%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : CSR002+2 : 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 : n028.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 1.44s 1.76s
% Output : CNFRefutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 22
% Syntax : Number of formulae : 98 ( 34 unt; 0 def)
% Number of atoms : 499 ( 216 equ)
% Maximal formula atoms : 194 ( 5 avg)
% Number of connectives : 581 ( 180 ~; 283 |; 98 &)
% ( 12 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 52 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-3 aty)
% Number of variables : 163 ( 7 sgn 92 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
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(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/sandbox2/benchmark/Axioms/CSR001+0.ax',keep_not_released) ).
fof(plus0_1,axiom,
plus(n0,n1) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus0_1) ).
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(happens_terminates_not_holds,axiom,
! [X4,X5,X2] :
( ( happens(X4,X5)
& terminates(X4,X2,X5) )
=> ~ holdsAt(X2,plus(X5,n1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+0.ax',happens_terminates_not_holds) ).
fof(terminates_all_defn,axiom,
! [X4,X2,X5] :
( terminates(X4,X2,X5)
<=> ( ( X4 = tapOff
& X2 = filling )
| ( X4 = overflow
& X2 = filling ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+1.ax',terminates_all_defn) ).
fof(releases_all_defn,axiom,
! [X4,X2,X5] :
( releases(X4,X2,X5)
<=> ? [X9] :
( X4 = tapOn
& X2 = waterLevel(X9) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+1.ax',releases_all_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/sandbox2/benchmark/Axioms/CSR001+1.ax',happens_all_defn) ).
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(filling_not_waterLevel,axiom,
! [X12] : filling != waterLevel(X12),
file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+1.ax',filling_not_waterLevel) ).
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(less3,axiom,
! [X12] :
( less(X12,n3)
<=> less_or_equal(X12,n2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less3) ).
fof(less2,axiom,
! [X12] :
( less(X12,n2)
<=> less_or_equal(X12,n1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less2) ).
fof(less_property,axiom,
! [X12,X13] :
( less(X12,X13)
<=> ( ~ less(X13,X12)
& X13 != X12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_property) ).
fof(plus1_1,axiom,
plus(n1,n1) = n2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus1_1) ).
fof(not_filling_4,conjecture,
~ holdsAt(filling,n4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_filling_4) ).
fof(plus1_2,axiom,
plus(n1,n2) = n3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus1_2) ).
fof(plus1_3,axiom,
plus(n1,n3) = n4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus1_3) ).
fof(waterLevel_3,lemma,
holdsAt(waterLevel(n3),n3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',waterLevel_3) ).
fof(less1,axiom,
! [X12] :
( less(X12,n1)
<=> less_or_equal(X12,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less1) ).
fof(c_0_21,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_22,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_21])])]) ).
fof(c_0_23,plain,
! [X181,X182] : plus(X181,X182) = plus(X182,X181),
inference(variable_rename,[status(thm)],[symmetry_of_plus]) ).
fof(c_0_24,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_25,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]) ).
cnf(c_0_26,plain,
( ~ initiates(X1,X2,X3)
| ~ happens(X1,X3)
| ~ releasedAt(X2,plus(X3,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
plus(X1,X2) = plus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
plus(n0,n1) = n1,
inference(split_conjunct,[status(thm)],[plus0_1]) ).
fof(c_0_29,axiom,
! [X4,X2,X5] :
( initiates(X4,X2,X5)
<=> epred1_3(X2,X4,X5) ),
inference(apply_def,[status(thm)],[initiates_all_defn,c_0_24]) ).
fof(c_0_30,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]) ).
fof(c_0_31,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_32,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_33,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_25])])])]) ).
cnf(c_0_34,plain,
( ~ releasedAt(X1,plus(n1,X2))
| ~ initiates(X3,X1,X2)
| ~ happens(X3,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_35,plain,
plus(n1,n0) = n1,
inference(rw,[status(thm)],[c_0_28,c_0_27]) ).
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_29])]) ).
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_24])])])])])]) ).
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,
! [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_30])]) ).
cnf(c_0_40,plain,
( terminates(X1,X2,X3)
| X1 != overflow
| X2 != filling ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_41,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_42,plain,
! [X177] : filling != waterLevel(X177),
inference(variable_rename,[status(thm)],[filling_not_waterLevel]) ).
cnf(c_0_43,plain,
( X1 = waterLevel(esk9_2(X2,X1))
| ~ releases(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_44,plain,
( releases(esk8_2(X1,X2),X1,X2)
| releasedAt(X1,X2)
| ~ releasedAt(X1,plus(X2,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_45,plain,
( ~ releasedAt(X1,n1)
| ~ initiates(X2,X1,n0)
| ~ happens(X2,n0) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_46,plain,
( initiates(X2,X1,X3)
| ~ epred1_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_47,plain,
( epred1_3(X2,X1,X3)
| X1 != tapOn
| X2 != filling ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_48,plain,
( happens(X1,X2)
| X1 != tapOn
| X2 != n0 ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_49,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_50,plain,
( ~ happens(X1,X2)
| ~ terminates(X1,X3,X2)
| ~ holdsAt(X3,plus(X2,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_51,plain,
terminates(overflow,filling,X1),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_40])]) ).
cnf(c_0_52,plain,
( happens(X2,X1)
| ~ holdsAt(waterLevel(n3),X1)
| ~ holdsAt(filling,X1)
| X2 != overflow ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_53,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])]) ).
fof(c_0_54,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_55,plain,
( less_or_equal(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_56,plain,
filling != waterLevel(X1),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_57,plain,
( waterLevel(esk9_2(esk8_2(X1,X2),X1)) = X1
| releasedAt(X1,X2)
| ~ releasedAt(X1,plus(X2,n1)) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_58,plain,
( ~ epred1_3(X1,X2,n0)
| ~ releasedAt(X1,n1)
| ~ happens(X2,n0) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_59,plain,
epred1_3(filling,tapOn,X1),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_47])]) ).
cnf(c_0_60,plain,
happens(tapOn,n0),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_48])]) ).
fof(c_0_61,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_49])])])]) ).
cnf(c_0_62,plain,
( ~ holdsAt(filling,plus(X1,n1))
| ~ happens(overflow,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_63,plain,
( happens(overflow,X1)
| ~ holdsAt(waterLevel(n3),X1)
| ~ holdsAt(filling,X1) ),
inference(er,[status(thm)],[c_0_52]) ).
fof(c_0_64,plain,
! [X12,X13] :
( less(X12,X13)
<=> ( ~ less(X13,X12)
& X13 != X12 ) ),
inference(fof_simplification,[status(thm)],[less_property]) ).
cnf(c_0_65,plain,
( less(X1,n3)
| ~ less_or_equal(X1,n2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_66,plain,
( less_or_equal(X1,X2)
| ~ less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_67,plain,
( less(X1,n2)
| ~ less_or_equal(X1,n1) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_68,plain,
less_or_equal(X1,X1),
inference(er,[status(thm)],[c_0_55]) ).
cnf(c_0_69,plain,
( releasedAt(filling,X1)
| ~ releasedAt(filling,plus(X1,n1)) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57])]) ).
cnf(c_0_70,plain,
plus(n1,n1) = n2,
inference(split_conjunct,[status(thm)],[plus1_1]) ).
cnf(c_0_71,plain,
~ releasedAt(filling,n1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60])]) ).
cnf(c_0_72,plain,
( holdsAt(filling,X1)
| X1 = n0
| ~ happens(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_73,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_61]) ).
cnf(c_0_74,plain,
( ~ holdsAt(filling,plus(X1,n1))
| ~ holdsAt(waterLevel(n3),X1)
| ~ holdsAt(filling,X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
fof(c_0_75,negated_conjecture,
holdsAt(filling,n4),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[not_filling_4])]) ).
fof(c_0_76,plain,
! [X195,X196] :
( ( ~ less(X196,X195)
| ~ less(X195,X196) )
& ( X196 != X195
| ~ less(X195,X196) )
& ( less(X196,X195)
| X196 = X195
| less(X195,X196) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_64])])]) ).
cnf(c_0_77,plain,
( less(X1,n3)
| ~ less(X1,n2) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_78,plain,
less(n1,n2),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_79,plain,
( releasedAt(filling,X1)
| ~ releasedAt(filling,plus(n1,X1)) ),
inference(spm,[status(thm)],[c_0_69,c_0_27]) ).
cnf(c_0_80,plain,
plus(n1,n2) = n3,
inference(split_conjunct,[status(thm)],[plus1_2]) ).
cnf(c_0_81,plain,
~ releasedAt(filling,n2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]) ).
cnf(c_0_82,plain,
( X1 = n0
| releasedAt(X2,plus(X1,n1))
| holdsAt(filling,X1)
| holdsAt(X2,X1)
| ~ holdsAt(X2,plus(X1,n1)) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_83,plain,
( ~ holdsAt(filling,plus(n1,X1))
| ~ holdsAt(waterLevel(n3),X1)
| ~ holdsAt(filling,X1) ),
inference(spm,[status(thm)],[c_0_74,c_0_27]) ).
cnf(c_0_84,plain,
plus(n1,n3) = n4,
inference(split_conjunct,[status(thm)],[plus1_3]) ).
cnf(c_0_85,negated_conjecture,
holdsAt(filling,n4),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_86,lemma,
holdsAt(waterLevel(n3),n3),
inference(split_conjunct,[status(thm)],[waterLevel_3]) ).
fof(c_0_87,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])]) ).
cnf(c_0_88,plain,
( ~ less(X1,X2)
| ~ less(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_89,plain,
less(n1,n3),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_90,plain,
~ releasedAt(filling,n3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]) ).
cnf(c_0_91,plain,
( X1 = n0
| releasedAt(filling,X1)
| holdsAt(filling,X1)
| ~ holdsAt(filling,plus(X1,n1)) ),
inference(spm,[status(thm)],[c_0_69,c_0_82]) ).
cnf(c_0_92,plain,
~ holdsAt(filling,n3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85]),c_0_86])]) ).
cnf(c_0_93,plain,
( less(X1,n1)
| ~ less_or_equal(X1,n0) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_94,plain,
~ less(n3,n1),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_95,plain,
n3 = n0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_27]),c_0_84]),c_0_85])]),c_0_92]) ).
cnf(c_0_96,plain,
less(n0,n1),
inference(spm,[status(thm)],[c_0_93,c_0_68]) ).
cnf(c_0_97,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_95]),c_0_96])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : CSR002+2 : 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
% 0.13/0.32 % Computer : n028.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon May 4 16:26:16 EDT 2026
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % start to proof: theBenchmark
% 1.44/1.76 % Version : CSE_E---1.7
% 1.44/1.76 % Problem : theBenchmark.p
% 1.44/1.76 % SZS status Theorem for theBenchmark.p
% 1.44/1.76 % SZS output start CNFRefutation
% See solution above
% 1.44/1.76 % Total time : 1.368s
%------------------------------------------------------------------------------