%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PRO005+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 08:20:54 AM UTC 2026
% Result : Theorem 5.32s 1.28s
% Output : CNFRefutation 5.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 18
% Syntax : Number of formulae : 122 ( 36 unt; 0 def)
% Number of atoms : 365 ( 22 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 381 ( 138 ~; 166 |; 63 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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; 6 con; 0-3 aty)
% Number of variables : 192 ( 12 sgn 91 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_02,axiom,
! [X8,X9,X10,X11] :
( ( ~ min_precedes(X10,X11,X8)
& arboreal(X10)
& leaf_occ(X11,X9)
& subactivity_occurrence(X10,X9)
& occurrence_of(X9,X8) )
=> X11 = X10 ),
file('theBenchmark.p',sos_02) ).
fof(sos_06,axiom,
! [X21,X22,X23] :
( min_precedes(X22,X23,X21)
=> ? [X24] :
( subactivity_occurrence(X23,X24)
& subactivity_occurrence(X22,X24)
& occurrence_of(X24,X21) ) ),
file('theBenchmark.p',sos_06) ).
fof(sos_07,axiom,
! [X25,X26] :
( ( ~ atomic(X26)
& leaf(X25,X26) )
=> ? [X27] :
( leaf_occ(X25,X27)
& occurrence_of(X27,X26) ) ),
file('theBenchmark.p',sos_07) ).
fof(sos_08,axiom,
! [X28,X29,X30] :
( ( occurrence_of(X28,X30)
& occurrence_of(X28,X29) )
=> X29 = X30 ),
file('theBenchmark.p',sos_08) ).
fof(sos_09,axiom,
! [X31,X32,X33] :
( ( leaf_occ(X32,X31)
& occurrence_of(X31,X33) )
=> ~ ? [X34] : min_precedes(X32,X34,X33) ),
file('theBenchmark.p',sos_09) ).
fof(sos_10,axiom,
! [X35,X36,X37] :
( ( root_occ(X36,X35)
& occurrence_of(X35,X37) )
=> ~ ? [X38] : min_precedes(X38,X36,X37) ),
file('theBenchmark.p',sos_10) ).
fof(sos_15,axiom,
! [X47,X48] :
( leaf(X47,X48)
<=> ( ~ ? [X50] : min_precedes(X47,X50,X48)
& ( ? [X49] : min_precedes(X49,X47,X48)
| root(X47,X48) ) ) ),
file('theBenchmark.p',sos_15) ).
fof(sos_18,axiom,
! [X55,X56] :
( leaf_occ(X55,X56)
<=> ? [X57] :
( leaf(X55,X57)
& subactivity_occurrence(X55,X56)
& occurrence_of(X56,X57) ) ),
file('theBenchmark.p',sos_18) ).
fof(sos_19,axiom,
! [X58,X59] :
( root_occ(X58,X59)
<=> ? [X60] :
( root(X58,X60)
& subactivity_occurrence(X58,X59)
& occurrence_of(X59,X60) ) ),
file('theBenchmark.p',sos_19) ).
fof(sos_25,axiom,
! [X75,X76,X77] :
( next_subocc(X75,X76,X77)
=> ( arboreal(X76)
& arboreal(X75) ) ),
file('theBenchmark.p',sos_25) ).
fof(sos_26,axiom,
! [X78,X79,X80] :
( next_subocc(X78,X79,X80)
<=> ( ~ ? [X81] :
( min_precedes(X81,X79,X80)
& min_precedes(X78,X81,X80) )
& min_precedes(X78,X79,X80) ) ),
file('theBenchmark.p',sos_26) ).
fof(sos_32,axiom,
! [X101] :
( occurrence_of(X101,tptp0)
=> ? [X102,X103] :
( next_subocc(X102,X103,tptp0)
& leaf_occ(X103,X101)
& ( occurrence_of(X103,tptp2)
| occurrence_of(X103,tptp3) )
& root_occ(X102,X101)
& occurrence_of(X102,tptp4) ) ),
file('theBenchmark.p',sos_32) ).
fof(sos_45,axiom,
! [X104,X105] :
( ( ~ leaf_occ(X104,X105)
& arboreal(X104)
& subactivity_occurrence(X104,X105)
& occurrence_of(X105,tptp0) )
=> root_occ(X104,X105) ),
file('theBenchmark.p',sos_45) ).
fof(sos_46,axiom,
! [X106,X107] :
( ( ~ leaf_occ(X106,X107)
& arboreal(X106)
& subactivity_occurrence(X106,X107)
& occurrence_of(X107,tptp0) )
=> ? [X108] :
( next_subocc(X106,X108,tptp0)
& occurrence_of(X108,tptp1) ) ),
file('theBenchmark.p',sos_46) ).
fof(goals,conjecture,
~ ? [X109] : occurrence_of(X109,tptp0),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ~ ? [X109] : occurrence_of(X109,tptp0),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_16,plain,
! [X47,X48] :
( ( ? [X50] : min_precedes(X47,X50,X48)
| ( ! [X49] : ~ min_precedes(X49,X47,X48)
& ~ root(X47,X48) )
| leaf(X47,X48) )
& ( ( ! [X111] : ~ min_precedes(X47,X111,X48)
& ( ? [X110] : min_precedes(X110,X47,X48)
| root(X47,X48) ) )
| ~ leaf(X47,X48) ) ),
inference(fof_nnf,[status(thm)],[sos_15]) ).
fof(sk_sos_15_sk,plain,
! [X47,X48] :
( ( min_precedes(X47,sK0(X47,X48),X48)
| ( ! [X49] : ~ min_precedes(X49,X47,X48)
& ~ root(X47,X48) )
| leaf(X47,X48) )
& ( ( ! [X111] : ~ min_precedes(X47,X111,X48)
& ( min_precedes(sK7(X47,X48),X47,X48)
| root(X47,X48) ) )
| ~ leaf(X47,X48) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK0]),skolemize(X110,sK7(X47,X48)),skolemize(X50,sK0(X47,X48))],[nnf_16]) ).
fof(sk_sos_15,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( min_precedes(VAR_0,sK0(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,sK0(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(sK7(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_15_sk]) ).
cnf(c_57,plain,
( min_precedes(A,sK0(A,B),B)
| ~ min_precedes(C,A,B)
| leaf(A,B) ),
inference(split_conjunct,[status(thm)],[sk_sos_15]) ).
fof(nnf_8,plain,
! [X25,X26] :
( ? [X27] :
( leaf_occ(X25,X27)
& occurrence_of(X27,X26) )
| atomic(X26)
| ~ leaf(X25,X26) ),
inference(fof_nnf,[status(thm)],[sos_07]) ).
fof(sk_sos_07_sk,plain,
! [X25,X26] :
( ( leaf_occ(X25,sK1(X25,X26))
& occurrence_of(sK1(X25,X26),X26) )
| atomic(X26)
| ~ leaf(X25,X26) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X27,sK1(X25,X26))],[nnf_8]) ).
fof(sk_sos_07,plain,
( ! [VAR_0,VAR_1] :
( leaf_occ(VAR_0,sK1(VAR_0,VAR_1))
| atomic(VAR_1)
| ~ leaf(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( occurrence_of(sK1(VAR_0,VAR_1),VAR_1)
| atomic(VAR_1)
| ~ leaf(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_sos_07_sk]) ).
cnf(c_59,plain,
( leaf_occ(A,sK1(A,B))
| atomic(B)
| ~ leaf(A,B) ),
inference(split_conjunct,[status(thm)],[sk_sos_07]) ).
cnf(c_60,plain,
( occurrence_of(sK1(A,B),B)
| atomic(B)
| ~ leaf(A,B) ),
inference(split_conjunct,[status(thm)],[sk_sos_07]) ).
cnf(c_83,plain,
( min_precedes(A,B,C)
| ~ next_subocc(A,B,C) ),
inference(clausify,[status(thm)],[sos_26]) ).
cnf(c_84,plain,
( arboreal(B)
| ~ next_subocc(A,B,C) ),
inference(clausify,[status(thm)],[sos_25]) ).
cnf(c_85,plain,
( arboreal(A)
| ~ next_subocc(A,B,C) ),
inference(clausify,[status(thm)],[sos_25]) ).
fof(nnf_33,plain,
! [X101] :
( ? [X102,X103] :
( next_subocc(X102,X103,tptp0)
& leaf_occ(X103,X101)
& ( occurrence_of(X103,tptp2)
| occurrence_of(X103,tptp3) )
& root_occ(X102,X101)
& occurrence_of(X102,tptp4) )
| ~ occurrence_of(X101,tptp0) ),
inference(fof_nnf,[status(thm)],[sos_32]) ).
fof(sk_sos_32_sk,plain,
! [X101] :
( ( next_subocc(sK2(X101),sK3(X101),tptp0)
& leaf_occ(sK3(X101),X101)
& ( occurrence_of(sK3(X101),tptp2)
| occurrence_of(sK3(X101),tptp3) )
& root_occ(sK2(X101),X101)
& occurrence_of(sK2(X101),tptp4) )
| ~ occurrence_of(X101,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X102,sK2(X101)),skolemize(X103,sK3(X101))],[nnf_33]) ).
fof(sk_sos_32,plain,
( ! [VAR_0] :
( next_subocc(sK2(VAR_0),sK3(VAR_0),tptp0)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( leaf_occ(sK3(VAR_0),VAR_0)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( occurrence_of(sK3(VAR_0),tptp2)
| occurrence_of(sK3(VAR_0),tptp3)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( root_occ(sK2(VAR_0),VAR_0)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( occurrence_of(sK2(VAR_0),tptp4)
| ~ occurrence_of(VAR_0,tptp0) ) ),
inference(cnf_transformation,[status(thm)],[sk_sos_32_sk]) ).
cnf(c_87,plain,
( next_subocc(sK2(A),sK3(A),tptp0)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
fof(nnf_35,plain,
! [X106,X107] :
( ? [X108] :
( next_subocc(X106,X108,tptp0)
& occurrence_of(X108,tptp1) )
| leaf_occ(X106,X107)
| ~ arboreal(X106)
| ~ subactivity_occurrence(X106,X107)
| ~ occurrence_of(X107,tptp0) ),
inference(fof_nnf,[status(thm)],[sos_46]) ).
fof(sk_sos_46_sk,plain,
! [X106,X107] :
( ( next_subocc(X106,sK4(X106,X107),tptp0)
& occurrence_of(sK4(X106,X107),tptp1) )
| leaf_occ(X106,X107)
| ~ arboreal(X106)
| ~ subactivity_occurrence(X106,X107)
| ~ occurrence_of(X107,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X108,sK4(X106,X107))],[nnf_35]) ).
fof(sk_sos_46,plain,
( ! [VAR_0,VAR_1] :
( next_subocc(VAR_1,sK4(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(sK4(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_46_sk]) ).
cnf(c_88,plain,
( next_subocc(B,sK4(B,A),tptp0)
| leaf_occ(B,A)
| ~ arboreal(B)
| ~ subactivity_occurrence(B,A)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_46]) ).
cnf(c_89,plain,
( arboreal(sK4(B,A))
| leaf_occ(B,A)
| ~ arboreal(B)
| ~ subactivity_occurrence(B,A)
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_88,c_84]) ).
cnf(c_90,plain,
( min_precedes(B,sK4(B,A),tptp0)
| leaf_occ(B,A)
| ~ arboreal(B)
| ~ subactivity_occurrence(B,A)
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_88,c_83]) ).
cnf(c_92,plain,
( arboreal(sK2(A))
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_87,c_85]) ).
cnf(c_94,plain,
( min_precedes(sK2(A),sK3(A),tptp0)
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_87,c_83]) ).
cnf(c_135,plain,
( occurrence_of(sK1(B,C),C)
| atomic(C)
| min_precedes(B,sK0(B,C),C)
| ~ min_precedes(A,B,C) ),
inference(resolve,[status(thm)],[c_57,c_60]) ).
cnf(c_136,plain,
( leaf_occ(B,sK1(B,C))
| atomic(C)
| min_precedes(B,sK0(B,C),C)
| ~ min_precedes(A,B,C) ),
inference(resolve,[status(thm)],[c_57,c_59]) ).
fof(nnf_36,plain,
? [X109] : occurrence_of(X109,tptp0),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
occurrence_of(sK5,tptp0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X109,sK5)],[nnf_36]) ).
cnf(c_150,negated_conjecture,
occurrence_of(sK5,tptp0),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_151,plain,
( occurrence_of(sK4(B,A),tptp1)
| leaf_occ(B,A)
| ~ arboreal(B)
| ~ subactivity_occurrence(B,A)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_46]) ).
cnf(c_152,plain,
( root_occ(B,A)
| leaf_occ(B,A)
| ~ arboreal(B)
| ~ subactivity_occurrence(B,A)
| ~ occurrence_of(A,tptp0) ),
inference(clausify,[status(thm)],[sos_45]) ).
fof(sos_43,axiom,
tptp1 != tptp2,
file('theBenchmark.p',sos_43) ).
cnf(c_154,plain,
tptp1 != tptp2,
inference(clausify,[status(thm)],[sos_43]) ).
cnf(c_155,plain,
tptp2 != tptp1,
inference(copy,[status(thm)],[c_154]) ).
fof(sos_42,axiom,
tptp1 != tptp3,
file('theBenchmark.p',sos_42) ).
cnf(c_156,plain,
tptp1 != tptp3,
inference(clausify,[status(thm)],[sos_42]) ).
cnf(c_157,plain,
tptp3 != tptp1,
inference(copy,[status(thm)],[c_156]) ).
fof(sos_34,axiom,
~ atomic(tptp0),
file('theBenchmark.p',sos_34) ).
cnf(c_165,plain,
~ atomic(tptp0),
inference(clausify,[status(thm)],[sos_34]) ).
cnf(c_166,plain,
( leaf_occ(sK3(A),A)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_167,plain,
( occurrence_of(sK3(A),tptp2)
| occurrence_of(sK3(A),tptp3)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_168,plain,
( root_occ(sK2(A),A)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_179,plain,
( subactivity_occurrence(A,B)
| ~ root_occ(A,B) ),
inference(clausify,[status(thm)],[sos_19]) ).
cnf(c_181,plain,
( subactivity_occurrence(A,B)
| ~ leaf_occ(A,B) ),
inference(clausify,[status(thm)],[sos_18]) ).
cnf(c_187,plain,
( ~ min_precedes(D,C,B)
| ~ root_occ(C,A)
| ~ occurrence_of(A,B) ),
inference(clausify,[status(thm)],[sos_10]) ).
cnf(c_188,plain,
( ~ min_precedes(C,D,B)
| ~ leaf_occ(C,A)
| ~ occurrence_of(A,B) ),
inference(clausify,[status(thm)],[sos_09]) ).
cnf(c_189,plain,
( C = B
| ~ occurrence_of(A,C)
| ~ occurrence_of(A,B) ),
inference(clausify,[status(thm)],[sos_08]) ).
fof(nnf_7,plain,
! [X21,X22,X23] :
( ? [X24] :
( subactivity_occurrence(X23,X24)
& subactivity_occurrence(X22,X24)
& occurrence_of(X24,X21) )
| ~ min_precedes(X22,X23,X21) ),
inference(fof_nnf,[status(thm)],[sos_06]) ).
fof(sk_sos_06_sk,plain,
! [X21,X22,X23] :
( ( subactivity_occurrence(X23,sK6(X21,X22,X23))
& subactivity_occurrence(X22,sK6(X21,X22,X23))
& occurrence_of(sK6(X21,X22,X23),X21) )
| ~ min_precedes(X22,X23,X21) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X24,sK6(X21,X22,X23))],[nnf_7]) ).
fof(sk_sos_06,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( subactivity_occurrence(VAR_1,sK6(VAR_2,VAR_0,VAR_1))
| ~ min_precedes(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1,VAR_2] :
( subactivity_occurrence(VAR_0,sK6(VAR_2,VAR_0,VAR_1))
| ~ min_precedes(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1,VAR_2] :
( occurrence_of(sK6(VAR_2,VAR_0,VAR_1),VAR_2)
| ~ min_precedes(VAR_0,VAR_1,VAR_2) ) ),
inference(cnf_transformation,[status(thm)],[sk_sos_06_sk]) ).
cnf(c_190,plain,
( subactivity_occurrence(B,sK6(C,A,B))
| ~ min_precedes(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_sos_06]) ).
cnf(c_192,plain,
( occurrence_of(sK6(C,A,B),C)
| ~ min_precedes(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_sos_06]) ).
cnf(c_194,plain,
( D = C
| min_precedes(C,D,B)
| ~ arboreal(C)
| ~ leaf_occ(D,A)
| ~ subactivity_occurrence(C,A)
| ~ occurrence_of(A,B) ),
inference(clausify,[status(thm)],[sos_02]) ).
cnf(c_238,plain,
min_precedes(sK2(sK5),sK3(sK5),tptp0),
inference(resolve,[status(thm)],[c_150,c_94]) ).
cnf(c_240,plain,
arboreal(sK2(sK5)),
inference(resolve,[status(thm)],[c_150,c_92]) ).
cnf(c_248,plain,
root_occ(sK2(sK5),sK5),
inference(resolve,[status(thm)],[c_168,c_150]) ).
cnf(c_259,plain,
( ~ min_precedes(A,B,tptp0)
| ~ leaf_occ(A,sK5) ),
inference(resolve,[status(thm)],[c_188,c_150]) ).
cnf(c_317,plain,
subactivity_occurrence(sK2(sK5),sK5),
inference(resolve,[status(thm)],[c_248,c_179]) ).
cnf(c_4666,plain,
( occurrence_of(sK4(sK2(sK5),sK5),tptp1)
| leaf_occ(sK2(sK5),sK5)
| ~ arboreal(sK2(sK5))
| ~ occurrence_of(sK5,tptp0) ),
inference(resolve,[status(thm)],[c_317,c_151]) ).
cnf(c_4667,negated_conjecture,
( occurrence_of(sK4(sK2(sK5),sK5),tptp1)
| leaf_occ(sK2(sK5),sK5)
| ~ arboreal(sK2(sK5)) ),
inference(resolve,[status(thm)],[c_150,c_4666]) ).
cnf(c_354,negated_conjecture,
( occurrence_of(sK4(sK2(sK5),sK5),tptp1)
| leaf_occ(sK2(sK5),sK5) ),
inference(resolve,[status(thm)],[c_240,c_4667]) ).
cnf(c_4668,plain,
( min_precedes(sK2(sK5),sK4(sK2(sK5),sK5),tptp0)
| leaf_occ(sK2(sK5),sK5)
| ~ arboreal(sK2(sK5))
| ~ occurrence_of(sK5,tptp0) ),
inference(resolve,[status(thm)],[c_317,c_90]) ).
cnf(c_4669,negated_conjecture,
( min_precedes(sK2(sK5),sK4(sK2(sK5),sK5),tptp0)
| leaf_occ(sK2(sK5),sK5)
| ~ arboreal(sK2(sK5)) ),
inference(resolve,[status(thm)],[c_150,c_4668]) ).
cnf(c_358,negated_conjecture,
( min_precedes(sK2(sK5),sK4(sK2(sK5),sK5),tptp0)
| leaf_occ(sK2(sK5),sK5) ),
inference(resolve,[status(thm)],[c_240,c_4669]) ).
cnf(c_4670,plain,
( arboreal(sK4(sK2(sK5),sK5))
| leaf_occ(sK2(sK5),sK5)
| ~ arboreal(sK2(sK5))
| ~ occurrence_of(sK5,tptp0) ),
inference(resolve,[status(thm)],[c_317,c_89]) ).
cnf(c_4671,negated_conjecture,
( arboreal(sK4(sK2(sK5),sK5))
| leaf_occ(sK2(sK5),sK5)
| ~ arboreal(sK2(sK5)) ),
inference(resolve,[status(thm)],[c_150,c_4670]) ).
cnf(c_359,negated_conjecture,
( arboreal(sK4(sK2(sK5),sK5))
| leaf_occ(sK2(sK5),sK5) ),
inference(resolve,[status(thm)],[c_240,c_4671]) ).
cnf(c_385,plain,
~ leaf_occ(sK2(sK5),sK5),
inference(resolve,[status(thm)],[c_238,c_259]) ).
cnf(c_412,negated_conjecture,
arboreal(sK4(sK2(sK5),sK5)),
inference(resolve,[status(thm)],[c_385,c_359]) ).
cnf(c_413,negated_conjecture,
min_precedes(sK2(sK5),sK4(sK2(sK5),sK5),tptp0),
inference(resolve,[status(thm)],[c_385,c_358]) ).
cnf(c_417,negated_conjecture,
occurrence_of(sK4(sK2(sK5),sK5),tptp1),
inference(resolve,[status(thm)],[c_385,c_354]) ).
cnf(c_4672,plain,
( C = sK4(sK2(sK5),sK5)
| min_precedes(sK4(sK2(sK5),sK5),C,B)
| ~ leaf_occ(C,A)
| ~ subactivity_occurrence(sK4(sK2(sK5),sK5),A)
| ~ occurrence_of(A,B) ),
inference(resolve,[status(thm)],[c_412,c_194]) ).
cnf(c_450,plain,
( sK4(sK2(sK5),sK5) = C
| min_precedes(sK4(sK2(sK5),sK5),C,B)
| ~ leaf_occ(C,A)
| ~ subactivity_occurrence(sK4(sK2(sK5),sK5),A)
| ~ occurrence_of(A,B) ),
inference(copy,[status(thm)],[c_4672]) ).
cnf(c_532,plain,
( tptp1 = A
| ~ occurrence_of(sK4(sK2(sK5),sK5),A) ),
inference(resolve,[status(thm)],[c_417,c_189]) ).
cnf(c_725,plain,
occurrence_of(sK6(tptp0,sK2(sK5),sK4(sK2(sK5),sK5)),tptp0),
inference(resolve,[status(thm)],[c_413,c_192]) ).
cnf(c_727,plain,
subactivity_occurrence(sK4(sK2(sK5),sK5),sK6(tptp0,sK2(sK5),sK4(sK2(sK5),sK5))),
inference(resolve,[status(thm)],[c_413,c_190]) ).
cnf(c_728,plain,
( ~ root_occ(sK4(sK2(sK5),sK5),A)
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_413,c_187]) ).
cnf(c_4673,plain,
( leaf_occ(sK4(sK2(sK5),sK5),sK1(sK4(sK2(sK5),sK5),tptp0))
| atomic(tptp0)
| min_precedes(sK4(sK2(sK5),sK5),sK0(sK4(sK2(sK5),sK5),tptp0),tptp0) ),
inference(resolve,[status(thm)],[c_413,c_136]) ).
cnf(c_738,plain,
( leaf_occ(sK4(sK2(sK5),sK5),sK1(sK4(sK2(sK5),sK5),tptp0))
| min_precedes(sK4(sK2(sK5),sK5),sK0(sK4(sK2(sK5),sK5),tptp0),tptp0) ),
inference(resolve,[status(thm)],[c_165,c_4673]) ).
cnf(c_4674,plain,
( occurrence_of(sK1(sK4(sK2(sK5),sK5),tptp0),tptp0)
| atomic(tptp0)
| min_precedes(sK4(sK2(sK5),sK5),sK0(sK4(sK2(sK5),sK5),tptp0),tptp0) ),
inference(resolve,[status(thm)],[c_413,c_135]) ).
cnf(c_739,plain,
( occurrence_of(sK1(sK4(sK2(sK5),sK5),tptp0),tptp0)
| min_precedes(sK4(sK2(sK5),sK5),sK0(sK4(sK2(sK5),sK5),tptp0),tptp0) ),
inference(resolve,[status(thm)],[c_165,c_4674]) ).
cnf(c_1420,plain,
~ root_occ(sK4(sK2(sK5),sK5),sK6(tptp0,sK2(sK5),sK4(sK2(sK5),sK5))),
inference(resolve,[status(thm)],[c_725,c_728]) ).
cnf(c_1446,plain,
( ~ min_precedes(A,B,tptp0)
| ~ leaf_occ(A,sK6(tptp0,sK2(sK5),sK4(sK2(sK5),sK5))) ),
inference(resolve,[status(thm)],[c_725,c_188]) ).
cnf(c_4675,plain,
( root_occ(sK4(sK2(sK5),sK5),sK6(tptp0,sK2(sK5),sK4(sK2(sK5),sK5)))
| leaf_occ(sK4(sK2(sK5),sK5),sK6(tptp0,sK2(sK5),sK4(sK2(sK5),sK5)))
| ~ arboreal(sK4(sK2(sK5),sK5))
| ~ occurrence_of(sK6(tptp0,sK2(sK5),sK4(sK2(sK5),sK5)),tptp0) ),
inference(resolve,[status(thm)],[c_727,c_152]) ).
cnf(c_4676,plain,
( root_occ(sK4(sK2(sK5),sK5),sK6(tptp0,sK2(sK5),sK4(sK2(sK5),sK5)))
| leaf_occ(sK4(sK2(sK5),sK5),sK6(tptp0,sK2(sK5),sK4(sK2(sK5),sK5)))
| ~ arboreal(sK4(sK2(sK5),sK5)) ),
inference(resolve,[status(thm)],[c_725,c_4675]) ).
cnf(c_4677,plain,
( root_occ(sK4(sK2(sK5),sK5),sK6(tptp0,sK2(sK5),sK4(sK2(sK5),sK5)))
| leaf_occ(sK4(sK2(sK5),sK5),sK6(tptp0,sK2(sK5),sK4(sK2(sK5),sK5))) ),
inference(resolve,[status(thm)],[c_412,c_4676]) ).
cnf(c_1874,plain,
leaf_occ(sK4(sK2(sK5),sK5),sK6(tptp0,sK2(sK5),sK4(sK2(sK5),sK5))),
inference(resolve,[status(thm)],[c_1420,c_4677]) ).
cnf(c_1976,plain,
~ min_precedes(sK4(sK2(sK5),sK5),A,tptp0),
inference(resolve,[status(thm)],[c_1874,c_1446]) ).
cnf(c_2003,plain,
occurrence_of(sK1(sK4(sK2(sK5),sK5),tptp0),tptp0),
inference(resolve,[status(thm)],[c_1976,c_739]) ).
cnf(c_2004,plain,
leaf_occ(sK4(sK2(sK5),sK5),sK1(sK4(sK2(sK5),sK5),tptp0)),
inference(resolve,[status(thm)],[c_1976,c_738]) ).
cnf(c_4678,plain,
( sK4(sK2(sK5),sK5) = A
| min_precedes(sK4(sK2(sK5),sK5),A,tptp0)
| ~ leaf_occ(A,sK1(sK4(sK2(sK5),sK5),tptp0))
| ~ subactivity_occurrence(sK4(sK2(sK5),sK5),sK1(sK4(sK2(sK5),sK5),tptp0)) ),
inference(resolve,[status(thm)],[c_2003,c_450]) ).
cnf(c_2018,plain,
( sK4(sK2(sK5),sK5) = A
| ~ leaf_occ(A,sK1(sK4(sK2(sK5),sK5),tptp0))
| ~ subactivity_occurrence(sK4(sK2(sK5),sK5),sK1(sK4(sK2(sK5),sK5),tptp0)) ),
inference(resolve,[status(thm)],[c_1976,c_4678]) ).
cnf(c_2052,plain,
( occurrence_of(sK3(sK1(sK4(sK2(sK5),sK5),tptp0)),tptp2)
| occurrence_of(sK3(sK1(sK4(sK2(sK5),sK5),tptp0)),tptp3) ),
inference(resolve,[status(thm)],[c_2003,c_167]) ).
cnf(c_2053,plain,
leaf_occ(sK3(sK1(sK4(sK2(sK5),sK5),tptp0)),sK1(sK4(sK2(sK5),sK5),tptp0)),
inference(resolve,[status(thm)],[c_2003,c_166]) ).
cnf(c_2085,plain,
subactivity_occurrence(sK4(sK2(sK5),sK5),sK1(sK4(sK2(sK5),sK5),tptp0)),
inference(resolve,[status(thm)],[c_2004,c_181]) ).
cnf(c_2094,plain,
( sK4(sK2(sK5),sK5) = A
| ~ leaf_occ(A,sK1(sK4(sK2(sK5),sK5),tptp0)) ),
inference(resolve,[status(thm)],[c_2085,c_2018]) ).
cnf(c_4679,plain,
sK4(sK2(sK5),sK5) = sK3(sK1(sK4(sK2(sK5),sK5),tptp0)),
inference(resolve,[status(thm)],[c_2053,c_2094]) ).
cnf(c_4660,plain,
sK3(sK1(sK4(sK2(sK5),sK5),tptp0)) = sK4(sK2(sK5),sK5),
inference(copy,[status(thm)],[c_4679]) ).
cnf(c_4680,plain,
( occurrence_of(sK3(sK1(sK4(sK2(sK5),sK5),tptp0)),tptp2)
| occurrence_of(sK4(sK2(sK5),sK5),tptp3) ),
inference(paramod,[status(thm)],[c_4660,c_2052]) ).
cnf(c_4661,plain,
( occurrence_of(sK4(sK2(sK5),sK5),tptp2)
| occurrence_of(sK4(sK2(sK5),sK5),tptp3) ),
inference(paramod,[status(thm)],[c_4660,c_4680]) ).
cnf(c_4681,plain,
( tptp1 = tptp3
| occurrence_of(sK4(sK2(sK5),sK5),tptp2) ),
inference(resolve,[status(thm)],[c_4661,c_532]) ).
cnf(c_4682,plain,
( tptp3 = tptp1
| occurrence_of(sK4(sK2(sK5),sK5),tptp2) ),
inference(copy,[status(thm)],[c_4681]) ).
cnf(c_4663,plain,
occurrence_of(sK4(sK2(sK5),sK5),tptp2),
inference(resolve,[status(thm)],[c_157,c_4682]) ).
cnf(c_4683,plain,
tptp1 = tptp2,
inference(resolve,[status(thm)],[c_4663,c_532]) ).
cnf(c_4684,plain,
tptp2 = tptp1,
inference(copy,[status(thm)],[c_4683]) ).
cnf(c_4665,plain,
$false,
inference(resolve,[status(thm)],[c_155,c_4684]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : PRO005+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n014.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 04:55:46 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.42 % Process 2185500 was started by sandbox on n014,
% 0.15/0.42 % Sat Sep 26 04:55:46 2026
% 0.15/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.44
% 0.15/0.44 % From the command line: assign(max_seconds, 300).
% 5.32/1.28
% 5.32/1.28 % given #500 (A,wt=32): 443 occurrence_of(f14(c1),tptp2) | leaf_occ(A,f14(c1)) | -subactivity_occurrence(A,f14(c1)) | -min_precedes(B,A,tptp3) | min_precedes(A,f8(A,tptp3),tptp3). [resolve(247,a,128,b)].
% 5.32/1.28
% 5.32/1.28 % given #1000 (T,wt=38): 2913 -occurrence_of(f14(f3(tptp0,f7(f14(c1),tptp0),f14(c1))),A) | atomic(A). [resolve(1376,a,184,b)].
% 5.32/1.28
% 5.32/1.28 % SZS status Theorem for theBenchmark
% 5.32/1.28
% 5.32/1.28 % Proof 1 at 0.68 (+ 0.13) seconds.
% 5.32/1.28 % Length of proof is 82.
% 5.32/1.28 % Level of proof is 16.
% 5.32/1.28 % Maximum clause weight is 45.000.
% 5.32/1.28 % Given clauses 1079.
% 5.32/1.28
% 5.32/1.28 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------