%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PRO005+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 : n016.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 11.97s 1.98s
% Output : CNFRefutation 11.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 17
% Syntax : Number of formulae : 116 ( 36 unt; 0 def)
% Number of atoms : 337 ( 21 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 350 ( 129 ~; 148 |; 60 &)
% ( 3 <=>; 10 =>; 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; 6 con; 0-3 aty)
% Number of variables : 180 ( 10 sgn 89 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
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_32,axiom,
! [X95] :
( occurrence_of(X95,tptp0)
=> ? [X96,X97] :
( next_subocc(X96,X97,tptp0)
& leaf_occ(X97,X95)
& ( occurrence_of(X97,tptp2)
| occurrence_of(X97,tptp3) )
& root_occ(X96,X95)
& occurrence_of(X96,tptp4) ) ),
file('theBenchmark.p',sos_32) ).
fof(sos_45,axiom,
! [X98,X99] :
( ( ~ leaf_occ(X98,X99)
& arboreal(X98)
& subactivity_occurrence(X98,X99)
& occurrence_of(X99,tptp0) )
=> root_occ(X98,X99) ),
file('theBenchmark.p',sos_45) ).
fof(sos_46,axiom,
! [X100,X101] :
( ( ~ leaf_occ(X100,X101)
& arboreal(X100)
& subactivity_occurrence(X100,X101)
& occurrence_of(X101,tptp0) )
=> ? [X102] :
( next_subocc(X100,X102,tptp0)
& occurrence_of(X102,tptp1) ) ),
file('theBenchmark.p',sos_46) ).
fof(goals,conjecture,
~ ? [X103] : occurrence_of(X103,tptp0),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ~ ? [X103] : occurrence_of(X103,tptp0),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_39,plain,
( min_precedes(A,B,C)
| ~ next_subocc(A,B,C) ),
inference(clausify,[status(thm)],[sos_04]) ).
cnf(c_41,plain,
( arboreal(A)
| ~ next_subocc(A,B,C) ),
inference(clausify,[status(thm)],[sos_05]) ).
cnf(c_42,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,tptp2)
| 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),tptp2)
| 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),tptp2)
| 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_43,plain,
( next_subocc(sK0(A),sK1(A),tptp0)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
fof(nnf_35,plain,
! [X100,X101] :
( ? [X102] :
( next_subocc(X100,X102,tptp0)
& occurrence_of(X102,tptp1) )
| leaf_occ(X100,X101)
| ~ arboreal(X100)
| ~ subactivity_occurrence(X100,X101)
| ~ occurrence_of(X101,tptp0) ),
inference(fof_nnf,[status(thm)],[sos_46]) ).
fof(sk_sos_46_sk,plain,
! [X100,X101] :
( ( next_subocc(X100,sK2(X100,X101),tptp0)
& occurrence_of(sK2(X100,X101),tptp1) )
| leaf_occ(X100,X101)
| ~ arboreal(X100)
| ~ subactivity_occurrence(X100,X101)
| ~ occurrence_of(X101,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X102,sK2(X100,X101))],[nnf_35]) ).
fof(sk_sos_46,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_46_sk]) ).
cnf(c_44,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_46]) ).
cnf(c_114,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_44,c_39]) ).
cnf(c_116,plain,
( arboreal(sK2(B,A))
| leaf_occ(B,A)
| ~ arboreal(B)
| ~ subactivity_occurrence(B,A)
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_44,c_42]) ).
cnf(c_117,plain,
( min_precedes(sK0(A),sK1(A),tptp0)
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_43,c_39]) ).
cnf(c_119,plain,
( arboreal(sK0(A))
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_43,c_41]) ).
fof(nnf_36,plain,
? [X103] : occurrence_of(X103,tptp0),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
occurrence_of(sK3,tptp0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X103,sK3)],[nnf_36]) ).
cnf(c_127,negated_conjecture,
occurrence_of(sK3,tptp0),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_128,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_46]) ).
cnf(c_129,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_131,plain,
tptp1 != tptp2,
inference(clausify,[status(thm)],[sos_43]) ).
cnf(c_132,plain,
tptp2 != tptp1,
inference(copy,[status(thm)],[c_131]) ).
fof(sos_42,axiom,
tptp1 != tptp3,
file('theBenchmark.p',sos_42) ).
cnf(c_133,plain,
tptp1 != tptp3,
inference(clausify,[status(thm)],[sos_42]) ).
cnf(c_134,plain,
tptp3 != tptp1,
inference(copy,[status(thm)],[c_133]) ).
fof(sos_34,axiom,
~ atomic(tptp0),
file('theBenchmark.p',sos_34) ).
cnf(c_142,plain,
~ atomic(tptp0),
inference(clausify,[status(thm)],[sos_34]) ).
cnf(c_143,plain,
( leaf_occ(sK1(A),A)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_144,plain,
( occurrence_of(sK1(A),tptp2)
| occurrence_of(sK1(A),tptp3)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_145,plain,
( root_occ(sK0(A),A)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
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,sK4(X70,X71,X72))
& subactivity_occurrence(X71,sK4(X70,X71,X72))
& occurrence_of(sK4(X70,X71,X72),X70) )
| ~ min_precedes(X71,X72,X70) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X73,sK4(X70,X71,X72))],[nnf_25]) ).
fof(sk_sos_24,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( subactivity_occurrence(VAR_1,sK4(VAR_2,VAR_0,VAR_1))
| ~ min_precedes(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1,VAR_2] :
( subactivity_occurrence(VAR_0,sK4(VAR_2,VAR_0,VAR_1))
| ~ min_precedes(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1,VAR_2] :
( occurrence_of(sK4(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_153,plain,
( subactivity_occurrence(B,sK4(C,A,B))
| ~ min_precedes(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_sos_24]) ).
cnf(c_155,plain,
( occurrence_of(sK4(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,sK5(X67,X68))
& occurrence_of(sK5(X67,X68),X68) )
| atomic(X68)
| ~ leaf(X67,X68) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X69,sK5(X67,X68))],[nnf_24]) ).
fof(sk_sos_23,plain,
( ! [VAR_0,VAR_1] :
( leaf_occ(VAR_0,sK5(VAR_0,VAR_1))
| atomic(VAR_1)
| ~ leaf(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( occurrence_of(sK5(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_156,plain,
( leaf_occ(A,sK5(A,B))
| atomic(B)
| ~ leaf(A,B) ),
inference(split_conjunct,[status(thm)],[sk_sos_23]) ).
cnf(c_157,plain,
( occurrence_of(sK5(A,B),B)
| atomic(B)
| ~ leaf(A,B) ),
inference(split_conjunct,[status(thm)],[sk_sos_23]) ).
cnf(c_158,plain,
( C = B
| ~ occurrence_of(A,C)
| ~ occurrence_of(A,B) ),
inference(clausify,[status(thm)],[sos_22]) ).
cnf(c_159,plain,
( ~ min_precedes(C,D,B)
| ~ leaf_occ(C,A)
| ~ occurrence_of(A,B) ),
inference(clausify,[status(thm)],[sos_21]) ).
cnf(c_160,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) )
& ( ( ! [X104] : ~ min_precedes(X42,X104,X43)
& ( ? [X105] : min_precedes(X105,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,sK6(X42,X43),X43)
| ( ! [X44] : ~ min_precedes(X44,X42,X43)
& ~ root(X42,X43) )
| leaf(X42,X43) )
& ( ( ! [X104] : ~ min_precedes(X42,X104,X43)
& ( min_precedes(sK8(X42,X43),X42,X43)
| root(X42,X43) ) )
| ~ leaf(X42,X43) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK6]),skolemize(X105,sK8(X42,X43)),skolemize(X45,sK6(X42,X43))],[nnf_15]) ).
fof(sk_sos_14,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( min_precedes(VAR_0,sK6(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,sK6(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(sK8(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_163,plain,
( min_precedes(A,sK6(A,B),B)
| ~ min_precedes(C,A,B)
| leaf(A,B) ),
inference(split_conjunct,[status(thm)],[sk_sos_14]) ).
cnf(c_171,plain,
( subactivity_occurrence(A,B)
| ~ root_occ(A,B) ),
inference(clausify,[status(thm)],[sos_10]) ).
cnf(c_174,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_213,plain,
arboreal(sK0(sK3)),
inference(resolve,[status(thm)],[c_127,c_119]) ).
cnf(c_215,plain,
min_precedes(sK0(sK3),sK1(sK3),tptp0),
inference(resolve,[status(thm)],[c_127,c_117]) ).
cnf(c_216,plain,
( arboreal(sK2(A,sK3))
| leaf_occ(A,sK3)
| ~ arboreal(A)
| ~ subactivity_occurrence(A,sK3) ),
inference(resolve,[status(thm)],[c_127,c_116]) ).
cnf(c_258,plain,
root_occ(sK0(sK3),sK3),
inference(resolve,[status(thm)],[c_145,c_127]) ).
cnf(c_263,plain,
( ~ min_precedes(A,B,tptp0)
| ~ leaf_occ(A,sK3) ),
inference(resolve,[status(thm)],[c_159,c_127]) ).
cnf(c_314,plain,
subactivity_occurrence(sK0(sK3),sK3),
inference(resolve,[status(thm)],[c_258,c_171]) ).
cnf(c_343,plain,
~ leaf_occ(sK0(sK3),sK3),
inference(resolve,[status(thm)],[c_215,c_263]) ).
cnf(c_10822,plain,
( arboreal(sK2(sK0(sK3),sK3))
| leaf_occ(sK0(sK3),sK3)
| ~ subactivity_occurrence(sK0(sK3),sK3) ),
inference(resolve,[status(thm)],[c_216,c_213]) ).
cnf(c_10823,plain,
( arboreal(sK2(sK0(sK3),sK3))
| leaf_occ(sK0(sK3),sK3) ),
inference(resolve,[status(thm)],[c_314,c_10822]) ).
cnf(c_377,plain,
arboreal(sK2(sK0(sK3),sK3)),
inference(resolve,[status(thm)],[c_343,c_10823]) ).
cnf(c_10824,plain,
( occurrence_of(sK2(sK0(sK3),sK3),tptp1)
| leaf_occ(sK0(sK3),sK3)
| ~ arboreal(sK0(sK3))
| ~ occurrence_of(sK3,tptp0) ),
inference(resolve,[status(thm)],[c_314,c_128]) ).
cnf(c_10825,negated_conjecture,
( occurrence_of(sK2(sK0(sK3),sK3),tptp1)
| leaf_occ(sK0(sK3),sK3)
| ~ arboreal(sK0(sK3)) ),
inference(resolve,[status(thm)],[c_127,c_10824]) ).
cnf(c_10826,negated_conjecture,
( occurrence_of(sK2(sK0(sK3),sK3),tptp1)
| leaf_occ(sK0(sK3),sK3) ),
inference(resolve,[status(thm)],[c_213,c_10825]) ).
cnf(c_380,negated_conjecture,
occurrence_of(sK2(sK0(sK3),sK3),tptp1),
inference(resolve,[status(thm)],[c_343,c_10826]) ).
cnf(c_10827,plain,
( min_precedes(sK0(sK3),sK2(sK0(sK3),sK3),tptp0)
| leaf_occ(sK0(sK3),sK3)
| ~ arboreal(sK0(sK3))
| ~ occurrence_of(sK3,tptp0) ),
inference(resolve,[status(thm)],[c_314,c_114]) ).
cnf(c_10828,negated_conjecture,
( min_precedes(sK0(sK3),sK2(sK0(sK3),sK3),tptp0)
| leaf_occ(sK0(sK3),sK3)
| ~ arboreal(sK0(sK3)) ),
inference(resolve,[status(thm)],[c_127,c_10827]) ).
cnf(c_10829,negated_conjecture,
( min_precedes(sK0(sK3),sK2(sK0(sK3),sK3),tptp0)
| leaf_occ(sK0(sK3),sK3) ),
inference(resolve,[status(thm)],[c_213,c_10828]) ).
cnf(c_382,negated_conjecture,
min_precedes(sK0(sK3),sK2(sK0(sK3),sK3),tptp0),
inference(resolve,[status(thm)],[c_343,c_10829]) ).
cnf(c_468,plain,
( root_occ(sK2(sK0(sK3),sK3),A)
| leaf_occ(sK2(sK0(sK3),sK3),A)
| ~ subactivity_occurrence(sK2(sK0(sK3),sK3),A)
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_377,c_129]) ).
cnf(c_534,plain,
( tptp1 = A
| ~ occurrence_of(sK2(sK0(sK3),sK3),A) ),
inference(resolve,[status(thm)],[c_380,c_158]) ).
cnf(c_813,plain,
( min_precedes(sK2(sK0(sK3),sK3),sK6(sK2(sK0(sK3),sK3),tptp0),tptp0)
| leaf(sK2(sK0(sK3),sK3),tptp0) ),
inference(resolve,[status(thm)],[c_382,c_163]) ).
cnf(c_814,plain,
( ~ root_occ(sK2(sK0(sK3),sK3),A)
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_382,c_160]) ).
cnf(c_815,plain,
occurrence_of(sK4(tptp0,sK0(sK3),sK2(sK0(sK3),sK3)),tptp0),
inference(resolve,[status(thm)],[c_382,c_155]) ).
cnf(c_817,plain,
subactivity_occurrence(sK2(sK0(sK3),sK3),sK4(tptp0,sK0(sK3),sK2(sK0(sK3),sK3))),
inference(resolve,[status(thm)],[c_382,c_153]) ).
cnf(c_2192,plain,
~ root_occ(sK2(sK0(sK3),sK3),sK4(tptp0,sK0(sK3),sK2(sK0(sK3),sK3))),
inference(resolve,[status(thm)],[c_815,c_814]) ).
cnf(c_10830,plain,
( root_occ(sK2(sK0(sK3),sK3),sK4(tptp0,sK0(sK3),sK2(sK0(sK3),sK3)))
| leaf_occ(sK2(sK0(sK3),sK3),sK4(tptp0,sK0(sK3),sK2(sK0(sK3),sK3)))
| ~ subactivity_occurrence(sK2(sK0(sK3),sK3),sK4(tptp0,sK0(sK3),sK2(sK0(sK3),sK3))) ),
inference(resolve,[status(thm)],[c_815,c_468]) ).
cnf(c_10831,plain,
( root_occ(sK2(sK0(sK3),sK3),sK4(tptp0,sK0(sK3),sK2(sK0(sK3),sK3)))
| leaf_occ(sK2(sK0(sK3),sK3),sK4(tptp0,sK0(sK3),sK2(sK0(sK3),sK3))) ),
inference(resolve,[status(thm)],[c_817,c_10830]) ).
cnf(c_2198,plain,
leaf_occ(sK2(sK0(sK3),sK3),sK4(tptp0,sK0(sK3),sK2(sK0(sK3),sK3))),
inference(resolve,[status(thm)],[c_2192,c_10831]) ).
cnf(c_2235,plain,
( ~ min_precedes(A,B,tptp0)
| ~ leaf_occ(A,sK4(tptp0,sK0(sK3),sK2(sK0(sK3),sK3))) ),
inference(resolve,[status(thm)],[c_815,c_159]) ).
cnf(c_3703,plain,
~ min_precedes(sK2(sK0(sK3),sK3),A,tptp0),
inference(resolve,[status(thm)],[c_2198,c_2235]) ).
cnf(c_3715,plain,
leaf(sK2(sK0(sK3),sK3),tptp0),
inference(resolve,[status(thm)],[c_3703,c_813]) ).
cnf(c_10832,plain,
( occurrence_of(sK5(sK2(sK0(sK3),sK3),tptp0),tptp0)
| atomic(tptp0) ),
inference(resolve,[status(thm)],[c_3715,c_157]) ).
cnf(c_3718,plain,
occurrence_of(sK5(sK2(sK0(sK3),sK3),tptp0),tptp0),
inference(resolve,[status(thm)],[c_142,c_10832]) ).
cnf(c_10833,plain,
( leaf_occ(sK2(sK0(sK3),sK3),sK5(sK2(sK0(sK3),sK3),tptp0))
| atomic(tptp0) ),
inference(resolve,[status(thm)],[c_3715,c_156]) ).
cnf(c_3719,plain,
leaf_occ(sK2(sK0(sK3),sK3),sK5(sK2(sK0(sK3),sK3),tptp0)),
inference(resolve,[status(thm)],[c_142,c_10833]) ).
cnf(c_10834,plain,
( B = A
| ~ leaf_occ(B,sK5(sK2(sK0(sK3),sK3),tptp0))
| ~ leaf_occ(A,sK5(sK2(sK0(sK3),sK3),tptp0))
| atomic(tptp0) ),
inference(resolve,[status(thm)],[c_3718,c_174]) ).
cnf(c_3766,plain,
( B = A
| ~ leaf_occ(B,sK5(sK2(sK0(sK3),sK3),tptp0))
| ~ leaf_occ(A,sK5(sK2(sK0(sK3),sK3),tptp0)) ),
inference(resolve,[status(thm)],[c_142,c_10834]) ).
cnf(c_3776,plain,
( occurrence_of(sK1(sK5(sK2(sK0(sK3),sK3),tptp0)),tptp2)
| occurrence_of(sK1(sK5(sK2(sK0(sK3),sK3),tptp0)),tptp3) ),
inference(resolve,[status(thm)],[c_3718,c_144]) ).
cnf(c_3777,plain,
leaf_occ(sK1(sK5(sK2(sK0(sK3),sK3),tptp0)),sK5(sK2(sK0(sK3),sK3),tptp0)),
inference(resolve,[status(thm)],[c_3718,c_143]) ).
cnf(c_10835,plain,
( A = sK2(sK0(sK3),sK3)
| ~ leaf_occ(A,sK5(sK2(sK0(sK3),sK3),tptp0)) ),
inference(resolve,[status(thm)],[c_3766,c_3719]) ).
cnf(c_10674,plain,
( sK2(sK0(sK3),sK3) = A
| ~ leaf_occ(A,sK5(sK2(sK0(sK3),sK3),tptp0)) ),
inference(copy,[status(thm)],[c_10835]) ).
cnf(c_10836,plain,
sK2(sK0(sK3),sK3) = sK1(sK5(sK2(sK0(sK3),sK3),tptp0)),
inference(resolve,[status(thm)],[c_3777,c_10674]) ).
cnf(c_10765,plain,
sK1(sK5(sK2(sK0(sK3),sK3),tptp0)) = sK2(sK0(sK3),sK3),
inference(copy,[status(thm)],[c_10836]) ).
cnf(c_10837,plain,
( occurrence_of(sK1(sK5(sK2(sK0(sK3),sK3),tptp0)),tptp2)
| occurrence_of(sK2(sK0(sK3),sK3),tptp3) ),
inference(paramod,[status(thm)],[c_10765,c_3776]) ).
cnf(c_10768,plain,
( occurrence_of(sK2(sK0(sK3),sK3),tptp2)
| occurrence_of(sK2(sK0(sK3),sK3),tptp3) ),
inference(paramod,[status(thm)],[c_10765,c_10837]) ).
cnf(c_10838,plain,
( tptp1 = tptp3
| occurrence_of(sK2(sK0(sK3),sK3),tptp2) ),
inference(resolve,[status(thm)],[c_10768,c_534]) ).
cnf(c_10839,plain,
( tptp3 = tptp1
| occurrence_of(sK2(sK0(sK3),sK3),tptp2) ),
inference(copy,[status(thm)],[c_10838]) ).
cnf(c_10786,plain,
occurrence_of(sK2(sK0(sK3),sK3),tptp2),
inference(resolve,[status(thm)],[c_134,c_10839]) ).
cnf(c_10840,plain,
tptp1 = tptp2,
inference(resolve,[status(thm)],[c_10786,c_534]) ).
cnf(c_10841,plain,
tptp2 = tptp1,
inference(copy,[status(thm)],[c_10840]) ).
cnf(c_10821,plain,
$false,
inference(resolve,[status(thm)],[c_132,c_10841]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PRO005+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 05:00:16 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 29942 was started by sandbox2 on n016,
% 0.10/0.37 % Sat Sep 26 05:00:16 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 11.97/1.98
% 11.97/1.98 % given #500 (W,wt=28): 1035 root_occ(f16(c1),A) | -occurrence_of(A,f7(f16(c1))) | -subactivity_occurrence(f16(c1),A). [resolve(346,a,494,a)].
% 11.97/1.98
% 11.97/1.98 % given #1000 (T,wt=32): 3466 earlier(f15(c1),f17(f15(c1),f9(tptp0,f15(c1),f16(c1)))). [resolve(882,a,178,a)].
% 11.97/1.98
% 11.97/1.98 % given #1500 (T,wt=35): 2658 -occurrence_of(f9(tptp0,f4(f16(c1),tptp0),f16(c1)),tptp2) | atomic(f6(f16(c1),tptp3)). [resolve(2575,a,923,b)].
% 11.97/1.98
% 11.97/1.98 % given #2000 (T,wt=35): 8892 leaf(f17(f15(c1),c1),tptp1) | earlier(f15(c1),f5(f17(f15(c1),c1),tptp1)). [resolve(8868,b,827,a)].
% 11.97/1.98
% 11.97/1.98 % SZS status Theorem for theBenchmark
% 11.97/1.98
% 11.97/1.98 % Proof 1 at 1.24 (+ 0.27) seconds.
% 11.97/1.98 % Length of proof is 75.
% 11.97/1.98 % Level of proof is 17.
% 11.97/1.98 % Maximum clause weight is 43.000.
% 11.97/1.98 % Given clauses 2275.
% 11.97/1.98
% 11.97/1.98 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------