%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PRO004+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 : Sun Sep 27 08:20:53 AM UTC 2026
% Result : Theorem 17.04s 2.91s
% Output : CNFRefutation 17.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 18
% Syntax : Number of formulae : 135 ( 39 unt; 0 def)
% Number of atoms : 398 ( 22 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 419 ( 156 ~; 181 |; 67 &)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 219 ( 10 sgn 103 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_02,axiom,
! [X7,X8,X9,X10] :
( ( root_occ(X8,X9)
& root_occ(X7,X9)
& occurrence_of(X9,X10) )
=> X7 = X8 ),
file('theBenchmark.p',sos_02) ).
fof(sos_03,axiom,
! [X11,X12,X13,X14] :
( ( leaf_occ(X12,X13)
& leaf_occ(X11,X13)
& ~ atomic(X14)
& occurrence_of(X13,X14) )
=> X11 = X12 ),
file('theBenchmark.p',sos_03) ).
fof(sos_04,axiom,
! [X15,X16,X17] :
( next_subocc(X15,X16,X17)
<=> ( ~ ? [X18] :
( min_precedes(X18,X16,X17)
& min_precedes(X15,X18,X17) )
& min_precedes(X15,X16,X17) ) ),
file('theBenchmark.p',sos_04) ).
fof(sos_05,axiom,
! [X19,X20,X21] :
( next_subocc(X19,X20,X21)
=> ( arboreal(X20)
& arboreal(X19) ) ),
file('theBenchmark.p',sos_05) ).
fof(sos_10,axiom,
! [X32,X33] :
( root_occ(X32,X33)
<=> ? [X34] :
( root(X32,X34)
& subactivity_occurrence(X32,X33)
& occurrence_of(X33,X34) ) ),
file('theBenchmark.p',sos_10) ).
fof(sos_14,axiom,
! [X42,X43] :
( leaf(X42,X43)
<=> ( ~ ? [X45] : min_precedes(X42,X45,X43)
& ( ? [X44] : min_precedes(X44,X42,X43)
| root(X42,X43) ) ) ),
file('theBenchmark.p',sos_14) ).
fof(sos_20,axiom,
! [X56,X57,X58] :
( ( root_occ(X57,X56)
& occurrence_of(X56,X58) )
=> ~ ? [X59] : min_precedes(X59,X57,X58) ),
file('theBenchmark.p',sos_20) ).
fof(sos_21,axiom,
! [X60,X61,X62] :
( ( leaf_occ(X61,X60)
& occurrence_of(X60,X62) )
=> ~ ? [X63] : min_precedes(X61,X63,X62) ),
file('theBenchmark.p',sos_21) ).
fof(sos_22,axiom,
! [X64,X65,X66] :
( ( occurrence_of(X64,X66)
& occurrence_of(X64,X65) )
=> X65 = X66 ),
file('theBenchmark.p',sos_22) ).
fof(sos_23,axiom,
! [X67,X68] :
( ( ~ atomic(X68)
& leaf(X67,X68) )
=> ? [X69] :
( leaf_occ(X67,X69)
& occurrence_of(X69,X68) ) ),
file('theBenchmark.p',sos_23) ).
fof(sos_24,axiom,
! [X70,X71,X72] :
( min_precedes(X71,X72,X70)
=> ? [X73] :
( subactivity_occurrence(X72,X73)
& subactivity_occurrence(X71,X73)
& occurrence_of(X73,X70) ) ),
file('theBenchmark.p',sos_24) ).
fof(sos_30,axiom,
! [X91,X92] :
( ( ~ atomic(X91)
& occurrence_of(X92,X91) )
=> ? [X93] :
( subactivity_occurrence(X93,X92)
& root(X93,X91) ) ),
file('theBenchmark.p',sos_30) ).
fof(sos_32,axiom,
! [X95] :
( occurrence_of(X95,tptp0)
=> ? [X96,X97] :
( next_subocc(X96,X97,tptp0)
& leaf_occ(X97,X95)
& occurrence_of(X97,tptp3)
& root_occ(X96,X95)
& occurrence_of(X96,tptp4) ) ),
file('theBenchmark.p',sos_32) ).
fof(sos_46,axiom,
! [X100,X101] :
( ( ~ leaf_occ(X100,X101)
& arboreal(X100)
& subactivity_occurrence(X100,X101)
& occurrence_of(X101,tptp0) )
=> root_occ(X100,X101) ),
file('theBenchmark.p',sos_46) ).
fof(sos_47,axiom,
! [X102,X103] :
( ( ~ leaf_occ(X102,X103)
& arboreal(X102)
& subactivity_occurrence(X102,X103)
& occurrence_of(X103,tptp0) )
=> ? [X104] :
( next_subocc(X102,X104,tptp0)
& occurrence_of(X104,tptp1) ) ),
file('theBenchmark.p',sos_47) ).
fof(goals,conjecture,
~ ? [X105] : occurrence_of(X105,tptp0),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ~ ? [X105] : occurrence_of(X105,tptp0),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_40,plain,
( min_precedes(A,B,C)
| ~ next_subocc(A,B,C) ),
inference(clausify,[status(thm)],[sos_04]) ).
cnf(c_42,plain,
( arboreal(A)
| ~ next_subocc(A,B,C) ),
inference(clausify,[status(thm)],[sos_05]) ).
cnf(c_43,plain,
( arboreal(B)
| ~ next_subocc(A,B,C) ),
inference(clausify,[status(thm)],[sos_05]) ).
fof(nnf_33,plain,
! [X95] :
( ? [X96,X97] :
( next_subocc(X96,X97,tptp0)
& leaf_occ(X97,X95)
& occurrence_of(X97,tptp3)
& root_occ(X96,X95)
& occurrence_of(X96,tptp4) )
| ~ occurrence_of(X95,tptp0) ),
inference(fof_nnf,[status(thm)],[sos_32]) ).
fof(sk_sos_32_sk,plain,
! [X95] :
( ( next_subocc(sK0(X95),sK1(X95),tptp0)
& leaf_occ(sK1(X95),X95)
& occurrence_of(sK1(X95),tptp3)
& root_occ(sK0(X95),X95)
& occurrence_of(sK0(X95),tptp4) )
| ~ occurrence_of(X95,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X96,sK0(X95)),skolemize(X97,sK1(X95))],[nnf_33]) ).
fof(sk_sos_32,plain,
( ! [VAR_0] :
( next_subocc(sK0(VAR_0),sK1(VAR_0),tptp0)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( leaf_occ(sK1(VAR_0),VAR_0)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( occurrence_of(sK1(VAR_0),tptp3)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( root_occ(sK0(VAR_0),VAR_0)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( occurrence_of(sK0(VAR_0),tptp4)
| ~ occurrence_of(VAR_0,tptp0) ) ),
inference(cnf_transformation,[status(thm)],[sk_sos_32_sk]) ).
cnf(c_44,plain,
( next_subocc(sK0(A),sK1(A),tptp0)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
fof(nnf_36,plain,
! [X102,X103] :
( ? [X104] :
( next_subocc(X102,X104,tptp0)
& occurrence_of(X104,tptp1) )
| leaf_occ(X102,X103)
| ~ arboreal(X102)
| ~ subactivity_occurrence(X102,X103)
| ~ occurrence_of(X103,tptp0) ),
inference(fof_nnf,[status(thm)],[sos_47]) ).
fof(sk_sos_47_sk,plain,
! [X102,X103] :
( ( next_subocc(X102,sK2(X102,X103),tptp0)
& occurrence_of(sK2(X102,X103),tptp1) )
| leaf_occ(X102,X103)
| ~ arboreal(X102)
| ~ subactivity_occurrence(X102,X103)
| ~ occurrence_of(X103,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X104,sK2(X102,X103))],[nnf_36]) ).
fof(sk_sos_47,plain,
( ! [VAR_0,VAR_1] :
( next_subocc(VAR_1,sK2(VAR_1,VAR_0),tptp0)
| leaf_occ(VAR_1,VAR_0)
| ~ arboreal(VAR_1)
| ~ subactivity_occurrence(VAR_1,VAR_0)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0,VAR_1] :
( occurrence_of(sK2(VAR_1,VAR_0),tptp1)
| leaf_occ(VAR_1,VAR_0)
| ~ arboreal(VAR_1)
| ~ subactivity_occurrence(VAR_1,VAR_0)
| ~ occurrence_of(VAR_0,tptp0) ) ),
inference(cnf_transformation,[status(thm)],[sk_sos_47_sk]) ).
cnf(c_45,plain,
( next_subocc(B,sK2(B,A),tptp0)
| leaf_occ(B,A)
| ~ arboreal(B)
| ~ subactivity_occurrence(B,A)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_47]) ).
cnf(c_52,plain,
( ~ root(A,C)
| ~ subactivity_occurrence(A,B)
| ~ occurrence_of(B,C)
| root_occ(A,B) ),
inference(clausify,[status(thm)],[sos_10]) ).
fof(nnf_31,plain,
! [X91,X92] :
( ? [X93] :
( subactivity_occurrence(X93,X92)
& root(X93,X91) )
| atomic(X91)
| ~ occurrence_of(X92,X91) ),
inference(fof_nnf,[status(thm)],[sos_30]) ).
fof(sk_sos_30_sk,plain,
! [X91,X92] :
( ( subactivity_occurrence(sK3(X91,X92),X92)
& root(sK3(X91,X92),X91) )
| atomic(X91)
| ~ occurrence_of(X92,X91) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X93,sK3(X91,X92))],[nnf_31]) ).
fof(sk_sos_30,plain,
( ! [VAR_0,VAR_1] :
( subactivity_occurrence(sK3(VAR_1,VAR_0),VAR_0)
| atomic(VAR_1)
| ~ occurrence_of(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( root(sK3(VAR_1,VAR_0),VAR_1)
| atomic(VAR_1)
| ~ occurrence_of(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_sos_30_sk]) ).
cnf(c_59,plain,
( root(sK3(B,A),B)
| atomic(B)
| ~ occurrence_of(A,B) ),
inference(split_conjunct,[status(thm)],[sk_sos_30]) ).
cnf(c_105,plain,
( ~ subactivity_occurrence(sK3(B,A),C)
| ~ occurrence_of(C,B)
| root_occ(sK3(B,A),C)
| atomic(B)
| ~ occurrence_of(A,B) ),
inference(resolve,[status(thm)],[c_59,c_52]) ).
cnf(c_115,plain,
( min_precedes(B,sK2(B,A),tptp0)
| leaf_occ(B,A)
| ~ arboreal(B)
| ~ subactivity_occurrence(B,A)
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_45,c_40]) ).
cnf(c_117,plain,
( arboreal(sK2(B,A))
| leaf_occ(B,A)
| ~ arboreal(B)
| ~ subactivity_occurrence(B,A)
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_45,c_43]) ).
cnf(c_118,plain,
( min_precedes(sK0(A),sK1(A),tptp0)
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_44,c_40]) ).
cnf(c_120,plain,
( arboreal(sK0(A))
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_44,c_42]) ).
fof(nnf_37,plain,
? [X105] : occurrence_of(X105,tptp0),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
occurrence_of(sK4,tptp0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X105,sK4)],[nnf_37]) ).
cnf(c_128,negated_conjecture,
occurrence_of(sK4,tptp0),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_129,plain,
( occurrence_of(sK2(B,A),tptp1)
| leaf_occ(B,A)
| ~ arboreal(B)
| ~ subactivity_occurrence(B,A)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_47]) ).
cnf(c_130,plain,
( root_occ(B,A)
| leaf_occ(B,A)
| ~ arboreal(B)
| ~ subactivity_occurrence(B,A)
| ~ occurrence_of(A,tptp0) ),
inference(clausify,[status(thm)],[sos_46]) ).
fof(sos_42,axiom,
tptp1 != tptp3,
file('theBenchmark.p',sos_42) ).
cnf(c_135,plain,
tptp1 != tptp3,
inference(clausify,[status(thm)],[sos_42]) ).
cnf(c_136,plain,
tptp3 != tptp1,
inference(copy,[status(thm)],[c_135]) ).
fof(sos_34,axiom,
~ atomic(tptp0),
file('theBenchmark.p',sos_34) ).
cnf(c_145,plain,
~ atomic(tptp0),
inference(clausify,[status(thm)],[sos_34]) ).
cnf(c_146,plain,
( leaf_occ(sK1(A),A)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_147,plain,
( occurrence_of(sK1(A),tptp3)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_148,plain,
( root_occ(sK0(A),A)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_150,plain,
( subactivity_occurrence(sK3(B,A),A)
| atomic(B)
| ~ occurrence_of(A,B) ),
inference(split_conjunct,[status(thm)],[sk_sos_30]) ).
fof(nnf_25,plain,
! [X70,X71,X72] :
( ? [X73] :
( subactivity_occurrence(X72,X73)
& subactivity_occurrence(X71,X73)
& occurrence_of(X73,X70) )
| ~ min_precedes(X71,X72,X70) ),
inference(fof_nnf,[status(thm)],[sos_24]) ).
fof(sk_sos_24_sk,plain,
! [X70,X71,X72] :
( ( subactivity_occurrence(X72,sK5(X70,X71,X72))
& subactivity_occurrence(X71,sK5(X70,X71,X72))
& occurrence_of(sK5(X70,X71,X72),X70) )
| ~ min_precedes(X71,X72,X70) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X73,sK5(X70,X71,X72))],[nnf_25]) ).
fof(sk_sos_24,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( subactivity_occurrence(VAR_1,sK5(VAR_2,VAR_0,VAR_1))
| ~ min_precedes(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1,VAR_2] :
( subactivity_occurrence(VAR_0,sK5(VAR_2,VAR_0,VAR_1))
| ~ min_precedes(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1,VAR_2] :
( occurrence_of(sK5(VAR_2,VAR_0,VAR_1),VAR_2)
| ~ min_precedes(VAR_0,VAR_1,VAR_2) ) ),
inference(cnf_transformation,[status(thm)],[sk_sos_24_sk]) ).
cnf(c_156,plain,
( subactivity_occurrence(B,sK5(C,A,B))
| ~ min_precedes(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_sos_24]) ).
cnf(c_158,plain,
( occurrence_of(sK5(C,A,B),C)
| ~ min_precedes(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_sos_24]) ).
fof(nnf_24,plain,
! [X67,X68] :
( ? [X69] :
( leaf_occ(X67,X69)
& occurrence_of(X69,X68) )
| atomic(X68)
| ~ leaf(X67,X68) ),
inference(fof_nnf,[status(thm)],[sos_23]) ).
fof(sk_sos_23_sk,plain,
! [X67,X68] :
( ( leaf_occ(X67,sK6(X67,X68))
& occurrence_of(sK6(X67,X68),X68) )
| atomic(X68)
| ~ leaf(X67,X68) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X69,sK6(X67,X68))],[nnf_24]) ).
fof(sk_sos_23,plain,
( ! [VAR_0,VAR_1] :
( leaf_occ(VAR_0,sK6(VAR_0,VAR_1))
| atomic(VAR_1)
| ~ leaf(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( occurrence_of(sK6(VAR_0,VAR_1),VAR_1)
| atomic(VAR_1)
| ~ leaf(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_sos_23_sk]) ).
cnf(c_159,plain,
( leaf_occ(A,sK6(A,B))
| atomic(B)
| ~ leaf(A,B) ),
inference(split_conjunct,[status(thm)],[sk_sos_23]) ).
cnf(c_160,plain,
( occurrence_of(sK6(A,B),B)
| atomic(B)
| ~ leaf(A,B) ),
inference(split_conjunct,[status(thm)],[sk_sos_23]) ).
cnf(c_161,plain,
( C = B
| ~ occurrence_of(A,C)
| ~ occurrence_of(A,B) ),
inference(clausify,[status(thm)],[sos_22]) ).
cnf(c_162,plain,
( ~ min_precedes(C,D,B)
| ~ leaf_occ(C,A)
| ~ occurrence_of(A,B) ),
inference(clausify,[status(thm)],[sos_21]) ).
cnf(c_163,plain,
( ~ min_precedes(D,C,B)
| ~ root_occ(C,A)
| ~ occurrence_of(A,B) ),
inference(clausify,[status(thm)],[sos_20]) ).
fof(nnf_15,plain,
! [X42,X43] :
( ( ? [X45] : min_precedes(X42,X45,X43)
| ( ! [X44] : ~ min_precedes(X44,X42,X43)
& ~ root(X42,X43) )
| leaf(X42,X43) )
& ( ( ! [X106] : ~ min_precedes(X42,X106,X43)
& ( ? [X107] : min_precedes(X107,X42,X43)
| root(X42,X43) ) )
| ~ leaf(X42,X43) ) ),
inference(fof_nnf,[status(thm)],[sos_14]) ).
fof(sk_sos_14_sk,plain,
! [X42,X43] :
( ( min_precedes(X42,sK7(X42,X43),X43)
| ( ! [X44] : ~ min_precedes(X44,X42,X43)
& ~ root(X42,X43) )
| leaf(X42,X43) )
& ( ( ! [X106] : ~ min_precedes(X42,X106,X43)
& ( min_precedes(sK10(X42,X43),X42,X43)
| root(X42,X43) ) )
| ~ leaf(X42,X43) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK7]),skolemize(X107,sK10(X42,X43)),skolemize(X45,sK7(X42,X43))],[nnf_15]) ).
fof(sk_sos_14,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( min_precedes(VAR_0,sK7(VAR_0,VAR_1),VAR_1)
| ~ min_precedes(VAR_2,VAR_0,VAR_1)
| leaf(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( min_precedes(VAR_0,sK7(VAR_0,VAR_1),VAR_1)
| ~ root(VAR_0,VAR_1)
| leaf(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ min_precedes(VAR_0,VAR_2,VAR_1)
| ~ leaf(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( min_precedes(sK10(VAR_0,VAR_1),VAR_0,VAR_1)
| root(VAR_0,VAR_1)
| ~ leaf(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_sos_14_sk]) ).
cnf(c_166,plain,
( min_precedes(A,sK7(A,B),B)
| ~ min_precedes(C,A,B)
| leaf(A,B) ),
inference(split_conjunct,[status(thm)],[sk_sos_14]) ).
cnf(c_174,plain,
( subactivity_occurrence(A,B)
| ~ root_occ(A,B) ),
inference(clausify,[status(thm)],[sos_10]) ).
cnf(c_177,plain,
( D = C
| ~ leaf_occ(D,A)
| ~ leaf_occ(C,A)
| atomic(B)
| ~ occurrence_of(A,B) ),
inference(clausify,[status(thm)],[sos_03]) ).
cnf(c_178,plain,
( D = C
| ~ root_occ(D,A)
| ~ root_occ(C,A)
| ~ occurrence_of(A,B) ),
inference(clausify,[status(thm)],[sos_02]) ).
cnf(c_206,plain,
( ~ subactivity_occurrence(sK3(B,A),A)
| root_occ(sK3(B,A),A)
| atomic(B)
| ~ occurrence_of(A,B) ),
inference(factor,[status(thm)],[c_105]) ).
cnf(c_216,plain,
arboreal(sK0(sK4)),
inference(resolve,[status(thm)],[c_128,c_120]) ).
cnf(c_218,plain,
min_precedes(sK0(sK4),sK1(sK4),tptp0),
inference(resolve,[status(thm)],[c_128,c_118]) ).
cnf(c_219,plain,
( arboreal(sK2(A,sK4))
| leaf_occ(A,sK4)
| ~ arboreal(A)
| ~ subactivity_occurrence(A,sK4) ),
inference(resolve,[status(thm)],[c_128,c_117]) ).
cnf(c_221,plain,
( min_precedes(A,sK2(A,sK4),tptp0)
| leaf_occ(A,sK4)
| ~ arboreal(A)
| ~ subactivity_occurrence(A,sK4) ),
inference(resolve,[status(thm)],[c_128,c_115]) ).
cnf(c_261,plain,
root_occ(sK0(sK4),sK4),
inference(resolve,[status(thm)],[c_148,c_128]) ).
cnf(c_3194,negated_conjecture,
( subactivity_occurrence(sK3(tptp0,sK4),sK4)
| atomic(tptp0) ),
inference(resolve,[status(thm)],[c_150,c_128]) ).
cnf(c_263,negated_conjecture,
subactivity_occurrence(sK3(tptp0,sK4),sK4),
inference(resolve,[status(thm)],[c_145,c_3194]) ).
cnf(c_266,plain,
( ~ min_precedes(A,B,tptp0)
| ~ leaf_occ(A,sK4) ),
inference(resolve,[status(thm)],[c_162,c_128]) ).
cnf(c_275,plain,
( B = A
| ~ root_occ(B,sK4)
| ~ root_occ(A,sK4) ),
inference(resolve,[status(thm)],[c_178,c_128]) ).
cnf(c_3195,negated_conjecture,
( ~ subactivity_occurrence(sK3(tptp0,sK4),sK4)
| root_occ(sK3(tptp0,sK4),sK4)
| atomic(tptp0) ),
inference(resolve,[status(thm)],[c_206,c_128]) ).
cnf(c_3196,negated_conjecture,
( ~ subactivity_occurrence(sK3(tptp0,sK4),sK4)
| root_occ(sK3(tptp0,sK4),sK4) ),
inference(resolve,[status(thm)],[c_145,c_3195]) ).
cnf(c_289,negated_conjecture,
root_occ(sK3(tptp0,sK4),sK4),
inference(resolve,[status(thm)],[c_263,c_3196]) ).
cnf(c_312,plain,
~ leaf_occ(sK0(sK4),sK4),
inference(resolve,[status(thm)],[c_218,c_266]) ).
cnf(c_359,plain,
subactivity_occurrence(sK0(sK4),sK4),
inference(resolve,[status(thm)],[c_261,c_174]) ).
cnf(c_3197,plain,
( arboreal(sK2(sK0(sK4),sK4))
| leaf_occ(sK0(sK4),sK4)
| ~ subactivity_occurrence(sK0(sK4),sK4) ),
inference(resolve,[status(thm)],[c_219,c_216]) ).
cnf(c_3198,plain,
( arboreal(sK2(sK0(sK4),sK4))
| leaf_occ(sK0(sK4),sK4) ),
inference(resolve,[status(thm)],[c_359,c_3197]) ).
cnf(c_392,plain,
arboreal(sK2(sK0(sK4),sK4)),
inference(resolve,[status(thm)],[c_312,c_3198]) ).
cnf(c_3199,plain,
( min_precedes(sK0(sK4),sK2(sK0(sK4),sK4),tptp0)
| leaf_occ(sK0(sK4),sK4)
| ~ subactivity_occurrence(sK0(sK4),sK4) ),
inference(resolve,[status(thm)],[c_221,c_216]) ).
cnf(c_3200,plain,
( min_precedes(sK0(sK4),sK2(sK0(sK4),sK4),tptp0)
| leaf_occ(sK0(sK4),sK4) ),
inference(resolve,[status(thm)],[c_359,c_3199]) ).
cnf(c_397,plain,
min_precedes(sK0(sK4),sK2(sK0(sK4),sK4),tptp0),
inference(resolve,[status(thm)],[c_312,c_3200]) ).
cnf(c_3201,plain,
( occurrence_of(sK2(sK0(sK4),sK4),tptp1)
| leaf_occ(sK0(sK4),sK4)
| ~ arboreal(sK0(sK4))
| ~ occurrence_of(sK4,tptp0) ),
inference(resolve,[status(thm)],[c_359,c_129]) ).
cnf(c_3202,negated_conjecture,
( occurrence_of(sK2(sK0(sK4),sK4),tptp1)
| leaf_occ(sK0(sK4),sK4)
| ~ arboreal(sK0(sK4)) ),
inference(resolve,[status(thm)],[c_128,c_3201]) ).
cnf(c_3203,negated_conjecture,
( occurrence_of(sK2(sK0(sK4),sK4),tptp1)
| leaf_occ(sK0(sK4),sK4) ),
inference(resolve,[status(thm)],[c_216,c_3202]) ).
cnf(c_426,negated_conjecture,
occurrence_of(sK2(sK0(sK4),sK4),tptp1),
inference(resolve,[status(thm)],[c_312,c_3203]) ).
cnf(c_3204,plain,
( A = sK0(sK4)
| ~ root_occ(A,sK4) ),
inference(resolve,[status(thm)],[c_275,c_261]) ).
cnf(c_491,plain,
( sK0(sK4) = A
| ~ root_occ(A,sK4) ),
inference(copy,[status(thm)],[c_3204]) ).
cnf(c_504,plain,
( root_occ(sK2(sK0(sK4),sK4),A)
| leaf_occ(sK2(sK0(sK4),sK4),A)
| ~ subactivity_occurrence(sK2(sK0(sK4),sK4),A)
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_392,c_130]) ).
cnf(c_514,plain,
sK0(sK4) = sK3(tptp0,sK4),
inference(resolve,[status(thm)],[c_491,c_289]) ).
cnf(c_3205,plain,
( root_occ(sK2(sK0(sK4),sK4),A)
| leaf_occ(sK2(sK0(sK4),sK4),A)
| ~ subactivity_occurrence(sK2(sK3(tptp0,sK4),sK4),A)
| ~ occurrence_of(A,tptp0) ),
inference(paramod,[status(thm)],[c_514,c_504]) ).
cnf(c_3206,plain,
( root_occ(sK2(sK0(sK4),sK4),A)
| leaf_occ(sK2(sK3(tptp0,sK4),sK4),A)
| ~ subactivity_occurrence(sK2(sK3(tptp0,sK4),sK4),A)
| ~ occurrence_of(A,tptp0) ),
inference(paramod,[status(thm)],[c_514,c_3205]) ).
cnf(c_518,plain,
( root_occ(sK2(sK3(tptp0,sK4),sK4),A)
| leaf_occ(sK2(sK3(tptp0,sK4),sK4),A)
| ~ subactivity_occurrence(sK2(sK3(tptp0,sK4),sK4),A)
| ~ occurrence_of(A,tptp0) ),
inference(paramod,[status(thm)],[c_514,c_3206]) ).
cnf(c_536,negated_conjecture,
occurrence_of(sK2(sK3(tptp0,sK4),sK4),tptp1),
inference(paramod,[status(thm)],[c_514,c_426]) ).
cnf(c_3207,plain,
min_precedes(sK3(tptp0,sK4),sK2(sK0(sK4),sK4),tptp0),
inference(paramod,[status(thm)],[c_514,c_397]) ).
cnf(c_538,plain,
min_precedes(sK3(tptp0,sK4),sK2(sK3(tptp0,sK4),sK4),tptp0),
inference(paramod,[status(thm)],[c_514,c_3207]) ).
cnf(c_703,plain,
( tptp1 = A
| ~ occurrence_of(sK2(sK3(tptp0,sK4),sK4),A) ),
inference(resolve,[status(thm)],[c_536,c_161]) ).
cnf(c_929,plain,
( min_precedes(sK2(sK3(tptp0,sK4),sK4),sK7(sK2(sK3(tptp0,sK4),sK4),tptp0),tptp0)
| leaf(sK2(sK3(tptp0,sK4),sK4),tptp0) ),
inference(resolve,[status(thm)],[c_538,c_166]) ).
cnf(c_930,plain,
( ~ root_occ(sK2(sK3(tptp0,sK4),sK4),A)
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_538,c_163]) ).
cnf(c_931,plain,
occurrence_of(sK5(tptp0,sK3(tptp0,sK4),sK2(sK3(tptp0,sK4),sK4)),tptp0),
inference(resolve,[status(thm)],[c_538,c_158]) ).
cnf(c_933,plain,
subactivity_occurrence(sK2(sK3(tptp0,sK4),sK4),sK5(tptp0,sK3(tptp0,sK4),sK2(sK3(tptp0,sK4),sK4))),
inference(resolve,[status(thm)],[c_538,c_156]) ).
cnf(c_1597,plain,
~ root_occ(sK2(sK3(tptp0,sK4),sK4),sK5(tptp0,sK3(tptp0,sK4),sK2(sK3(tptp0,sK4),sK4))),
inference(resolve,[status(thm)],[c_931,c_930]) ).
cnf(c_3208,plain,
( root_occ(sK2(sK3(tptp0,sK4),sK4),sK5(tptp0,sK3(tptp0,sK4),sK2(sK3(tptp0,sK4),sK4)))
| leaf_occ(sK2(sK3(tptp0,sK4),sK4),sK5(tptp0,sK3(tptp0,sK4),sK2(sK3(tptp0,sK4),sK4)))
| ~ subactivity_occurrence(sK2(sK3(tptp0,sK4),sK4),sK5(tptp0,sK3(tptp0,sK4),sK2(sK3(tptp0,sK4),sK4))) ),
inference(resolve,[status(thm)],[c_931,c_518]) ).
cnf(c_3209,plain,
( root_occ(sK2(sK3(tptp0,sK4),sK4),sK5(tptp0,sK3(tptp0,sK4),sK2(sK3(tptp0,sK4),sK4)))
| leaf_occ(sK2(sK3(tptp0,sK4),sK4),sK5(tptp0,sK3(tptp0,sK4),sK2(sK3(tptp0,sK4),sK4))) ),
inference(resolve,[status(thm)],[c_933,c_3208]) ).
cnf(c_1601,plain,
leaf_occ(sK2(sK3(tptp0,sK4),sK4),sK5(tptp0,sK3(tptp0,sK4),sK2(sK3(tptp0,sK4),sK4))),
inference(resolve,[status(thm)],[c_1597,c_3209]) ).
cnf(c_1611,plain,
( ~ min_precedes(A,B,tptp0)
| ~ leaf_occ(A,sK5(tptp0,sK3(tptp0,sK4),sK2(sK3(tptp0,sK4),sK4))) ),
inference(resolve,[status(thm)],[c_931,c_162]) ).
cnf(c_3210,plain,
( ~ leaf_occ(sK2(sK3(tptp0,sK4),sK4),sK5(tptp0,sK3(tptp0,sK4),sK2(sK3(tptp0,sK4),sK4)))
| leaf(sK2(sK3(tptp0,sK4),sK4),tptp0) ),
inference(resolve,[status(thm)],[c_929,c_1611]) ).
cnf(c_2010,plain,
leaf(sK2(sK3(tptp0,sK4),sK4),tptp0),
inference(resolve,[status(thm)],[c_1601,c_3210]) ).
cnf(c_3211,plain,
( occurrence_of(sK6(sK2(sK3(tptp0,sK4),sK4),tptp0),tptp0)
| atomic(tptp0) ),
inference(resolve,[status(thm)],[c_2010,c_160]) ).
cnf(c_2015,plain,
occurrence_of(sK6(sK2(sK3(tptp0,sK4),sK4),tptp0),tptp0),
inference(resolve,[status(thm)],[c_145,c_3211]) ).
cnf(c_3212,plain,
( leaf_occ(sK2(sK3(tptp0,sK4),sK4),sK6(sK2(sK3(tptp0,sK4),sK4),tptp0))
| atomic(tptp0) ),
inference(resolve,[status(thm)],[c_2010,c_159]) ).
cnf(c_2016,plain,
leaf_occ(sK2(sK3(tptp0,sK4),sK4),sK6(sK2(sK3(tptp0,sK4),sK4),tptp0)),
inference(resolve,[status(thm)],[c_145,c_3212]) ).
cnf(c_3213,plain,
( B = A
| ~ leaf_occ(B,sK6(sK2(sK3(tptp0,sK4),sK4),tptp0))
| ~ leaf_occ(A,sK6(sK2(sK3(tptp0,sK4),sK4),tptp0))
| atomic(tptp0) ),
inference(resolve,[status(thm)],[c_2015,c_177]) ).
cnf(c_2031,plain,
( B = A
| ~ leaf_occ(B,sK6(sK2(sK3(tptp0,sK4),sK4),tptp0))
| ~ leaf_occ(A,sK6(sK2(sK3(tptp0,sK4),sK4),tptp0)) ),
inference(resolve,[status(thm)],[c_145,c_3213]) ).
cnf(c_2040,plain,
occurrence_of(sK1(sK6(sK2(sK3(tptp0,sK4),sK4),tptp0)),tptp3),
inference(resolve,[status(thm)],[c_2015,c_147]) ).
cnf(c_2041,plain,
leaf_occ(sK1(sK6(sK2(sK3(tptp0,sK4),sK4),tptp0)),sK6(sK2(sK3(tptp0,sK4),sK4),tptp0)),
inference(resolve,[status(thm)],[c_2015,c_146]) ).
cnf(c_3214,plain,
( A = sK2(sK3(tptp0,sK4),sK4)
| ~ leaf_occ(A,sK6(sK2(sK3(tptp0,sK4),sK4),tptp0)) ),
inference(resolve,[status(thm)],[c_2031,c_2016]) ).
cnf(c_3143,plain,
( sK2(sK3(tptp0,sK4),sK4) = A
| ~ leaf_occ(A,sK6(sK2(sK3(tptp0,sK4),sK4),tptp0)) ),
inference(copy,[status(thm)],[c_3214]) ).
cnf(c_3215,plain,
sK2(sK3(tptp0,sK4),sK4) = sK1(sK6(sK2(sK3(tptp0,sK4),sK4),tptp0)),
inference(resolve,[status(thm)],[c_3143,c_2041]) ).
cnf(c_3144,plain,
sK1(sK6(sK2(sK3(tptp0,sK4),sK4),tptp0)) = sK2(sK3(tptp0,sK4),sK4),
inference(copy,[status(thm)],[c_3215]) ).
cnf(c_3173,plain,
occurrence_of(sK2(sK3(tptp0,sK4),sK4),tptp3),
inference(paramod,[status(thm)],[c_3144,c_2040]) ).
cnf(c_3216,plain,
tptp1 = tptp3,
inference(resolve,[status(thm)],[c_3173,c_703]) ).
cnf(c_3217,plain,
tptp3 = tptp1,
inference(copy,[status(thm)],[c_3216]) ).
cnf(c_3193,plain,
$false,
inference(resolve,[status(thm)],[c_136,c_3217]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PRO004+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n014.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sat Sep 26 04:55:02 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 2184726 was started by sandbox2 on n014,
% 0.08/0.37 % Sat Sep 26 04:55:02 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.39
% 0.08/0.39 % From the command line: assign(max_seconds, 300).
% 17.04/2.91
% 17.04/2.91 % given #500 (F,wt=22): 1152 -leaf_occ(A,f16(f9(tptp0,f14(tptp0,c1),f16(c1)))) | -min_precedes(A,B,tptp3). [resolve(777,a,162,a)].
% 17.04/2.91
% 17.04/2.91 % given #1000 (W,wt=20): 2063 -occurrence_of(f10(f17(f14(tptp0,c1),c1),tptp0),A) | tptp0 = A. [resolve(2017,a,161,b)].
% 17.04/2.91
% 17.04/2.91 % given #1500 (F,wt=30): 2337 -root_occ(f17(f14(tptp0,c1),f9(tptp0,f14(tptp0,c1),f16(c1))),f9(tptp0,f14(tptp0,c1),f5(f14(tptp0,c1),tptp0))). [resolve(1030,a,1328,b)].
% 17.04/2.91
% 17.04/2.91 % given #2000 (W,wt=27): 2587 atocc(f16(f10(f17(f14(tptp0,c1),c1),tptp0)),f12(tptp0,f4(f16(c1),tptp0),f16(c1))). [resolve(2586,b,2067,a)].
% 17.04/2.91
% 17.04/2.91 % SZS status Theorem for theBenchmark
% 17.04/2.91
% 17.04/2.91 % Proof 1 at 1.78 (+ 0.48) seconds.
% 17.04/2.91 % Length of proof is 88.
% 17.04/2.91 % Level of proof is 16.
% 17.04/2.91 % Maximum clause weight is 30.000.
% 17.04/2.91 % Given clauses 2024.
% 17.04/2.91
% 17.04/2.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------