%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PRO009+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 : n005.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 08:20:56 AM UTC 2026
% Result : Theorem 0.79s 0.75s
% Output : CNFRefutation 0.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 69 ( 17 unt; 0 def)
% Number of atoms : 224 ( 15 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 250 ( 95 ~; 95 |; 49 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-1 aty)
% Number of variables : 97 ( 3 sgn 42 !; 13 ?)
% 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_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_20,axiom,
! [X61,X62] :
( earlier(X61,X62)
=> ~ earlier(X62,X61) ),
file('theBenchmark.p',sos_20) ).
fof(sos_21,axiom,
! [X63,X64] :
( precedes(X63,X64)
<=> ( legal(X64)
& earlier(X63,X64) ) ),
file('theBenchmark.p',sos_21) ).
fof(sos_24,axiom,
! [X72,X73,X74] :
( min_precedes(X72,X73,X74)
=> precedes(X72,X73) ),
file('theBenchmark.p',sos_24) ).
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_30,axiom,
! [X94,X95,X96] :
( ( earlier(X95,X96)
& earlier(X94,X95) )
=> earlier(X94,X96) ),
file('theBenchmark.p',sos_30) ).
fof(sos_32,axiom,
! [X101] :
( occurrence_of(X101,tptp0)
=> ? [X102,X103,X104] :
( leaf_occ(X104,X101)
& next_subocc(X103,X104,tptp0)
& ( occurrence_of(X104,tptp1)
| occurrence_of(X104,tptp2) )
& next_subocc(X102,X103,tptp0)
& occurrence_of(X103,tptp4)
& root_occ(X102,X101)
& occurrence_of(X102,tptp3) ) ),
file('theBenchmark.p',sos_32) ).
fof(goals,conjecture,
! [X105] :
( occurrence_of(X105,tptp0)
=> ? [X106,X107] :
( leaf_occ(X107,X105)
& min_precedes(X106,X107,tptp0)
& ( occurrence_of(X107,tptp1)
| occurrence_of(X107,tptp2) )
& root_occ(X106,X105)
& occurrence_of(X106,tptp3) ) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X105] :
( occurrence_of(X105,tptp0)
=> ? [X106,X107] :
( leaf_occ(X107,X105)
& min_precedes(X106,X107,tptp0)
& ( occurrence_of(X107,tptp1)
| occurrence_of(X107,tptp2) )
& root_occ(X106,X105)
& occurrence_of(X106,tptp3) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_81,plain,
( min_precedes(A,B,C)
| ~ next_subocc(A,B,C) ),
inference(clausify,[status(thm)],[sos_26]) ).
cnf(c_83,plain,
( arboreal(A)
| ~ next_subocc(A,B,C) ),
inference(clausify,[status(thm)],[sos_25]) ).
fof(nnf_33,plain,
! [X101] :
( ? [X102,X103,X104] :
( leaf_occ(X104,X101)
& next_subocc(X103,X104,tptp0)
& ( occurrence_of(X104,tptp1)
| occurrence_of(X104,tptp2) )
& next_subocc(X102,X103,tptp0)
& occurrence_of(X103,tptp4)
& root_occ(X102,X101)
& occurrence_of(X102,tptp3) )
| ~ occurrence_of(X101,tptp0) ),
inference(fof_nnf,[status(thm)],[sos_32]) ).
fof(sk_sos_32_sk,plain,
! [X101] :
( ( leaf_occ(sK2(X101),X101)
& next_subocc(sK1(X101),sK2(X101),tptp0)
& ( occurrence_of(sK2(X101),tptp1)
| occurrence_of(sK2(X101),tptp2) )
& next_subocc(sK0(X101),sK1(X101),tptp0)
& occurrence_of(sK1(X101),tptp4)
& root_occ(sK0(X101),X101)
& occurrence_of(sK0(X101),tptp3) )
| ~ occurrence_of(X101,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X102,sK0(X101)),skolemize(X103,sK1(X101)),skolemize(X104,sK2(X101))],[nnf_33]) ).
fof(sk_sos_32,plain,
( ! [VAR_0] :
( leaf_occ(sK2(VAR_0),VAR_0)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( next_subocc(sK1(VAR_0),sK2(VAR_0),tptp0)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( occurrence_of(sK2(VAR_0),tptp1)
| occurrence_of(sK2(VAR_0),tptp2)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( next_subocc(sK0(VAR_0),sK1(VAR_0),tptp0)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( occurrence_of(sK1(VAR_0),tptp4)
| ~ 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),tptp3)
| ~ occurrence_of(VAR_0,tptp0) ) ),
inference(cnf_transformation,[status(thm)],[sk_sos_32_sk]) ).
cnf(c_85,plain,
( next_subocc(sK0(A),sK1(A),tptp0)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_86,plain,
( next_subocc(sK1(A),sK2(A),tptp0)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_88,plain,
( min_precedes(sK1(A),sK2(A),tptp0)
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_86,c_81]) ).
cnf(c_90,plain,
( arboreal(sK0(A))
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_85,c_83]) ).
cnf(c_92,plain,
( min_precedes(sK0(A),sK1(A),tptp0)
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_85,c_81]) ).
fof(nnf_34,plain,
? [X105] :
( ! [X106,X107] :
( ~ leaf_occ(X107,X105)
| ~ min_precedes(X106,X107,tptp0)
| ( ~ occurrence_of(X107,tptp1)
& ~ occurrence_of(X107,tptp2) )
| ~ root_occ(X106,X105)
| ~ occurrence_of(X106,tptp3) )
& occurrence_of(X105,tptp0) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg_sk,plain,
( ! [X106,X107] :
( ~ leaf_occ(X107,sK3)
| ~ min_precedes(X106,X107,tptp0)
| ( ~ occurrence_of(X107,tptp1)
& ~ occurrence_of(X107,tptp2) )
| ~ root_occ(X106,sK3)
| ~ occurrence_of(X106,tptp3) )
& occurrence_of(sK3,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X105,sK3)],[nnf_34]) ).
fof(sk_goals_neg,plain,
( ! [VAR_0,VAR_1] :
( ~ leaf_occ(VAR_1,sK3)
| ~ min_precedes(VAR_0,VAR_1,tptp0)
| ~ occurrence_of(VAR_1,tptp1)
| ~ root_occ(VAR_0,sK3)
| ~ occurrence_of(VAR_0,tptp3) )
& ! [VAR_0,VAR_1] :
( ~ leaf_occ(VAR_1,sK3)
| ~ min_precedes(VAR_0,VAR_1,tptp0)
| ~ occurrence_of(VAR_1,tptp2)
| ~ root_occ(VAR_0,sK3)
| ~ occurrence_of(VAR_0,tptp3) )
& occurrence_of(sK3,tptp0) ),
inference(cnf_transformation,[status(thm)],[sk_goals_neg_sk]) ).
cnf(c_148,negated_conjecture,
( ~ leaf_occ(B,sK3)
| ~ min_precedes(A,B,tptp0)
| ~ occurrence_of(B,tptp1)
| ~ root_occ(A,sK3)
| ~ occurrence_of(A,tptp3) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_149,negated_conjecture,
( ~ leaf_occ(B,sK3)
| ~ min_precedes(A,B,tptp0)
| ~ occurrence_of(B,tptp2)
| ~ root_occ(A,sK3)
| ~ occurrence_of(A,tptp3) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_150,negated_conjecture,
occurrence_of(sK3,tptp0),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_162,plain,
( leaf_occ(sK2(A),A)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_163,plain,
( occurrence_of(sK2(A),tptp1)
| occurrence_of(sK2(A),tptp2)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_165,plain,
( root_occ(sK0(A),A)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_166,plain,
( occurrence_of(sK0(A),tptp3)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_168,plain,
( earlier(A,C)
| ~ earlier(B,C)
| ~ earlier(A,B) ),
inference(clausify,[status(thm)],[sos_30]) ).
cnf(c_172,plain,
( precedes(A,B)
| ~ min_precedes(A,B,C) ),
inference(clausify,[status(thm)],[sos_24]) ).
cnf(c_174,plain,
( earlier(A,B)
| ~ precedes(A,B) ),
inference(clausify,[status(thm)],[sos_21]) ).
cnf(c_175,plain,
( ~ earlier(B,A)
| ~ earlier(A,B) ),
inference(clausify,[status(thm)],[sos_20]) ).
cnf(c_176,plain,
( subactivity_occurrence(A,B)
| ~ root_occ(A,B) ),
inference(clausify,[status(thm)],[sos_19]) ).
cnf(c_191,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_220,plain,
~ earlier(A,A),
inference(factor,[status(thm)],[c_175]) ).
cnf(c_225,plain,
min_precedes(sK0(sK3),sK1(sK3),tptp0),
inference(resolve,[status(thm)],[c_150,c_92]) ).
cnf(c_227,plain,
arboreal(sK0(sK3)),
inference(resolve,[status(thm)],[c_150,c_90]) ).
cnf(c_228,plain,
min_precedes(sK1(sK3),sK2(sK3),tptp0),
inference(resolve,[status(thm)],[c_150,c_88]) ).
cnf(c_230,plain,
leaf_occ(sK2(sK3),sK3),
inference(resolve,[status(thm)],[c_162,c_150]) ).
cnf(c_231,plain,
( occurrence_of(sK2(sK3),tptp1)
| occurrence_of(sK2(sK3),tptp2) ),
inference(resolve,[status(thm)],[c_163,c_150]) ).
cnf(c_233,plain,
root_occ(sK0(sK3),sK3),
inference(resolve,[status(thm)],[c_165,c_150]) ).
cnf(c_234,plain,
occurrence_of(sK0(sK3),tptp3),
inference(resolve,[status(thm)],[c_166,c_150]) ).
cnf(c_293,plain,
subactivity_occurrence(sK0(sK3),sK3),
inference(resolve,[status(thm)],[c_233,c_176]) ).
cnf(c_602,negated_conjecture,
( B = A
| min_precedes(A,B,tptp0)
| ~ arboreal(A)
| ~ leaf_occ(B,sK3)
| ~ subactivity_occurrence(A,sK3) ),
inference(resolve,[status(thm)],[c_191,c_150]) ).
cnf(c_603,negated_conjecture,
( A = sK0(sK3)
| min_precedes(sK0(sK3),A,tptp0)
| ~ arboreal(sK0(sK3))
| ~ leaf_occ(A,sK3) ),
inference(resolve,[status(thm)],[c_602,c_293]) ).
cnf(c_604,negated_conjecture,
( sK2(sK3) = sK0(sK3)
| min_precedes(sK0(sK3),sK2(sK3),tptp0)
| ~ arboreal(sK0(sK3)) ),
inference(resolve,[status(thm)],[c_603,c_230]) ).
cnf(c_347,negated_conjecture,
( sK2(sK3) = sK0(sK3)
| min_precedes(sK0(sK3),sK2(sK3),tptp0) ),
inference(resolve,[status(thm)],[c_604,c_227]) ).
cnf(c_466,plain,
precedes(sK0(sK3),sK1(sK3)),
inference(resolve,[status(thm)],[c_225,c_172]) ).
cnf(c_491,plain,
earlier(sK0(sK3),sK1(sK3)),
inference(resolve,[status(thm)],[c_466,c_174]) ).
cnf(c_504,plain,
precedes(sK1(sK3),sK2(sK3)),
inference(resolve,[status(thm)],[c_228,c_172]) ).
cnf(c_539,plain,
earlier(sK1(sK3),sK2(sK3)),
inference(resolve,[status(thm)],[c_504,c_174]) ).
cnf(c_605,plain,
( earlier(sK0(sK3),A)
| ~ earlier(sK1(sK3),A) ),
inference(resolve,[status(thm)],[c_168,c_491]) ).
cnf(c_543,plain,
earlier(sK0(sK3),sK2(sK3)),
inference(resolve,[status(thm)],[c_605,c_539]) ).
cnf(c_606,negated_conjecture,
( ~ leaf_occ(sK2(sK3),sK3)
| ~ occurrence_of(sK2(sK3),tptp1)
| ~ root_occ(sK0(sK3),sK3)
| ~ occurrence_of(sK0(sK3),tptp3)
| sK2(sK3) = sK0(sK3) ),
inference(resolve,[status(thm)],[c_347,c_148]) ).
cnf(c_607,negated_conjecture,
( ~ leaf_occ(sK2(sK3),sK3)
| ~ occurrence_of(sK2(sK3),tptp1)
| ~ root_occ(sK0(sK3),sK3)
| sK2(sK3) = sK0(sK3) ),
inference(resolve,[status(thm)],[c_234,c_606]) ).
cnf(c_608,negated_conjecture,
( ~ leaf_occ(sK2(sK3),sK3)
| ~ occurrence_of(sK2(sK3),tptp1)
| sK2(sK3) = sK0(sK3) ),
inference(resolve,[status(thm)],[c_233,c_607]) ).
cnf(c_581,negated_conjecture,
( ~ occurrence_of(sK2(sK3),tptp1)
| sK2(sK3) = sK0(sK3) ),
inference(resolve,[status(thm)],[c_230,c_608]) ).
cnf(c_609,negated_conjecture,
( ~ leaf_occ(A,sK3)
| ~ min_precedes(sK0(sK3),A,tptp0)
| ~ occurrence_of(A,tptp2)
| ~ root_occ(sK0(sK3),sK3) ),
inference(resolve,[status(thm)],[c_149,c_234]) ).
cnf(c_610,negated_conjecture,
( ~ leaf_occ(A,sK3)
| ~ min_precedes(sK0(sK3),A,tptp0)
| ~ occurrence_of(A,tptp2) ),
inference(resolve,[status(thm)],[c_609,c_233]) ).
cnf(c_611,negated_conjecture,
( occurrence_of(sK2(sK3),tptp1)
| ~ leaf_occ(sK2(sK3),sK3)
| ~ min_precedes(sK0(sK3),sK2(sK3),tptp0) ),
inference(resolve,[status(thm)],[c_610,c_231]) ).
cnf(c_612,negated_conjecture,
( sK2(sK3) = sK0(sK3)
| occurrence_of(sK2(sK3),tptp1)
| ~ leaf_occ(sK2(sK3),sK3) ),
inference(resolve,[status(thm)],[c_611,c_347]) ).
cnf(c_592,negated_conjecture,
( sK2(sK3) = sK0(sK3)
| occurrence_of(sK2(sK3),tptp1) ),
inference(resolve,[status(thm)],[c_612,c_230]) ).
cnf(c_613,plain,
( sK2(sK3) = sK0(sK3)
| sK2(sK3) = sK0(sK3) ),
inference(resolve,[status(thm)],[c_592,c_581]) ).
cnf(c_595,plain,
sK2(sK3) = sK0(sK3),
inference(copy,[status(thm)],[c_613]) ).
cnf(c_614,plain,
earlier(sK0(sK3),sK0(sK3)),
inference(paramod,[status(thm)],[c_595,c_543]) ).
cnf(c_601,plain,
$false,
inference(resolve,[status(thm)],[c_220,c_614]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : PRO009+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.44 % Computer : n005.cluster.edu
% 0.11/0.44 % Model : x86_64 x86_64
% 0.11/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.44 % Memory : 8046.5625MB
% 0.11/0.44 % OS : Linux 6.8.0-71-generic
% 0.11/0.44 % CPULimit : 300
% 0.11/0.44 % WCLimit : 300
% 0.11/0.44 % DateTime : Sat Sep 26 04:57:47 UTC 2026
% 0.11/0.44 % CPUTime :
% 0.11/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.45 % Process 1236047 was started by sandbox on n005,
% 0.11/0.45 % Sat Sep 26 04:57:47 2026
% 0.11/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.46
% 0.11/0.46 % From the command line: assign(max_seconds, 300).
% 0.79/0.75
% 0.79/0.75 % SZS status Theorem for theBenchmark
% 0.79/0.75
% 0.79/0.75 % Proof 1 at 0.08 (+ 0.02) seconds.
% 0.79/0.75 % Length of proof is 49.
% 0.79/0.75 % Level of proof is 7.
% 0.79/0.75 % Maximum clause weight is 23.000.
% 0.79/0.75 % Given clauses 191.
% 0.79/0.75
% 0.79/0.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------