%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : CSR001+2 : TPTP v9.2.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:13:50 PM UTC 2026
% Result : Theorem 3.80s 3.07s
% Output : CNFRefutation 3.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 34
% Syntax : Number of formulae : 247 ( 61 unt; 0 def)
% Number of atoms : 883 ( 278 equ)
% Maximal formula atoms : 194 ( 3 avg)
% Number of connectives : 1015 ( 379 ~; 500 |; 112 &)
% ( 15 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 52 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 12 con; 0-3 aty)
% Number of variables : 451 ( 52 sgn 123 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(keep_holding,axiom,
! [X2,X5] :
( ( holdsAt(X2,X5)
& ~ releasedAt(X2,plus(X5,n1))
& ~ ? [X4] :
( happens(X4,X5)
& terminates(X4,X2,X5) ) )
=> holdsAt(X2,plus(X5,n1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+0.ax',keep_holding) ).
fof(keep_not_released,axiom,
! [X2,X5] :
( ( ~ releasedAt(X2,X5)
& ~ ? [X4] :
( happens(X4,X5)
& releases(X4,X2,X5) ) )
=> ~ releasedAt(X2,plus(X5,n1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+0.ax',keep_not_released) ).
fof(terminates_all_defn,axiom,
! [X4,X2,X5] :
( terminates(X4,X2,X5)
<=> ( ( X4 = tapOff
& X2 = filling )
| ( X4 = overflow
& X2 = filling ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax',terminates_all_defn) ).
fof(stoppedin_defn,axiom,
! [X1,X2,X3] :
( stoppedIn(X1,X2,X3)
<=> ? [X4,X5] :
( happens(X4,X5)
& less(X1,X5)
& less(X5,X3)
& terminates(X4,X2,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+0.ax',stoppedin_defn) ).
fof(happens_all_defn,axiom,
! [X4,X5] :
( happens(X4,X5)
<=> ( ( X4 = tapOn
& X5 = n0 )
| ( holdsAt(waterLevel(n3),X5)
& holdsAt(filling,X5)
& X4 = overflow ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax',happens_all_defn) ).
fof(happens_not_released,axiom,
! [X4,X5,X2] :
( ( happens(X4,X5)
& ( initiates(X4,X2,X5)
| terminates(X4,X2,X5) ) )
=> ~ releasedAt(X2,plus(X5,n1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+0.ax',happens_not_released) ).
fof(releases_all_defn,axiom,
! [X4,X2,X5] :
( releases(X4,X2,X5)
<=> ? [X9] :
( X4 = tapOn
& X2 = waterLevel(X9) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax',releases_all_defn) ).
fof(symmetry_of_plus,axiom,
! [X12,X13] : plus(X12,X13) = plus(X13,X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_plus) ).
fof(waterLevel_4,conjecture,
holdsAt(waterLevel(n3),n4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',waterLevel_4) ).
fof(less_or_equal,axiom,
! [X12,X13] :
( less_or_equal(X12,X13)
<=> ( less(X12,X13)
| X12 = X13 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal) ).
fof(initiates_all_defn,axiom,
! [X4,X2,X5] :
( initiates(X4,X2,X5)
<=> ( ( X4 = tapOn
& X2 = filling )
| ( X4 = overflow
& X2 = spilling )
| ? [X9] :
( holdsAt(waterLevel(X9),X5)
& X4 = tapOff
& X2 = waterLevel(X9) )
| ? [X9] :
( holdsAt(waterLevel(X9),X5)
& X4 = overflow
& X2 = waterLevel(X9) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax',initiates_all_defn) ).
fof(waterLevel_3,lemma,
holdsAt(waterLevel(n3),n3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',waterLevel_3) ).
fof(plus1_3,axiom,
plus(n1,n3) = n4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus1_3) ).
fof(filling_not_waterLevel,axiom,
! [X12] : filling != waterLevel(X12),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax',filling_not_waterLevel) ).
fof(less3,axiom,
! [X12] :
( less(X12,n3)
<=> less_or_equal(X12,n2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less3) ).
fof(less6,axiom,
! [X12] :
( less(X12,n6)
<=> less_or_equal(X12,n5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less6) ).
fof(less5,axiom,
! [X12] :
( less(X12,n5)
<=> less_or_equal(X12,n4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less5) ).
fof(tapOff_not_overflow,axiom,
tapOff != overflow,
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax',tapOff_not_overflow) ).
fof(tapOff_not_tapOn,axiom,
tapOff != tapOn,
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax',tapOff_not_tapOn) ).
fof(less1,axiom,
! [X12] :
( less(X12,n1)
<=> less_or_equal(X12,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less1) ).
fof(less0,axiom,
~ ? [X12] : less(X12,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less0) ).
fof(plus0_1,axiom,
plus(n0,n1) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus0_1) ).
fof(startedin_defn,axiom,
! [X1,X3,X2] :
( startedIn(X1,X2,X3)
<=> ? [X4,X5] :
( happens(X4,X5)
& less(X1,X5)
& less(X5,X3)
& initiates(X4,X2,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+0.ax',startedin_defn) ).
fof(plus1_1,axiom,
plus(n1,n1) = n2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus1_1) ).
fof(less4,axiom,
! [X12] :
( less(X12,n4)
<=> less_or_equal(X12,n3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less4) ).
fof(happens_holds,axiom,
! [X4,X5,X2] :
( ( happens(X4,X5)
& initiates(X4,X2,X5) )
=> holdsAt(X2,plus(X5,n1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+0.ax',happens_holds) ).
fof(less2,axiom,
! [X12] :
( less(X12,n2)
<=> less_or_equal(X12,n1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less2) ).
fof(filling_not_spilling,axiom,
filling != spilling,
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax',filling_not_spilling) ).
fof(plus1_2,axiom,
plus(n1,n2) = n3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus1_2) ).
fof(overflow_not_tapOn,axiom,
overflow != tapOn,
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax',overflow_not_tapOn) ).
fof(spilling_not_waterLevel,axiom,
! [X12] : spilling != waterLevel(X12),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax',spilling_not_waterLevel) ).
fof(happens_terminates_not_holds,axiom,
! [X4,X5,X2] :
( ( happens(X4,X5)
& terminates(X4,X2,X5) )
=> ~ holdsAt(X2,plus(X5,n1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+0.ax',happens_terminates_not_holds) ).
fof(not_spilling_0,hypothesis,
~ holdsAt(spilling,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_spilling_0) ).
fof(c_0_33,plain,
! [X2,X5] :
( ( holdsAt(X2,X5)
& ~ releasedAt(X2,plus(X5,n1))
& ~ ? [X4] :
( happens(X4,X5)
& terminates(X4,X2,X5) ) )
=> holdsAt(X2,plus(X5,n1)) ),
inference(fof_simplification,[status(thm)],[keep_holding]) ).
fof(c_0_34,plain,
! [X2,X5] :
( ( ~ releasedAt(X2,X5)
& ~ ? [X4] :
( happens(X4,X5)
& releases(X4,X2,X5) ) )
=> ~ releasedAt(X2,plus(X5,n1)) ),
inference(fof_simplification,[status(thm)],[keep_not_released]) ).
fof(c_0_35,plain,
! [X157,X158,X159] :
( ( X157 = overflow
| X157 = tapOff
| ~ terminates(X157,X158,X159) )
& ( X158 = filling
| X157 = tapOff
| ~ terminates(X157,X158,X159) )
& ( X157 = overflow
| X158 = filling
| ~ terminates(X157,X158,X159) )
& ( X158 = filling
| X158 = filling
| ~ terminates(X157,X158,X159) )
& ( X157 != tapOff
| X158 != filling
| terminates(X157,X158,X159) )
& ( X157 != overflow
| X158 != filling
| terminates(X157,X158,X159) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[terminates_all_defn])])]) ).
fof(c_0_36,plain,
! [X100,X101,X102,X105,X106,X107,X108,X109] :
( ( happens(esk1_3(X100,X101,X102),esk2_3(X100,X101,X102))
| ~ stoppedIn(X100,X101,X102) )
& ( less(X100,esk2_3(X100,X101,X102))
| ~ stoppedIn(X100,X101,X102) )
& ( less(esk2_3(X100,X101,X102),X102)
| ~ stoppedIn(X100,X101,X102) )
& ( terminates(esk1_3(X100,X101,X102),X101,esk2_3(X100,X101,X102))
| ~ stoppedIn(X100,X101,X102) )
& ( ~ happens(X108,X109)
| ~ less(X105,X109)
| ~ less(X109,X107)
| ~ terminates(X108,X106,X109)
| stoppedIn(X105,X106,X107) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[stoppedin_defn])])])])])]) ).
fof(c_0_37,plain,
! [X130,X131] :
( ( happens(esk5_2(X130,X131),X131)
| ~ holdsAt(X130,X131)
| releasedAt(X130,plus(X131,n1))
| holdsAt(X130,plus(X131,n1)) )
& ( terminates(esk5_2(X130,X131),X130,X131)
| ~ holdsAt(X130,X131)
| releasedAt(X130,plus(X131,n1))
| holdsAt(X130,plus(X131,n1)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])])]) ).
fof(c_0_38,plain,
! [X168,X169] :
( ( holdsAt(waterLevel(n3),X169)
| X168 = tapOn
| ~ happens(X168,X169) )
& ( holdsAt(filling,X169)
| X168 = tapOn
| ~ happens(X168,X169) )
& ( X168 = overflow
| X168 = tapOn
| ~ happens(X168,X169) )
& ( holdsAt(waterLevel(n3),X169)
| X169 = n0
| ~ happens(X168,X169) )
& ( holdsAt(filling,X169)
| X169 = n0
| ~ happens(X168,X169) )
& ( X168 = overflow
| X169 = n0
| ~ happens(X168,X169) )
& ( X168 != tapOn
| X169 != n0
| happens(X168,X169) )
& ( ~ holdsAt(waterLevel(n3),X169)
| ~ holdsAt(filling,X169)
| X168 != overflow
| happens(X168,X169) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[happens_all_defn])])]) ).
fof(c_0_39,plain,
! [X4,X5,X2] :
( ( happens(X4,X5)
& ( initiates(X4,X2,X5)
| terminates(X4,X2,X5) ) )
=> ~ releasedAt(X2,plus(X5,n1)) ),
inference(fof_simplification,[status(thm)],[happens_not_released]) ).
fof(c_0_40,plain,
! [X5,X4,X2] :
( epred1_3(X2,X4,X5)
<=> ( ( X4 = tapOn
& X2 = filling )
| ( X4 = overflow
& X2 = spilling )
| ? [X9] :
( holdsAt(waterLevel(X9),X5)
& X4 = tapOff
& X2 = waterLevel(X9) )
| ? [X9] :
( holdsAt(waterLevel(X9),X5)
& X4 = overflow
& X2 = waterLevel(X9) ) ) ),
introduced(definition) ).
fof(c_0_41,plain,
! [X160,X161,X162,X164,X165,X166,X167] :
( ( X160 = tapOn
| ~ releases(X160,X161,X162) )
& ( X161 = waterLevel(esk9_2(X160,X161))
| ~ releases(X160,X161,X162) )
& ( X164 != tapOn
| X165 != waterLevel(X166)
| releases(X164,X165,X167) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[releases_all_defn])])])])])]) ).
fof(c_0_42,plain,
! [X139,X140] :
( ( happens(esk8_2(X139,X140),X140)
| releasedAt(X139,X140)
| ~ releasedAt(X139,plus(X140,n1)) )
& ( releases(esk8_2(X139,X140),X139,X140)
| releasedAt(X139,X140)
| ~ releasedAt(X139,plus(X140,n1)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])])]) ).
cnf(c_0_43,plain,
( X1 = filling
| X1 = filling
| ~ terminates(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_44,plain,
( stoppedIn(X3,X5,X4)
| ~ happens(X1,X2)
| ~ less(X3,X2)
| ~ less(X2,X4)
| ~ terminates(X1,X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_45,plain,
( terminates(esk5_2(X1,X2),X1,X2)
| releasedAt(X1,plus(X2,n1))
| holdsAt(X1,plus(X2,n1))
| ~ holdsAt(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_46,plain,
( happens(esk5_2(X1,X2),X2)
| releasedAt(X1,plus(X2,n1))
| holdsAt(X1,plus(X2,n1))
| ~ holdsAt(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_47,plain,
! [X181,X182] : plus(X181,X182) = plus(X182,X181),
inference(variable_rename,[status(thm)],[symmetry_of_plus]) ).
fof(c_0_48,negated_conjecture,
~ holdsAt(waterLevel(n3),n4),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[waterLevel_4])]) ).
fof(c_0_49,plain,
! [X183,X184] :
( ( ~ less_or_equal(X183,X184)
| less(X183,X184)
| X183 = X184 )
& ( ~ less(X183,X184)
| less_or_equal(X183,X184) )
& ( X183 != X184
| less_or_equal(X183,X184) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[less_or_equal])])]) ).
cnf(c_0_50,plain,
( X1 = overflow
| X1 = tapOn
| ~ happens(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_51,plain,
( happens(esk1_3(X1,X2,X3),esk2_3(X1,X2,X3))
| ~ stoppedIn(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_52,plain,
( X1 = overflow
| X1 = tapOff
| ~ terminates(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_53,plain,
( terminates(esk1_3(X1,X2,X3),X2,esk2_3(X1,X2,X3))
| ~ stoppedIn(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_54,plain,
! [X151,X152,X153] :
( ( ~ initiates(X151,X153,X152)
| ~ happens(X151,X152)
| ~ releasedAt(X153,plus(X152,n1)) )
& ( ~ terminates(X151,X153,X152)
| ~ happens(X151,X152)
| ~ releasedAt(X153,plus(X152,n1)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])]) ).
fof(c_0_55,axiom,
! [X4,X2,X5] :
( initiates(X4,X2,X5)
<=> epred1_3(X2,X4,X5) ),
inference(apply_def,[status(thm)],[initiates_all_defn,c_0_40]) ).
cnf(c_0_56,plain,
( X1 = tapOn
| ~ releases(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_57,plain,
( releases(esk8_2(X1,X2),X1,X2)
| releasedAt(X1,X2)
| ~ releasedAt(X1,plus(X2,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_58,plain,
( X1 = filling
| ~ terminates(X2,X1,X3) ),
inference(cn,[status(thm)],[c_0_43]) ).
cnf(c_0_59,plain,
( releasedAt(X1,plus(X2,n1))
| holdsAt(X1,plus(X2,n1))
| stoppedIn(X3,X1,X4)
| ~ holdsAt(X1,X2)
| ~ less(X3,X2)
| ~ less(X2,X4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]) ).
cnf(c_0_60,lemma,
holdsAt(waterLevel(n3),n3),
inference(split_conjunct,[status(thm)],[waterLevel_3]) ).
cnf(c_0_61,plain,
plus(X1,X2) = plus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_62,plain,
plus(n1,n3) = n4,
inference(split_conjunct,[status(thm)],[plus1_3]) ).
cnf(c_0_63,negated_conjecture,
~ holdsAt(waterLevel(n3),n4),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
fof(c_0_64,plain,
! [X177] : filling != waterLevel(X177),
inference(variable_rename,[status(thm)],[filling_not_waterLevel]) ).
fof(c_0_65,plain,
! [X188] :
( ( ~ less(X188,n3)
| less_or_equal(X188,n2) )
& ( ~ less_or_equal(X188,n2)
| less(X188,n3) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[less3])]) ).
cnf(c_0_66,plain,
( less_or_equal(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
fof(c_0_67,plain,
! [X191] :
( ( ~ less(X191,n6)
| less_or_equal(X191,n5) )
& ( ~ less_or_equal(X191,n5)
| less(X191,n6) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[less6])]) ).
fof(c_0_68,plain,
! [X190] :
( ( ~ less(X190,n5)
| less_or_equal(X190,n4) )
& ( ~ less_or_equal(X190,n4)
| less(X190,n5) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[less5])]) ).
cnf(c_0_69,plain,
( terminates(X1,X2,X3)
| X1 != overflow
| X2 != filling ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_70,plain,
( esk1_3(X1,X2,X3) = overflow
| esk1_3(X1,X2,X3) = tapOn
| ~ stoppedIn(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_71,plain,
( esk1_3(X1,X2,X3) = tapOff
| esk1_3(X1,X2,X3) = overflow
| ~ stoppedIn(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_72,plain,
tapOff != overflow,
inference(split_conjunct,[status(thm)],[tapOff_not_overflow]) ).
cnf(c_0_73,plain,
tapOff != tapOn,
inference(split_conjunct,[status(thm)],[tapOff_not_tapOn]) ).
fof(c_0_74,plain,
! [X186] :
( ( ~ less(X186,n1)
| less_or_equal(X186,n0) )
& ( ~ less_or_equal(X186,n0)
| less(X186,n1) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[less1])]) ).
fof(c_0_75,plain,
! [X185] : ~ less(X185,n0),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[less0])]) ).
cnf(c_0_76,plain,
( ~ initiates(X1,X2,X3)
| ~ happens(X1,X3)
| ~ releasedAt(X2,plus(X3,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_77,plain,
plus(n0,n1) = n1,
inference(split_conjunct,[status(thm)],[plus0_1]) ).
fof(c_0_78,plain,
! [X198,X199,X200,X203,X204,X205,X206,X207] :
( ( holdsAt(waterLevel(esk11_3(X198,X199,X200)),X198)
| holdsAt(waterLevel(esk10_3(X198,X199,X200)),X198)
| X199 = overflow
| X199 = tapOn
| ~ epred1_3(X200,X199,X198) )
& ( X199 = overflow
| holdsAt(waterLevel(esk10_3(X198,X199,X200)),X198)
| X199 = overflow
| X199 = tapOn
| ~ epred1_3(X200,X199,X198) )
& ( X200 = waterLevel(esk11_3(X198,X199,X200))
| holdsAt(waterLevel(esk10_3(X198,X199,X200)),X198)
| X199 = overflow
| X199 = tapOn
| ~ epred1_3(X200,X199,X198) )
& ( holdsAt(waterLevel(esk11_3(X198,X199,X200)),X198)
| X199 = tapOff
| X199 = overflow
| X199 = tapOn
| ~ epred1_3(X200,X199,X198) )
& ( X199 = overflow
| X199 = tapOff
| X199 = overflow
| X199 = tapOn
| ~ epred1_3(X200,X199,X198) )
& ( X200 = waterLevel(esk11_3(X198,X199,X200))
| X199 = tapOff
| X199 = overflow
| X199 = tapOn
| ~ epred1_3(X200,X199,X198) )
& ( holdsAt(waterLevel(esk11_3(X198,X199,X200)),X198)
| X200 = waterLevel(esk10_3(X198,X199,X200))
| X199 = overflow
| X199 = tapOn
| ~ epred1_3(X200,X199,X198) )
& ( X199 = overflow
| X200 = waterLevel(esk10_3(X198,X199,X200))
| X199 = overflow
| X199 = tapOn
| ~ epred1_3(X200,X199,X198) )
& ( X200 = waterLevel(esk11_3(X198,X199,X200))
| X200 = waterLevel(esk10_3(X198,X199,X200))
| X199 = overflow
| X199 = tapOn
| ~ epred1_3(X200,X199,X198) )
& ( holdsAt(waterLevel(esk11_3(X198,X199,X200)),X198)
| holdsAt(waterLevel(esk10_3(X198,X199,X200)),X198)
| X200 = spilling
| X199 = tapOn
| ~ epred1_3(X200,X199,X198) )
& ( X199 = overflow
| holdsAt(waterLevel(esk10_3(X198,X199,X200)),X198)
| X200 = spilling
| X199 = tapOn
| ~ epred1_3(X200,X199,X198) )
& ( X200 = waterLevel(esk11_3(X198,X199,X200))
| holdsAt(waterLevel(esk10_3(X198,X199,X200)),X198)
| X200 = spilling
| X199 = tapOn
| ~ epred1_3(X200,X199,X198) )
& ( holdsAt(waterLevel(esk11_3(X198,X199,X200)),X198)
| X199 = tapOff
| X200 = spilling
| X199 = tapOn
| ~ epred1_3(X200,X199,X198) )
& ( X199 = overflow
| X199 = tapOff
| X200 = spilling
| X199 = tapOn
| ~ epred1_3(X200,X199,X198) )
& ( X200 = waterLevel(esk11_3(X198,X199,X200))
| X199 = tapOff
| X200 = spilling
| X199 = tapOn
| ~ epred1_3(X200,X199,X198) )
& ( holdsAt(waterLevel(esk11_3(X198,X199,X200)),X198)
| X200 = waterLevel(esk10_3(X198,X199,X200))
| X200 = spilling
| X199 = tapOn
| ~ epred1_3(X200,X199,X198) )
& ( X199 = overflow
| X200 = waterLevel(esk10_3(X198,X199,X200))
| X200 = spilling
| X199 = tapOn
| ~ epred1_3(X200,X199,X198) )
& ( X200 = waterLevel(esk11_3(X198,X199,X200))
| X200 = waterLevel(esk10_3(X198,X199,X200))
| X200 = spilling
| X199 = tapOn
| ~ epred1_3(X200,X199,X198) )
& ( holdsAt(waterLevel(esk11_3(X198,X199,X200)),X198)
| holdsAt(waterLevel(esk10_3(X198,X199,X200)),X198)
| X199 = overflow
| X200 = filling
| ~ epred1_3(X200,X199,X198) )
& ( X199 = overflow
| holdsAt(waterLevel(esk10_3(X198,X199,X200)),X198)
| X199 = overflow
| X200 = filling
| ~ epred1_3(X200,X199,X198) )
& ( X200 = waterLevel(esk11_3(X198,X199,X200))
| holdsAt(waterLevel(esk10_3(X198,X199,X200)),X198)
| X199 = overflow
| X200 = filling
| ~ epred1_3(X200,X199,X198) )
& ( holdsAt(waterLevel(esk11_3(X198,X199,X200)),X198)
| X199 = tapOff
| X199 = overflow
| X200 = filling
| ~ epred1_3(X200,X199,X198) )
& ( X199 = overflow
| X199 = tapOff
| X199 = overflow
| X200 = filling
| ~ epred1_3(X200,X199,X198) )
& ( X200 = waterLevel(esk11_3(X198,X199,X200))
| X199 = tapOff
| X199 = overflow
| X200 = filling
| ~ epred1_3(X200,X199,X198) )
& ( holdsAt(waterLevel(esk11_3(X198,X199,X200)),X198)
| X200 = waterLevel(esk10_3(X198,X199,X200))
| X199 = overflow
| X200 = filling
| ~ epred1_3(X200,X199,X198) )
& ( X199 = overflow
| X200 = waterLevel(esk10_3(X198,X199,X200))
| X199 = overflow
| X200 = filling
| ~ epred1_3(X200,X199,X198) )
& ( X200 = waterLevel(esk11_3(X198,X199,X200))
| X200 = waterLevel(esk10_3(X198,X199,X200))
| X199 = overflow
| X200 = filling
| ~ epred1_3(X200,X199,X198) )
& ( holdsAt(waterLevel(esk11_3(X198,X199,X200)),X198)
| holdsAt(waterLevel(esk10_3(X198,X199,X200)),X198)
| X200 = spilling
| X200 = filling
| ~ epred1_3(X200,X199,X198) )
& ( X199 = overflow
| holdsAt(waterLevel(esk10_3(X198,X199,X200)),X198)
| X200 = spilling
| X200 = filling
| ~ epred1_3(X200,X199,X198) )
& ( X200 = waterLevel(esk11_3(X198,X199,X200))
| holdsAt(waterLevel(esk10_3(X198,X199,X200)),X198)
| X200 = spilling
| X200 = filling
| ~ epred1_3(X200,X199,X198) )
& ( holdsAt(waterLevel(esk11_3(X198,X199,X200)),X198)
| X199 = tapOff
| X200 = spilling
| X200 = filling
| ~ epred1_3(X200,X199,X198) )
& ( X199 = overflow
| X199 = tapOff
| X200 = spilling
| X200 = filling
| ~ epred1_3(X200,X199,X198) )
& ( X200 = waterLevel(esk11_3(X198,X199,X200))
| X199 = tapOff
| X200 = spilling
| X200 = filling
| ~ epred1_3(X200,X199,X198) )
& ( holdsAt(waterLevel(esk11_3(X198,X199,X200)),X198)
| X200 = waterLevel(esk10_3(X198,X199,X200))
| X200 = spilling
| X200 = filling
| ~ epred1_3(X200,X199,X198) )
& ( X199 = overflow
| X200 = waterLevel(esk10_3(X198,X199,X200))
| X200 = spilling
| X200 = filling
| ~ epred1_3(X200,X199,X198) )
& ( X200 = waterLevel(esk11_3(X198,X199,X200))
| X200 = waterLevel(esk10_3(X198,X199,X200))
| X200 = spilling
| X200 = filling
| ~ epred1_3(X200,X199,X198) )
& ( X204 != tapOn
| X205 != filling
| epred1_3(X205,X204,X203) )
& ( X204 != overflow
| X205 != spilling
| epred1_3(X205,X204,X203) )
& ( ~ holdsAt(waterLevel(X206),X203)
| X204 != tapOff
| X205 != waterLevel(X206)
| epred1_3(X205,X204,X203) )
& ( ~ holdsAt(waterLevel(X207),X203)
| X204 != overflow
| X205 != waterLevel(X207)
| epred1_3(X205,X204,X203) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])])])])]) ).
fof(c_0_79,plain,
! [X154,X155,X156] :
( ( ~ initiates(X154,X155,X156)
| epred1_3(X155,X154,X156) )
& ( ~ epred1_3(X155,X154,X156)
| initiates(X154,X155,X156) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])]) ).
fof(c_0_80,plain,
! [X110,X111,X112,X115,X116,X117,X118,X119] :
( ( happens(esk3_3(X110,X111,X112),esk4_3(X110,X111,X112))
| ~ startedIn(X110,X112,X111) )
& ( less(X110,esk4_3(X110,X111,X112))
| ~ startedIn(X110,X112,X111) )
& ( less(esk4_3(X110,X111,X112),X111)
| ~ startedIn(X110,X112,X111) )
& ( initiates(esk3_3(X110,X111,X112),X112,esk4_3(X110,X111,X112))
| ~ startedIn(X110,X112,X111) )
& ( ~ happens(X118,X119)
| ~ less(X115,X119)
| ~ less(X119,X116)
| ~ initiates(X118,X117,X119)
| startedIn(X115,X117,X116) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[startedin_defn])])])])])]) ).
cnf(c_0_81,plain,
plus(n1,n1) = n2,
inference(split_conjunct,[status(thm)],[plus1_1]) ).
cnf(c_0_82,plain,
( happens(esk8_2(X1,X2),X2)
| releasedAt(X1,X2)
| ~ releasedAt(X1,plus(X2,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_83,plain,
( esk8_2(X1,X2) = tapOn
| releasedAt(X1,X2)
| ~ releasedAt(X1,plus(X2,n1)) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_84,plain,
( X1 = filling
| ~ stoppedIn(X2,X1,X3) ),
inference(spm,[status(thm)],[c_0_58,c_0_53]) ).
cnf(c_0_85,lemma,
( releasedAt(waterLevel(n3),n4)
| stoppedIn(X1,waterLevel(n3),X2)
| ~ less(X1,n3)
| ~ less(n3,X2) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]),c_0_62]),c_0_61]),c_0_62]),c_0_63]) ).
cnf(c_0_86,plain,
filling != waterLevel(X1),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_87,plain,
( less(X1,n3)
| ~ less_or_equal(X1,n2) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_88,plain,
less_or_equal(X1,X1),
inference(er,[status(thm)],[c_0_66]) ).
cnf(c_0_89,plain,
( less(X1,n6)
| ~ less_or_equal(X1,n5) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_90,plain,
( less_or_equal(X1,X2)
| ~ less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_91,plain,
( less(X1,n5)
| ~ less_or_equal(X1,n4) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
fof(c_0_92,plain,
! [X189] :
( ( ~ less(X189,n4)
| less_or_equal(X189,n3) )
& ( ~ less_or_equal(X189,n3)
| less(X189,n4) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[less4])]) ).
fof(c_0_93,plain,
! [X142,X143,X144] :
( ~ happens(X142,X143)
| ~ initiates(X142,X144,X143)
| holdsAt(X144,plus(X143,n1)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[happens_holds])]) ).
cnf(c_0_94,plain,
terminates(overflow,filling,X1),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_69])]) ).
cnf(c_0_95,plain,
( esk1_3(X1,X2,X3) = overflow
| ~ stoppedIn(X1,X2,X3) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]),c_0_73]) ).
fof(c_0_96,plain,
! [X187] :
( ( ~ less(X187,n2)
| less_or_equal(X187,n1) )
& ( ~ less_or_equal(X187,n1)
| less(X187,n2) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[less2])]) ).
cnf(c_0_97,plain,
( less(X1,X2)
| X1 = X2
| ~ less_or_equal(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_98,plain,
( less_or_equal(X1,n0)
| ~ less(X1,n1) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_99,plain,
~ less(X1,n0),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_100,plain,
( ~ releasedAt(X1,plus(n1,X2))
| ~ initiates(X3,X1,X2)
| ~ happens(X3,X2) ),
inference(spm,[status(thm)],[c_0_76,c_0_61]) ).
cnf(c_0_101,plain,
plus(n1,n0) = n1,
inference(rw,[status(thm)],[c_0_77,c_0_61]) ).
cnf(c_0_102,plain,
( X1 = waterLevel(esk11_3(X2,X3,X1))
| X1 = waterLevel(esk10_3(X2,X3,X1))
| X1 = spilling
| X3 = tapOn
| ~ epred1_3(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_103,plain,
filling != spilling,
inference(split_conjunct,[status(thm)],[filling_not_spilling]) ).
cnf(c_0_104,plain,
( epred1_3(X2,X1,X3)
| ~ initiates(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_105,plain,
( initiates(esk3_3(X1,X2,X3),X3,esk4_3(X1,X2,X3))
| ~ startedIn(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_106,plain,
( ~ releasedAt(X1,n2)
| ~ initiates(X2,X1,n1)
| ~ happens(X2,n1) ),
inference(spm,[status(thm)],[c_0_76,c_0_81]) ).
cnf(c_0_107,plain,
( initiates(X2,X1,X3)
| ~ epred1_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_108,plain,
( epred1_3(X4,X3,X2)
| ~ holdsAt(waterLevel(X1),X2)
| X3 != overflow
| X4 != waterLevel(X1) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_109,plain,
( releasedAt(X1,X2)
| happens(tapOn,X2)
| ~ releasedAt(X1,plus(X2,n1)) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_110,lemma,
( releasedAt(waterLevel(n3),n4)
| ~ less(X1,n3)
| ~ less(n3,X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86]) ).
cnf(c_0_111,plain,
less(n2,n3),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_112,plain,
( less(X1,n6)
| ~ less(X1,n5) ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_113,plain,
( less(X1,n5)
| ~ less(X1,n4) ),
inference(spm,[status(thm)],[c_0_91,c_0_90]) ).
cnf(c_0_114,plain,
( less(X1,n4)
| ~ less_or_equal(X1,n3) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_115,plain,
( holdsAt(X3,plus(X2,n1))
| ~ happens(X1,X2)
| ~ initiates(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_116,plain,
( stoppedIn(X1,filling,X2)
| ~ less(X1,X3)
| ~ less(X3,X2)
| ~ happens(overflow,X3) ),
inference(spm,[status(thm)],[c_0_44,c_0_94]) ).
cnf(c_0_117,plain,
( happens(overflow,esk2_3(X1,X2,X3))
| ~ stoppedIn(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_51,c_0_95]) ).
cnf(c_0_118,plain,
( less_or_equal(X1,n1)
| ~ less(X1,n2) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_119,plain,
( X1 = n0
| ~ less(X1,n1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_99]) ).
cnf(c_0_120,plain,
( less(esk2_3(X1,X2,X3),X3)
| ~ stoppedIn(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_121,plain,
( epred1_3(X2,X1,X3)
| X1 != tapOn
| X2 != filling ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_122,plain,
( X1 = waterLevel(esk9_2(X2,X1))
| ~ releases(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_123,plain,
( ~ releasedAt(X1,n1)
| ~ initiates(X2,X1,n0)
| ~ happens(X2,n0) ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_124,plain,
( happens(X1,X2)
| X1 != tapOn
| X2 != n0 ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_125,plain,
( X1 = overflow
| X2 = n0
| ~ happens(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_126,plain,
( happens(esk3_3(X1,X2,X3),esk4_3(X1,X2,X3))
| ~ startedIn(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_127,plain,
( X1 = tapOn
| ~ epred1_3(filling,X1,X2) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_102])]),c_0_86]),c_0_103]) ).
cnf(c_0_128,plain,
( epred1_3(X1,esk3_3(X2,X3,X1),esk4_3(X2,X3,X1))
| ~ startedIn(X2,X1,X3) ),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_129,plain,
( ~ epred1_3(X1,X2,n1)
| ~ releasedAt(X1,n2)
| ~ happens(X2,n1) ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_130,plain,
( epred1_3(waterLevel(X1),overflow,X2)
| ~ holdsAt(waterLevel(X1),X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_108])]) ).
cnf(c_0_131,plain,
( releasedAt(X1,X2)
| happens(tapOn,X2)
| ~ releasedAt(X1,plus(n1,X2)) ),
inference(spm,[status(thm)],[c_0_109,c_0_61]) ).
cnf(c_0_132,plain,
plus(n1,n2) = n3,
inference(split_conjunct,[status(thm)],[plus1_2]) ).
cnf(c_0_133,lemma,
( releasedAt(waterLevel(n3),n4)
| ~ less(n3,X1) ),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_134,plain,
( less(X1,n6)
| ~ less(X1,n4) ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_135,plain,
less(n3,n4),
inference(spm,[status(thm)],[c_0_114,c_0_88]) ).
cnf(c_0_136,plain,
( holdsAt(X1,plus(X2,n1))
| ~ epred1_3(X1,X3,X2)
| ~ happens(X3,X2) ),
inference(spm,[status(thm)],[c_0_115,c_0_107]) ).
cnf(c_0_137,plain,
( stoppedIn(X1,filling,X2)
| ~ less(X1,esk2_3(X3,X4,X5))
| ~ less(esk2_3(X3,X4,X5),X2)
| ~ stoppedIn(X3,X4,X5) ),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_138,plain,
( less(X1,esk2_3(X1,X2,X3))
| ~ stoppedIn(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_139,plain,
( X1 = n1
| less(X1,n1)
| ~ less(X1,n2) ),
inference(spm,[status(thm)],[c_0_97,c_0_118]) ).
cnf(c_0_140,plain,
( esk2_3(X1,X2,n1) = n0
| ~ stoppedIn(X1,X2,n1) ),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_141,plain,
epred1_3(filling,tapOn,X1),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_121])]) ).
cnf(c_0_142,plain,
( waterLevel(esk9_2(esk8_2(X1,X2),X1)) = X1
| releasedAt(X1,X2)
| ~ releasedAt(X1,plus(X2,n1)) ),
inference(spm,[status(thm)],[c_0_122,c_0_57]) ).
cnf(c_0_143,plain,
( ~ epred1_3(X1,X2,n0)
| ~ releasedAt(X1,n1)
| ~ happens(X2,n0) ),
inference(spm,[status(thm)],[c_0_123,c_0_107]) ).
cnf(c_0_144,plain,
happens(tapOn,n0),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_124])]) ).
cnf(c_0_145,plain,
( esk3_3(X1,X2,X3) = overflow
| esk4_3(X1,X2,X3) = n0
| ~ startedIn(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_146,plain,
( esk3_3(X1,X2,filling) = tapOn
| ~ startedIn(X1,filling,X2) ),
inference(spm,[status(thm)],[c_0_127,c_0_128]) ).
cnf(c_0_147,plain,
overflow != tapOn,
inference(split_conjunct,[status(thm)],[overflow_not_tapOn]) ).
cnf(c_0_148,plain,
( ~ releasedAt(waterLevel(X1),n2)
| ~ holdsAt(waterLevel(X1),n1)
| ~ happens(overflow,n1) ),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_149,plain,
( releasedAt(X1,n2)
| happens(tapOn,n2)
| ~ releasedAt(X1,n3) ),
inference(spm,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_150,plain,
( releasedAt(X1,n3)
| happens(tapOn,n3)
| ~ releasedAt(X1,n4) ),
inference(spm,[status(thm)],[c_0_131,c_0_62]) ).
cnf(c_0_151,lemma,
releasedAt(waterLevel(n3),n4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_135])]) ).
cnf(c_0_152,plain,
( holdsAt(waterLevel(X1),plus(X2,n1))
| ~ holdsAt(waterLevel(X1),X2)
| ~ happens(overflow,X2) ),
inference(spm,[status(thm)],[c_0_136,c_0_130]) ).
cnf(c_0_153,plain,
( happens(X2,X1)
| ~ holdsAt(waterLevel(n3),X1)
| ~ holdsAt(filling,X1)
| X2 != overflow ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_154,plain,
( holdsAt(waterLevel(n3),X1)
| X2 = tapOn
| ~ happens(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_155,plain,
( stoppedIn(X1,filling,X2)
| ~ less(esk2_3(X1,X3,X4),X2)
| ~ stoppedIn(X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_156,plain,
( esk2_3(X1,X2,n2) = n1
| less(esk2_3(X1,X2,n2),n1)
| ~ stoppedIn(X1,X2,n2) ),
inference(spm,[status(thm)],[c_0_139,c_0_120]) ).
cnf(c_0_157,plain,
~ stoppedIn(X1,X2,n1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_140]),c_0_99]) ).
cnf(c_0_158,plain,
( holdsAt(filling,plus(X1,n1))
| ~ happens(tapOn,X1) ),
inference(spm,[status(thm)],[c_0_136,c_0_141]) ).
cnf(c_0_159,plain,
( releasedAt(filling,X1)
| ~ releasedAt(filling,plus(X1,n1)) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_142])]) ).
cnf(c_0_160,plain,
~ releasedAt(filling,n1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_141]),c_0_144])]) ).
cnf(c_0_161,plain,
( startedIn(X3,X5,X4)
| ~ happens(X1,X2)
| ~ less(X3,X2)
| ~ less(X2,X4)
| ~ initiates(X1,X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_162,plain,
( less(X1,esk4_3(X1,X2,X3))
| ~ startedIn(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_163,plain,
( esk4_3(X1,X2,filling) = n0
| ~ startedIn(X1,filling,X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_147]) ).
cnf(c_0_164,plain,
( happens(tapOn,n2)
| ~ releasedAt(waterLevel(X1),n3)
| ~ holdsAt(waterLevel(X1),n1)
| ~ happens(overflow,n1) ),
inference(spm,[status(thm)],[c_0_148,c_0_149]) ).
cnf(c_0_165,lemma,
( releasedAt(waterLevel(n3),n3)
| happens(tapOn,n3) ),
inference(spm,[status(thm)],[c_0_150,c_0_151]) ).
cnf(c_0_166,lemma,
~ happens(overflow,n3),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_60]),c_0_61]),c_0_62]),c_0_63]) ).
cnf(c_0_167,plain,
( happens(overflow,X1)
| ~ holdsAt(waterLevel(n3),X1)
| ~ holdsAt(filling,X1) ),
inference(er,[status(thm)],[c_0_153]) ).
cnf(c_0_168,plain,
( holdsAt(waterLevel(n3),esk2_3(X1,X2,X3))
| ~ stoppedIn(X1,X2,X3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_117]),c_0_147]) ).
cnf(c_0_169,plain,
( esk2_3(X1,X2,n2) = n1
| ~ stoppedIn(X1,X2,n2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_157]) ).
cnf(c_0_170,plain,
holdsAt(filling,n1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_144]),c_0_61]),c_0_101]) ).
cnf(c_0_171,plain,
~ releasedAt(filling,n2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_81]),c_0_160]) ).
cnf(c_0_172,plain,
( less(X1,n2)
| ~ less_or_equal(X1,n1) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
fof(c_0_173,plain,
! [X178] : spilling != waterLevel(X178),
inference(variable_rename,[status(thm)],[spilling_not_waterLevel]) ).
cnf(c_0_174,plain,
( X1 = overflow
| X2 = waterLevel(esk10_3(X3,X1,X2))
| X1 = overflow
| X2 = filling
| ~ epred1_3(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
fof(c_0_175,plain,
! [X4,X5,X2] :
( ( happens(X4,X5)
& terminates(X4,X2,X5) )
=> ~ holdsAt(X2,plus(X5,n1)) ),
inference(fof_simplification,[status(thm)],[happens_terminates_not_holds]) ).
cnf(c_0_176,plain,
( startedIn(X1,X2,X3)
| ~ epred1_3(X2,X4,X5)
| ~ less(X1,X5)
| ~ less(X5,X3)
| ~ happens(X4,X5) ),
inference(spm,[status(thm)],[c_0_161,c_0_107]) ).
cnf(c_0_177,plain,
~ startedIn(X1,filling,X2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_163]),c_0_99]) ).
cnf(c_0_178,lemma,
( happens(tapOn,n3)
| happens(tapOn,n2)
| ~ holdsAt(waterLevel(n3),n1)
| ~ happens(overflow,n1) ),
inference(spm,[status(thm)],[c_0_164,c_0_165]) ).
cnf(c_0_179,lemma,
~ holdsAt(filling,n3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_167]),c_0_60])]) ).
cnf(c_0_180,plain,
( holdsAt(waterLevel(n3),n1)
| ~ stoppedIn(X1,X2,n2) ),
inference(spm,[status(thm)],[c_0_168,c_0_169]) ).
cnf(c_0_181,plain,
( holdsAt(filling,n2)
| stoppedIn(X1,filling,X2)
| ~ less(X1,n1)
| ~ less(n1,X2) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_170]),c_0_81]),c_0_81]),c_0_171]) ).
cnf(c_0_182,plain,
less(n1,n2),
inference(spm,[status(thm)],[c_0_172,c_0_88]) ).
cnf(c_0_183,plain,
( less(X1,n1)
| ~ less_or_equal(X1,n0) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_184,plain,
( happens(overflow,n1)
| ~ stoppedIn(X1,X2,n2) ),
inference(spm,[status(thm)],[c_0_117,c_0_169]) ).
cnf(c_0_185,plain,
spilling != waterLevel(X1),
inference(split_conjunct,[status(thm)],[c_0_173]) ).
cnf(c_0_186,plain,
( X2 = filling
| X1 = overflow
| X2 = waterLevel(esk10_3(X3,X1,X2))
| ~ epred1_3(X2,X1,X3) ),
inference(cn,[status(thm)],[c_0_174]) ).
fof(c_0_187,plain,
! [X145,X146,X147] :
( ~ happens(X145,X146)
| ~ terminates(X145,X147,X146)
| ~ holdsAt(X147,plus(X146,n1)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_175])]) ).
cnf(c_0_188,plain,
( ~ less(X1,X2)
| ~ less(X2,X3)
| ~ happens(tapOn,X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_141]),c_0_177]) ).
cnf(c_0_189,plain,
( happens(tapOn,n3)
| ~ holdsAt(waterLevel(n3),n1)
| ~ happens(overflow,n1) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_178]),c_0_61]),c_0_132]),c_0_179]) ).
cnf(c_0_190,plain,
( holdsAt(waterLevel(n3),n1)
| holdsAt(filling,n2)
| ~ less(X1,n1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_181]),c_0_182])]) ).
cnf(c_0_191,plain,
less(n0,n1),
inference(spm,[status(thm)],[c_0_183,c_0_88]) ).
cnf(c_0_192,plain,
( holdsAt(filling,n2)
| happens(overflow,n1)
| ~ less(X1,n1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_181]),c_0_182])]) ).
cnf(c_0_193,plain,
( X1 = overflow
| ~ epred1_3(spilling,X1,X2) ),
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_186])]),c_0_103]) ).
cnf(c_0_194,plain,
( ~ happens(X1,X2)
| ~ terminates(X1,X3,X2)
| ~ holdsAt(X3,plus(X2,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_187]) ).
cnf(c_0_195,plain,
( ~ holdsAt(waterLevel(n3),n1)
| ~ less(X1,n3)
| ~ less(n3,X2)
| ~ happens(overflow,n1) ),
inference(spm,[status(thm)],[c_0_188,c_0_189]) ).
cnf(c_0_196,plain,
( holdsAt(waterLevel(n3),n1)
| holdsAt(filling,n2) ),
inference(spm,[status(thm)],[c_0_190,c_0_191]) ).
cnf(c_0_197,plain,
( holdsAt(filling,n2)
| happens(overflow,n1) ),
inference(spm,[status(thm)],[c_0_192,c_0_191]) ).
cnf(c_0_198,plain,
( esk3_3(X1,X2,spilling) = overflow
| ~ startedIn(X1,spilling,X2) ),
inference(spm,[status(thm)],[c_0_193,c_0_128]) ).
cnf(c_0_199,plain,
( ~ holdsAt(filling,plus(X1,n1))
| ~ happens(overflow,X1) ),
inference(spm,[status(thm)],[c_0_194,c_0_94]) ).
cnf(c_0_200,plain,
( holdsAt(filling,n2)
| ~ less(X1,n3)
| ~ less(n3,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_196]),c_0_197]) ).
cnf(c_0_201,plain,
( epred1_3(X2,X1,X3)
| X1 != overflow
| X2 != spilling ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_202,plain,
( esk8_2(X1,X2) = overflow
| X2 = n0
| releasedAt(X1,X2)
| ~ releasedAt(X1,plus(X2,n1)) ),
inference(spm,[status(thm)],[c_0_125,c_0_82]) ).
cnf(c_0_203,plain,
( happens(overflow,esk4_3(X1,X2,spilling))
| ~ startedIn(X1,spilling,X2) ),
inference(spm,[status(thm)],[c_0_126,c_0_198]) ).
cnf(c_0_204,plain,
( ~ holdsAt(filling,plus(n1,esk2_3(X1,X2,X3)))
| ~ stoppedIn(X1,X2,X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_117]),c_0_61]) ).
cnf(c_0_205,plain,
( holdsAt(filling,n2)
| ~ less(n3,X1) ),
inference(spm,[status(thm)],[c_0_200,c_0_111]) ).
cnf(c_0_206,plain,
epred1_3(spilling,overflow,X1),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_201])]) ).
cnf(c_0_207,plain,
( X1 = n0
| releasedAt(X2,X1)
| ~ releasedAt(X2,plus(X1,n1)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_83]),c_0_147]) ).
cnf(c_0_208,plain,
( stoppedIn(X1,filling,X2)
| ~ startedIn(X3,spilling,X4)
| ~ less(X1,esk4_3(X3,X4,spilling))
| ~ less(esk4_3(X3,X4,spilling),X2) ),
inference(spm,[status(thm)],[c_0_116,c_0_203]) ).
cnf(c_0_209,plain,
( less_or_equal(X1,n2)
| ~ less(X1,n3) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_210,plain,
( ~ holdsAt(filling,n2)
| ~ stoppedIn(X1,X2,n2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_169]),c_0_81]) ).
cnf(c_0_211,plain,
holdsAt(filling,n2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_205,c_0_134]),c_0_135])]) ).
cnf(c_0_212,plain,
( startedIn(X1,spilling,X2)
| ~ less(X1,X3)
| ~ less(X3,X2)
| ~ happens(overflow,X3) ),
inference(spm,[status(thm)],[c_0_176,c_0_206]) ).
cnf(c_0_213,plain,
( ~ releasedAt(X1,n3)
| ~ initiates(X2,X1,n2)
| ~ happens(X2,n2) ),
inference(spm,[status(thm)],[c_0_100,c_0_132]) ).
cnf(c_0_214,plain,
( X1 = n0
| releasedAt(X2,X1)
| ~ releasedAt(X2,plus(n1,X1)) ),
inference(spm,[status(thm)],[c_0_207,c_0_61]) ).
cnf(c_0_215,plain,
( stoppedIn(X1,filling,X2)
| ~ startedIn(X1,spilling,X3)
| ~ less(esk4_3(X1,X3,spilling),X2) ),
inference(spm,[status(thm)],[c_0_208,c_0_162]) ).
cnf(c_0_216,plain,
( X1 = n2
| less(X1,n2)
| ~ less(X1,n3) ),
inference(spm,[status(thm)],[c_0_97,c_0_209]) ).
cnf(c_0_217,plain,
~ stoppedIn(X1,X2,n2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_210,c_0_211])]) ).
cnf(c_0_218,plain,
( startedIn(X1,spilling,X2)
| ~ less(X1,esk2_3(X3,X4,X5))
| ~ less(esk2_3(X3,X4,X5),X2)
| ~ stoppedIn(X3,X4,X5) ),
inference(spm,[status(thm)],[c_0_212,c_0_117]) ).
cnf(c_0_219,plain,
( releasedAt(filling,X1)
| ~ releasedAt(filling,plus(n1,X1)) ),
inference(spm,[status(thm)],[c_0_159,c_0_61]) ).
cnf(c_0_220,plain,
( ~ epred1_3(X1,X2,n2)
| ~ releasedAt(X1,n3)
| ~ happens(X2,n2) ),
inference(spm,[status(thm)],[c_0_213,c_0_107]) ).
cnf(c_0_221,plain,
( n3 = n0
| releasedAt(X1,n3)
| ~ releasedAt(X1,n4) ),
inference(spm,[status(thm)],[c_0_214,c_0_62]) ).
cnf(c_0_222,plain,
( esk4_3(X1,X2,spilling) = n2
| ~ startedIn(X1,spilling,X2)
| ~ less(esk4_3(X1,X2,spilling),n3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_216]),c_0_217]) ).
cnf(c_0_223,plain,
( less(esk4_3(X1,X2,X3),X2)
| ~ startedIn(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_224,plain,
( startedIn(X1,spilling,X2)
| ~ less(esk2_3(X1,X3,X4),X2)
| ~ stoppedIn(X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_218,c_0_138]) ).
cnf(c_0_225,plain,
~ releasedAt(filling,n3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_219,c_0_132]),c_0_171]) ).
cnf(c_0_226,plain,
( ~ releasedAt(waterLevel(X1),n3)
| ~ holdsAt(waterLevel(X1),n2)
| ~ happens(overflow,n2) ),
inference(spm,[status(thm)],[c_0_220,c_0_130]) ).
cnf(c_0_227,lemma,
( n3 = n0
| releasedAt(waterLevel(n3),n3) ),
inference(spm,[status(thm)],[c_0_221,c_0_151]) ).
cnf(c_0_228,plain,
( holdsAt(waterLevel(n3),esk4_3(X1,X2,spilling))
| ~ startedIn(X1,spilling,X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_203]),c_0_147]) ).
cnf(c_0_229,plain,
( esk4_3(X1,n3,spilling) = n2
| ~ startedIn(X1,spilling,n3) ),
inference(spm,[status(thm)],[c_0_222,c_0_223]) ).
cnf(c_0_230,plain,
( startedIn(X1,spilling,X2)
| ~ stoppedIn(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_224,c_0_120]) ).
cnf(c_0_231,plain,
( stoppedIn(X1,filling,X2)
| ~ less(X1,n2)
| ~ less(n2,X2) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_211]),c_0_61]),c_0_132]),c_0_61]),c_0_132]),c_0_225]),c_0_179]) ).
cnf(c_0_232,plain,
( holdsAt(X1,plus(n1,esk4_3(X2,X3,X1)))
| ~ startedIn(X2,X1,X3) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_105]),c_0_61]),c_0_126]) ).
cnf(c_0_233,plain,
( n3 = n0
| ~ holdsAt(waterLevel(n3),n2)
| ~ happens(overflow,n2) ),
inference(spm,[status(thm)],[c_0_226,c_0_227]) ).
cnf(c_0_234,plain,
( holdsAt(waterLevel(n3),n2)
| ~ startedIn(X1,spilling,n3) ),
inference(spm,[status(thm)],[c_0_228,c_0_229]) ).
cnf(c_0_235,plain,
( startedIn(X1,spilling,X2)
| ~ less(X1,n2)
| ~ less(n2,X2) ),
inference(spm,[status(thm)],[c_0_230,c_0_231]) ).
cnf(c_0_236,plain,
( holdsAt(spilling,n3)
| ~ startedIn(X1,spilling,n3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_232,c_0_229]),c_0_132]) ).
cnf(c_0_237,plain,
( n3 = n0
| ~ holdsAt(waterLevel(n3),n2)
| ~ holdsAt(filling,n2) ),
inference(spm,[status(thm)],[c_0_233,c_0_167]) ).
cnf(c_0_238,plain,
( holdsAt(waterLevel(n3),n2)
| ~ less(X1,n2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_234,c_0_235]),c_0_111])]) ).
cnf(c_0_239,plain,
( holdsAt(spilling,n3)
| ~ less(X1,n2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_236,c_0_235]),c_0_111])]) ).
cnf(c_0_240,plain,
( n3 = n0
| ~ holdsAt(waterLevel(n3),n2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_237,c_0_211])]) ).
cnf(c_0_241,plain,
holdsAt(waterLevel(n3),n2),
inference(spm,[status(thm)],[c_0_238,c_0_182]) ).
fof(c_0_242,hypothesis,
~ holdsAt(spilling,n0),
inference(fof_simplification,[status(thm)],[not_spilling_0]) ).
cnf(c_0_243,plain,
holdsAt(spilling,n3),
inference(spm,[status(thm)],[c_0_239,c_0_182]) ).
cnf(c_0_244,plain,
n3 = n0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_240,c_0_241])]) ).
cnf(c_0_245,hypothesis,
~ holdsAt(spilling,n0),
inference(split_conjunct,[status(thm)],[c_0_242]) ).
cnf(c_0_246,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_243,c_0_244]),c_0_245]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : CSR001+2 : TPTP v9.2.1. Bugfixed v3.1.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n026.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 16:26:23 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 3.80/3.07 % Version : CSE_E---1.7
% 3.80/3.07 % Problem : theBenchmark.p
% 3.80/3.07 % SZS status Theorem for theBenchmark.p
% 3.80/3.07 % SZS output start CNFRefutation
% See solution above
% 3.80/3.08 % Total time : 2.374s
%------------------------------------------------------------------------------