%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : CSR012+1 : TPTP v9.2.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n005.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 04:13:52 PM UTC 2026
% Result : Theorem 1.85s 1.87s
% Output : CNFRefutation 1.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 17
% Syntax : Number of formulae : 81 ( 26 unt; 0 def)
% Number of atoms : 458 ( 180 equ)
% Maximal formula atoms : 194 ( 5 avg)
% Number of connectives : 536 ( 159 ~; 270 |; 92 &)
% ( 7 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 52 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-4 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-3 aty)
% Number of variables : 173 ( 5 sgn 90 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(change_of_waterLevel,axiom,
! [X10,X5,X11,X7] :
( ( holdsAt(waterLevel(X10),X5)
& X11 = plus(X10,X7) )
=> trajectory(filling,X5,waterLevel(X11),X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+1.ax',change_of_waterLevel) ).
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/sandbox2/benchmark/Axioms/CSR001+0.ax',happens_not_released) ).
fof(symmetry_of_plus,axiom,
! [X12,X13] : plus(X12,X13) = plus(X13,X12),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_plus) ).
fof(less_or_equal,axiom,
! [X12,X13] :
( less_or_equal(X12,X13)
<=> ( less(X12,X13)
| X12 = X13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal) ).
fof(less1,axiom,
! [X12] :
( less(X12,n1)
<=> less_or_equal(X12,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less1) ).
fof(less0,axiom,
~ ? [X12] : less(X12,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less0) ).
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/sandbox2/benchmark/Axioms/CSR001+1.ax',initiates_all_defn) ).
fof(change_holding,axiom,
! [X4,X5,X2,X6,X7] :
( ( happens(X4,X5)
& initiates(X4,X2,X5)
& less(n0,X7)
& trajectory(X2,X5,X6,X7)
& ~ stoppedIn(X5,X2,plus(X5,X7)) )
=> holdsAt(X6,plus(X5,X7)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+0.ax',change_holding) ).
fof(plus0_1,axiom,
plus(n0,n1) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus0_1) ).
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/sandbox2/benchmark/Axioms/CSR001+0.ax',stoppedin_defn) ).
fof(happens_holds,axiom,
! [X4,X5,X2] :
( ( happens(X4,X5)
& initiates(X4,X2,X5) )
=> holdsAt(X2,plus(X5,n1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+0.ax',happens_holds) ).
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/sandbox2/benchmark/Axioms/CSR001+1.ax',happens_all_defn) ).
fof(waterLevel_1,conjecture,
holdsAt(waterLevel(n1),n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',waterLevel_1) ).
fof(keep_not_holding,axiom,
! [X2,X5] :
( ( ~ holdsAt(X2,X5)
& ~ releasedAt(X2,plus(X5,n1))
& ~ ? [X4] :
( happens(X4,X5)
& initiates(X4,X2,X5) ) )
=> ~ holdsAt(X2,plus(X5,n1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+0.ax',keep_not_holding) ).
fof(waterLevel_0,hypothesis,
holdsAt(waterLevel(n0),n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',waterLevel_0) ).
fof(not_filling_0,hypothesis,
~ holdsAt(filling,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_filling_0) ).
fof(c_0_16,plain,
! [X170,X171,X172,X173] :
( ~ holdsAt(waterLevel(X170),X171)
| X172 != plus(X170,X173)
| trajectory(filling,X171,waterLevel(X172),X173) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[change_of_waterLevel])]) ).
fof(c_0_17,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_18,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]) ).
cnf(c_0_19,plain,
( trajectory(filling,X2,waterLevel(X3),X4)
| ~ holdsAt(waterLevel(X1),X2)
| X3 != plus(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_20,plain,
! [X181,X182] : plus(X181,X182) = plus(X182,X181),
inference(variable_rename,[status(thm)],[symmetry_of_plus]) ).
fof(c_0_21,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])])]) ).
fof(c_0_22,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_23,plain,
! [X185] : ~ less(X185,n0),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[less0])]) ).
fof(c_0_24,axiom,
! [X4,X2,X5] :
( initiates(X4,X2,X5)
<=> epred1_3(X2,X4,X5) ),
inference(apply_def,[status(thm)],[initiates_all_defn,c_0_17]) ).
fof(c_0_25,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_18])])]) ).
fof(c_0_26,plain,
! [X4,X5,X2,X6,X7] :
( ( happens(X4,X5)
& initiates(X4,X2,X5)
& less(n0,X7)
& trajectory(X2,X5,X6,X7)
& ~ stoppedIn(X5,X2,plus(X5,X7)) )
=> holdsAt(X6,plus(X5,X7)) ),
inference(fof_simplification,[status(thm)],[change_holding]) ).
cnf(c_0_27,plain,
( trajectory(filling,X1,waterLevel(plus(X2,X3)),X3)
| ~ holdsAt(waterLevel(X2),X1) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_28,plain,
plus(X1,X2) = plus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,plain,
plus(n0,n1) = n1,
inference(split_conjunct,[status(thm)],[plus0_1]) ).
cnf(c_0_30,plain,
( less_or_equal(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_31,plain,
( less(X1,X2)
| X1 = X2
| ~ less_or_equal(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_32,plain,
( less_or_equal(X1,n0)
| ~ less(X1,n1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_33,plain,
~ less(X1,n0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_34,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_35,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])]) ).
fof(c_0_36,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_24])]) ).
fof(c_0_37,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_17])])])])])]) ).
cnf(c_0_38,plain,
( ~ initiates(X1,X2,X3)
| ~ happens(X1,X3)
| ~ releasedAt(X2,plus(X3,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_39,plain,
! [X120,X121,X122,X123,X124] :
( ~ happens(X120,X121)
| ~ initiates(X120,X122,X121)
| ~ less(n0,X124)
| ~ trajectory(X122,X121,X123,X124)
| stoppedIn(X121,X122,plus(X121,X124))
| holdsAt(X123,plus(X121,X124)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])]) ).
cnf(c_0_40,plain,
( trajectory(filling,X1,waterLevel(plus(X2,X3)),X2)
| ~ holdsAt(waterLevel(X3),X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_41,plain,
plus(n1,n0) = n1,
inference(rw,[status(thm)],[c_0_29,c_0_28]) ).
cnf(c_0_42,plain,
( less(X1,n1)
| ~ less_or_equal(X1,n0) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_43,plain,
less_or_equal(X1,X1),
inference(er,[status(thm)],[c_0_30]) ).
cnf(c_0_44,plain,
( X1 = n0
| ~ less(X1,n1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_45,plain,
( less(esk2_3(X1,X2,X3),X3)
| ~ stoppedIn(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_46,plain,
( holdsAt(X3,plus(X2,n1))
| ~ happens(X1,X2)
| ~ initiates(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_47,plain,
( initiates(X2,X1,X3)
| ~ epred1_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_48,plain,
( epred1_3(X2,X1,X3)
| X1 != tapOn
| X2 != filling ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_49,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])])]) ).
cnf(c_0_50,plain,
( ~ releasedAt(X1,plus(n1,X2))
| ~ initiates(X3,X1,X2)
| ~ happens(X3,X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_28]) ).
cnf(c_0_51,plain,
( stoppedIn(X2,X3,plus(X2,X4))
| holdsAt(X5,plus(X2,X4))
| ~ happens(X1,X2)
| ~ initiates(X1,X3,X2)
| ~ less(n0,X4)
| ~ trajectory(X3,X2,X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_52,plain,
( trajectory(filling,X1,waterLevel(n1),n1)
| ~ holdsAt(waterLevel(n0),X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_53,plain,
less(n0,n1),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
fof(c_0_54,negated_conjecture,
~ holdsAt(waterLevel(n1),n1),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[waterLevel_1])]) ).
cnf(c_0_55,plain,
( less(X1,esk2_3(X1,X2,X3))
| ~ stoppedIn(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_56,plain,
( esk2_3(X1,X2,n1) = n0
| ~ stoppedIn(X1,X2,n1) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
fof(c_0_57,plain,
! [X2,X5] :
( ( ~ holdsAt(X2,X5)
& ~ releasedAt(X2,plus(X5,n1))
& ~ ? [X4] :
( happens(X4,X5)
& initiates(X4,X2,X5) ) )
=> ~ holdsAt(X2,plus(X5,n1)) ),
inference(fof_simplification,[status(thm)],[keep_not_holding]) ).
cnf(c_0_58,plain,
( holdsAt(X1,plus(X2,n1))
| ~ epred1_3(X1,X3,X2)
| ~ happens(X3,X2) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_59,plain,
epred1_3(filling,tapOn,X1),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_48])]) ).
cnf(c_0_60,plain,
( happens(X1,X2)
| X1 != tapOn
| X2 != n0 ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_61,plain,
( ~ releasedAt(X1,n1)
| ~ initiates(X2,X1,n0)
| ~ happens(X2,n0) ),
inference(spm,[status(thm)],[c_0_50,c_0_41]) ).
cnf(c_0_62,plain,
( holdsAt(waterLevel(n1),plus(X1,n1))
| stoppedIn(X1,filling,plus(X1,n1))
| ~ holdsAt(waterLevel(n0),X1)
| ~ initiates(X2,filling,X1)
| ~ happens(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53])]) ).
cnf(c_0_63,hypothesis,
holdsAt(waterLevel(n0),n0),
inference(split_conjunct,[status(thm)],[waterLevel_0]) ).
cnf(c_0_64,negated_conjecture,
~ holdsAt(waterLevel(n1),n1),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_65,plain,
~ stoppedIn(X1,X2,n1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_33]) ).
fof(c_0_66,plain,
! [X133,X134] :
( ( happens(esk6_2(X133,X134),X134)
| holdsAt(X133,X134)
| releasedAt(X133,plus(X134,n1))
| ~ holdsAt(X133,plus(X134,n1)) )
& ( initiates(esk6_2(X133,X134),X133,X134)
| holdsAt(X133,X134)
| releasedAt(X133,plus(X134,n1))
| ~ holdsAt(X133,plus(X134,n1)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])])]) ).
cnf(c_0_67,plain,
( holdsAt(filling,plus(X1,n1))
| ~ happens(tapOn,X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_68,plain,
happens(tapOn,n0),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_60])]) ).
cnf(c_0_69,plain,
( ~ epred1_3(X1,X2,n0)
| ~ releasedAt(X1,n1)
| ~ happens(X2,n0) ),
inference(spm,[status(thm)],[c_0_61,c_0_47]) ).
fof(c_0_70,hypothesis,
~ holdsAt(filling,n0),
inference(fof_simplification,[status(thm)],[not_filling_0]) ).
cnf(c_0_71,hypothesis,
( ~ initiates(X1,filling,n0)
| ~ happens(X1,n0) ),
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_62,c_0_63]),c_0_28]),c_0_41]),c_0_28]),c_0_41]),c_0_64]),c_0_65]) ).
cnf(c_0_72,plain,
( initiates(esk6_2(X1,X2),X1,X2)
| holdsAt(X1,X2)
| releasedAt(X1,plus(X2,n1))
| ~ holdsAt(X1,plus(X2,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_73,plain,
holdsAt(filling,n1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_28]),c_0_41]) ).
cnf(c_0_74,plain,
~ releasedAt(filling,n1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_59]),c_0_68])]) ).
cnf(c_0_75,hypothesis,
~ holdsAt(filling,n0),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_76,plain,
( holdsAt(filling,X1)
| X2 = tapOn
| ~ happens(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_77,plain,
( happens(esk6_2(X1,X2),X2)
| holdsAt(X1,X2)
| releasedAt(X1,plus(X2,n1))
| ~ holdsAt(X1,plus(X2,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_78,hypothesis,
~ happens(esk6_2(filling,n0),n0),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_28]),c_0_41]),c_0_28]),c_0_41]),c_0_73])]),c_0_74]),c_0_75]) ).
cnf(c_0_79,plain,
( esk6_2(X1,X2) = tapOn
| releasedAt(X1,plus(X2,n1))
| holdsAt(filling,X2)
| holdsAt(X1,X2)
| ~ holdsAt(X1,plus(X2,n1)) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_80,hypothesis,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_28]),c_0_41]),c_0_68]),c_0_28]),c_0_41]),c_0_73])]),c_0_74]),c_0_75]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : CSR012+1 : TPTP v9.2.1. Bugfixed v3.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n005.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 16:26:45 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.85/1.87 % Version : CSE_E---1.7
% 1.85/1.87 % Problem : theBenchmark.p
% 1.85/1.87 % SZS status Theorem for theBenchmark.p
% 1.85/1.87 % SZS output start CNFRefutation
% See solution above
% 1.85/1.87 % Total time : 1.372s
%------------------------------------------------------------------------------