%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : PRO003+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 01:59:29 PM UTC 2026
% Result : Theorem 42.90s 11.89s
% Output : CNFRefutation 42.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 18
% Syntax : Number of formulae : 114 ( 50 unt; 0 def)
% Number of atoms : 297 ( 26 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 309 ( 126 ~; 121 |; 47 &)
% ( 4 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 155 ( 6 sgn 74 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_30,axiom,
! [X92,X93] :
( ( ~ atomic(X92)
& occurrence_of(X93,X92) )
=> ? [X94] :
( subactivity_occurrence(X94,X93)
& root(X94,X92) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_30) ).
fof(goals,conjecture,
~ ? [X102] : occurrence_of(X102,tptp0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(sos_34,axiom,
~ atomic(tptp0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_34) ).
fof(sos_10,axiom,
! [X33,X34] :
( root_occ(X33,X34)
<=> ? [X35] :
( root(X33,X35)
& subactivity_occurrence(X33,X34)
& occurrence_of(X34,X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_10) ).
fof(sos_45,axiom,
! [X99,X100] :
( ( root_occ(X99,X100)
& occurrence_of(X100,tptp0) )
=> ? [X101] :
( next_subocc(X99,X101,tptp0)
& occurrence_of(X101,tptp1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_45) ).
fof(sos_32,axiom,
! [X96] :
( occurrence_of(X96,tptp0)
=> ? [X97,X98] :
( next_subocc(X97,X98,tptp0)
& leaf_occ(X98,X96)
& occurrence_of(X98,tptp3)
& root_occ(X97,X96)
& occurrence_of(X97,tptp4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_32) ).
fof(sos_02,axiom,
! [X8,X9,X10,X11] :
( ( root_occ(X9,X10)
& root_occ(X8,X10)
& occurrence_of(X10,X11) )
=> X8 = X9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_02) ).
fof(sos_04,axiom,
! [X16,X17,X18] :
( next_subocc(X16,X17,X18)
<=> ( ~ ? [X19] :
( min_precedes(X19,X17,X18)
& min_precedes(X16,X19,X18) )
& min_precedes(X16,X17,X18) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_04) ).
fof(sos_24,axiom,
! [X71,X72,X73] :
( min_precedes(X72,X73,X71)
=> ? [X74] :
( subactivity_occurrence(X73,X74)
& subactivity_occurrence(X72,X74)
& occurrence_of(X74,X71) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_24) ).
fof(sos_13,axiom,
! [X41,X42] :
( occurrence_of(X41,X42)
=> ( arboreal(X41)
<=> atomic(X42) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_13) ).
fof(sos_29,axiom,
! [X90,X91] :
( occurrence_of(X91,X90)
=> ( activity_occurrence(X91)
& activity(X90) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_29) ).
fof(sos_28,axiom,
! [X86,X87,X88,X89] :
( ( subactivity_occurrence(X89,X87)
& subactivity_occurrence(X88,X87)
& arboreal(X89)
& arboreal(X88)
& occurrence_of(X87,X86) )
=> ( X88 = X89
| min_precedes(X89,X88,X86)
| min_precedes(X88,X89,X86) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_28) ).
fof(sos_38,axiom,
atomic(tptp1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_38) ).
fof(sos_11,axiom,
! [X36,X37] :
( leaf_occ(X36,X37)
<=> ? [X38] :
( leaf(X36,X38)
& subactivity_occurrence(X36,X37)
& occurrence_of(X37,X38) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_11) ).
fof(sos_22,axiom,
! [X65,X66,X67] :
( ( occurrence_of(X65,X67)
& occurrence_of(X65,X66) )
=> X66 = X67 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_22) ).
fof(sos_18,axiom,
! [X53] :
( activity_occurrence(X53)
=> ? [X54] :
( occurrence_of(X53,X54)
& activity(X54) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_18) ).
fof(sos_36,axiom,
atomic(tptp3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_36) ).
fof(sos_42,axiom,
tptp1 != tptp3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_42) ).
fof(c_0_18,plain,
! [X92,X93] :
( ( ~ atomic(X92)
& occurrence_of(X93,X92) )
=> ? [X94] :
( subactivity_occurrence(X94,X93)
& root(X94,X92) ) ),
inference(fof_simplification,[status(thm)],[sos_30]) ).
fof(c_0_19,negated_conjecture,
~ ~ ? [X102] : occurrence_of(X102,tptp0),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_20,plain,
~ atomic(tptp0),
inference(fof_simplification,[status(thm)],[sos_34]) ).
fof(c_0_21,plain,
! [X211,X212] :
( ( atomic(X211)
| ~ occurrence_of(X212,X211)
| subactivity_occurrence(esk14_2(X211,X212),X212) )
& ( atomic(X211)
| ~ occurrence_of(X212,X211)
| root(esk14_2(X211,X212),X211) ) ),
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_18])])])])]) ).
fof(c_0_22,negated_conjecture,
occurrence_of(esk18_0,tptp0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
fof(c_0_23,plain,
~ atomic(tptp0),
inference(fof_nnf,[status(thm)],[c_0_20]) ).
fof(c_0_24,plain,
! [X139,X140,X142,X143,X144] :
( ( root_occ(X142,X143)
| ~ root(X142,X144)
| ~ subactivity_occurrence(X142,X143)
| ~ occurrence_of(X143,X144) )
& ( ~ root_occ(X139,X140)
| root(X139,esk2_2(X139,X140)) )
& ( ~ root_occ(X139,X140)
| subactivity_occurrence(X139,X140) )
& ( ~ root_occ(X139,X140)
| occurrence_of(X140,esk2_2(X139,X140)) ) ),
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)],[sos_10])])])])])])]) ).
cnf(c_0_25,plain,
( ~ occurrence_of(X2,X1)
| atomic(X1)
| subactivity_occurrence(esk14_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,negated_conjecture,
occurrence_of(esk18_0,tptp0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
~ atomic(tptp0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_28,plain,
! [X218,X219] :
( ( ~ root_occ(X218,X219)
| ~ occurrence_of(X219,tptp0)
| next_subocc(X218,esk17_1(X218),tptp0) )
& ( ~ root_occ(X218,X219)
| ~ occurrence_of(X219,tptp0)
| occurrence_of(esk17_1(X218),tptp1) ) ),
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)],[sos_45])])])])])])]) ).
fof(c_0_29,plain,
! [X215] :
( ( ~ occurrence_of(X215,tptp0)
| next_subocc(esk15_1(X215),esk16_1(X215),tptp0) )
& ( ~ occurrence_of(X215,tptp0)
| leaf_occ(esk16_1(X215),X215) )
& ( ~ occurrence_of(X215,tptp0)
| occurrence_of(esk16_1(X215),tptp3) )
& ( ~ occurrence_of(X215,tptp0)
| root_occ(esk15_1(X215),X215) )
& ( ~ occurrence_of(X215,tptp0)
| occurrence_of(esk15_1(X215),tptp4) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_32])])])])]) ).
cnf(c_0_30,plain,
( ~ root(X3,X2)
| ~ subactivity_occurrence(X3,X1)
| ~ occurrence_of(X1,X2)
| root_occ(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,negated_conjecture,
subactivity_occurrence(esk14_2(tptp0,esk18_0),esk18_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_32,plain,
( ~ occurrence_of(X2,X1)
| atomic(X1)
| root(esk14_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_33,plain,
( ~ root_occ(X1,X2)
| ~ occurrence_of(X2,tptp0)
| next_subocc(X1,esk17_1(X1),tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,plain,
( ~ occurrence_of(X1,tptp0)
| root_occ(esk15_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_35,plain,
! [X110,X111,X112,X113] :
( X110 = X111
| ~ root_occ(X111,X112)
| ~ root_occ(X110,X112)
| ~ occurrence_of(X112,X113) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_02])])]) ).
cnf(c_0_36,negated_conjecture,
( ~ occurrence_of(esk18_0,X1)
| ~ root(esk14_2(tptp0,esk18_0),X1)
| root_occ(esk14_2(tptp0,esk18_0),esk18_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,negated_conjecture,
root(esk14_2(tptp0,esk18_0),tptp0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_26]),c_0_27]) ).
fof(c_0_38,plain,
! [X118,X119,X120,X121,X122,X123,X124] :
( ( next_subocc(X122,X123,X124)
| ~ min_precedes(X122,X123,X124)
| min_precedes(esk1_3(X122,X123,X124),X123,X124) )
& ( next_subocc(X122,X123,X124)
| ~ min_precedes(X122,X123,X124)
| min_precedes(X122,esk1_3(X122,X123,X124),X124) )
& ( ~ next_subocc(X118,X119,X120)
| ~ min_precedes(X121,X119,X120)
| ~ min_precedes(X118,X121,X120) )
& ( ~ next_subocc(X118,X119,X120)
| min_precedes(X118,X119,X120) ) ),
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)],[sos_04])])])])])])]) ).
cnf(c_0_39,negated_conjecture,
( ~ root_occ(X1,esk18_0)
| next_subocc(X1,esk17_1(X1),tptp0) ),
inference(spm,[status(thm)],[c_0_33,c_0_26]) ).
cnf(c_0_40,negated_conjecture,
root_occ(esk15_1(esk18_0),esk18_0),
inference(spm,[status(thm)],[c_0_34,c_0_26]) ).
cnf(c_0_41,plain,
( ~ root_occ(X4,X1)
| ~ root_occ(X3,X1)
| ~ occurrence_of(X1,X2)
| X3 = X4 ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_42,negated_conjecture,
root_occ(esk14_2(tptp0,esk18_0),esk18_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_26]),c_0_37])]) ).
fof(c_0_43,plain,
! [X190,X191,X192] :
( ( ~ min_precedes(X191,X192,X190)
| subactivity_occurrence(X192,esk9_3(X190,X191,X192)) )
& ( ~ min_precedes(X191,X192,X190)
| subactivity_occurrence(X191,esk9_3(X190,X191,X192)) )
& ( ~ min_precedes(X191,X192,X190)
| occurrence_of(esk9_3(X190,X191,X192),X190) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_24])])])])]) ).
cnf(c_0_44,plain,
( ~ next_subocc(X1,X2,X3)
| min_precedes(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_45,negated_conjecture,
next_subocc(esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)),tptp0),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_46,negated_conjecture,
( ~ occurrence_of(esk18_0,X2)
| ~ root_occ(X1,esk18_0)
| X1 = esk14_2(tptp0,esk18_0) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,plain,
( ~ root_occ(X2,X1)
| occurrence_of(X1,esk2_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_48,plain,
( ~ min_precedes(X1,X3,X2)
| subactivity_occurrence(X1,esk9_3(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_49,negated_conjecture,
min_precedes(esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)),tptp0),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,negated_conjecture,
( ~ occurrence_of(esk18_0,X1)
| esk14_2(tptp0,esk18_0) = esk15_1(esk18_0) ),
inference(spm,[status(thm)],[c_0_46,c_0_40]) ).
cnf(c_0_51,negated_conjecture,
occurrence_of(esk18_0,esk2_2(esk14_2(tptp0,esk18_0),esk18_0)),
inference(spm,[status(thm)],[c_0_47,c_0_42]) ).
cnf(c_0_52,negated_conjecture,
subactivity_occurrence(esk15_1(esk18_0),esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)))),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,negated_conjecture,
esk14_2(tptp0,esk18_0) = esk15_1(esk18_0),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_54,plain,
( ~ min_precedes(X2,X3,X1)
| occurrence_of(esk9_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_55,negated_conjecture,
( ~ occurrence_of(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0))),X1)
| ~ root(esk15_1(esk18_0),X1)
| root_occ(esk15_1(esk18_0),esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)))) ),
inference(spm,[status(thm)],[c_0_30,c_0_52]) ).
cnf(c_0_56,negated_conjecture,
root(esk15_1(esk18_0),tptp0),
inference(rw,[status(thm)],[c_0_37,c_0_53]) ).
cnf(c_0_57,negated_conjecture,
occurrence_of(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0))),tptp0),
inference(spm,[status(thm)],[c_0_54,c_0_49]) ).
cnf(c_0_58,negated_conjecture,
root_occ(esk15_1(esk18_0),esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57])]) ).
cnf(c_0_59,plain,
( ~ root_occ(X1,X2)
| ~ occurrence_of(X2,tptp0)
| occurrence_of(esk17_1(X1),tptp1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_60,negated_conjecture,
( ~ occurrence_of(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0))),X2)
| ~ root_occ(X1,esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0))))
| X1 = esk15_1(esk18_0) ),
inference(spm,[status(thm)],[c_0_41,c_0_58]) ).
cnf(c_0_61,negated_conjecture,
root_occ(esk15_1(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)))),esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)))),
inference(spm,[status(thm)],[c_0_34,c_0_57]) ).
fof(c_0_62,plain,
! [X153,X154] :
( ( ~ occurrence_of(X153,X154)
| arboreal(X153)
| ~ atomic(X154) )
& ( ~ occurrence_of(X153,X154)
| atomic(X154)
| ~ arboreal(X153) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_13])])])]) ).
cnf(c_0_63,negated_conjecture,
( ~ root_occ(X1,esk18_0)
| occurrence_of(esk17_1(X1),tptp1) ),
inference(spm,[status(thm)],[c_0_59,c_0_26]) ).
cnf(c_0_64,plain,
( ~ occurrence_of(X1,tptp0)
| next_subocc(esk15_1(X1),esk16_1(X1),tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_65,negated_conjecture,
( ~ occurrence_of(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0))),X1)
| esk15_1(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)))) = esk15_1(esk18_0) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
fof(c_0_66,plain,
! [X209,X210] :
( ( ~ occurrence_of(X210,X209)
| activity_occurrence(X210) )
& ( ~ occurrence_of(X210,X209)
| activity(X209) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_29])])])]) ).
cnf(c_0_67,plain,
( ~ occurrence_of(X1,tptp0)
| occurrence_of(esk16_1(X1),tptp3) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_68,plain,
! [X205,X206,X207,X208] :
( X207 = X208
| min_precedes(X208,X207,X205)
| min_precedes(X207,X208,X205)
| ~ subactivity_occurrence(X208,X206)
| ~ subactivity_occurrence(X207,X206)
| ~ arboreal(X208)
| ~ arboreal(X207)
| ~ occurrence_of(X206,X205) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_28])])]) ).
cnf(c_0_69,plain,
( ~ min_precedes(X3,X1,X2)
| subactivity_occurrence(X1,esk9_3(X2,X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_70,plain,
( ~ occurrence_of(X2,X1)
| ~ atomic(X1)
| arboreal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_71,negated_conjecture,
occurrence_of(esk17_1(esk15_1(esk18_0)),tptp1),
inference(spm,[status(thm)],[c_0_63,c_0_40]) ).
cnf(c_0_72,plain,
atomic(tptp1),
inference(split_conjunct,[status(thm)],[sos_38]) ).
fof(c_0_73,plain,
! [X145,X146,X148,X149,X150] :
( ( leaf_occ(X148,X149)
| ~ leaf(X148,X150)
| ~ subactivity_occurrence(X148,X149)
| ~ occurrence_of(X149,X150) )
& ( ~ leaf_occ(X145,X146)
| leaf(X145,esk3_2(X145,X146)) )
& ( ~ leaf_occ(X145,X146)
| subactivity_occurrence(X145,X146) )
& ( ~ leaf_occ(X145,X146)
| occurrence_of(X146,esk3_2(X145,X146)) ) ),
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)],[sos_11])])])])])])]) ).
cnf(c_0_74,plain,
( ~ occurrence_of(X1,tptp0)
| leaf_occ(esk16_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_75,plain,
( ~ next_subocc(X1,X4,X3)
| ~ min_precedes(X2,X4,X3)
| ~ min_precedes(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_76,negated_conjecture,
next_subocc(esk15_1(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)))),esk16_1(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)))),tptp0),
inference(spm,[status(thm)],[c_0_64,c_0_57]) ).
cnf(c_0_77,negated_conjecture,
esk15_1(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)))) = esk15_1(esk18_0),
inference(spm,[status(thm)],[c_0_65,c_0_57]) ).
fof(c_0_78,plain,
! [X184,X185,X186] :
( X185 = X186
| ~ occurrence_of(X184,X186)
| ~ occurrence_of(X184,X185) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_22])])]) ).
fof(c_0_79,plain,
! [X172] :
( ( ~ activity_occurrence(X172)
| occurrence_of(X172,esk7_1(X172)) )
& ( ~ activity_occurrence(X172)
| activity(esk7_1(X172)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_18])])])])]) ).
cnf(c_0_80,plain,
( ~ occurrence_of(X1,X2)
| activity_occurrence(X1) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_81,negated_conjecture,
occurrence_of(esk16_1(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)))),tptp3),
inference(spm,[status(thm)],[c_0_67,c_0_57]) ).
cnf(c_0_82,plain,
( ~ subactivity_occurrence(X4,X1)
| ~ subactivity_occurrence(X3,X1)
| ~ arboreal(X4)
| ~ arboreal(X3)
| ~ occurrence_of(X1,X2)
| X3 = X4
| min_precedes(X4,X3,X2)
| min_precedes(X3,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_83,negated_conjecture,
subactivity_occurrence(esk17_1(esk15_1(esk18_0)),esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)))),
inference(spm,[status(thm)],[c_0_69,c_0_49]) ).
cnf(c_0_84,negated_conjecture,
arboreal(esk17_1(esk15_1(esk18_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72])]) ).
cnf(c_0_85,plain,
( ~ leaf_occ(X1,X2)
| subactivity_occurrence(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_86,negated_conjecture,
leaf_occ(esk16_1(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)))),esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)))),
inference(spm,[status(thm)],[c_0_74,c_0_57]) ).
cnf(c_0_87,plain,
atomic(tptp3),
inference(split_conjunct,[status(thm)],[sos_36]) ).
cnf(c_0_88,negated_conjecture,
( ~ min_precedes(esk15_1(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)))),X1,tptp0)
| ~ min_precedes(X1,esk16_1(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)))),tptp0) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_89,negated_conjecture,
next_subocc(esk15_1(esk18_0),esk16_1(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)))),tptp0),
inference(rw,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_90,plain,
( ~ occurrence_of(X1,X3)
| ~ occurrence_of(X1,X2)
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_91,plain,
( ~ activity_occurrence(X1)
| occurrence_of(X1,esk7_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_92,negated_conjecture,
activity_occurrence(esk16_1(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0))))),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_93,negated_conjecture,
( ~ occurrence_of(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0))),X2)
| ~ arboreal(X1)
| ~ subactivity_occurrence(X1,esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0))))
| min_precedes(esk17_1(esk15_1(esk18_0)),X1,X2)
| min_precedes(X1,esk17_1(esk15_1(esk18_0)),X2)
| X1 = esk17_1(esk15_1(esk18_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84])]) ).
cnf(c_0_94,negated_conjecture,
subactivity_occurrence(esk16_1(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)))),esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)))),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_95,negated_conjecture,
arboreal(esk16_1(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0))))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_81]),c_0_87])]) ).
cnf(c_0_96,negated_conjecture,
( ~ min_precedes(esk15_1(esk18_0),X1,tptp0)
| ~ min_precedes(X1,esk16_1(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)))),tptp0) ),
inference(rw,[status(thm)],[c_0_88,c_0_77]) ).
cnf(c_0_97,negated_conjecture,
( ~ min_precedes(esk15_1(esk18_0),X1,tptp0)
| ~ min_precedes(X1,esk17_1(esk15_1(esk18_0)),tptp0) ),
inference(spm,[status(thm)],[c_0_75,c_0_45]) ).
cnf(c_0_98,negated_conjecture,
min_precedes(esk15_1(esk18_0),esk16_1(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)))),tptp0),
inference(spm,[status(thm)],[c_0_44,c_0_89]) ).
cnf(c_0_99,negated_conjecture,
activity_occurrence(esk17_1(esk15_1(esk18_0))),
inference(spm,[status(thm)],[c_0_80,c_0_71]) ).
fof(c_0_100,plain,
tptp1 != tptp3,
inference(fof_simplification,[status(thm)],[sos_42]) ).
cnf(c_0_101,negated_conjecture,
( ~ occurrence_of(esk16_1(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)))),X1)
| X1 = tptp3 ),
inference(spm,[status(thm)],[c_0_90,c_0_81]) ).
cnf(c_0_102,negated_conjecture,
occurrence_of(esk16_1(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)))),esk7_1(esk16_1(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)))))),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_103,negated_conjecture,
( ~ occurrence_of(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0))),X1)
| min_precedes(esk16_1(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)))),esk17_1(esk15_1(esk18_0)),X1)
| min_precedes(esk17_1(esk15_1(esk18_0)),esk16_1(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)))),X1)
| esk16_1(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)))) = esk17_1(esk15_1(esk18_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95])]) ).
cnf(c_0_104,negated_conjecture,
~ min_precedes(esk17_1(esk15_1(esk18_0)),esk16_1(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)))),tptp0),
inference(spm,[status(thm)],[c_0_96,c_0_49]) ).
cnf(c_0_105,negated_conjecture,
~ min_precedes(esk16_1(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)))),esk17_1(esk15_1(esk18_0)),tptp0),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_106,negated_conjecture,
( ~ occurrence_of(esk17_1(esk15_1(esk18_0)),X1)
| X1 = tptp1 ),
inference(spm,[status(thm)],[c_0_90,c_0_71]) ).
cnf(c_0_107,negated_conjecture,
occurrence_of(esk17_1(esk15_1(esk18_0)),esk7_1(esk17_1(esk15_1(esk18_0)))),
inference(spm,[status(thm)],[c_0_91,c_0_99]) ).
fof(c_0_108,plain,
tptp1 != tptp3,
inference(fof_nnf,[status(thm)],[c_0_100]) ).
cnf(c_0_109,negated_conjecture,
esk7_1(esk16_1(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0))))) = tptp3,
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_110,negated_conjecture,
esk16_1(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)))) = esk17_1(esk15_1(esk18_0)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_57]),c_0_104]),c_0_105]) ).
cnf(c_0_111,negated_conjecture,
esk7_1(esk17_1(esk15_1(esk18_0))) = tptp1,
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_112,plain,
tptp1 != tptp3,
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_113,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_110]),c_0_111]),c_0_112]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : PRO003+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/5.45 % Computer : n001.cluster.edu
% 0.18/5.45 % Model : x86_64 x86_64
% 0.18/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.45 % Memory : 8046.5625MB
% 0.18/5.45 % OS : Linux 6.8.0-71-generic
% 0.18/5.45 % CPULimit : 300
% 0.18/5.45 % WCLimit : 300
% 0.18/5.45 % DateTime : Mon Sep 21 03:46:20 UTC 2026
% 0.18/5.45 % CPUTime :
% 0.18/5.45 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/5.51 Running first-order theorem proving
% 0.22/5.51 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 42.90/11.89 % Version: 3.5.1
% 42.90/11.89 % Preprocessing class: FSLSSMSSSSSNFFN.
% 42.90/11.89 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 42.90/11.89 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 42.90/11.89 % Starting new_bool_3 with 300s (1) cores
% 42.90/11.89 % Starting new_bool_1 with 300s (1) cores
% 42.90/11.89 % Starting sh5l with 300s (1) cores
% 42.90/11.89 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2112657 completed with status 0
% 42.90/11.89 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 42.90/11.89 % Preprocessing class: FSLSSMSSSSSNFFN.
% 42.90/11.89 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 42.90/11.89 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 42.90/11.89 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 42.90/11.89 % No SInE strategy applied
% 42.90/11.89 % Search class: FGHSF-FFMM32-SFFFFFNN
% 42.90/11.89 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 42.90/11.89 % Starting SubtermCWHack with 136s (1) cores
% 42.90/11.89 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 42.90/11.89 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2SI with 136s (1) cores
% 42.90/11.89 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2g with 136s (1) cores
% 42.90/11.89 % Starting G-E--_107_C48_F1_PI_AE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 42.90/11.89 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2SI with pid 2112666 completed with status 0
% 42.90/11.89 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2SI
% 42.90/11.89 % Preprocessing class: FSLSSMSSSSSNFFN.
% 42.90/11.89 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 42.90/11.89 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 42.90/11.89 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 42.90/11.89 % No SInE strategy applied
% 42.90/11.89 % Search class: FGHSF-FFMM32-SFFFFFNN
% 42.90/11.89 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 42.90/11.89 % Starting SubtermCWHack with 136s (1) cores
% 42.90/11.89 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 42.90/11.89 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2SI with 136s (1) cores
% 42.90/11.89 % Preprocessing time : 0.003 s
% 42.90/11.89 % Presaturation interreduction done
% 42.90/11.89
% 42.90/11.89 % Proof found!
% 42.90/11.89 % SZS status Theorem
% 42.90/11.89 % SZS output start CNFRefutation
% See solution above
% 42.90/11.90 % Parsed axioms : 47
% 42.90/11.90 % Removed by relevancy pruning/SinE : 0
% 42.90/11.90 % Initial clauses : 83
% 42.90/11.90 % Removed in clause preprocessing : 0
% 42.90/11.90 % Initial clauses in saturation : 83
% 42.90/11.90 % Processed clauses : 12525
% 42.90/11.90 % ...of these trivial : 484
% 42.90/11.90 % ...subsumed : 2130
% 42.90/11.90 % ...remaining for further processing : 9911
% 42.90/11.90 % Other redundant clauses eliminated : 0
% 42.90/11.90 % Clauses deleted for lack of memory : 0
% 42.90/11.90 % Backward-subsumed : 639
% 42.90/11.90 % Backward-rewritten : 2582
% 42.90/11.90 % Generated clauses : 28409
% 42.90/11.90 % ...of the previous two non-redundant : 25207
% 42.90/11.90 % ...aggressively subsumed : 0
% 42.90/11.90 % Contextual simplify-reflections : 114
% 42.90/11.90 % Paramodulations : 28407
% 42.90/11.90 % Factorizations : 0
% 42.90/11.90 % NegExts : 0
% 42.90/11.90 % Equation resolutions : 0
% 42.90/11.90 % Disequality decompositions : 0
% 42.90/11.90 % Total rewrite steps : 9901
% 42.90/11.90 % ...of those cached : 8761
% 42.90/11.90 % Propositional unsat checks : 1
% 42.90/11.90 % Propositional check models : 1
% 42.90/11.90 % Propositional check unsatisfiable : 0
% 42.90/11.90 % Propositional clauses : 0
% 42.90/11.90 % Propositional clauses after purity: 0
% 42.90/11.90 % Propositional unsat core size : 0
% 42.90/11.90 % Propositional preprocessing time : 0.000
% 42.90/11.90 % Propositional encoding time : 0.007
% 42.90/11.90 % Propositional solver time : 0.028
% 42.90/11.90 % Success case prop preproc time : 0.000
% 42.90/11.90 % Success case prop encoding time : 0.000
% 42.90/11.90 % Success case prop solver time : 0.000
% 42.90/11.90 % Current number of processed clauses : 6605
% 42.90/11.90 % Positive orientable unit clauses : 1919
% 42.90/11.90 % Positive unorientable unit clauses: 0
% 42.90/11.90 % Negative unit clauses : 1340
% 42.90/11.90 % Non-unit-clauses : 3346
% 42.90/11.90 % Current number of unprocessed clauses: 11531
% 42.90/11.90 % ...number of literals in the above : 27001
% 42.90/11.90 % Current number of archived formulas : 0
% 42.90/11.90 % Current number of archived clauses : 3306
% 42.90/11.90 % Clause-clause subsumption calls (NU) : 1228216
% 42.90/11.90 % Rec. Clause-clause subsumption calls : 920126
% 42.90/11.90 % Non-unit clause-clause subsumptions : 1531
% 42.90/11.90 % Unit Clause-clause subsumption calls : 624589
% 42.90/11.90 % Rewrite failures with RHS unbound : 0
% 42.90/11.90 % BW rewrite match attempts : 17480
% 42.90/11.90 % BW rewrite match successes : 352
% 42.90/11.90 % Condensation attempts : 0
% 42.90/11.90 % Condensation successes : 0
% 42.90/11.90 % Termbank termtop insertions : 788798
% 42.90/11.90 % Search garbage collected termcells : 1199
% 42.90/11.90
% 42.90/11.90 % -------------------------------------------------
% 42.90/11.90 % User time : 5.672 s
% 42.90/11.90 % System time : 0.105 s
% 42.90/11.90 % Total time : 5.777 s
% 42.90/11.90 % Maximum resident set size: 3732 pages
% 42.90/11.90
% 42.90/11.90 % -------------------------------------------------
% 42.90/11.90 % User time : 29.921 s
% 42.90/11.90 % System time : 0.568 s
% 42.90/11.90 % Total time : 30.490 s
% 42.90/11.90 % Maximum resident set size: 4608 pages
% 42.90/11.90 % E exiting
%------------------------------------------------------------------------------