%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PRO009+3 : 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 : n006.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 0.82s 0.56s
% Output : CNFRefutation 0.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 61 ( 15 unt; 0 def)
% Number of atoms : 202 ( 15 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 228 ( 87 ~; 87 |; 45 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-1 aty)
% Number of variables : 86 ( 2 sgn 37 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_04,axiom,
! [X8,X9] :
( earlier(X8,X9)
=> ~ earlier(X9,X8) ),
file('theBenchmark.p',sos_04) ).
fof(sos_05,axiom,
! [X10,X11,X12] :
( ( earlier(X11,X12)
& earlier(X10,X11) )
=> earlier(X10,X12) ),
file('theBenchmark.p',sos_05) ).
fof(sos_10,axiom,
! [X21,X22] :
( precedes(X21,X22)
<=> ( legal(X22)
& earlier(X21,X22) ) ),
file('theBenchmark.p',sos_10) ).
fof(sos_15,axiom,
! [X38,X39,X40] :
( min_precedes(X38,X39,X40)
=> precedes(X38,X39) ),
file('theBenchmark.p',sos_15) ).
fof(sos_22,axiom,
! [X60,X61,X62] :
( next_subocc(X60,X61,X62)
<=> ( ~ ? [X63] :
( min_precedes(X63,X61,X62)
& min_precedes(X60,X63,X62) )
& min_precedes(X60,X61,X62) ) ),
file('theBenchmark.p',sos_22) ).
fof(sos_41,axiom,
! [X130,X131,X132,X133] :
( ( X131 != X132
& root_occ(X132,X130)
& leaf_occ(X131,X130)
& occurrence_of(X130,X133) )
=> min_precedes(X132,X131,X133) ),
file('theBenchmark.p',sos_41) ).
fof(sos_49,axiom,
! [X161] :
( occurrence_of(X161,tptp0)
=> ? [X162,X163,X164] :
( leaf_occ(X164,X161)
& next_subocc(X163,X164,tptp0)
& ( occurrence_of(X164,tptp1)
| occurrence_of(X164,tptp2) )
& next_subocc(X162,X163,tptp0)
& occurrence_of(X163,tptp4)
& root_occ(X162,X161)
& occurrence_of(X162,tptp3) ) ),
file('theBenchmark.p',sos_49) ).
fof(goals,conjecture,
! [X165] :
( occurrence_of(X165,tptp0)
=> ? [X166,X167] :
( leaf_occ(X167,X165)
& min_precedes(X166,X167,tptp0)
& ( occurrence_of(X167,tptp1)
| occurrence_of(X167,tptp2) )
& root_occ(X166,X165)
& occurrence_of(X166,tptp3) ) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X165] :
( occurrence_of(X165,tptp0)
=> ? [X166,X167] :
( leaf_occ(X167,X165)
& min_precedes(X166,X167,tptp0)
& ( occurrence_of(X167,tptp1)
| occurrence_of(X167,tptp2) )
& root_occ(X166,X165)
& occurrence_of(X166,tptp3) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_74,plain,
( precedes(A,B)
| ~ min_precedes(A,B,C) ),
inference(clausify,[status(thm)],[sos_15]) ).
cnf(c_79,plain,
( earlier(A,B)
| ~ precedes(A,B) ),
inference(clausify,[status(thm)],[sos_10]) ).
cnf(c_180,plain,
( ~ min_precedes(A,B,C)
| earlier(A,B) ),
inference(resolve,[status(thm)],[c_79,c_74]) ).
cnf(c_190,plain,
( ~ earlier(B,A)
| ~ earlier(A,B) ),
inference(clausify,[status(thm)],[sos_04]) ).
cnf(c_191,plain,
( earlier(A,C)
| ~ earlier(B,C)
| ~ earlier(A,B) ),
inference(clausify,[status(thm)],[sos_05]) ).
cnf(c_201,plain,
( min_precedes(A,B,C)
| ~ next_subocc(A,B,C) ),
inference(clausify,[status(thm)],[sos_22]) ).
cnf(c_224,plain,
( min_precedes(D,C,B)
| D = C
| ~ root_occ(D,A)
| ~ leaf_occ(C,A)
| ~ occurrence_of(A,B) ),
inference(clausify,[status(thm)],[sos_41]) ).
fof(nnf_50,plain,
! [X161] :
( ? [X162,X163,X164] :
( leaf_occ(X164,X161)
& next_subocc(X163,X164,tptp0)
& ( occurrence_of(X164,tptp1)
| occurrence_of(X164,tptp2) )
& next_subocc(X162,X163,tptp0)
& occurrence_of(X163,tptp4)
& root_occ(X162,X161)
& occurrence_of(X162,tptp3) )
| ~ occurrence_of(X161,tptp0) ),
inference(fof_nnf,[status(thm)],[sos_49]) ).
fof(sk_sos_49_sk,plain,
! [X161] :
( ( leaf_occ(sK2(X161),X161)
& next_subocc(sK1(X161),sK2(X161),tptp0)
& ( occurrence_of(sK2(X161),tptp1)
| occurrence_of(sK2(X161),tptp2) )
& next_subocc(sK0(X161),sK1(X161),tptp0)
& occurrence_of(sK1(X161),tptp4)
& root_occ(sK0(X161),X161)
& occurrence_of(sK0(X161),tptp3) )
| ~ occurrence_of(X161,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X162,sK0(X161)),skolemize(X163,sK1(X161)),skolemize(X164,sK2(X161))],[nnf_50]) ).
fof(sk_sos_49,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_49_sk]) ).
cnf(c_232,plain,
( occurrence_of(sK0(A),tptp3)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_49]) ).
cnf(c_233,plain,
( root_occ(sK0(A),A)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_49]) ).
cnf(c_235,plain,
( next_subocc(sK0(A),sK1(A),tptp0)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_49]) ).
cnf(c_236,plain,
( occurrence_of(sK2(A),tptp1)
| occurrence_of(sK2(A),tptp2)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_49]) ).
cnf(c_237,plain,
( next_subocc(sK1(A),sK2(A),tptp0)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_49]) ).
cnf(c_238,plain,
( leaf_occ(sK2(A),A)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_49]) ).
fof(nnf_51,plain,
? [X165] :
( ! [X166,X167] :
( ~ leaf_occ(X167,X165)
| ~ min_precedes(X166,X167,tptp0)
| ( ~ occurrence_of(X167,tptp1)
& ~ occurrence_of(X167,tptp2) )
| ~ root_occ(X166,X165)
| ~ occurrence_of(X166,tptp3) )
& occurrence_of(X165,tptp0) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg_sk,plain,
( ! [X166,X167] :
( ~ leaf_occ(X167,sK3)
| ~ min_precedes(X166,X167,tptp0)
| ( ~ occurrence_of(X167,tptp1)
& ~ occurrence_of(X167,tptp2) )
| ~ root_occ(X166,sK3)
| ~ occurrence_of(X166,tptp3) )
& occurrence_of(sK3,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X165,sK3)],[nnf_51]) ).
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_250,negated_conjecture,
occurrence_of(sK3,tptp0),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_251,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_252,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_320,plain,
~ earlier(A,A),
inference(factor,[status(thm)],[c_190]) ).
cnf(c_350,plain,
leaf_occ(sK2(sK3),sK3),
inference(resolve,[status(thm)],[c_250,c_238]) ).
cnf(c_351,plain,
next_subocc(sK1(sK3),sK2(sK3),tptp0),
inference(resolve,[status(thm)],[c_250,c_237]) ).
cnf(c_352,plain,
( occurrence_of(sK2(sK3),tptp1)
| occurrence_of(sK2(sK3),tptp2) ),
inference(resolve,[status(thm)],[c_250,c_236]) ).
cnf(c_353,plain,
next_subocc(sK0(sK3),sK1(sK3),tptp0),
inference(resolve,[status(thm)],[c_250,c_235]) ).
cnf(c_355,plain,
root_occ(sK0(sK3),sK3),
inference(resolve,[status(thm)],[c_250,c_233]) ).
cnf(c_356,plain,
occurrence_of(sK0(sK3),tptp3),
inference(resolve,[status(thm)],[c_250,c_232]) ).
cnf(c_756,negated_conjecture,
( min_precedes(B,A,tptp0)
| B = A
| ~ root_occ(B,sK3)
| ~ leaf_occ(A,sK3) ),
inference(resolve,[status(thm)],[c_224,c_250]) ).
cnf(c_757,negated_conjecture,
( min_precedes(A,sK2(sK3),tptp0)
| A = sK2(sK3)
| ~ root_occ(A,sK3) ),
inference(resolve,[status(thm)],[c_756,c_350]) ).
cnf(c_758,negated_conjecture,
( min_precedes(sK0(sK3),sK2(sK3),tptp0)
| sK0(sK3) = sK2(sK3) ),
inference(resolve,[status(thm)],[c_757,c_355]) ).
cnf(c_409,negated_conjecture,
( min_precedes(sK0(sK3),sK2(sK3),tptp0)
| sK2(sK3) = sK0(sK3) ),
inference(copy,[status(thm)],[c_758]) ).
cnf(c_415,plain,
min_precedes(sK1(sK3),sK2(sK3),tptp0),
inference(resolve,[status(thm)],[c_351,c_201]) ).
cnf(c_514,plain,
min_precedes(sK0(sK3),sK1(sK3),tptp0),
inference(resolve,[status(thm)],[c_353,c_201]) ).
cnf(c_556,plain,
earlier(sK1(sK3),sK2(sK3)),
inference(resolve,[status(thm)],[c_415,c_180]) ).
cnf(c_637,plain,
earlier(sK0(sK3),sK1(sK3)),
inference(resolve,[status(thm)],[c_514,c_180]) ).
cnf(c_759,plain,
( earlier(sK0(sK3),A)
| ~ earlier(sK1(sK3),A) ),
inference(resolve,[status(thm)],[c_191,c_637]) ).
cnf(c_652,plain,
earlier(sK0(sK3),sK2(sK3)),
inference(resolve,[status(thm)],[c_759,c_556]) ).
cnf(c_760,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_409,c_252]) ).
cnf(c_761,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_356,c_760]) ).
cnf(c_762,negated_conjecture,
( ~ leaf_occ(sK2(sK3),sK3)
| ~ occurrence_of(sK2(sK3),tptp1)
| sK2(sK3) = sK0(sK3) ),
inference(resolve,[status(thm)],[c_355,c_761]) ).
cnf(c_711,negated_conjecture,
( ~ occurrence_of(sK2(sK3),tptp1)
| sK2(sK3) = sK0(sK3) ),
inference(resolve,[status(thm)],[c_350,c_762]) ).
cnf(c_763,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_251,c_356]) ).
cnf(c_764,negated_conjecture,
( ~ leaf_occ(A,sK3)
| ~ min_precedes(sK0(sK3),A,tptp0)
| ~ occurrence_of(A,tptp2) ),
inference(resolve,[status(thm)],[c_763,c_355]) ).
cnf(c_765,negated_conjecture,
( occurrence_of(sK2(sK3),tptp1)
| ~ leaf_occ(sK2(sK3),sK3)
| ~ min_precedes(sK0(sK3),sK2(sK3),tptp0) ),
inference(resolve,[status(thm)],[c_764,c_352]) ).
cnf(c_766,negated_conjecture,
( sK2(sK3) = sK0(sK3)
| occurrence_of(sK2(sK3),tptp1)
| ~ leaf_occ(sK2(sK3),sK3) ),
inference(resolve,[status(thm)],[c_765,c_409]) ).
cnf(c_737,negated_conjecture,
( sK2(sK3) = sK0(sK3)
| occurrence_of(sK2(sK3),tptp1) ),
inference(resolve,[status(thm)],[c_766,c_350]) ).
cnf(c_767,plain,
( sK2(sK3) = sK0(sK3)
| sK2(sK3) = sK0(sK3) ),
inference(resolve,[status(thm)],[c_737,c_711]) ).
cnf(c_738,plain,
sK2(sK3) = sK0(sK3),
inference(copy,[status(thm)],[c_767]) ).
cnf(c_768,plain,
earlier(sK0(sK3),sK0(sK3)),
inference(paramod,[status(thm)],[c_738,c_652]) ).
cnf(c_755,plain,
$false,
inference(resolve,[status(thm)],[c_320,c_768]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PRO009+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n006.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 04:57:55 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 405580 was started by sandbox2 on n006,
% 0.08/0.35 % Sat Sep 26 04:57:55 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.82/0.56
% 0.82/0.56 % SZS status Theorem for theBenchmark
% 0.82/0.56
% 0.82/0.56 % Proof 1 at 0.15 (+ 0.03) seconds.
% 0.82/0.56 % Length of proof is 41.
% 0.82/0.56 % Level of proof is 6.
% 0.82/0.56 % Maximum clause weight is 21.000.
% 0.82/0.56 % Given clauses 262.
% 0.82/0.56
% 0.82/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------