%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PRO009+2 : 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 : n010.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 0.06s 0.40s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 42 ( 11 unt; 0 def)
% Number of atoms : 153 ( 0 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 186 ( 75 ~; 65 |; 41 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-1 aty)
% Number of variables : 59 ( 0 sgn 27 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos,axiom,
! [X0,X1,X2,X3] :
( ( min_precedes(X1,X2,X3)
& min_precedes(X0,X1,X3) )
=> min_precedes(X0,X2,X3) ),
file('theBenchmark.p',sos) ).
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_32,axiom,
! [X95] :
( occurrence_of(X95,tptp0)
=> ? [X96,X97,X98] :
( leaf_occ(X98,X95)
& next_subocc(X97,X98,tptp0)
& ( occurrence_of(X98,tptp1)
| occurrence_of(X98,tptp2) )
& next_subocc(X96,X97,tptp0)
& occurrence_of(X97,tptp4)
& root_occ(X96,X95)
& occurrence_of(X96,tptp3) ) ),
file('theBenchmark.p',sos_32) ).
fof(goals,conjecture,
! [X99] :
( occurrence_of(X99,tptp0)
=> ? [X100,X101] :
( leaf_occ(X101,X99)
& min_precedes(X100,X101,tptp0)
& ( occurrence_of(X101,tptp1)
| occurrence_of(X101,tptp2) )
& root_occ(X100,X99)
& occurrence_of(X100,tptp3) ) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X99] :
( occurrence_of(X99,tptp0)
=> ? [X100,X101] :
( leaf_occ(X101,X99)
& min_precedes(X100,X101,tptp0)
& ( occurrence_of(X101,tptp1)
| occurrence_of(X101,tptp2) )
& root_occ(X100,X99)
& occurrence_of(X100,tptp3) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_37,plain,
( min_precedes(A,B,C)
| ~ next_subocc(A,B,C) ),
inference(clausify,[status(thm)],[sos_04]) ).
fof(nnf_33,plain,
! [X95] :
( ? [X96,X97,X98] :
( leaf_occ(X98,X95)
& next_subocc(X97,X98,tptp0)
& ( occurrence_of(X98,tptp1)
| occurrence_of(X98,tptp2) )
& next_subocc(X96,X97,tptp0)
& occurrence_of(X97,tptp4)
& root_occ(X96,X95)
& occurrence_of(X96,tptp3) )
| ~ occurrence_of(X95,tptp0) ),
inference(fof_nnf,[status(thm)],[sos_32]) ).
fof(sk_sos_32_sk,plain,
! [X95] :
( ( leaf_occ(sK2(X95),X95)
& next_subocc(sK1(X95),sK2(X95),tptp0)
& ( occurrence_of(sK2(X95),tptp1)
| occurrence_of(sK2(X95),tptp2) )
& next_subocc(sK0(X95),sK1(X95),tptp0)
& occurrence_of(sK1(X95),tptp4)
& root_occ(sK0(X95),X95)
& occurrence_of(sK0(X95),tptp3) )
| ~ occurrence_of(X95,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X96,sK0(X95)),skolemize(X97,sK1(X95)),skolemize(X98,sK2(X95))],[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_41,plain,
( next_subocc(sK0(A),sK1(A),tptp0)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_42,plain,
( next_subocc(sK1(A),sK2(A),tptp0)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_112,plain,
( min_precedes(sK1(A),sK2(A),tptp0)
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_42,c_37]) ).
cnf(c_115,plain,
( min_precedes(sK0(A),sK1(A),tptp0)
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_41,c_37]) ).
fof(nnf_34,plain,
? [X99] :
( ! [X100,X101] :
( ~ leaf_occ(X101,X99)
| ~ min_precedes(X100,X101,tptp0)
| ( ~ occurrence_of(X101,tptp1)
& ~ occurrence_of(X101,tptp2) )
| ~ root_occ(X100,X99)
| ~ occurrence_of(X100,tptp3) )
& occurrence_of(X99,tptp0) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg_sk,plain,
( ! [X100,X101] :
( ~ leaf_occ(X101,sK3)
| ~ min_precedes(X100,X101,tptp0)
| ( ~ occurrence_of(X101,tptp1)
& ~ occurrence_of(X101,tptp2) )
| ~ root_occ(X100,sK3)
| ~ occurrence_of(X100,tptp3) )
& occurrence_of(sK3,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X99,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_125,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_126,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_127,negated_conjecture,
occurrence_of(sK3,tptp0),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_139,plain,
( leaf_occ(sK2(A),A)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_140,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_142,plain,
( root_occ(sK0(A),A)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_143,plain,
( occurrence_of(sK0(A),tptp3)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_174,plain,
( min_precedes(A,D,C)
| ~ min_precedes(B,D,C)
| ~ min_precedes(A,B,C) ),
inference(clausify,[status(thm)],[sos]) ).
cnf(c_211,plain,
min_precedes(sK0(sK3),sK1(sK3),tptp0),
inference(resolve,[status(thm)],[c_127,c_115]) ).
cnf(c_213,plain,
min_precedes(sK1(sK3),sK2(sK3),tptp0),
inference(resolve,[status(thm)],[c_127,c_112]) ).
cnf(c_216,plain,
leaf_occ(sK2(sK3),sK3),
inference(resolve,[status(thm)],[c_139,c_127]) ).
cnf(c_217,plain,
( occurrence_of(sK2(sK3),tptp1)
| occurrence_of(sK2(sK3),tptp2) ),
inference(resolve,[status(thm)],[c_140,c_127]) ).
cnf(c_219,plain,
root_occ(sK0(sK3),sK3),
inference(resolve,[status(thm)],[c_142,c_127]) ).
cnf(c_220,plain,
occurrence_of(sK0(sK3),tptp3),
inference(resolve,[status(thm)],[c_143,c_127]) ).
cnf(c_236,plain,
( min_precedes(sK0(sK3),A,tptp0)
| ~ min_precedes(sK1(sK3),A,tptp0) ),
inference(resolve,[status(thm)],[c_211,c_174]) ).
cnf(c_394,plain,
min_precedes(sK0(sK3),sK2(sK3),tptp0),
inference(resolve,[status(thm)],[c_236,c_213]) ).
cnf(c_439,negated_conjecture,
( ~ leaf_occ(sK2(sK3),sK3)
| ~ occurrence_of(sK2(sK3),tptp2)
| ~ root_occ(sK0(sK3),sK3)
| ~ occurrence_of(sK0(sK3),tptp3) ),
inference(resolve,[status(thm)],[c_394,c_126]) ).
cnf(c_440,negated_conjecture,
( ~ leaf_occ(sK2(sK3),sK3)
| ~ occurrence_of(sK2(sK3),tptp2)
| ~ root_occ(sK0(sK3),sK3) ),
inference(resolve,[status(thm)],[c_220,c_439]) ).
cnf(c_441,negated_conjecture,
( ~ leaf_occ(sK2(sK3),sK3)
| ~ occurrence_of(sK2(sK3),tptp2) ),
inference(resolve,[status(thm)],[c_219,c_440]) ).
cnf(c_428,negated_conjecture,
~ occurrence_of(sK2(sK3),tptp2),
inference(resolve,[status(thm)],[c_216,c_441]) ).
cnf(c_442,negated_conjecture,
( ~ leaf_occ(sK2(sK3),sK3)
| ~ occurrence_of(sK2(sK3),tptp1)
| ~ root_occ(sK0(sK3),sK3)
| ~ occurrence_of(sK0(sK3),tptp3) ),
inference(resolve,[status(thm)],[c_394,c_125]) ).
cnf(c_443,negated_conjecture,
( ~ leaf_occ(sK2(sK3),sK3)
| ~ occurrence_of(sK2(sK3),tptp1)
| ~ root_occ(sK0(sK3),sK3) ),
inference(resolve,[status(thm)],[c_220,c_442]) ).
cnf(c_444,negated_conjecture,
( ~ leaf_occ(sK2(sK3),sK3)
| ~ occurrence_of(sK2(sK3),tptp1) ),
inference(resolve,[status(thm)],[c_219,c_443]) ).
cnf(c_429,negated_conjecture,
~ occurrence_of(sK2(sK3),tptp1),
inference(resolve,[status(thm)],[c_216,c_444]) ).
cnf(c_445,plain,
occurrence_of(sK2(sK3),tptp1),
inference(resolve,[status(thm)],[c_428,c_217]) ).
cnf(c_438,plain,
$false,
inference(resolve,[status(thm)],[c_429,c_445]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PRO009+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.34 % Computer : n010.cluster.edu
% 0.06/0.34 % Model : x86_64 x86_64
% 0.06/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.34 % Memory : 8046.5625MB
% 0.06/0.34 % OS : Linux 6.8.0-71-generic
% 0.06/0.34 % CPULimit : 300
% 0.06/0.34 % WCLimit : 300
% 0.06/0.34 % DateTime : Sat Sep 26 04:58:29 UTC 2026
% 0.06/0.34 % CPUTime :
% 0.06/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.06/0.35 % Process 2521325 was started by sandbox on n010,
% 0.06/0.35 % Sat Sep 26 04:58:29 2026
% 0.06/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.06/0.36
% 0.06/0.36 % From the command line: assign(max_seconds, 300).
% 0.06/0.40
% 0.06/0.40 % SZS status Theorem for theBenchmark
% 0.06/0.40
% 0.06/0.40 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.06/0.40 % Length of proof is 28.
% 0.06/0.40 % Level of proof is 7.
% 0.06/0.40 % Maximum clause weight is 21.000.
% 0.06/0.40 % Given clauses 170.
% 0.06/0.40
% 0.06/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------