%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : PRO004+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 0.14s 5.54s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of formulae : 87 ( 34 unt; 0 def)
% Number of atoms : 252 ( 15 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 279 ( 114 ~; 100 |; 49 &)
% ( 3 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 141 ( 4 sgn 79 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
~ ? [X106] : occurrence_of(X106,tptp0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
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/sandbox/benchmark/theBenchmark.p',sos_32) ).
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/sandbox/benchmark/theBenchmark.p',sos_04) ).
fof(sos_47,axiom,
! [X103,X104] :
( ( ~ leaf_occ(X103,X104)
& arboreal(X103)
& subactivity_occurrence(X103,X104)
& occurrence_of(X104,tptp0) )
=> ? [X105] :
( next_subocc(X103,X105,tptp0)
& occurrence_of(X105,tptp1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_47) ).
fof(sos_21,axiom,
! [X61,X62,X63] :
( ( leaf_occ(X62,X61)
& occurrence_of(X61,X63) )
=> ~ ? [X64] : min_precedes(X62,X64,X63) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_21) ).
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/sandbox/benchmark/theBenchmark.p',sos_10) ).
fof(sos_13,axiom,
! [X41,X42] :
( occurrence_of(X41,X42)
=> ( arboreal(X41)
<=> atomic(X42) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_13) ).
fof(sos_35,axiom,
atomic(tptp4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_35) ).
fof(sos_45,axiom,
! [X99,X100] :
( ( ~ leaf_occ(X99,X100)
& arboreal(X99)
& subactivity_occurrence(X99,X100)
& occurrence_of(X100,tptp0) )
=> root_occ(X99,X100) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_45) ).
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/sandbox/benchmark/theBenchmark.p',sos_24) ).
fof(sos_20,axiom,
! [X57,X58,X59] :
( ( root_occ(X58,X57)
& occurrence_of(X57,X59) )
=> ~ ? [X60] : min_precedes(X60,X58,X59) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_20) ).
fof(sos_05,axiom,
! [X20,X21,X22] :
( next_subocc(X20,X21,X22)
=> ( arboreal(X21)
& arboreal(X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_05) ).
fof(sos_03,axiom,
! [X12,X13,X14,X15] :
( ( leaf_occ(X13,X14)
& leaf_occ(X12,X14)
& ~ atomic(X15)
& occurrence_of(X14,X15) )
=> X12 = X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_03) ).
fof(sos_34,axiom,
~ atomic(tptp0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_34) ).
fof(sos_22,axiom,
! [X65,X66,X67] :
( ( occurrence_of(X65,X67)
& occurrence_of(X65,X66) )
=> X66 = X67 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_22) ).
fof(sos_42,axiom,
tptp1 != tptp3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_42) ).
fof(c_0_16,negated_conjecture,
~ ~ ? [X106] : occurrence_of(X106,tptp0),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_17,plain,
! [X219] :
( ( ~ occurrence_of(X219,tptp0)
| next_subocc(esk15_1(X219),esk16_1(X219),tptp0) )
& ( ~ occurrence_of(X219,tptp0)
| leaf_occ(esk16_1(X219),X219) )
& ( ~ occurrence_of(X219,tptp0)
| occurrence_of(esk16_1(X219),tptp3) )
& ( ~ occurrence_of(X219,tptp0)
| root_occ(esk15_1(X219),X219) )
& ( ~ occurrence_of(X219,tptp0)
| occurrence_of(esk15_1(X219),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])])])])]) ).
fof(c_0_18,negated_conjecture,
occurrence_of(esk18_0,tptp0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
fof(c_0_19,plain,
! [X122,X123,X124,X125,X126,X127,X128] :
( ( next_subocc(X126,X127,X128)
| ~ min_precedes(X126,X127,X128)
| min_precedes(esk1_3(X126,X127,X128),X127,X128) )
& ( next_subocc(X126,X127,X128)
| ~ min_precedes(X126,X127,X128)
| min_precedes(X126,esk1_3(X126,X127,X128),X128) )
& ( ~ next_subocc(X122,X123,X124)
| ~ min_precedes(X125,X123,X124)
| ~ min_precedes(X122,X125,X124) )
& ( ~ next_subocc(X122,X123,X124)
| min_precedes(X122,X123,X124) ) ),
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_20,plain,
( ~ occurrence_of(X1,tptp0)
| next_subocc(esk15_1(X1),esk16_1(X1),tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,negated_conjecture,
occurrence_of(esk18_0,tptp0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_22,plain,
! [X103,X104] :
( ( ~ leaf_occ(X103,X104)
& arboreal(X103)
& subactivity_occurrence(X103,X104)
& occurrence_of(X104,tptp0) )
=> ? [X105] :
( next_subocc(X103,X105,tptp0)
& occurrence_of(X105,tptp1) ) ),
inference(fof_simplification,[status(thm)],[sos_47]) ).
fof(c_0_23,plain,
! [X184,X185,X186,X187] :
( ~ min_precedes(X185,X187,X186)
| ~ leaf_occ(X185,X184)
| ~ occurrence_of(X184,X186) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_21])])])]) ).
cnf(c_0_24,plain,
( ~ next_subocc(X1,X2,X3)
| min_precedes(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,negated_conjecture,
next_subocc(esk15_1(esk18_0),esk16_1(esk18_0),tptp0),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_26,plain,
! [X226,X227] :
( ( leaf_occ(X226,X227)
| ~ arboreal(X226)
| ~ subactivity_occurrence(X226,X227)
| ~ occurrence_of(X227,tptp0)
| next_subocc(X226,esk17_1(X226),tptp0) )
& ( leaf_occ(X226,X227)
| ~ arboreal(X226)
| ~ subactivity_occurrence(X226,X227)
| ~ occurrence_of(X227,tptp0)
| occurrence_of(esk17_1(X226),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)],[c_0_22])])])])])])]) ).
fof(c_0_27,plain,
! [X143,X144,X146,X147,X148] :
( ( root_occ(X146,X147)
| ~ root(X146,X148)
| ~ subactivity_occurrence(X146,X147)
| ~ occurrence_of(X147,X148) )
& ( ~ root_occ(X143,X144)
| root(X143,esk2_2(X143,X144)) )
& ( ~ root_occ(X143,X144)
| subactivity_occurrence(X143,X144) )
& ( ~ root_occ(X143,X144)
| occurrence_of(X144,esk2_2(X143,X144)) ) ),
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_28,plain,
( ~ occurrence_of(X1,tptp0)
| root_occ(esk15_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_29,plain,
! [X157,X158] :
( ( ~ occurrence_of(X157,X158)
| arboreal(X157)
| ~ atomic(X158) )
& ( ~ occurrence_of(X157,X158)
| atomic(X158)
| ~ arboreal(X157) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_13])])])]) ).
cnf(c_0_30,plain,
( ~ occurrence_of(X1,tptp0)
| occurrence_of(esk15_1(X1),tptp4) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_31,plain,
( ~ min_precedes(X3,X4,X2)
| ~ leaf_occ(X3,X1)
| ~ occurrence_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,negated_conjecture,
min_precedes(esk15_1(esk18_0),esk16_1(esk18_0),tptp0),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_33,plain,
( ~ arboreal(X1)
| ~ subactivity_occurrence(X1,X2)
| ~ occurrence_of(X2,tptp0)
| leaf_occ(X1,X2)
| next_subocc(X1,esk17_1(X1),tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_34,plain,
( ~ root_occ(X1,X2)
| subactivity_occurrence(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,negated_conjecture,
root_occ(esk15_1(esk18_0),esk18_0),
inference(spm,[status(thm)],[c_0_28,c_0_21]) ).
cnf(c_0_36,plain,
( ~ occurrence_of(X2,X1)
| ~ atomic(X1)
| arboreal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_37,negated_conjecture,
occurrence_of(esk15_1(esk18_0),tptp4),
inference(spm,[status(thm)],[c_0_30,c_0_21]) ).
cnf(c_0_38,plain,
atomic(tptp4),
inference(split_conjunct,[status(thm)],[sos_35]) ).
cnf(c_0_39,negated_conjecture,
( ~ occurrence_of(X1,tptp0)
| ~ leaf_occ(esk15_1(esk18_0),X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_40,negated_conjecture,
( ~ arboreal(X1)
| ~ subactivity_occurrence(X1,esk18_0)
| leaf_occ(X1,esk18_0)
| next_subocc(X1,esk17_1(X1),tptp0) ),
inference(spm,[status(thm)],[c_0_33,c_0_21]) ).
cnf(c_0_41,negated_conjecture,
subactivity_occurrence(esk15_1(esk18_0),esk18_0),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_42,negated_conjecture,
arboreal(esk15_1(esk18_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]) ).
cnf(c_0_43,negated_conjecture,
~ leaf_occ(esk15_1(esk18_0),esk18_0),
inference(spm,[status(thm)],[c_0_39,c_0_21]) ).
fof(c_0_44,plain,
! [X99,X100] :
( ( ~ leaf_occ(X99,X100)
& arboreal(X99)
& subactivity_occurrence(X99,X100)
& occurrence_of(X100,tptp0) )
=> root_occ(X99,X100) ),
inference(fof_simplification,[status(thm)],[sos_45]) ).
fof(c_0_45,plain,
! [X194,X195,X196] :
( ( ~ min_precedes(X195,X196,X194)
| subactivity_occurrence(X196,esk9_3(X194,X195,X196)) )
& ( ~ min_precedes(X195,X196,X194)
| subactivity_occurrence(X195,esk9_3(X194,X195,X196)) )
& ( ~ min_precedes(X195,X196,X194)
| occurrence_of(esk9_3(X194,X195,X196),X194) ) ),
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_46,negated_conjecture,
next_subocc(esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)),tptp0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]),c_0_43]) ).
fof(c_0_47,plain,
! [X180,X181,X182,X183] :
( ~ min_precedes(X183,X181,X182)
| ~ root_occ(X181,X180)
| ~ occurrence_of(X180,X182) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_20])])])]) ).
fof(c_0_48,plain,
! [X222,X223] :
( root_occ(X222,X223)
| leaf_occ(X222,X223)
| ~ arboreal(X222)
| ~ subactivity_occurrence(X222,X223)
| ~ occurrence_of(X223,tptp0) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])]) ).
cnf(c_0_49,plain,
( ~ min_precedes(X2,X3,X1)
| occurrence_of(esk9_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_50,negated_conjecture,
min_precedes(esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)),tptp0),
inference(spm,[status(thm)],[c_0_24,c_0_46]) ).
fof(c_0_51,plain,
! [X130,X131,X132] :
( ( ~ next_subocc(X130,X131,X132)
| arboreal(X131) )
& ( ~ next_subocc(X130,X131,X132)
| arboreal(X130) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_05])])])]) ).
cnf(c_0_52,plain,
( ~ min_precedes(X4,X3,X2)
| ~ root_occ(X3,X1)
| ~ occurrence_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
fof(c_0_53,plain,
! [X12,X13,X14,X15] :
( ( leaf_occ(X13,X14)
& leaf_occ(X12,X14)
& ~ atomic(X15)
& occurrence_of(X14,X15) )
=> X12 = X13 ),
inference(fof_simplification,[status(thm)],[sos_03]) ).
cnf(c_0_54,plain,
( ~ arboreal(X2)
| ~ subactivity_occurrence(X2,X1)
| ~ occurrence_of(X1,tptp0)
| root_occ(X2,X1)
| leaf_occ(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_55,negated_conjecture,
occurrence_of(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0))),tptp0),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_56,plain,
( ~ min_precedes(X3,X1,X2)
| subactivity_occurrence(X1,esk9_3(X2,X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_57,plain,
( ~ next_subocc(X2,X1,X3)
| arboreal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_58,negated_conjecture,
( ~ occurrence_of(X1,tptp0)
| ~ root_occ(esk17_1(esk15_1(esk18_0)),X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_50]) ).
fof(c_0_59,plain,
! [X118,X119,X120,X121] :
( X118 = X119
| ~ leaf_occ(X119,X120)
| ~ leaf_occ(X118,X120)
| atomic(X121)
| ~ occurrence_of(X120,X121) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_53])])]) ).
cnf(c_0_60,negated_conjecture,
( ~ arboreal(X1)
| ~ subactivity_occurrence(X1,esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0))))
| root_occ(X1,esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0))))
| leaf_occ(X1,esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)))) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_61,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_56,c_0_50]) ).
cnf(c_0_62,negated_conjecture,
arboreal(esk17_1(esk15_1(esk18_0))),
inference(spm,[status(thm)],[c_0_57,c_0_46]) ).
cnf(c_0_63,negated_conjecture,
~ root_occ(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_58,c_0_55]) ).
cnf(c_0_64,plain,
( ~ leaf_occ(X4,X1)
| ~ leaf_occ(X3,X1)
| ~ occurrence_of(X1,X2)
| X3 = X4
| atomic(X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_65,negated_conjecture,
leaf_occ(esk17_1(esk15_1(esk18_0)),esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62])]),c_0_63]) ).
cnf(c_0_66,plain,
( ~ occurrence_of(X1,tptp0)
| leaf_occ(esk16_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_67,plain,
~ atomic(tptp0),
inference(fof_simplification,[status(thm)],[sos_34]) ).
cnf(c_0_68,plain,
( ~ arboreal(X1)
| ~ subactivity_occurrence(X1,X2)
| ~ occurrence_of(X2,tptp0)
| leaf_occ(X1,X2)
| occurrence_of(esk17_1(X1),tptp1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_69,negated_conjecture,
( ~ occurrence_of(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0))),X2)
| ~ leaf_occ(X1,esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0))))
| atomic(X2)
| X1 = esk17_1(esk15_1(esk18_0)) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_70,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_66,c_0_55]) ).
fof(c_0_71,plain,
~ atomic(tptp0),
inference(fof_nnf,[status(thm)],[c_0_67]) ).
fof(c_0_72,plain,
! [X188,X189,X190] :
( X189 = X190
| ~ occurrence_of(X188,X190)
| ~ occurrence_of(X188,X189) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_22])])]) ).
cnf(c_0_73,negated_conjecture,
( ~ arboreal(X1)
| ~ subactivity_occurrence(X1,esk18_0)
| occurrence_of(esk17_1(X1),tptp1)
| leaf_occ(X1,esk18_0) ),
inference(spm,[status(thm)],[c_0_68,c_0_21]) ).
cnf(c_0_74,plain,
( ~ occurrence_of(X1,tptp0)
| occurrence_of(esk16_1(X1),tptp3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_75,negated_conjecture,
( ~ occurrence_of(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0))),X1)
| atomic(X1)
| esk16_1(esk9_3(tptp0,esk15_1(esk18_0),esk17_1(esk15_1(esk18_0)))) = esk17_1(esk15_1(esk18_0)) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_76,plain,
~ atomic(tptp0),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
fof(c_0_77,plain,
tptp1 != tptp3,
inference(fof_simplification,[status(thm)],[sos_42]) ).
cnf(c_0_78,plain,
( ~ occurrence_of(X1,X3)
| ~ occurrence_of(X1,X2)
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_79,negated_conjecture,
occurrence_of(esk17_1(esk15_1(esk18_0)),tptp1),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_41]),c_0_42])]),c_0_43]) ).
cnf(c_0_80,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_74,c_0_55]) ).
cnf(c_0_81,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(spm,[status(thm)],[c_0_75,c_0_55]),c_0_76]) ).
fof(c_0_82,plain,
tptp1 != tptp3,
inference(fof_nnf,[status(thm)],[c_0_77]) ).
cnf(c_0_83,negated_conjecture,
( ~ occurrence_of(esk17_1(esk15_1(esk18_0)),X1)
| X1 = tptp1 ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_84,negated_conjecture,
occurrence_of(esk17_1(esk15_1(esk18_0)),tptp3),
inference(rw,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_85,plain,
tptp1 != tptp3,
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_86,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PRO004+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/5.37 % Computer : n007.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Mon Sep 21 03:38:56 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/5.41 Running first-order theorem proving
% 0.14/5.41 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
% 0.14/5.54 % Version: 3.5.1
% 0.14/5.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/5.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/5.54 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.54 % Starting new_bool_1 with 300s (1) cores
% 0.14/5.54 % Starting sh5l with 300s (1) cores
% 0.14/5.54 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 89195 completed with status 0
% 0.14/5.54 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.14/5.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/5.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/5.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/5.54 % No SInE strategy applied
% 0.14/5.54 % Search class: FGHSF-FFMM32-SFFFFFNN
% 0.14/5.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/5.54 % Starting SubtermCWHack with 136s (1) cores
% 0.14/5.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.14/5.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2SI with 136s (1) cores
% 0.14/5.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2g with 136s (1) cores
% 0.14/5.54 % Starting G-E--_107_C48_F1_PI_AE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 0.14/5.54 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2SI with pid 89203 completed with status 0
% 0.14/5.54 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2SI
% 0.14/5.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/5.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/5.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/5.54 % No SInE strategy applied
% 0.14/5.54 % Search class: FGHSF-FFMM32-SFFFFFNN
% 0.14/5.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/5.54 % Starting SubtermCWHack with 136s (1) cores
% 0.14/5.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.14/5.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2SI with 136s (1) cores
% 0.14/5.54 % Preprocessing time : 0.002 s
% 0.14/5.54 % Presaturation interreduction done
% 0.14/5.54
% 0.14/5.54 % Proof found!
% 0.14/5.54 % SZS status Theorem
% 0.14/5.54 % SZS output start CNFRefutation
% See solution above
% 0.14/5.54 % Parsed axioms : 49
% 0.14/5.54 % Removed by relevancy pruning/SinE : 0
% 0.14/5.54 % Initial clauses : 85
% 0.14/5.54 % Removed in clause preprocessing : 0
% 0.14/5.54 % Initial clauses in saturation : 85
% 0.14/5.54 % Processed clauses : 1167
% 0.14/5.54 % ...of these trivial : 25
% 0.14/5.54 % ...subsumed : 112
% 0.14/5.54 % ...remaining for further processing : 1030
% 0.14/5.54 % Other redundant clauses eliminated : 0
% 0.14/5.54 % Clauses deleted for lack of memory : 0
% 0.14/5.54 % Backward-subsumed : 7
% 0.14/5.54 % Backward-rewritten : 195
% 0.14/5.54 % Generated clauses : 1992
% 0.14/5.54 % ...of the previous two non-redundant : 1669
% 0.14/5.54 % ...aggressively subsumed : 0
% 0.14/5.54 % Contextual simplify-reflections : 0
% 0.14/5.54 % Paramodulations : 1991
% 0.14/5.54 % Factorizations : 0
% 0.14/5.54 % NegExts : 0
% 0.14/5.54 % Equation resolutions : 0
% 0.14/5.54 % Disequality decompositions : 0
% 0.14/5.54 % Total rewrite steps : 977
% 0.14/5.54 % ...of those cached : 789
% 0.14/5.54 % Propositional unsat checks : 0
% 0.14/5.54 % Propositional check models : 0
% 0.14/5.54 % Propositional check unsatisfiable : 0
% 0.14/5.54 % Propositional clauses : 0
% 0.14/5.54 % Propositional clauses after purity: 0
% 0.14/5.54 % Propositional unsat core size : 0
% 0.14/5.54 % Propositional preprocessing time : 0.000
% 0.14/5.54 % Propositional encoding time : 0.000
% 0.14/5.54 % Propositional solver time : 0.000
% 0.14/5.54 % Success case prop preproc time : 0.000
% 0.14/5.54 % Success case prop encoding time : 0.000
% 0.14/5.54 % Success case prop solver time : 0.000
% 0.14/5.54 % Current number of processed clauses : 743
% 0.14/5.54 % Positive orientable unit clauses : 333
% 0.14/5.54 % Positive unorientable unit clauses: 0
% 0.14/5.54 % Negative unit clauses : 179
% 0.14/5.54 % Non-unit-clauses : 231
% 0.14/5.54 % Current number of unprocessed clauses: 530
% 0.14/5.54 % ...number of literals in the above : 937
% 0.14/5.54 % Current number of archived formulas : 0
% 0.14/5.54 % Current number of archived clauses : 287
% 0.14/5.54 % Clause-clause subsumption calls (NU) : 15821
% 0.14/5.54 % Rec. Clause-clause subsumption calls : 10301
% 0.14/5.54 % Non-unit clause-clause subsumptions : 44
% 0.14/5.54 % Unit Clause-clause subsumption calls : 2113
% 0.14/5.54 % Rewrite failures with RHS unbound : 0
% 0.14/5.54 % BW rewrite match attempts : 359
% 0.14/5.54 % BW rewrite match successes : 42
% 0.14/5.54 % Condensation attempts : 0
% 0.14/5.54 % Condensation successes : 0
% 0.14/5.54 % Termbank termtop insertions : 44202
% 0.14/5.54 % Search garbage collected termcells : 1276
% 0.14/5.54
% 0.14/5.54 % -------------------------------------------------
% 0.14/5.54 % User time : 0.089 s
% 0.14/5.54 % System time : 0.018 s
% 0.14/5.54 % Total time : 0.107 s
% 0.14/5.54 % Maximum resident set size: 3996 pages
% 0.14/5.54
% 0.14/5.54 % -------------------------------------------------
% 0.14/5.54 % User time : 0.472 s
% 0.14/5.54 % System time : 0.047 s
% 0.14/5.54 % Total time : 0.519 s
% 0.14/5.54 % Maximum resident set size: 4864 pages
% 0.14/5.54 % E exiting
%------------------------------------------------------------------------------