%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : CSR002+2 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:15:51 PM UTC 2026
% Result : Theorem 0.41s 0.51s
% Output : CNFRefutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 23
% Syntax : Number of formulae : 109 ( 36 unt; 0 def)
% Number of atoms : 525 ( 219 equ)
% Maximal formula atoms : 194 ( 4 avg)
% Number of connectives : 608 ( 192 ~; 296 |; 99 &)
% ( 12 <=>; 9 =>; 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 : 189 ( 14 sgn 99 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(releases_all_defn,axiom,
! [X4,X2,X5] :
( releases(X4,X2,X5)
<=> ? [X9] :
( X2 = waterLevel(X9)
& X4 = tapOn ) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax',releases_all_defn) ).
fof(happens_releases,axiom,
! [X4,X5,X2] :
( ( releases(X4,X2,X5)
& happens(X4,X5) )
=> releasedAt(X2,plus(X5,n1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+0.ax',happens_releases) ).
fof(symmetry_of_plus,axiom,
! [X12,X13] : plus(X12,X13) = plus(X13,X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_plus) ).
fof(happens_all_defn,axiom,
! [X4,X5] :
( happens(X4,X5)
<=> ( ( X4 = overflow
& holdsAt(filling,X5)
& holdsAt(waterLevel(n3),X5) )
| ( X5 = n0
& X4 = tapOn ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax',happens_all_defn) ).
fof(keep_not_released,axiom,
! [X2,X5] :
( ( ~ ? [X4] :
( releases(X4,X2,X5)
& happens(X4,X5) )
& ~ releasedAt(X2,X5) )
=> ~ releasedAt(X2,plus(X5,n1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+0.ax',keep_not_released) ).
fof(happens_not_released,axiom,
! [X4,X5,X2] :
( ( ( terminates(X4,X2,X5)
| initiates(X4,X2,X5) )
& happens(X4,X5) )
=> ~ releasedAt(X2,plus(X5,n1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+0.ax',happens_not_released) ).
fof(happens_terminates_not_holds,axiom,
! [X4,X5,X2] :
( ( terminates(X4,X2,X5)
& happens(X4,X5) )
=> ~ holdsAt(X2,plus(X5,n1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+0.ax',happens_terminates_not_holds) ).
fof(terminates_all_defn,axiom,
! [X4,X2,X5] :
( terminates(X4,X2,X5)
<=> ( ( X2 = filling
& X4 = overflow )
| ( X2 = filling
& X4 = tapOff ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax',terminates_all_defn) ).
fof(plus0_1,axiom,
plus(n0,n1) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus0_1) ).
fof(less_or_equal,axiom,
! [X12,X13] :
( less_or_equal(X12,X13)
<=> ( X12 = X13
| less(X12,X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal) ).
fof(filling_not_waterLevel,axiom,
! [X12] : filling != waterLevel(X12),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax',filling_not_waterLevel) ).
fof(keep_not_holding,axiom,
! [X2,X5] :
( ( ~ ? [X4] :
( initiates(X4,X2,X5)
& happens(X4,X5) )
& ~ releasedAt(X2,plus(X5,n1))
& ~ holdsAt(X2,X5) )
=> ~ holdsAt(X2,plus(X5,n1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+0.ax',keep_not_holding) ).
fof(initiates_all_defn,axiom,
! [X4,X2,X5] :
( initiates(X4,X2,X5)
<=> ( ? [X9] :
( X2 = waterLevel(X9)
& X4 = overflow
& holdsAt(waterLevel(X9),X5) )
| ? [X9] :
( X2 = waterLevel(X9)
& X4 = tapOff
& holdsAt(waterLevel(X9),X5) )
| ( X2 = spilling
& X4 = overflow )
| ( X2 = filling
& X4 = tapOn ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+1.ax',initiates_all_defn) ).
fof(less3,axiom,
! [X12] :
( less(X12,n3)
<=> less_or_equal(X12,n2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less3) ).
fof(less2,axiom,
! [X12] :
( less(X12,n2)
<=> less_or_equal(X12,n1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less2) ).
fof(not_filling_4,conjecture,
~ holdsAt(filling,n4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_filling_4) ).
fof(less_property,axiom,
! [X12,X13] :
( less(X12,X13)
<=> ( X13 != X12
& ~ less(X13,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_property) ).
fof(plus1_1,axiom,
plus(n1,n1) = n2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus1_1) ).
fof(plus1_2,axiom,
plus(n1,n2) = n3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus1_2) ).
fof(plus1_3,axiom,
plus(n1,n3) = n4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus1_3) ).
fof(waterLevel_3,lemma,
holdsAt(waterLevel(n3),n3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',waterLevel_3) ).
fof(less1,axiom,
! [X12] :
( less(X12,n1)
<=> less_or_equal(X12,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less1) ).
fof(c_0_22,plain,
! [X74,X75,X76,X78,X79,X80,X81] :
( ( releases(X78,X79,X81)
| X79 != waterLevel(X80)
| X78 != tapOn )
& ( ~ releases(X74,X75,X76)
| X75 = waterLevel(esk9_2(X74,X75)) )
& ( ~ releases(X74,X75,X76)
| X74 = tapOn ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_23,plain,
! [X62,X63,X64] :
( releasedAt(X64,plus(X63,n1))
| ~ releases(X62,X64,X63)
| ~ happens(X62,X63) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[happens_releases])])]) ).
cnf(c_0_24,plain,
( X2 != waterLevel(X3)
| X1 != tapOn
| releases(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_25,plain,
( ~ releases(X1,X3,X2)
| ~ happens(X1,X2)
| releasedAt(X3,plus(X2,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_26,plain,
releases(tapOn,waterLevel(X1),X2),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_24])]) ).
fof(c_0_27,plain,
! [X95,X96] : plus(X95,X96) = plus(X96,X95),
inference(variable_rename,[status(thm)],[symmetry_of_plus]) ).
fof(c_0_28,plain,
! [X82,X83] :
( ( happens(X82,X83)
| X82 != overflow
| ~ holdsAt(filling,X83)
| ~ holdsAt(waterLevel(n3),X83) )
& ( happens(X82,X83)
| X83 != n0
| X82 != tapOn )
& ( ~ happens(X82,X83)
| X83 = n0
| X82 = overflow )
& ( ~ happens(X82,X83)
| X83 = n0
| holdsAt(filling,X83) )
& ( ~ happens(X82,X83)
| X83 = n0
| holdsAt(waterLevel(n3),X83) )
& ( ~ happens(X82,X83)
| X82 = tapOn
| X82 = overflow )
& ( ~ happens(X82,X83)
| X82 = tapOn
| holdsAt(filling,X83) )
& ( ~ happens(X82,X83)
| X82 = tapOn
| holdsAt(waterLevel(n3),X83) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[happens_all_defn])])])]) ).
fof(c_0_29,plain,
! [X2,X5] :
( ( ~ ? [X4] :
( releases(X4,X2,X5)
& happens(X4,X5) )
& ~ releasedAt(X2,X5) )
=> ~ releasedAt(X2,plus(X5,n1)) ),
inference(fof_simplification,[status(thm)],[keep_not_released]) ).
fof(c_0_30,plain,
! [X4,X5,X2] :
( ( ( terminates(X4,X2,X5)
| initiates(X4,X2,X5) )
& happens(X4,X5) )
=> ~ releasedAt(X2,plus(X5,n1)) ),
inference(fof_simplification,[status(thm)],[happens_not_released]) ).
fof(c_0_31,plain,
! [X4,X5,X2] :
( ( terminates(X4,X2,X5)
& happens(X4,X5) )
=> ~ holdsAt(X2,plus(X5,n1)) ),
inference(fof_simplification,[status(thm)],[happens_terminates_not_holds]) ).
fof(c_0_32,plain,
! [X71,X72,X73] :
( ( terminates(X71,X72,X73)
| X72 != filling
| X71 != overflow )
& ( terminates(X71,X72,X73)
| X72 != filling
| X71 != tapOff )
& ( ~ terminates(X71,X72,X73)
| X72 = filling
| X72 = filling )
& ( ~ terminates(X71,X72,X73)
| X72 = filling
| X71 = overflow )
& ( ~ terminates(X71,X72,X73)
| X71 = tapOff
| X72 = filling )
& ( ~ terminates(X71,X72,X73)
| X71 = tapOff
| X71 = overflow ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[terminates_all_defn])])])]) ).
cnf(c_0_33,plain,
( ~ happens(tapOn,X2)
| releasedAt(waterLevel(X1),plus(X2,n1)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_34,plain,
plus(X1,X2) = plus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,plain,
plus(n0,n1) = n1,
inference(split_conjunct,[status(thm)],[plus0_1]) ).
cnf(c_0_36,plain,
( X2 != n0
| X1 != tapOn
| happens(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_37,plain,
! [X53,X54] :
( ( ~ releasedAt(X53,plus(X54,n1))
| releasedAt(X53,X54)
| releases(esk8_2(X53,X54),X53,X54) )
& ( ~ releasedAt(X53,plus(X54,n1))
| releasedAt(X53,X54)
| happens(esk8_2(X53,X54),X54) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])])])]) ).
fof(c_0_38,plain,
! [X65,X66,X67] :
( ( ~ releasedAt(X67,plus(X66,n1))
| ~ happens(X65,X66)
| ~ terminates(X65,X67,X66) )
& ( ~ releasedAt(X67,plus(X66,n1))
| ~ happens(X65,X66)
| ~ initiates(X65,X67,X66) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])])]) ).
fof(c_0_39,plain,
! [X5,X4,X2] :
( epred1_3(X2,X4,X5)
<=> ( ? [X9] :
( X2 = waterLevel(X9)
& X4 = overflow
& holdsAt(waterLevel(X9),X5) )
| ? [X9] :
( X2 = waterLevel(X9)
& X4 = tapOff
& holdsAt(waterLevel(X9),X5) )
| ( X2 = spilling
& X4 = overflow )
| ( X2 = filling
& X4 = tapOn ) ) ),
introduced(definition) ).
fof(c_0_40,plain,
! [X59,X60,X61] :
( ~ holdsAt(X61,plus(X60,n1))
| ~ terminates(X59,X61,X60)
| ~ happens(X59,X60) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])]) ).
cnf(c_0_41,plain,
( X2 != filling
| X1 != overflow
| terminates(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_42,plain,
! [X97,X98] :
( ( less_or_equal(X97,X98)
| X97 != X98 )
& ( less_or_equal(X97,X98)
| ~ less(X97,X98) )
& ( X97 = X98
| less(X97,X98)
| ~ less_or_equal(X97,X98) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[less_or_equal])])])]) ).
cnf(c_0_43,plain,
( ~ happens(tapOn,X2)
| releasedAt(waterLevel(X1),plus(n1,X2)) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_44,plain,
plus(n1,n0) = n1,
inference(rw,[status(thm)],[c_0_35,c_0_34]) ).
cnf(c_0_45,plain,
happens(tapOn,n0),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_36])]) ).
cnf(c_0_46,plain,
( ~ releases(X2,X1,X3)
| X1 = waterLevel(esk9_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_47,plain,
( ~ releasedAt(X1,plus(X2,n1))
| releasedAt(X1,X2)
| releases(esk8_2(X1,X2),X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_48,plain,
! [X12] : filling != waterLevel(X12),
inference(fof_simplification,[status(thm)],[filling_not_waterLevel]) ).
fof(c_0_49,plain,
! [X2,X5] :
( ( ~ ? [X4] :
( initiates(X4,X2,X5)
& happens(X4,X5) )
& ~ releasedAt(X2,plus(X5,n1))
& ~ holdsAt(X2,X5) )
=> ~ holdsAt(X2,plus(X5,n1)) ),
inference(fof_simplification,[status(thm)],[keep_not_holding]) ).
cnf(c_0_50,plain,
( ~ releasedAt(X2,plus(X3,n1))
| ~ happens(X1,X3)
| ~ initiates(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_51,axiom,
! [X4,X2,X5] :
( initiates(X4,X2,X5)
<=> epred1_3(X2,X4,X5) ),
inference(apply_def,[status(thm)],[initiates_all_defn,c_0_39]) ).
cnf(c_0_52,plain,
( ~ holdsAt(X3,plus(X2,n1))
| ~ terminates(X1,X3,X2)
| ~ happens(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_53,plain,
terminates(overflow,filling,X1),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_41])]) ).
cnf(c_0_54,plain,
( X2 != overflow
| ~ holdsAt(filling,X1)
| ~ holdsAt(waterLevel(n3),X1)
| happens(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_55,plain,
! [X102] :
( ( less(X102,n3)
| ~ less_or_equal(X102,n2) )
& ( less_or_equal(X102,n2)
| ~ less(X102,n3) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[less3])])]) ).
fof(c_0_56,plain,
! [X101] :
( ( less(X101,n2)
| ~ less_or_equal(X101,n1) )
& ( less_or_equal(X101,n1)
| ~ less(X101,n2) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[less2])])]) ).
cnf(c_0_57,plain,
( X1 != X2
| less_or_equal(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_58,plain,
releasedAt(waterLevel(X1),n1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).
cnf(c_0_59,plain,
( ~ releasedAt(X1,plus(X2,n1))
| releasedAt(X1,X2)
| waterLevel(esk9_2(esk8_2(X1,X2),X1)) = X1 ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
fof(c_0_60,plain,
! [X91] : filling != waterLevel(X91),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_48])]) ).
fof(c_0_61,plain,
! [X47,X48] :
( ( ~ holdsAt(X47,plus(X48,n1))
| releasedAt(X47,plus(X48,n1))
| holdsAt(X47,X48)
| initiates(esk6_2(X47,X48),X47,X48) )
& ( ~ holdsAt(X47,plus(X48,n1))
| releasedAt(X47,plus(X48,n1))
| holdsAt(X47,X48)
| happens(esk6_2(X47,X48),X48) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])])])]) ).
cnf(c_0_62,plain,
( ~ happens(X3,X2)
| ~ initiates(X3,X1,X2)
| ~ releasedAt(X1,plus(n1,X2)) ),
inference(spm,[status(thm)],[c_0_50,c_0_34]) ).
fof(c_0_63,plain,
! [X68,X69,X70] :
( ( initiates(X68,X69,X70)
| ~ epred1_3(X69,X68,X70) )
& ( epred1_3(X69,X68,X70)
| ~ initiates(X68,X69,X70) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_51])])]) ).
fof(c_0_64,plain,
! [X112,X113,X114,X117,X118,X119,X120,X121] :
( ( epred1_3(X119,X118,X117)
| X119 != waterLevel(X121)
| X118 != overflow
| ~ holdsAt(waterLevel(X121),X117) )
& ( epred1_3(X119,X118,X117)
| X119 != waterLevel(X120)
| X118 != tapOff
| ~ holdsAt(waterLevel(X120),X117) )
& ( epred1_3(X119,X118,X117)
| X119 != spilling
| X118 != overflow )
& ( epred1_3(X119,X118,X117)
| X119 != filling
| X118 != tapOn )
& ( ~ epred1_3(X114,X113,X112)
| X114 = filling
| X114 = spilling
| X114 = waterLevel(esk10_3(X112,X113,X114))
| X114 = waterLevel(esk11_3(X112,X113,X114)) )
& ( ~ epred1_3(X114,X113,X112)
| X114 = filling
| X114 = spilling
| X114 = waterLevel(esk10_3(X112,X113,X114))
| X113 = overflow )
& ( ~ epred1_3(X114,X113,X112)
| X114 = filling
| X114 = spilling
| X114 = waterLevel(esk10_3(X112,X113,X114))
| holdsAt(waterLevel(esk11_3(X112,X113,X114)),X112) )
& ( ~ epred1_3(X114,X113,X112)
| X114 = filling
| X114 = spilling
| X113 = tapOff
| X114 = waterLevel(esk11_3(X112,X113,X114)) )
& ( ~ epred1_3(X114,X113,X112)
| X114 = filling
| X114 = spilling
| X113 = tapOff
| X113 = overflow )
& ( ~ epred1_3(X114,X113,X112)
| X114 = filling
| X114 = spilling
| X113 = tapOff
| holdsAt(waterLevel(esk11_3(X112,X113,X114)),X112) )
& ( ~ epred1_3(X114,X113,X112)
| X114 = filling
| X114 = spilling
| holdsAt(waterLevel(esk10_3(X112,X113,X114)),X112)
| X114 = waterLevel(esk11_3(X112,X113,X114)) )
& ( ~ epred1_3(X114,X113,X112)
| X114 = filling
| X114 = spilling
| holdsAt(waterLevel(esk10_3(X112,X113,X114)),X112)
| X113 = overflow )
& ( ~ epred1_3(X114,X113,X112)
| X114 = filling
| X114 = spilling
| holdsAt(waterLevel(esk10_3(X112,X113,X114)),X112)
| holdsAt(waterLevel(esk11_3(X112,X113,X114)),X112) )
& ( ~ epred1_3(X114,X113,X112)
| X114 = filling
| X113 = overflow
| X114 = waterLevel(esk10_3(X112,X113,X114))
| X114 = waterLevel(esk11_3(X112,X113,X114)) )
& ( ~ epred1_3(X114,X113,X112)
| X114 = filling
| X113 = overflow
| X114 = waterLevel(esk10_3(X112,X113,X114))
| X113 = overflow )
& ( ~ epred1_3(X114,X113,X112)
| X114 = filling
| X113 = overflow
| X114 = waterLevel(esk10_3(X112,X113,X114))
| holdsAt(waterLevel(esk11_3(X112,X113,X114)),X112) )
& ( ~ epred1_3(X114,X113,X112)
| X114 = filling
| X113 = overflow
| X113 = tapOff
| X114 = waterLevel(esk11_3(X112,X113,X114)) )
& ( ~ epred1_3(X114,X113,X112)
| X114 = filling
| X113 = overflow
| X113 = tapOff
| X113 = overflow )
& ( ~ epred1_3(X114,X113,X112)
| X114 = filling
| X113 = overflow
| X113 = tapOff
| holdsAt(waterLevel(esk11_3(X112,X113,X114)),X112) )
& ( ~ epred1_3(X114,X113,X112)
| X114 = filling
| X113 = overflow
| holdsAt(waterLevel(esk10_3(X112,X113,X114)),X112)
| X114 = waterLevel(esk11_3(X112,X113,X114)) )
& ( ~ epred1_3(X114,X113,X112)
| X114 = filling
| X113 = overflow
| holdsAt(waterLevel(esk10_3(X112,X113,X114)),X112)
| X113 = overflow )
& ( ~ epred1_3(X114,X113,X112)
| X114 = filling
| X113 = overflow
| holdsAt(waterLevel(esk10_3(X112,X113,X114)),X112)
| holdsAt(waterLevel(esk11_3(X112,X113,X114)),X112) )
& ( ~ epred1_3(X114,X113,X112)
| X113 = tapOn
| X114 = spilling
| X114 = waterLevel(esk10_3(X112,X113,X114))
| X114 = waterLevel(esk11_3(X112,X113,X114)) )
& ( ~ epred1_3(X114,X113,X112)
| X113 = tapOn
| X114 = spilling
| X114 = waterLevel(esk10_3(X112,X113,X114))
| X113 = overflow )
& ( ~ epred1_3(X114,X113,X112)
| X113 = tapOn
| X114 = spilling
| X114 = waterLevel(esk10_3(X112,X113,X114))
| holdsAt(waterLevel(esk11_3(X112,X113,X114)),X112) )
& ( ~ epred1_3(X114,X113,X112)
| X113 = tapOn
| X114 = spilling
| X113 = tapOff
| X114 = waterLevel(esk11_3(X112,X113,X114)) )
& ( ~ epred1_3(X114,X113,X112)
| X113 = tapOn
| X114 = spilling
| X113 = tapOff
| X113 = overflow )
& ( ~ epred1_3(X114,X113,X112)
| X113 = tapOn
| X114 = spilling
| X113 = tapOff
| holdsAt(waterLevel(esk11_3(X112,X113,X114)),X112) )
& ( ~ epred1_3(X114,X113,X112)
| X113 = tapOn
| X114 = spilling
| holdsAt(waterLevel(esk10_3(X112,X113,X114)),X112)
| X114 = waterLevel(esk11_3(X112,X113,X114)) )
& ( ~ epred1_3(X114,X113,X112)
| X113 = tapOn
| X114 = spilling
| holdsAt(waterLevel(esk10_3(X112,X113,X114)),X112)
| X113 = overflow )
& ( ~ epred1_3(X114,X113,X112)
| X113 = tapOn
| X114 = spilling
| holdsAt(waterLevel(esk10_3(X112,X113,X114)),X112)
| holdsAt(waterLevel(esk11_3(X112,X113,X114)),X112) )
& ( ~ epred1_3(X114,X113,X112)
| X113 = tapOn
| X113 = overflow
| X114 = waterLevel(esk10_3(X112,X113,X114))
| X114 = waterLevel(esk11_3(X112,X113,X114)) )
& ( ~ epred1_3(X114,X113,X112)
| X113 = tapOn
| X113 = overflow
| X114 = waterLevel(esk10_3(X112,X113,X114))
| X113 = overflow )
& ( ~ epred1_3(X114,X113,X112)
| X113 = tapOn
| X113 = overflow
| X114 = waterLevel(esk10_3(X112,X113,X114))
| holdsAt(waterLevel(esk11_3(X112,X113,X114)),X112) )
& ( ~ epred1_3(X114,X113,X112)
| X113 = tapOn
| X113 = overflow
| X113 = tapOff
| X114 = waterLevel(esk11_3(X112,X113,X114)) )
& ( ~ epred1_3(X114,X113,X112)
| X113 = tapOn
| X113 = overflow
| X113 = tapOff
| X113 = overflow )
& ( ~ epred1_3(X114,X113,X112)
| X113 = tapOn
| X113 = overflow
| X113 = tapOff
| holdsAt(waterLevel(esk11_3(X112,X113,X114)),X112) )
& ( ~ epred1_3(X114,X113,X112)
| X113 = tapOn
| X113 = overflow
| holdsAt(waterLevel(esk10_3(X112,X113,X114)),X112)
| X114 = waterLevel(esk11_3(X112,X113,X114)) )
& ( ~ epred1_3(X114,X113,X112)
| X113 = tapOn
| X113 = overflow
| holdsAt(waterLevel(esk10_3(X112,X113,X114)),X112)
| X113 = overflow )
& ( ~ epred1_3(X114,X113,X112)
| X113 = tapOn
| X113 = overflow
| holdsAt(waterLevel(esk10_3(X112,X113,X114)),X112)
| holdsAt(waterLevel(esk11_3(X112,X113,X114)),X112) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_39])])])])])])]) ).
cnf(c_0_65,plain,
( ~ happens(overflow,X1)
| ~ holdsAt(filling,plus(X1,n1)) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_66,plain,
( ~ holdsAt(filling,X1)
| ~ holdsAt(waterLevel(n3),X1)
| happens(overflow,X1) ),
inference(er,[status(thm)],[c_0_54]) ).
fof(c_0_67,negated_conjecture,
~ ~ holdsAt(filling,n4),
inference(assume_negation,[status(cth)],[not_filling_4]) ).
fof(c_0_68,plain,
! [X12,X13] :
( less(X12,X13)
<=> ( X13 != X12
& ~ less(X13,X12) ) ),
inference(fof_simplification,[status(thm)],[less_property]) ).
cnf(c_0_69,plain,
( ~ less_or_equal(X1,n2)
| less(X1,n3) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_70,plain,
( ~ less(X1,X2)
| less_or_equal(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_71,plain,
( ~ less_or_equal(X1,n1)
| less(X1,n2) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_72,plain,
less_or_equal(X1,X1),
inference(er,[status(thm)],[c_0_57]) ).
cnf(c_0_73,plain,
( ~ releasedAt(X1,plus(X2,n1))
| releasedAt(X1,X2)
| releasedAt(X1,n1) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_74,plain,
plus(n1,n1) = n2,
inference(split_conjunct,[status(thm)],[plus1_1]) ).
cnf(c_0_75,plain,
filling != waterLevel(X1),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_76,plain,
( ~ happens(X2,X1)
| X1 = n0
| holdsAt(filling,X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_77,plain,
( ~ holdsAt(X1,plus(X2,n1))
| releasedAt(X1,plus(X2,n1))
| holdsAt(X1,X2)
| happens(esk6_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_78,plain,
( ~ happens(X2,n0)
| ~ initiates(X2,X1,n0)
| ~ releasedAt(X1,n1) ),
inference(spm,[status(thm)],[c_0_62,c_0_44]) ).
cnf(c_0_79,plain,
( ~ epred1_3(X1,X2,X3)
| initiates(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_80,plain,
( X2 != filling
| X1 != tapOn
| epred1_3(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_81,plain,
( ~ holdsAt(filling,X1)
| ~ holdsAt(waterLevel(n3),X1)
| ~ holdsAt(filling,plus(X1,n1)) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
fof(c_0_82,negated_conjecture,
holdsAt(filling,n4),
inference(fof_simplification,[status(thm)],[c_0_67]) ).
fof(c_0_83,plain,
! [X109,X110] :
( ( less(X109,X110)
| X110 = X109
| less(X110,X109) )
& ( ~ less(X109,X110)
| X110 != X109 )
& ( ~ less(X109,X110)
| ~ less(X110,X109) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_68])])])]) ).
cnf(c_0_84,plain,
( ~ less(X1,n2)
| less(X1,n3) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_85,plain,
less(n1,n2),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_86,plain,
( ~ releasedAt(X1,plus(n1,X2))
| releasedAt(X1,X2)
| releasedAt(X1,n1) ),
inference(spm,[status(thm)],[c_0_73,c_0_34]) ).
cnf(c_0_87,plain,
plus(n1,n2) = n3,
inference(split_conjunct,[status(thm)],[plus1_2]) ).
cnf(c_0_88,plain,
( ~ releasedAt(X1,n2)
| releasedAt(X1,n1) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_89,plain,
( ~ releasedAt(filling,plus(X1,n1))
| releasedAt(filling,X1) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_59])]) ).
cnf(c_0_90,plain,
( ~ holdsAt(X2,plus(X1,n1))
| holdsAt(X2,X1)
| holdsAt(filling,X1)
| releasedAt(X2,plus(X1,n1))
| X1 = n0 ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_91,plain,
( ~ happens(X2,n0)
| ~ releasedAt(X1,n1)
| ~ epred1_3(X1,X2,n0) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_92,plain,
epred1_3(filling,tapOn,X1),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_80])]) ).
cnf(c_0_93,plain,
( ~ holdsAt(filling,X1)
| ~ holdsAt(waterLevel(n3),X1)
| ~ holdsAt(filling,plus(n1,X1)) ),
inference(spm,[status(thm)],[c_0_81,c_0_34]) ).
cnf(c_0_94,plain,
plus(n1,n3) = n4,
inference(split_conjunct,[status(thm)],[plus1_3]) ).
cnf(c_0_95,negated_conjecture,
holdsAt(filling,n4),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_96,lemma,
holdsAt(waterLevel(n3),n3),
inference(split_conjunct,[status(thm)],[waterLevel_3]) ).
fof(c_0_97,plain,
! [X100] :
( ( less(X100,n1)
| ~ less_or_equal(X100,n0) )
& ( less_or_equal(X100,n0)
| ~ less(X100,n1) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[less1])])]) ).
cnf(c_0_98,plain,
( ~ less(X2,X1)
| ~ less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_99,plain,
less(n1,n3),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_100,plain,
( ~ releasedAt(X1,n3)
| releasedAt(X1,n1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_88]) ).
cnf(c_0_101,plain,
( ~ holdsAt(filling,plus(X1,n1))
| holdsAt(filling,X1)
| releasedAt(filling,X1)
| X1 = n0 ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_102,plain,
~ releasedAt(filling,n1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_45])]) ).
cnf(c_0_103,plain,
~ holdsAt(filling,n3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95]),c_0_96])]) ).
cnf(c_0_104,plain,
( ~ less_or_equal(X1,n0)
| less(X1,n1) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_105,plain,
~ less(n3,n1),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_106,plain,
n3 = 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(spm,[status(thm)],[c_0_100,c_0_101]),c_0_34]),c_0_94]),c_0_95])]),c_0_102]),c_0_103]) ).
cnf(c_0_107,plain,
less(n0,n1),
inference(spm,[status(thm)],[c_0_104,c_0_72]) ).
cnf(c_0_108,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_106]),c_0_107])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CSR002+2 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n019.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 14:23:21 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.41/0.51 % Version: 3.5.1
% 0.41/0.51 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.41/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.41/0.51 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.41/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.41/0.51 % Starting new_bool_1 with 300s (1) cores
% 0.41/0.51 % Starting sh5l with 300s (1) cores
% 0.41/0.51 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 2807848 completed with status 0
% 0.41/0.51 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.41/0.51 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.41/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.41/0.51 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.41/0.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.41/0.51 % No SInE strategy applied
% 0.41/0.51 % Search class: FGHSF-FSLM32-SFFFFFNN
% 0.41/0.51 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.41/0.51 % Starting SubtermCWHack with 136s (1) cores
% 0.41/0.51 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.41/0.51 % Starting G-E--_107_C41_F1_PI_AE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 0.41/0.51 % Starting new_bool_3 with 136s (1) cores
% 0.41/0.51 % Starting U----_116_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN1 with 136s (1) cores
% 0.41/0.51 % SubtermCWHack with pid 2807854 completed with status 0
% 0.41/0.51 % Result found by SubtermCWHack
% 0.41/0.51 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.41/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.41/0.51 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.41/0.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.41/0.51 % No SInE strategy applied
% 0.41/0.51 % Search class: FGHSF-FSLM32-SFFFFFNN
% 0.41/0.51 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.41/0.51 % Starting SubtermCWHack with 136s (1) cores
% 0.41/0.51 % Preprocessing time : 0.002 s
% 0.41/0.51
% 0.41/0.51 % Proof found!
% 0.41/0.51 % SZS status Theorem
% 0.41/0.51 % SZS output start CNFRefutation
% See solution above
% 0.41/0.51 % Parsed axioms : 56
% 0.41/0.51 % Removed by relevancy pruning/SinE : 0
% 0.41/0.51 % Initial clauses : 138
% 0.41/0.51 % Removed in clause preprocessing : 1
% 0.41/0.51 % Initial clauses in saturation : 137
% 0.41/0.51 % Processed clauses : 1565
% 0.41/0.51 % ...of these trivial : 0
% 0.41/0.51 % ...subsumed : 874
% 0.41/0.51 % ...remaining for further processing : 691
% 0.41/0.51 % Other redundant clauses eliminated : 65
% 0.41/0.51 % Clauses deleted for lack of memory : 0
% 0.41/0.51 % Backward-subsumed : 49
% 0.41/0.51 % Backward-rewritten : 156
% 0.41/0.51 % Generated clauses : 3376
% 0.41/0.51 % ...of the previous two non-redundant : 3021
% 0.41/0.51 % ...aggressively subsumed : 0
% 0.41/0.51 % Contextual simplify-reflections : 4
% 0.41/0.51 % Paramodulations : 3310
% 0.41/0.51 % Factorizations : 7
% 0.41/0.51 % NegExts : 0
% 0.41/0.51 % Equation resolutions : 67
% 0.41/0.51 % Disequality decompositions : 0
% 0.41/0.51 % Total rewrite steps : 643
% 0.41/0.51 % ...of those cached : 604
% 0.41/0.51 % Propositional unsat checks : 0
% 0.41/0.51 % Propositional check models : 0
% 0.41/0.51 % Propositional check unsatisfiable : 0
% 0.41/0.51 % Propositional clauses : 0
% 0.41/0.51 % Propositional clauses after purity: 0
% 0.41/0.51 % Propositional unsat core size : 0
% 0.41/0.51 % Propositional preprocessing time : 0.000
% 0.41/0.51 % Propositional encoding time : 0.000
% 0.41/0.51 % Propositional solver time : 0.000
% 0.41/0.51 % Success case prop preproc time : 0.000
% 0.41/0.51 % Success case prop encoding time : 0.000
% 0.41/0.51 % Success case prop solver time : 0.000
% 0.41/0.51 % Current number of processed clauses : 474
% 0.41/0.51 % Positive orientable unit clauses : 26
% 0.41/0.51 % Positive unorientable unit clauses: 1
% 0.41/0.51 % Negative unit clauses : 89
% 0.41/0.51 % Non-unit-clauses : 358
% 0.41/0.51 % Current number of unprocessed clauses: 1403
% 0.41/0.51 % ...number of literals in the above : 7192
% 0.41/0.51 % Current number of archived formulas : 0
% 0.41/0.51 % Current number of archived clauses : 205
% 0.41/0.51 % Clause-clause subsumption calls (NU) : 32668
% 0.41/0.51 % Rec. Clause-clause subsumption calls : 17747
% 0.41/0.51 % Non-unit clause-clause subsumptions : 516
% 0.41/0.51 % Unit Clause-clause subsumption calls : 18889
% 0.41/0.51 % Rewrite failures with RHS unbound : 0
% 0.41/0.51 % BW rewrite match attempts : 23
% 0.41/0.51 % BW rewrite match successes : 23
% 0.41/0.51 % Condensation attempts : 0
% 0.41/0.51 % Condensation successes : 0
% 0.41/0.51 % Termbank termtop insertions : 46098
% 0.41/0.51 % Search garbage collected termcells : 1496
% 0.41/0.51
% 0.41/0.51 % -------------------------------------------------
% 0.41/0.51 % User time : 0.066 s
% 0.41/0.51 % System time : 0.009 s
% 0.41/0.51 % Total time : 0.074 s
% 0.41/0.51 % Maximum resident set size: 3948 pages
% 0.41/0.51
% 0.41/0.51 % -------------------------------------------------
% 0.41/0.51 % User time : 0.312 s
% 0.41/0.51 % System time : 0.034 s
% 0.41/0.51 % Total time : 0.345 s
% 0.41/0.51 % Maximum resident set size: 4864 pages
% 0.41/0.51 % E exiting
%------------------------------------------------------------------------------