%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : PRO004+4 : 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 : n019.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 05:01:51 PM UTC 2026
% Result : Theorem 23.51s 15.29s
% Output : CNFRefutation 23.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 23
% Syntax : Number of formulae : 148 ( 33 unt; 0 def)
% Number of atoms : 438 ( 32 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 487 ( 197 ~; 194 |; 70 &)
% ( 5 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 5 con; 0-3 aty)
% Number of variables : 262 ( 10 sgn 115 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
~ ? [X112] : occurrence_of(X112,tptp0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(sos_08,axiom,
! [X29,X30,X31] :
( ( occurrence_of(X29,X30)
& occurrence_of(X29,X31) )
=> X30 = X31 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_08) ).
fof(sos_18,axiom,
! [X56,X57] :
( leaf_occ(X56,X57)
<=> ? [X58] :
( occurrence_of(X57,X58)
& subactivity_occurrence(X56,X57)
& leaf(X56,X58) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_18) ).
fof(sos_07,axiom,
! [X26,X27] :
( ( leaf(X26,X27)
& ~ atomic(X27) )
=> ? [X28] :
( occurrence_of(X28,X27)
& leaf_occ(X26,X28) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_07) ).
fof(sos,axiom,
! [X1,X2] :
( ( occurrence_of(X2,X1)
& ~ atomic(X1) )
=> ? [X3] :
( root(X3,X1)
& subactivity_occurrence(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos) ).
fof(sos_34,axiom,
~ atomic(tptp0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_34) ).
fof(sos_19,axiom,
! [X59,X60] :
( root_occ(X59,X60)
<=> ? [X61] :
( occurrence_of(X60,X61)
& subactivity_occurrence(X59,X60)
& root(X59,X61) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_19) ).
fof(sos_29,axiom,
! [X91,X92,X93,X94] :
( ( occurrence_of(X93,X94)
& root_occ(X91,X93)
& root_occ(X92,X93) )
=> X91 = X92 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_29) ).
fof(sos_32,axiom,
! [X102] :
( occurrence_of(X102,tptp0)
=> ? [X103,X104] :
( occurrence_of(X103,tptp4)
& root_occ(X103,X102)
& occurrence_of(X104,tptp3)
& leaf_occ(X104,X102)
& next_subocc(X103,X104,tptp0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_32) ).
fof(sos_26,axiom,
! [X79,X80,X81] :
( next_subocc(X79,X80,X81)
<=> ( min_precedes(X79,X80,X81)
& ~ ? [X82] :
( min_precedes(X79,X82,X81)
& min_precedes(X82,X80,X81) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_26) ).
fof(sos_15,axiom,
! [X48,X49] :
( leaf(X48,X49)
<=> ( ( root(X48,X49)
| ? [X50] : min_precedes(X50,X48,X49) )
& ~ ? [X51] : min_precedes(X48,X51,X49) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_15) ).
fof(sos_03,axiom,
! [X13,X14] :
( occurrence_of(X14,X13)
=> ( activity(X13)
& activity_occurrence(X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_03) ).
fof(sos_17,axiom,
! [X54,X55] :
( root(X54,X55)
=> legal(X54) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_17) ).
fof(sos_12,axiom,
! [X42] :
( activity_occurrence(X42)
=> ? [X43] :
( activity(X43)
& occurrence_of(X42,X43) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_12) ).
fof(sos_47,axiom,
! [X109,X110] :
( ( occurrence_of(X110,tptp0)
& subactivity_occurrence(X109,X110)
& arboreal(X109)
& ~ leaf_occ(X109,X110) )
=> ? [X111] :
( occurrence_of(X111,tptp1)
& next_subocc(X109,X111,tptp0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_47) ).
fof(sos_13,axiom,
! [X44] :
( legal(X44)
=> arboreal(X44) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_13) ).
fof(sos_45,axiom,
! [X105,X106] :
( ( occurrence_of(X106,tptp0)
& subactivity_occurrence(X105,X106)
& arboreal(X105)
& ~ leaf_occ(X105,X106) )
=> root_occ(X105,X106) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_45) ).
fof(sos_06,axiom,
! [X22,X23,X24] :
( min_precedes(X23,X24,X22)
=> ? [X25] :
( occurrence_of(X25,X22)
& subactivity_occurrence(X23,X25)
& subactivity_occurrence(X24,X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_06) ).
fof(sos_16,axiom,
! [X52,X53] :
( occurrence_of(X52,X53)
=> ( arboreal(X52)
<=> atomic(X53) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_16) ).
fof(sos_22,axiom,
! [X66,X67,X68] :
( min_precedes(X66,X67,X68)
=> ~ root(X67,X68) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_22) ).
fof(sos_38,axiom,
atomic(tptp1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_38) ).
fof(sos_28,axiom,
! [X87,X88,X89,X90] :
( ( occurrence_of(X89,X90)
& ~ atomic(X90)
& leaf_occ(X87,X89)
& leaf_occ(X88,X89) )
=> X87 = X88 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_28) ).
fof(sos_42,axiom,
tptp1 != tptp3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_42) ).
fof(c_0_23,negated_conjecture,
~ ~ ? [X112] : occurrence_of(X112,tptp0),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_24,plain,
! [X253,X254,X255] :
( ~ occurrence_of(X253,X254)
| ~ occurrence_of(X253,X255)
| X254 = X255 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_08])]) ).
fof(c_0_25,negated_conjecture,
occurrence_of(esk16_0,tptp0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])]) ).
cnf(c_0_26,plain,
( X2 = X3
| ~ occurrence_of(X1,X2)
| ~ occurrence_of(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_27,negated_conjecture,
occurrence_of(esk16_0,tptp0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_28,plain,
! [X287,X288,X290,X291,X292] :
( ( occurrence_of(X288,esk9_2(X287,X288))
| ~ leaf_occ(X287,X288) )
& ( subactivity_occurrence(X287,X288)
| ~ leaf_occ(X287,X288) )
& ( leaf(X287,esk9_2(X287,X288))
| ~ leaf_occ(X287,X288) )
& ( ~ occurrence_of(X291,X292)
| ~ subactivity_occurrence(X290,X291)
| ~ leaf(X290,X292)
| leaf_occ(X290,X291) ) ),
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_18])])])])])]) ).
fof(c_0_29,plain,
! [X26,X27] :
( ( leaf(X26,X27)
& ~ atomic(X27) )
=> ? [X28] :
( occurrence_of(X28,X27)
& leaf_occ(X26,X28) ) ),
inference(fof_simplification,[status(thm)],[sos_07]) ).
cnf(c_0_30,negated_conjecture,
( X1 = tptp0
| ~ occurrence_of(esk16_0,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
( occurrence_of(X1,esk9_2(X2,X1))
| ~ leaf_occ(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_32,plain,
! [X1,X2] :
( ( occurrence_of(X2,X1)
& ~ atomic(X1) )
=> ? [X3] :
( root(X3,X1)
& subactivity_occurrence(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[sos]) ).
fof(c_0_33,plain,
! [X250,X251] :
( ( occurrence_of(esk4_2(X250,X251),X251)
| ~ leaf(X250,X251)
| atomic(X251) )
& ( leaf_occ(X250,esk4_2(X250,X251))
| ~ leaf(X250,X251)
| atomic(X251) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])])]) ).
cnf(c_0_34,plain,
( leaf(X1,esk9_2(X1,X2))
| ~ leaf_occ(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,negated_conjecture,
( esk9_2(X1,esk16_0) = tptp0
| ~ leaf_occ(X1,esk16_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
fof(c_0_36,plain,
~ atomic(tptp0),
inference(fof_simplification,[status(thm)],[sos_34]) ).
fof(c_0_37,plain,
! [X225,X226] :
( ( root(esk1_2(X225,X226),X225)
| ~ occurrence_of(X226,X225)
| atomic(X225) )
& ( subactivity_occurrence(esk1_2(X225,X226),X226)
| ~ occurrence_of(X226,X225)
| atomic(X225) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])])]) ).
cnf(c_0_38,plain,
( leaf_occ(X1,esk4_2(X1,X2))
| atomic(X2)
| ~ leaf(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_39,negated_conjecture,
( leaf(X1,tptp0)
| ~ leaf_occ(X1,esk16_0) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,plain,
~ atomic(tptp0),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_41,plain,
! [X293,X294,X296,X297,X298] :
( ( occurrence_of(X294,esk10_2(X293,X294))
| ~ root_occ(X293,X294) )
& ( subactivity_occurrence(X293,X294)
| ~ root_occ(X293,X294) )
& ( root(X293,esk10_2(X293,X294))
| ~ root_occ(X293,X294) )
& ( ~ occurrence_of(X297,X298)
| ~ subactivity_occurrence(X296,X297)
| ~ root(X296,X298)
| root_occ(X296,X297) ) ),
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_19])])])])])]) ).
cnf(c_0_42,plain,
( subactivity_occurrence(esk1_2(X1,X2),X2)
| atomic(X1)
| ~ occurrence_of(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_43,plain,
! [X332,X333,X334,X335] :
( ~ occurrence_of(X334,X335)
| ~ root_occ(X332,X334)
| ~ root_occ(X333,X334)
| X332 = X333 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_29])]) ).
fof(c_0_44,plain,
! [X343] :
( ( occurrence_of(esk13_1(X343),tptp4)
| ~ occurrence_of(X343,tptp0) )
& ( root_occ(esk13_1(X343),X343)
| ~ occurrence_of(X343,tptp0) )
& ( occurrence_of(esk14_1(X343),tptp3)
| ~ occurrence_of(X343,tptp0) )
& ( leaf_occ(esk14_1(X343),X343)
| ~ occurrence_of(X343,tptp0) )
& ( next_subocc(esk13_1(X343),esk14_1(X343),tptp0)
| ~ occurrence_of(X343,tptp0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_32])])])]) ).
cnf(c_0_45,plain,
( subactivity_occurrence(X1,X2)
| ~ leaf_occ(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_46,negated_conjecture,
( leaf_occ(X1,esk4_2(X1,tptp0))
| ~ leaf_occ(X1,esk16_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
cnf(c_0_47,plain,
( root_occ(X3,X1)
| ~ occurrence_of(X1,X2)
| ~ subactivity_occurrence(X3,X1)
| ~ root(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_48,negated_conjecture,
subactivity_occurrence(esk1_2(tptp0,esk16_0),esk16_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_27]),c_0_40]) ).
cnf(c_0_49,plain,
( root(esk1_2(X1,X2),X1)
| atomic(X1)
| ~ occurrence_of(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_50,plain,
! [X316,X317,X318,X319,X320,X321,X322] :
( ( min_precedes(X316,X317,X318)
| ~ next_subocc(X316,X317,X318) )
& ( ~ min_precedes(X316,X319,X318)
| ~ min_precedes(X319,X317,X318)
| ~ next_subocc(X316,X317,X318) )
& ( min_precedes(X320,esk12_3(X320,X321,X322),X322)
| ~ min_precedes(X320,X321,X322)
| next_subocc(X320,X321,X322) )
& ( min_precedes(esk12_3(X320,X321,X322),X321,X322)
| ~ min_precedes(X320,X321,X322)
| next_subocc(X320,X321,X322) ) ),
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_26])])])])])]) ).
cnf(c_0_51,plain,
( X3 = X4
| ~ occurrence_of(X1,X2)
| ~ root_occ(X3,X1)
| ~ root_occ(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_52,plain,
( root_occ(esk13_1(X1),X1)
| ~ occurrence_of(X1,tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_53,plain,
( occurrence_of(esk4_2(X1,X2),X2)
| atomic(X2)
| ~ leaf(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_54,negated_conjecture,
( subactivity_occurrence(X1,esk4_2(X1,tptp0))
| ~ leaf_occ(X1,esk16_0) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_55,negated_conjecture,
( root_occ(esk1_2(tptp0,esk16_0),esk16_0)
| ~ root(esk1_2(tptp0,esk16_0),X1)
| ~ occurrence_of(esk16_0,X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_56,negated_conjecture,
root(esk1_2(tptp0,esk16_0),tptp0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_27]),c_0_40]) ).
cnf(c_0_57,plain,
( occurrence_of(X1,esk10_2(X2,X1))
| ~ root_occ(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_58,plain,
! [X275,X276,X278,X279,X280,X281] :
( ( root(X275,X276)
| min_precedes(esk7_2(X275,X276),X275,X276)
| ~ leaf(X275,X276) )
& ( ~ min_precedes(X275,X278,X276)
| ~ leaf(X275,X276) )
& ( ~ root(X279,X280)
| min_precedes(X279,esk8_2(X279,X280),X280)
| leaf(X279,X280) )
& ( ~ min_precedes(X281,X279,X280)
| min_precedes(X279,esk8_2(X279,X280),X280)
| leaf(X279,X280) ) ),
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_15])])])])])]) ).
cnf(c_0_59,plain,
( min_precedes(X1,X2,X3)
| ~ next_subocc(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_60,plain,
( next_subocc(esk13_1(X1),esk14_1(X1),tptp0)
| ~ occurrence_of(X1,tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_61,plain,
( X1 = esk13_1(X2)
| ~ root_occ(X1,X2)
| ~ occurrence_of(X2,tptp0)
| ~ occurrence_of(X2,X3) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_62,negated_conjecture,
( occurrence_of(esk4_2(X1,tptp0),tptp0)
| ~ leaf_occ(X1,esk16_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_39]),c_0_40]) ).
cnf(c_0_63,negated_conjecture,
( root_occ(X1,esk4_2(X1,tptp0))
| ~ leaf_occ(X1,esk16_0)
| ~ root(X1,X2)
| ~ occurrence_of(esk4_2(X1,tptp0),X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_54]) ).
cnf(c_0_64,negated_conjecture,
root_occ(esk1_2(tptp0,esk16_0),esk16_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_27])]) ).
fof(c_0_65,plain,
! [X237,X238] :
( ( activity(X237)
| ~ occurrence_of(X238,X237) )
& ( activity_occurrence(X238)
| ~ occurrence_of(X238,X237) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_03])])]) ).
fof(c_0_66,plain,
! [X285,X286] :
( ~ root(X285,X286)
| legal(X285) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_17])]) ).
cnf(c_0_67,plain,
( root(X1,esk10_2(X1,X2))
| ~ root_occ(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_68,negated_conjecture,
( esk10_2(X1,esk16_0) = tptp0
| ~ root_occ(X1,esk16_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_57]) ).
cnf(c_0_69,plain,
( ~ min_precedes(X1,X2,X3)
| ~ leaf(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_70,plain,
( min_precedes(esk13_1(X1),esk14_1(X1),tptp0)
| ~ occurrence_of(X1,tptp0) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_71,negated_conjecture,
( X1 = esk13_1(esk4_2(X2,tptp0))
| ~ leaf_occ(X2,esk16_0)
| ~ root_occ(X1,esk4_2(X2,tptp0))
| ~ occurrence_of(esk4_2(X2,tptp0),X3) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_72,negated_conjecture,
( root_occ(X1,esk4_2(X1,tptp0))
| ~ leaf_occ(X1,esk16_0)
| ~ root(X1,tptp0) ),
inference(spm,[status(thm)],[c_0_63,c_0_62]) ).
cnf(c_0_73,negated_conjecture,
( X1 = esk1_2(tptp0,esk16_0)
| ~ root_occ(X1,esk16_0)
| ~ occurrence_of(esk16_0,X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_64]) ).
fof(c_0_74,plain,
! [X266] :
( ( activity(esk5_1(X266))
| ~ activity_occurrence(X266) )
& ( occurrence_of(X266,esk5_1(X266))
| ~ activity_occurrence(X266) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_12])])])]) ).
cnf(c_0_75,plain,
( activity_occurrence(X1)
| ~ occurrence_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
fof(c_0_76,plain,
! [X109,X110] :
( ( occurrence_of(X110,tptp0)
& subactivity_occurrence(X109,X110)
& arboreal(X109)
& ~ leaf_occ(X109,X110) )
=> ? [X111] :
( occurrence_of(X111,tptp1)
& next_subocc(X109,X111,tptp0) ) ),
inference(fof_simplification,[status(thm)],[sos_47]) ).
fof(c_0_77,plain,
! [X268] :
( ~ legal(X268)
| arboreal(X268) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_13])]) ).
cnf(c_0_78,plain,
( legal(X1)
| ~ root(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_79,negated_conjecture,
( root(X1,tptp0)
| ~ root_occ(X1,esk16_0) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_80,plain,
( ~ leaf(esk13_1(X1),tptp0)
| ~ occurrence_of(X1,tptp0) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_81,negated_conjecture,
( esk13_1(esk4_2(X1,tptp0)) = X1
| ~ leaf_occ(X1,esk16_0)
| ~ root(X1,tptp0)
| ~ occurrence_of(esk4_2(X1,tptp0),X2) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_82,negated_conjecture,
( esk1_2(tptp0,esk16_0) = esk13_1(esk16_0)
| ~ occurrence_of(esk16_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_52]),c_0_27])]) ).
cnf(c_0_83,plain,
( occurrence_of(X1,esk5_1(X1))
| ~ activity_occurrence(X1) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_84,negated_conjecture,
activity_occurrence(esk16_0),
inference(spm,[status(thm)],[c_0_75,c_0_27]) ).
fof(c_0_85,plain,
! [X105,X106] :
( ( occurrence_of(X106,tptp0)
& subactivity_occurrence(X105,X106)
& arboreal(X105)
& ~ leaf_occ(X105,X106) )
=> root_occ(X105,X106) ),
inference(fof_simplification,[status(thm)],[sos_45]) ).
fof(c_0_86,plain,
! [X350,X351] :
( ( occurrence_of(esk15_1(X350),tptp1)
| ~ occurrence_of(X351,tptp0)
| ~ subactivity_occurrence(X350,X351)
| ~ arboreal(X350)
| leaf_occ(X350,X351) )
& ( next_subocc(X350,esk15_1(X350),tptp0)
| ~ occurrence_of(X351,tptp0)
| ~ subactivity_occurrence(X350,X351)
| ~ arboreal(X350)
| leaf_occ(X350,X351) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_76])])])])])]) ).
cnf(c_0_87,plain,
( arboreal(X1)
| ~ legal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_88,negated_conjecture,
( legal(X1)
| ~ root_occ(X1,esk16_0) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_89,negated_conjecture,
( ~ leaf_occ(esk13_1(X1),esk16_0)
| ~ occurrence_of(X1,tptp0) ),
inference(spm,[status(thm)],[c_0_80,c_0_39]) ).
cnf(c_0_90,negated_conjecture,
( esk13_1(esk4_2(X1,tptp0)) = X1
| ~ leaf_occ(X1,esk16_0)
| ~ root(X1,tptp0) ),
inference(spm,[status(thm)],[c_0_81,c_0_62]) ).
cnf(c_0_91,negated_conjecture,
esk1_2(tptp0,esk16_0) = esk13_1(esk16_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84])]) ).
fof(c_0_92,plain,
! [X346,X347] :
( ~ occurrence_of(X347,tptp0)
| ~ subactivity_occurrence(X346,X347)
| ~ arboreal(X346)
| leaf_occ(X346,X347)
| root_occ(X346,X347) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_85])]) ).
fof(c_0_93,plain,
! [X246,X247,X248] :
( ( occurrence_of(esk3_3(X246,X247,X248),X246)
| ~ min_precedes(X247,X248,X246) )
& ( subactivity_occurrence(X247,esk3_3(X246,X247,X248))
| ~ min_precedes(X247,X248,X246) )
& ( subactivity_occurrence(X248,esk3_3(X246,X247,X248))
| ~ min_precedes(X247,X248,X246) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_06])])])]) ).
cnf(c_0_94,plain,
( next_subocc(X1,esk15_1(X1),tptp0)
| leaf_occ(X1,X2)
| ~ occurrence_of(X2,tptp0)
| ~ subactivity_occurrence(X1,X2)
| ~ arboreal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_95,plain,
( subactivity_occurrence(X1,X2)
| ~ root_occ(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_96,negated_conjecture,
( arboreal(X1)
| ~ root_occ(X1,esk16_0) ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_97,negated_conjecture,
( ~ leaf_occ(X1,esk16_0)
| ~ root(X1,tptp0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_62]) ).
cnf(c_0_98,negated_conjecture,
root(esk13_1(esk16_0),tptp0),
inference(rw,[status(thm)],[c_0_56,c_0_91]) ).
cnf(c_0_99,plain,
( occurrence_of(esk15_1(X1),tptp1)
| leaf_occ(X1,X2)
| ~ occurrence_of(X2,tptp0)
| ~ subactivity_occurrence(X1,X2)
| ~ arboreal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_100,plain,
( X1 = esk5_1(X2)
| ~ occurrence_of(X2,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_83]),c_0_75]) ).
cnf(c_0_101,plain,
( leaf_occ(X2,X1)
| root_occ(X2,X1)
| ~ occurrence_of(X1,tptp0)
| ~ subactivity_occurrence(X2,X1)
| ~ arboreal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_102,plain,
( occurrence_of(esk3_3(X1,X2,X3),X1)
| ~ min_precedes(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_103,negated_conjecture,
( next_subocc(X1,esk15_1(X1),tptp0)
| leaf_occ(X1,esk16_0)
| ~ arboreal(X1)
| ~ subactivity_occurrence(X1,esk16_0) ),
inference(spm,[status(thm)],[c_0_94,c_0_27]) ).
cnf(c_0_104,plain,
( subactivity_occurrence(esk13_1(X1),X1)
| ~ occurrence_of(X1,tptp0) ),
inference(spm,[status(thm)],[c_0_95,c_0_52]) ).
cnf(c_0_105,negated_conjecture,
arboreal(esk13_1(esk16_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_52]),c_0_27])]) ).
cnf(c_0_106,negated_conjecture,
~ leaf_occ(esk13_1(esk16_0),esk16_0),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
fof(c_0_107,plain,
! [X283,X284] :
( ( ~ arboreal(X283)
| atomic(X284)
| ~ occurrence_of(X283,X284) )
& ( ~ atomic(X284)
| arboreal(X283)
| ~ occurrence_of(X283,X284) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_16])])]) ).
cnf(c_0_108,negated_conjecture,
( leaf_occ(X1,esk16_0)
| occurrence_of(esk15_1(X1),tptp1)
| ~ arboreal(X1)
| ~ subactivity_occurrence(X1,esk16_0) ),
inference(spm,[status(thm)],[c_0_99,c_0_27]) ).
fof(c_0_109,plain,
! [X66,X67,X68] :
( min_precedes(X66,X67,X68)
=> ~ root(X67,X68) ),
inference(fof_simplification,[status(thm)],[sos_22]) ).
cnf(c_0_110,plain,
( esk10_2(X1,X2) = esk5_1(X2)
| ~ root_occ(X1,X2) ),
inference(spm,[status(thm)],[c_0_100,c_0_57]) ).
cnf(c_0_111,plain,
( leaf_occ(X1,esk3_3(tptp0,X2,X3))
| root_occ(X1,esk3_3(tptp0,X2,X3))
| ~ arboreal(X1)
| ~ min_precedes(X2,X3,tptp0)
| ~ subactivity_occurrence(X1,esk3_3(tptp0,X2,X3)) ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_112,plain,
( subactivity_occurrence(X1,esk3_3(X2,X3,X1))
| ~ min_precedes(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_113,negated_conjecture,
next_subocc(esk13_1(esk16_0),esk15_1(esk13_1(esk16_0)),tptp0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_105]),c_0_27])]),c_0_106]) ).
cnf(c_0_114,plain,
( arboreal(X2)
| ~ atomic(X1)
| ~ occurrence_of(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_115,negated_conjecture,
occurrence_of(esk15_1(esk13_1(esk16_0)),tptp1),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_104]),c_0_105]),c_0_27])]),c_0_106]) ).
cnf(c_0_116,plain,
atomic(tptp1),
inference(split_conjunct,[status(thm)],[sos_38]) ).
fof(c_0_117,plain,
! [X303,X304,X305] :
( ~ min_precedes(X303,X304,X305)
| ~ root(X304,X305) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_109])]) ).
cnf(c_0_118,plain,
( esk9_2(X1,X2) = esk5_1(X2)
| ~ leaf_occ(X1,X2) ),
inference(spm,[status(thm)],[c_0_100,c_0_31]) ).
cnf(c_0_119,plain,
( root(X1,esk5_1(X2))
| ~ root_occ(X1,X2) ),
inference(spm,[status(thm)],[c_0_67,c_0_110]) ).
cnf(c_0_120,plain,
( esk5_1(esk3_3(X1,X2,X3)) = X1
| ~ min_precedes(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_100,c_0_102]) ).
cnf(c_0_121,plain,
( leaf_occ(X1,esk3_3(tptp0,X2,X1))
| root_occ(X1,esk3_3(tptp0,X2,X1))
| ~ arboreal(X1)
| ~ min_precedes(X2,X1,tptp0) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_122,negated_conjecture,
min_precedes(esk13_1(esk16_0),esk15_1(esk13_1(esk16_0)),tptp0),
inference(spm,[status(thm)],[c_0_59,c_0_113]) ).
cnf(c_0_123,negated_conjecture,
arboreal(esk15_1(esk13_1(esk16_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_124,plain,
( ~ min_precedes(X1,X2,X3)
| ~ root(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_125,plain,
( leaf(X1,esk5_1(X2))
| ~ leaf_occ(X1,X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_118]) ).
cnf(c_0_126,plain,
( root(X1,X2)
| ~ min_precedes(X3,X4,X2)
| ~ root_occ(X1,esk3_3(X2,X3,X4)) ),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_127,negated_conjecture,
( leaf_occ(esk15_1(esk13_1(esk16_0)),esk3_3(tptp0,esk13_1(esk16_0),esk15_1(esk13_1(esk16_0))))
| root_occ(esk15_1(esk13_1(esk16_0)),esk3_3(tptp0,esk13_1(esk16_0),esk15_1(esk13_1(esk16_0)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_123])]) ).
cnf(c_0_128,negated_conjecture,
~ root(esk15_1(esk13_1(esk16_0)),tptp0),
inference(spm,[status(thm)],[c_0_124,c_0_122]) ).
fof(c_0_129,plain,
! [X87,X88,X89,X90] :
( ( occurrence_of(X89,X90)
& ~ atomic(X90)
& leaf_occ(X87,X89)
& leaf_occ(X88,X89) )
=> X87 = X88 ),
inference(fof_simplification,[status(thm)],[sos_28]) ).
cnf(c_0_130,plain,
( leaf(X1,X2)
| ~ min_precedes(X3,X4,X2)
| ~ leaf_occ(X1,esk3_3(X2,X3,X4)) ),
inference(spm,[status(thm)],[c_0_125,c_0_120]) ).
cnf(c_0_131,negated_conjecture,
leaf_occ(esk15_1(esk13_1(esk16_0)),esk3_3(tptp0,esk13_1(esk16_0),esk15_1(esk13_1(esk16_0)))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_122])]),c_0_128]) ).
fof(c_0_132,plain,
! [X328,X329,X330,X331] :
( ~ occurrence_of(X330,X331)
| atomic(X331)
| ~ leaf_occ(X328,X330)
| ~ leaf_occ(X329,X330)
| X328 = X329 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_129])]) ).
cnf(c_0_133,negated_conjecture,
leaf(esk15_1(esk13_1(esk16_0)),tptp0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_122])]) ).
cnf(c_0_134,plain,
( atomic(X2)
| X3 = X4
| ~ occurrence_of(X1,X2)
| ~ leaf_occ(X3,X1)
| ~ leaf_occ(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_132]) ).
cnf(c_0_135,negated_conjecture,
leaf_occ(esk15_1(esk13_1(esk16_0)),esk4_2(esk15_1(esk13_1(esk16_0)),tptp0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_133]),c_0_40]) ).
cnf(c_0_136,negated_conjecture,
( X1 = esk15_1(esk13_1(esk16_0))
| atomic(X2)
| ~ leaf_occ(X1,esk4_2(esk15_1(esk13_1(esk16_0)),tptp0))
| ~ occurrence_of(esk4_2(esk15_1(esk13_1(esk16_0)),tptp0),X2) ),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_137,plain,
( leaf_occ(esk14_1(X1),X1)
| ~ occurrence_of(X1,tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_138,negated_conjecture,
occurrence_of(esk4_2(esk15_1(esk13_1(esk16_0)),tptp0),tptp0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_133]),c_0_40]) ).
cnf(c_0_139,plain,
( occurrence_of(esk14_1(X1),tptp3)
| ~ occurrence_of(X1,tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_140,negated_conjecture,
( esk14_1(esk4_2(esk15_1(esk13_1(esk16_0)),tptp0)) = esk15_1(esk13_1(esk16_0))
| atomic(X1)
| ~ occurrence_of(esk4_2(esk15_1(esk13_1(esk16_0)),tptp0),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_138])]) ).
cnf(c_0_141,negated_conjecture,
esk5_1(esk4_2(esk15_1(esk13_1(esk16_0)),tptp0)) = tptp0,
inference(spm,[status(thm)],[c_0_100,c_0_138]) ).
cnf(c_0_142,negated_conjecture,
activity_occurrence(esk4_2(esk15_1(esk13_1(esk16_0)),tptp0)),
inference(spm,[status(thm)],[c_0_75,c_0_138]) ).
cnf(c_0_143,plain,
( esk5_1(esk14_1(X1)) = tptp3
| ~ occurrence_of(X1,tptp0) ),
inference(spm,[status(thm)],[c_0_100,c_0_139]) ).
cnf(c_0_144,negated_conjecture,
esk14_1(esk4_2(esk15_1(esk13_1(esk16_0)),tptp0)) = esk15_1(esk13_1(esk16_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_83]),c_0_141]),c_0_142])]),c_0_40]) ).
cnf(c_0_145,negated_conjecture,
esk5_1(esk15_1(esk13_1(esk16_0))) = tptp1,
inference(spm,[status(thm)],[c_0_100,c_0_115]) ).
cnf(c_0_146,plain,
tptp1 != tptp3,
inference(split_conjunct,[status(thm)],[sos_42]) ).
cnf(c_0_147,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_145]),c_0_138])]),c_0_146]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PRO004+4 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n019.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 01:29:44 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 23.51/15.29 % Version : CSE_E---1.7
% 23.51/15.29 % Problem : theBenchmark.p
% 23.51/15.29 % SZS status Theorem for theBenchmark.p
% 23.51/15.29 % SZS output start CNFRefutation
% See solution above
% 23.61/15.35 % Total time : 12.395s
%------------------------------------------------------------------------------