%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : PRO012+3 : TPTP v9.2.1. Released v4.0.0.
% 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 : n022.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 05:01:55 PM UTC 2026
% Result : Theorem 3.30s 3.00s
% Output : CNFRefutation 3.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 15
% Syntax : Number of formulae : 123 ( 45 unt; 0 def)
% Number of atoms : 344 ( 30 equ)
% Maximal formula atoms : 17 ( 2 avg)
% Number of connectives : 362 ( 141 ~; 147 |; 56 &)
% ( 3 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 182 ( 8 sgn 89 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_27,axiom,
! [X77,X78] :
( ( occurrence_of(X78,X77)
& ~ atomic(X77) )
=> ? [X79] :
( root(X79,X77)
& subactivity_occurrence(X79,X78) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_27) ).
fof(goals,conjecture,
! [X167] :
( occurrence_of(X167,tptp0)
=> ? [X168,X169] :
( occurrence_of(X168,tptp3)
& root_occ(X168,X167)
& ( occurrence_of(X169,tptp2)
| occurrence_of(X169,tptp1) )
& min_precedes(X168,X169,tptp0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(sos_51,axiom,
~ atomic(tptp0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_51) ).
fof(sos_33,axiom,
! [X100,X101] :
( root_occ(X100,X101)
<=> ? [X102] :
( occurrence_of(X101,X102)
& subactivity_occurrence(X100,X101)
& root(X100,X102) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_33) ).
fof(sos_35,axiom,
! [X106,X107,X108,X109] :
( ( occurrence_of(X108,X109)
& root_occ(X106,X108)
& root_occ(X107,X108) )
=> X106 = X107 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_35) ).
fof(sos_49,axiom,
! [X162] :
( occurrence_of(X162,tptp0)
=> ? [X163,X164,X165] :
( occurrence_of(X163,tptp3)
& root_occ(X163,X162)
& occurrence_of(X164,tptp4)
& min_precedes(X163,X164,tptp0)
& ( occurrence_of(X165,tptp2)
| occurrence_of(X165,tptp1) )
& min_precedes(X164,X165,tptp0)
& ! [X166] :
( min_precedes(X163,X166,tptp0)
=> ( X166 = X164
| X166 = X165 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_49) ).
fof(sos_25,axiom,
! [X70,X71,X72] :
( min_precedes(X71,X72,X70)
=> ? [X73] :
( occurrence_of(X73,X70)
& subactivity_occurrence(X71,X73)
& subactivity_occurrence(X72,X73) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_25) ).
fof(sos_21,axiom,
! [X57,X58] :
( leaf(X57,X58)
<=> ( ( root(X57,X58)
| ? [X59] : min_precedes(X59,X57,X58) )
& ~ ? [X60] : min_precedes(X57,X60,X58) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_21) ).
fof(sos_29,axiom,
! [X84,X85,X86,X87] :
( ( min_precedes(X84,X85,X86)
& occurrence_of(X87,X86)
& subactivity_occurrence(X85,X87) )
=> subactivity_occurrence(X84,X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_29) ).
fof(sos_15,axiom,
! [X39,X40,X41] :
( min_precedes(X39,X40,X41)
=> precedes(X39,X40) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_15) ).
fof(sos_42,axiom,
! [X135,X136,X137,X138] :
( ( occurrence_of(X136,X135)
& subactivity_occurrence(X137,X136)
& root_occ(X138,X136)
& arboreal(X137)
& ~ min_precedes(X138,X137,X135) )
=> X138 = X137 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_42) ).
fof(sos_10,axiom,
! [X22,X23] :
( precedes(X22,X23)
<=> ( earlier(X22,X23)
& legal(X23) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_10) ).
fof(sos_08,axiom,
! [X19] :
( legal(X19)
=> arboreal(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_08) ).
fof(sos_05,axiom,
! [X11,X12,X13] :
( ( earlier(X11,X12)
& earlier(X12,X13) )
=> earlier(X11,X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_05) ).
fof(sos_18,axiom,
! [X46,X47,X48,X49] :
( ( min_precedes(X46,X47,X49)
& min_precedes(X46,X48,X49)
& precedes(X47,X48) )
=> min_precedes(X47,X48,X49) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_18) ).
fof(c_0_15,plain,
! [X77,X78] :
( ( occurrence_of(X78,X77)
& ~ atomic(X77) )
=> ? [X79] :
( root(X79,X77)
& subactivity_occurrence(X79,X78) ) ),
inference(fof_simplification,[status(thm)],[sos_27]) ).
fof(c_0_16,negated_conjecture,
~ ! [X167] :
( occurrence_of(X167,tptp0)
=> ? [X168,X169] :
( occurrence_of(X168,tptp3)
& root_occ(X168,X167)
& ( occurrence_of(X169,tptp2)
| occurrence_of(X169,tptp1) )
& min_precedes(X168,X169,tptp0) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_17,plain,
! [X426,X427] :
( ( root(esk12_2(X426,X427),X426)
| ~ occurrence_of(X427,X426)
| atomic(X426) )
& ( subactivity_occurrence(esk12_2(X426,X427),X427)
| ~ occurrence_of(X427,X426)
| atomic(X426) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
fof(c_0_18,negated_conjecture,
! [X523,X524] :
( occurrence_of(esk20_0,tptp0)
& ( ~ occurrence_of(X524,tptp2)
| ~ occurrence_of(X523,tptp3)
| ~ root_occ(X523,esk20_0)
| ~ min_precedes(X523,X524,tptp0) )
& ( ~ occurrence_of(X524,tptp1)
| ~ occurrence_of(X523,tptp3)
| ~ root_occ(X523,esk20_0)
| ~ min_precedes(X523,X524,tptp0) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])])]) ).
fof(c_0_19,plain,
~ atomic(tptp0),
inference(fof_simplification,[status(thm)],[sos_51]) ).
fof(c_0_20,plain,
! [X449,X450,X452,X453,X454] :
( ( occurrence_of(X450,esk14_2(X449,X450))
| ~ root_occ(X449,X450) )
& ( subactivity_occurrence(X449,X450)
| ~ root_occ(X449,X450) )
& ( root(X449,esk14_2(X449,X450))
| ~ root_occ(X449,X450) )
& ( ~ occurrence_of(X453,X454)
| ~ subactivity_occurrence(X452,X453)
| ~ root(X452,X454)
| root_occ(X452,X453) ) ),
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)],[sos_33])])])])])]) ).
cnf(c_0_21,plain,
( subactivity_occurrence(esk12_2(X1,X2),X2)
| atomic(X1)
| ~ occurrence_of(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
occurrence_of(esk20_0,tptp0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
~ atomic(tptp0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
( root_occ(X3,X1)
| ~ occurrence_of(X1,X2)
| ~ subactivity_occurrence(X3,X1)
| ~ root(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
subactivity_occurrence(esk12_2(tptp0,esk20_0),esk20_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_26,plain,
( root(esk12_2(X1,X2),X1)
| atomic(X1)
| ~ occurrence_of(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_27,plain,
! [X461,X462,X463,X464] :
( ~ occurrence_of(X463,X464)
| ~ root_occ(X461,X463)
| ~ root_occ(X462,X463)
| X461 = X462 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_35])]) ).
cnf(c_0_28,negated_conjecture,
( root_occ(esk12_2(tptp0,esk20_0),esk20_0)
| ~ root(esk12_2(tptp0,esk20_0),X1)
| ~ occurrence_of(esk20_0,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
root(esk12_2(tptp0,esk20_0),tptp0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_22]),c_0_23]) ).
fof(c_0_30,plain,
! [X517,X521] :
( ( occurrence_of(esk17_1(X517),tptp3)
| ~ occurrence_of(X517,tptp0) )
& ( root_occ(esk17_1(X517),X517)
| ~ occurrence_of(X517,tptp0) )
& ( occurrence_of(esk18_1(X517),tptp4)
| ~ occurrence_of(X517,tptp0) )
& ( min_precedes(esk17_1(X517),esk18_1(X517),tptp0)
| ~ occurrence_of(X517,tptp0) )
& ( occurrence_of(esk19_1(X517),tptp2)
| occurrence_of(esk19_1(X517),tptp1)
| ~ occurrence_of(X517,tptp0) )
& ( min_precedes(esk18_1(X517),esk19_1(X517),tptp0)
| ~ occurrence_of(X517,tptp0) )
& ( ~ min_precedes(esk17_1(X517),X521,tptp0)
| X521 = esk18_1(X517)
| X521 = esk19_1(X517)
| ~ occurrence_of(X517,tptp0) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_49])])])])]) ).
cnf(c_0_31,plain,
( X3 = X4
| ~ occurrence_of(X1,X2)
| ~ root_occ(X3,X1)
| ~ root_occ(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,negated_conjecture,
root_occ(esk12_2(tptp0,esk20_0),esk20_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_22]),c_0_29])]) ).
cnf(c_0_33,plain,
( root_occ(esk17_1(X1),X1)
| ~ occurrence_of(X1,tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_34,plain,
! [X419,X420,X421] :
( ( occurrence_of(esk10_3(X419,X420,X421),X419)
| ~ min_precedes(X420,X421,X419) )
& ( subactivity_occurrence(X420,esk10_3(X419,X420,X421))
| ~ min_precedes(X420,X421,X419) )
& ( subactivity_occurrence(X421,esk10_3(X419,X420,X421))
| ~ min_precedes(X420,X421,X419) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_25])])])]) ).
cnf(c_0_35,plain,
( min_precedes(esk17_1(X1),esk18_1(X1),tptp0)
| ~ occurrence_of(X1,tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,negated_conjecture,
( X1 = esk12_2(tptp0,esk20_0)
| ~ root_occ(X1,esk20_0)
| ~ occurrence_of(esk20_0,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,negated_conjecture,
root_occ(esk17_1(esk20_0),esk20_0),
inference(spm,[status(thm)],[c_0_33,c_0_22]) ).
cnf(c_0_38,plain,
( subactivity_occurrence(X1,esk10_3(X2,X1,X3))
| ~ min_precedes(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_39,negated_conjecture,
min_precedes(esk17_1(esk20_0),esk18_1(esk20_0),tptp0),
inference(spm,[status(thm)],[c_0_35,c_0_22]) ).
cnf(c_0_40,negated_conjecture,
( esk12_2(tptp0,esk20_0) = esk17_1(esk20_0)
| ~ occurrence_of(esk20_0,X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,negated_conjecture,
subactivity_occurrence(esk17_1(esk20_0),esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0))),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,negated_conjecture,
esk12_2(tptp0,esk20_0) = esk17_1(esk20_0),
inference(spm,[status(thm)],[c_0_40,c_0_22]) ).
cnf(c_0_43,plain,
( occurrence_of(esk10_3(X1,X2,X3),X1)
| ~ min_precedes(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_44,negated_conjecture,
( root_occ(esk17_1(esk20_0),esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0)))
| ~ root(esk17_1(esk20_0),X1)
| ~ occurrence_of(esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0)),X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_41]) ).
cnf(c_0_45,negated_conjecture,
root(esk17_1(esk20_0),tptp0),
inference(rw,[status(thm)],[c_0_29,c_0_42]) ).
cnf(c_0_46,negated_conjecture,
occurrence_of(esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0)),tptp0),
inference(spm,[status(thm)],[c_0_43,c_0_39]) ).
fof(c_0_47,plain,
! [X395,X396,X398,X399,X400,X401] :
( ( root(X395,X396)
| min_precedes(esk6_2(X395,X396),X395,X396)
| ~ leaf(X395,X396) )
& ( ~ min_precedes(X395,X398,X396)
| ~ leaf(X395,X396) )
& ( ~ root(X399,X400)
| min_precedes(X399,esk7_2(X399,X400),X400)
| leaf(X399,X400) )
& ( ~ min_precedes(X401,X399,X400)
| min_precedes(X399,esk7_2(X399,X400),X400)
| leaf(X399,X400) ) ),
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)],[sos_21])])])])])]) ).
cnf(c_0_48,negated_conjecture,
root_occ(esk17_1(esk20_0),esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46])]) ).
cnf(c_0_49,plain,
( ~ min_precedes(X1,X2,X3)
| ~ leaf(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_50,plain,
( occurrence_of(esk17_1(X1),tptp3)
| ~ occurrence_of(X1,tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_51,negated_conjecture,
( X1 = esk17_1(esk20_0)
| ~ root_occ(X1,esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0)))
| ~ occurrence_of(esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0)),X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_48]) ).
cnf(c_0_52,negated_conjecture,
root_occ(esk17_1(esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0))),esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0))),
inference(spm,[status(thm)],[c_0_33,c_0_46]) ).
cnf(c_0_53,plain,
( X2 = esk18_1(X1)
| X2 = esk19_1(X1)
| ~ min_precedes(esk17_1(X1),X2,tptp0)
| ~ occurrence_of(X1,tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_54,plain,
( min_precedes(X1,esk7_2(X1,X2),X2)
| leaf(X1,X2)
| ~ root(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_55,negated_conjecture,
~ leaf(esk17_1(esk20_0),tptp0),
inference(spm,[status(thm)],[c_0_49,c_0_39]) ).
cnf(c_0_56,negated_conjecture,
( ~ occurrence_of(X1,tptp1)
| ~ occurrence_of(X2,tptp3)
| ~ root_occ(X2,esk20_0)
| ~ min_precedes(X2,X1,tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_57,negated_conjecture,
occurrence_of(esk17_1(esk20_0),tptp3),
inference(spm,[status(thm)],[c_0_50,c_0_22]) ).
cnf(c_0_58,plain,
( occurrence_of(esk19_1(X1),tptp2)
| occurrence_of(esk19_1(X1),tptp1)
| ~ occurrence_of(X1,tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_59,negated_conjecture,
( ~ occurrence_of(X1,tptp2)
| ~ occurrence_of(X2,tptp3)
| ~ root_occ(X2,esk20_0)
| ~ min_precedes(X2,X1,tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_60,negated_conjecture,
( esk17_1(esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0))) = esk17_1(esk20_0)
| ~ occurrence_of(esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0)),X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
fof(c_0_61,plain,
! [X433,X434,X435,X436] :
( ~ min_precedes(X433,X434,X435)
| ~ occurrence_of(X436,X435)
| ~ subactivity_occurrence(X434,X436)
| subactivity_occurrence(X433,X436) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_29])]) ).
cnf(c_0_62,negated_conjecture,
( X1 = esk19_1(esk20_0)
| X1 = esk18_1(esk20_0)
| ~ min_precedes(esk17_1(esk20_0),X1,tptp0) ),
inference(spm,[status(thm)],[c_0_53,c_0_22]) ).
cnf(c_0_63,negated_conjecture,
min_precedes(esk17_1(esk20_0),esk7_2(esk17_1(esk20_0),tptp0),tptp0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_45]),c_0_55]) ).
cnf(c_0_64,negated_conjecture,
( ~ min_precedes(esk17_1(esk20_0),X1,tptp0)
| ~ occurrence_of(X1,tptp1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_37]),c_0_57])]) ).
cnf(c_0_65,negated_conjecture,
( occurrence_of(esk19_1(esk20_0),tptp1)
| occurrence_of(esk19_1(esk20_0),tptp2) ),
inference(spm,[status(thm)],[c_0_58,c_0_22]) ).
cnf(c_0_66,negated_conjecture,
( ~ min_precedes(esk17_1(esk20_0),X1,tptp0)
| ~ occurrence_of(X1,tptp2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_37]),c_0_57])]) ).
cnf(c_0_67,negated_conjecture,
min_precedes(esk17_1(esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0))),esk18_1(esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0))),tptp0),
inference(spm,[status(thm)],[c_0_35,c_0_46]) ).
cnf(c_0_68,negated_conjecture,
esk17_1(esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0))) = esk17_1(esk20_0),
inference(spm,[status(thm)],[c_0_60,c_0_46]) ).
cnf(c_0_69,plain,
( subactivity_occurrence(X1,X4)
| ~ min_precedes(X1,X2,X3)
| ~ occurrence_of(X4,X3)
| ~ subactivity_occurrence(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_70,negated_conjecture,
( esk7_2(esk17_1(esk20_0),tptp0) = esk18_1(esk20_0)
| esk7_2(esk17_1(esk20_0),tptp0) = esk19_1(esk20_0) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_71,negated_conjecture,
~ min_precedes(esk17_1(esk20_0),esk19_1(esk20_0),tptp0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66]) ).
cnf(c_0_72,plain,
( min_precedes(esk18_1(X1),esk19_1(X1),tptp0)
| ~ occurrence_of(X1,tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_73,negated_conjecture,
min_precedes(esk17_1(esk20_0),esk18_1(esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0))),tptp0),
inference(rw,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_74,negated_conjecture,
( subactivity_occurrence(esk17_1(esk20_0),X1)
| ~ subactivity_occurrence(esk7_2(esk17_1(esk20_0),tptp0),X1)
| ~ occurrence_of(X1,tptp0) ),
inference(spm,[status(thm)],[c_0_69,c_0_63]) ).
cnf(c_0_75,negated_conjecture,
esk7_2(esk17_1(esk20_0),tptp0) = esk18_1(esk20_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_70]),c_0_71]) ).
cnf(c_0_76,negated_conjecture,
min_precedes(esk18_1(esk20_0),esk19_1(esk20_0),tptp0),
inference(spm,[status(thm)],[c_0_72,c_0_22]) ).
cnf(c_0_77,negated_conjecture,
( esk18_1(esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0))) = esk18_1(esk20_0)
| esk18_1(esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0))) = esk19_1(esk20_0) ),
inference(spm,[status(thm)],[c_0_62,c_0_73]) ).
cnf(c_0_78,negated_conjecture,
( subactivity_occurrence(esk17_1(esk20_0),X1)
| ~ subactivity_occurrence(esk18_1(esk20_0),X1)
| ~ occurrence_of(X1,tptp0) ),
inference(rw,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_79,negated_conjecture,
occurrence_of(esk10_3(tptp0,esk18_1(esk20_0),esk19_1(esk20_0)),tptp0),
inference(spm,[status(thm)],[c_0_43,c_0_76]) ).
cnf(c_0_80,negated_conjecture,
subactivity_occurrence(esk18_1(esk20_0),esk10_3(tptp0,esk18_1(esk20_0),esk19_1(esk20_0))),
inference(spm,[status(thm)],[c_0_38,c_0_76]) ).
fof(c_0_81,plain,
! [X377,X378,X379] :
( ~ min_precedes(X377,X378,X379)
| precedes(X377,X378) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_15])]) ).
cnf(c_0_82,negated_conjecture,
min_precedes(esk18_1(esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0))),esk19_1(esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0))),tptp0),
inference(spm,[status(thm)],[c_0_72,c_0_46]) ).
cnf(c_0_83,negated_conjecture,
esk18_1(esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0))) = esk18_1(esk20_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_77]),c_0_71]) ).
fof(c_0_84,plain,
! [X135,X136,X137,X138] :
( ( occurrence_of(X136,X135)
& subactivity_occurrence(X137,X136)
& root_occ(X138,X136)
& arboreal(X137)
& ~ min_precedes(X138,X137,X135) )
=> X138 = X137 ),
inference(fof_simplification,[status(thm)],[sos_42]) ).
cnf(c_0_85,negated_conjecture,
subactivity_occurrence(esk17_1(esk20_0),esk10_3(tptp0,esk18_1(esk20_0),esk19_1(esk20_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80])]) ).
fof(c_0_86,plain,
! [X360,X361] :
( ( earlier(X360,X361)
| ~ precedes(X360,X361) )
& ( legal(X361)
| ~ precedes(X360,X361) )
& ( ~ earlier(X360,X361)
| ~ legal(X361)
| precedes(X360,X361) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_10])])]) ).
cnf(c_0_87,plain,
( precedes(X1,X2)
| ~ min_precedes(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_88,negated_conjecture,
min_precedes(esk18_1(esk20_0),esk19_1(esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0))),tptp0),
inference(rw,[status(thm)],[c_0_82,c_0_83]) ).
fof(c_0_89,plain,
! [X490,X491,X492,X493] :
( ~ occurrence_of(X491,X490)
| ~ subactivity_occurrence(X492,X491)
| ~ root_occ(X493,X491)
| ~ arboreal(X492)
| min_precedes(X493,X492,X490)
| X493 = X492 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_84])]) ).
cnf(c_0_90,negated_conjecture,
( root_occ(esk17_1(esk20_0),esk10_3(tptp0,esk18_1(esk20_0),esk19_1(esk20_0)))
| ~ root(esk17_1(esk20_0),X1)
| ~ occurrence_of(esk10_3(tptp0,esk18_1(esk20_0),esk19_1(esk20_0)),X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_85]) ).
fof(c_0_91,plain,
! [X357] :
( ~ legal(X357)
| arboreal(X357) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_08])]) ).
cnf(c_0_92,plain,
( legal(X1)
| ~ precedes(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_93,negated_conjecture,
precedes(esk18_1(esk20_0),esk19_1(esk20_0)),
inference(spm,[status(thm)],[c_0_87,c_0_76]) ).
fof(c_0_94,plain,
! [X349,X350,X351] :
( ~ earlier(X349,X350)
| ~ earlier(X350,X351)
| earlier(X349,X351) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_05])]) ).
cnf(c_0_95,plain,
( earlier(X1,X2)
| ~ precedes(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_96,negated_conjecture,
precedes(esk18_1(esk20_0),esk19_1(esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0)))),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
fof(c_0_97,plain,
! [X384,X385,X386,X387] :
( ~ min_precedes(X384,X385,X387)
| ~ min_precedes(X384,X386,X387)
| ~ precedes(X385,X386)
| min_precedes(X385,X386,X387) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_18])]) ).
cnf(c_0_98,plain,
( min_precedes(X4,X3,X2)
| X4 = X3
| ~ occurrence_of(X1,X2)
| ~ subactivity_occurrence(X3,X1)
| ~ root_occ(X4,X1)
| ~ arboreal(X3) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_99,negated_conjecture,
root_occ(esk17_1(esk20_0),esk10_3(tptp0,esk18_1(esk20_0),esk19_1(esk20_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_45]),c_0_79])]) ).
cnf(c_0_100,plain,
( subactivity_occurrence(X1,esk10_3(X2,X3,X1))
| ~ min_precedes(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_101,plain,
( arboreal(X1)
| ~ legal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_102,negated_conjecture,
legal(esk19_1(esk20_0)),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_103,plain,
( earlier(X1,X3)
| ~ earlier(X1,X2)
| ~ earlier(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_104,negated_conjecture,
earlier(esk18_1(esk20_0),esk19_1(esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0)))),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_105,negated_conjecture,
precedes(esk17_1(esk20_0),esk18_1(esk20_0)),
inference(spm,[status(thm)],[c_0_87,c_0_39]) ).
cnf(c_0_106,plain,
( min_precedes(X2,X4,X3)
| ~ min_precedes(X1,X2,X3)
| ~ min_precedes(X1,X4,X3)
| ~ precedes(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_107,negated_conjecture,
( X1 = esk17_1(esk20_0)
| min_precedes(esk17_1(esk20_0),X1,X2)
| ~ subactivity_occurrence(X1,esk10_3(tptp0,esk18_1(esk20_0),esk19_1(esk20_0)))
| ~ arboreal(X1)
| ~ occurrence_of(esk10_3(tptp0,esk18_1(esk20_0),esk19_1(esk20_0)),X2) ),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_108,negated_conjecture,
subactivity_occurrence(esk19_1(esk20_0),esk10_3(tptp0,esk18_1(esk20_0),esk19_1(esk20_0))),
inference(spm,[status(thm)],[c_0_100,c_0_76]) ).
cnf(c_0_109,negated_conjecture,
arboreal(esk19_1(esk20_0)),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_110,negated_conjecture,
( earlier(X1,esk19_1(esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0))))
| ~ earlier(X1,esk18_1(esk20_0)) ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_111,negated_conjecture,
earlier(esk17_1(esk20_0),esk18_1(esk20_0)),
inference(spm,[status(thm)],[c_0_95,c_0_105]) ).
cnf(c_0_112,negated_conjecture,
( min_precedes(X1,esk19_1(esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0))),tptp0)
| ~ min_precedes(esk18_1(esk20_0),X1,tptp0)
| ~ precedes(X1,esk19_1(esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0)))) ),
inference(spm,[status(thm)],[c_0_106,c_0_88]) ).
cnf(c_0_113,negated_conjecture,
( esk19_1(esk20_0) = esk17_1(esk20_0)
| min_precedes(esk17_1(esk20_0),esk19_1(esk20_0),X1)
| ~ occurrence_of(esk10_3(tptp0,esk18_1(esk20_0),esk19_1(esk20_0)),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_109])]) ).
cnf(c_0_114,plain,
( precedes(X1,X2)
| ~ earlier(X1,X2)
| ~ legal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_115,negated_conjecture,
earlier(esk17_1(esk20_0),esk19_1(esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0)))),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_116,negated_conjecture,
legal(esk19_1(esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0)))),
inference(spm,[status(thm)],[c_0_92,c_0_96]) ).
cnf(c_0_117,negated_conjecture,
( occurrence_of(esk19_1(esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0))),tptp1)
| occurrence_of(esk19_1(esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0))),tptp2) ),
inference(spm,[status(thm)],[c_0_58,c_0_46]) ).
cnf(c_0_118,negated_conjecture,
( min_precedes(esk19_1(esk20_0),esk19_1(esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0))),tptp0)
| ~ precedes(esk19_1(esk20_0),esk19_1(esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0)))) ),
inference(spm,[status(thm)],[c_0_112,c_0_76]) ).
cnf(c_0_119,negated_conjecture,
esk19_1(esk20_0) = esk17_1(esk20_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_79]),c_0_71]) ).
cnf(c_0_120,negated_conjecture,
precedes(esk17_1(esk20_0),esk19_1(esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_116])]) ).
cnf(c_0_121,negated_conjecture,
~ min_precedes(esk17_1(esk20_0),esk19_1(esk10_3(tptp0,esk17_1(esk20_0),esk18_1(esk20_0))),tptp0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_117]),c_0_66]) ).
cnf(c_0_122,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_118,c_0_119]),c_0_119]),c_0_120])]),c_0_121]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : PRO012+3 : TPTP v9.2.1. Released v4.0.0.
% 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
% 0.15/0.32 % Computer : n022.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 01:30:21 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 3.30/3.00 % Version : CSE_E---1.7
% 3.30/3.00 % Problem : theBenchmark.p
% 3.30/3.00 % SZS status Theorem for theBenchmark.p
% 3.30/3.00 % SZS output start CNFRefutation
% See solution above
% 3.30/3.00 % Total time : 2.371s
%------------------------------------------------------------------------------