_137103,c_140098,c_142008]) ).
tcf(c_142076,plain,
~ happens(overflow,n1),
inference(backward_subsumption_resolution,[status(thm)],[c_81154,c_142070]) ).
tcf(c_143073,plain,
waterLevel(sK3(n1,overflow,waterLevel(n1))) = waterLevel(n1),
inference(superposition,[status(thm)],[c_143065,c_5561]) ).
tcf(c_143396,plain,
! [X0: $i] :
( holdsAt(waterLevel(n1),plus(X0,n1))
| ~ happens(tapOff,X0)
| ~ holdsAt(waterLevel(sK3(n1,overflow,waterLevel(n1))),X0) ),
inference(superposition,[status(thm)],[c_143073,c_5952]) ).
tcf(c_143479,plain,
! [X0: $i] :
( holdsAt(waterLevel(n1),plus(X0,n1))
| ~ happens(tapOff,X0)
| ~ holdsAt(waterLevel(n1),X0) ),
inference(light_normalisation,[status(thm)],[c_143396,c_143073]) ).
tcf(c_144952,plain,
! [X0: $i] : ~ happens(tapOff,X0),
inference(global_subsumption_just,[status(thm)],[c_143479,c_113,c_104,c_123879]) ).
tcf(c_146824,plain,
( happens(tapOff,sK8(n0,filling,n2))
| ( n3 = n2 )
| ( sK7(n0,filling,n2) = overflow )
| ~ stoppedIn(n0,filling,n2) ),
inference(superposition,[status(thm)],[c_112198,c_89]) ).
tcf(c_146825,plain,
( ( n3 = n2 )
| ( sK7(n0,filling,n2) = overflow )
| ~ stoppedIn(n0,filling,n2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_146824,c_144952]) ).
tcf(c_147137,plain,
( ( n3 = n2 )
| ( sK7(n0,filling,n2) = overflow ) ),
inference(global_subsumption_just,[status(thm)],[c_146825,c_111574,c_146825]) ).
tcf(c_147144,plain,
( happens(overflow,sK8(n0,filling,n2))
| ( n3 = n2 )
| ~ stoppedIn(n0,filling,n2) ),
inference(superposition,[status(thm)],[c_147137,c_89]) ).
tcf(c_147148,plain,
( happens(overflow,sK8(n0,filling,n2))
| ( n3 = n2 ) ),
inference(global_subsumption_just,[status(thm)],[c_147144,c_111574,c_147144]) ).
tcf(c_148752,plain,
( happens(overflow,n0)
| ( n3 = n2 )
| ( sK8(n0,filling,n2) = n1 ) ),
inference(superposition,[status(thm)],[c_112202,c_147148]) ).
tcf(c_148753,plain,
( ( n3 = n2 )
| ( sK8(n0,filling,n2) = n1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_148752,c_8174]) ).
tcf(c_148949,plain,
( happens(overflow,n1)
| ( n3 = n2 ) ),
inference(superposition,[status(thm)],[c_148753,c_147148]) ).
tcf(c_148950,plain,
n3 = n2,
inference(forward_subsumption_resolution,[status(thm)],[c_148949,c_142076]) ).
tcf(c_149228,plain,
less(n3,n3),
inference(demodulation,[status(thm)],[c_1272,c_148950]) ).
tcf(c_149229,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_149228,c_99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CSR011+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n007.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Fri Sep 25 08:04:38 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 46.88/8.38 % SZS status Started for theBenchmark.p
% 46.88/8.38 % SZS status Theorem for theBenchmark.p
% 46.88/8.38
% 46.88/8.38 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 46.88/8.38
% 46.88/8.38 % ------ iProver source info
% 46.88/8.38
% 46.88/8.38 % git: date: 2026-07-19 20:42:38 +0200
% 46.88/8.38 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 46.88/8.38 % git: non_committed_changes: false
% 46.88/8.38
% 46.88/8.38 % ------ Parsing...
% 46.88/8.38 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 46.88/8.38
% 46.88/8.38 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e %
% 46.88/8.38
% 46.88/8.38 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 46.88/8.38
% 46.88/8.38 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 46.88/8.38 % ------ Proving...
% 46.88/8.38 % ------ Problem Properties
% 46.88/8.38
% 46.88/8.38 %
% 46.88/8.38 % clauses 81
% 46.88/8.38 % conjectures 1
% 46.88/8.38 % EPR 44
% 46.88/8.38 % Horn 60
% 46.88/8.38 % unary 31
% 46.88/8.38 % binary 20
% 46.88/8.38 % lits 175
% 46.88/8.38 % lits eq 47
% 46.88/8.38 % fd_pure 0
% 46.88/8.38 % fd_pseudo 0
% 46.88/8.38 % fd_cond 17
% 46.88/8.38 % fd_pseudo_cond 3
% 46.88/8.38 % AC symbols 0
% 46.88/8.38
% 46.88/8.38 % ------ Schedule dynamic 5 is on
% 46.88/8.38
% 46.88/8.38 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 46.88/8.38
% 46.88/8.38
% 46.88/8.38 % ------
% 46.88/8.38 % Current options:
% 46.88/8.38 % ------
% 46.88/8.38
% 46.88/8.38
% 46.88/8.38 %
% 46.88/8.38
% 46.88/8.38 % ------ Proving...
% 46.88/8.38 %
% 46.88/8.38
% 46.88/8.38 % SZS status Theorem for theBenchmark.p
% 46.88/8.38
% 46.88/8.38 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 46.88/8.39
% 46.88/8.39
%------------------------------------------------------------------------------