%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PRO010+3 : 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 : n011.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 0.59s 0.48s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 50 ( 12 unt; 0 def)
% Number of atoms : 203 ( 7 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 208 ( 55 ~; 78 |; 62 &)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 110 ( 6 sgn 61 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_02,axiom,
! [X4,X5,X6] :
( ( occurrence_of(X4,X6)
& occurrence_of(X4,X5) )
=> X5 = X6 ),
file('theBenchmark.p',sos_02) ).
fof(sos_07,axiom,
! [X16,X17] :
( occurrence_of(X16,X17)
=> ( arboreal(X16)
<=> atomic(X17) ) ),
file('theBenchmark.p',sos_07) ).
fof(sos_26,axiom,
! [X73,X74] :
( ( ~ atomic(X73)
& root(X74,X73) )
=> ? [X75] :
( subactivity_occurrence(X74,X75)
& occurrence_of(X75,X73) ) ),
file('theBenchmark.p',sos_26) ).
fof(sos_27,axiom,
! [X76,X77] :
( ( ~ atomic(X76)
& occurrence_of(X77,X76) )
=> ? [X78] :
( subactivity_occurrence(X78,X77)
& root(X78,X76) ) ),
file('theBenchmark.p',sos_27) ).
fof(sos_46,axiom,
! [X148,X149,X150] :
( min_precedes(X148,X149,X150)
=> arboreal(X148) ),
file('theBenchmark.p',sos_46) ).
fof(sos_49,axiom,
! [X161] :
( occurrence_of(X161,tptp0)
=> ? [X162,X163,X164] :
( leaf_occ(X164,X161)
& next_subocc(X163,X164,tptp0)
& ( occurrence_of(X164,tptp2)
| occurrence_of(X164,tptp1) )
& 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] :
( ( occurrence_of(X167,tptp2)
=> ~ ? [X169] :
( min_precedes(X166,X169,tptp0)
& occurrence_of(X169,tptp1) ) )
& ( occurrence_of(X167,tptp1)
=> ~ ? [X168] :
( min_precedes(X166,X168,tptp0)
& occurrence_of(X168,tptp2) ) )
& leaf_occ(X167,X165) ) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X165] :
( occurrence_of(X165,tptp0)
=> ? [X166,X167] :
( ( occurrence_of(X167,tptp2)
=> ~ ? [X169] :
( min_precedes(X166,X169,tptp0)
& occurrence_of(X169,tptp1) ) )
& ( occurrence_of(X167,tptp1)
=> ~ ? [X168] :
( min_precedes(X166,X168,tptp0)
& occurrence_of(X168,tptp2) ) )
& leaf_occ(X167,X165) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_27,plain,
! [X73,X74] :
( ? [X75] :
( subactivity_occurrence(X74,X75)
& occurrence_of(X75,X73) )
| atomic(X73)
| ~ root(X74,X73) ),
inference(fof_nnf,[status(thm)],[sos_26]) ).
fof(sk_sos_26_sk,plain,
! [X73,X74] :
( ( subactivity_occurrence(X74,sK0(X73,X74))
& occurrence_of(sK0(X73,X74),X73) )
| atomic(X73)
| ~ root(X74,X73) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X75,sK0(X73,X74))],[nnf_27]) ).
fof(sk_sos_26,plain,
( ! [VAR_0,VAR_1] :
( subactivity_occurrence(VAR_0,sK0(VAR_1,VAR_0))
| atomic(VAR_1)
| ~ root(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( occurrence_of(sK0(VAR_1,VAR_0),VAR_1)
| atomic(VAR_1)
| ~ root(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_sos_26_sk]) ).
cnf(c_87,plain,
( occurrence_of(sK0(B,A),B)
| atomic(B)
| ~ root(A,B) ),
inference(split_conjunct,[status(thm)],[sk_sos_26]) ).
fof(nnf_28,plain,
! [X76,X77] :
( ? [X78] :
( subactivity_occurrence(X78,X77)
& root(X78,X76) )
| atomic(X76)
| ~ occurrence_of(X77,X76) ),
inference(fof_nnf,[status(thm)],[sos_27]) ).
fof(sk_sos_27_sk,plain,
! [X76,X77] :
( ( subactivity_occurrence(sK1(X76,X77),X77)
& root(sK1(X76,X77),X76) )
| atomic(X76)
| ~ occurrence_of(X77,X76) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X78,sK1(X76,X77))],[nnf_28]) ).
fof(sk_sos_27,plain,
( ! [VAR_0,VAR_1] :
( subactivity_occurrence(sK1(VAR_1,VAR_0),VAR_0)
| atomic(VAR_1)
| ~ occurrence_of(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( root(sK1(VAR_1,VAR_0),VAR_1)
| atomic(VAR_1)
| ~ occurrence_of(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_sos_27_sk]) ).
cnf(c_89,plain,
( root(sK1(B,A),B)
| atomic(B)
| ~ occurrence_of(A,B) ),
inference(split_conjunct,[status(thm)],[sk_sos_27]) ).
cnf(c_189,plain,
( C = B
| ~ occurrence_of(A,C)
| ~ occurrence_of(A,B) ),
inference(clausify,[status(thm)],[sos_02]) ).
cnf(c_193,plain,
( atomic(B)
| ~ arboreal(A)
| ~ occurrence_of(A,B) ),
inference(clausify,[status(thm)],[sos_07]) ).
cnf(c_229,plain,
( arboreal(A)
| ~ min_precedes(A,B,C) ),
inference(clausify,[status(thm)],[sos_46]) ).
fof(nnf_50,plain,
! [X161] :
( ? [X162,X163,X164] :
( leaf_occ(X164,X161)
& next_subocc(X163,X164,tptp0)
& ( occurrence_of(X164,tptp2)
| occurrence_of(X164,tptp1) )
& 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(sK7(X161),sK2(X161),tptp0)
& ( occurrence_of(sK2(X161),tptp2)
| occurrence_of(sK2(X161),tptp1) )
& next_subocc(sK6(X161),sK7(X161),tptp0)
& occurrence_of(sK7(X161),tptp4)
& root_occ(sK6(X161),X161)
& occurrence_of(sK6(X161),tptp3) )
| ~ occurrence_of(X161,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK2]),skolemize(X162,sK6(X161)),skolemize(X163,sK7(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(sK7(VAR_0),sK2(VAR_0),tptp0)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( occurrence_of(sK2(VAR_0),tptp2)
| occurrence_of(sK2(VAR_0),tptp1)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( next_subocc(sK6(VAR_0),sK7(VAR_0),tptp0)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( occurrence_of(sK7(VAR_0),tptp4)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( root_occ(sK6(VAR_0),VAR_0)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( occurrence_of(sK6(VAR_0),tptp3)
| ~ occurrence_of(VAR_0,tptp0) ) ),
inference(cnf_transformation,[status(thm)],[sk_sos_49_sk]) ).
cnf(c_238,plain,
( leaf_occ(sK2(A),A)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_49]) ).
fof(sos_51,axiom,
~ atomic(tptp0),
file('theBenchmark.p',sos_51) ).
cnf(c_239,plain,
~ atomic(tptp0),
inference(clausify,[status(thm)],[sos_51]) ).
fof(sos_61,axiom,
tptp1 != tptp2,
file('theBenchmark.p',sos_61) ).
cnf(c_249,plain,
tptp1 != tptp2,
inference(clausify,[status(thm)],[sos_61]) ).
cnf(c_250,plain,
tptp2 != tptp1,
inference(copy,[status(thm)],[c_249]) ).
fof(nnf_51,plain,
? [X165] :
( ! [X166,X167] :
( ( ? [X169] :
( min_precedes(X166,X169,tptp0)
& occurrence_of(X169,tptp1) )
& occurrence_of(X167,tptp2) )
| ( ? [X168] :
( min_precedes(X166,X168,tptp0)
& occurrence_of(X168,tptp2) )
& occurrence_of(X167,tptp1) )
| ~ leaf_occ(X167,X165) )
& occurrence_of(X165,tptp0) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg_sk,plain,
( ! [X166,X167] :
( ( min_precedes(X166,sK4(X166,X167),tptp0)
& occurrence_of(sK4(X166,X167),tptp1)
& occurrence_of(X167,tptp2) )
| ( min_precedes(X166,sK5(X166,X167),tptp0)
& occurrence_of(sK5(X166,X167),tptp2)
& occurrence_of(X167,tptp1) )
| ~ leaf_occ(X167,sK3) )
& occurrence_of(sK3,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK5,sK4]),skolemize(X165,sK3),skolemize(X168,sK5(X166,X167)),skolemize(X169,sK4(X166,X167))],[nnf_51]) ).
fof(sk_goals_neg,plain,
( ! [VAR_0,VAR_1] :
( min_precedes(VAR_1,sK4(VAR_1,VAR_0),tptp0)
| min_precedes(VAR_1,sK5(VAR_1,VAR_0),tptp0)
| ~ leaf_occ(VAR_0,sK3) )
& ! [VAR_0,VAR_1] :
( occurrence_of(sK4(VAR_1,VAR_0),tptp1)
| min_precedes(VAR_1,sK5(VAR_1,VAR_0),tptp0)
| ~ leaf_occ(VAR_0,sK3) )
& ! [VAR_0,VAR_1] :
( occurrence_of(VAR_0,tptp2)
| min_precedes(VAR_1,sK5(VAR_1,VAR_0),tptp0)
| ~ leaf_occ(VAR_0,sK3) )
& ! [VAR_0,VAR_1] :
( min_precedes(VAR_1,sK4(VAR_1,VAR_0),tptp0)
| occurrence_of(sK5(VAR_1,VAR_0),tptp2)
| ~ leaf_occ(VAR_0,sK3) )
& ! [VAR_0,VAR_1] :
( occurrence_of(sK4(VAR_1,VAR_0),tptp1)
| occurrence_of(sK5(VAR_1,VAR_0),tptp2)
| ~ leaf_occ(VAR_0,sK3) )
& ! [VAR_0,VAR_1] :
( occurrence_of(VAR_0,tptp2)
| occurrence_of(sK5(VAR_1,VAR_0),tptp2)
| ~ leaf_occ(VAR_0,sK3) )
& ! [VAR_0,VAR_1] :
( min_precedes(VAR_1,sK4(VAR_1,VAR_0),tptp0)
| occurrence_of(VAR_0,tptp1)
| ~ leaf_occ(VAR_0,sK3) )
& ! [VAR_0,VAR_1] :
( occurrence_of(sK4(VAR_1,VAR_0),tptp1)
| occurrence_of(VAR_0,tptp1)
| ~ leaf_occ(VAR_0,sK3) )
& ! [VAR_0] :
( occurrence_of(VAR_0,tptp2)
| occurrence_of(VAR_0,tptp1)
| ~ leaf_occ(VAR_0,sK3) )
& occurrence_of(sK3,tptp0) ),
inference(cnf_transformation,[status(thm)],[sk_goals_neg_sk]) ).
cnf(c_251,negated_conjecture,
occurrence_of(sK3,tptp0),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_254,negated_conjecture,
( min_precedes(B,sK4(B,A),tptp0)
| occurrence_of(A,tptp1)
| ~ leaf_occ(A,sK3) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_258,negated_conjecture,
( occurrence_of(A,tptp2)
| min_precedes(B,sK5(B,A),tptp0)
| ~ leaf_occ(A,sK3) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_294,plain,
( occurrence_of(sK0(B,sK1(B,A)),B)
| atomic(B)
| atomic(B)
| ~ occurrence_of(A,B) ),
inference(resolve,[status(thm)],[c_89,c_87]) ).
cnf(c_295,plain,
( occurrence_of(sK0(B,sK1(B,A)),B)
| atomic(B)
| ~ occurrence_of(A,B) ),
inference(copy,[status(thm)],[c_294]) ).
cnf(c_358,plain,
leaf_occ(sK2(sK3),sK3),
inference(resolve,[status(thm)],[c_251,c_238]) ).
cnf(c_1311,negated_conjecture,
( occurrence_of(sK0(tptp0,sK1(tptp0,sK3)),tptp0)
| atomic(tptp0) ),
inference(resolve,[status(thm)],[c_295,c_251]) ).
cnf(c_372,negated_conjecture,
occurrence_of(sK0(tptp0,sK1(tptp0,sK3)),tptp0),
inference(resolve,[status(thm)],[c_239,c_1311]) ).
cnf(c_383,plain,
( occurrence_of(sK2(sK3),tptp2)
| min_precedes(A,sK5(A,sK2(sK3)),tptp0) ),
inference(resolve,[status(thm)],[c_358,c_258]) ).
cnf(c_387,plain,
( min_precedes(A,sK4(A,sK2(sK3)),tptp0)
| occurrence_of(sK2(sK3),tptp1) ),
inference(resolve,[status(thm)],[c_358,c_254]) ).
cnf(c_1312,plain,
( atomic(tptp0)
| ~ arboreal(sK0(tptp0,sK1(tptp0,sK3))) ),
inference(resolve,[status(thm)],[c_372,c_193]) ).
cnf(c_770,plain,
~ arboreal(sK0(tptp0,sK1(tptp0,sK3))),
inference(resolve,[status(thm)],[c_239,c_1312]) ).
cnf(c_1107,plain,
( arboreal(A)
| occurrence_of(sK2(sK3),tptp2) ),
inference(resolve,[status(thm)],[c_383,c_229]) ).
cnf(c_1214,plain,
occurrence_of(sK2(sK3),tptp2),
inference(resolve,[status(thm)],[c_1107,c_770]) ).
cnf(c_1219,plain,
( tptp2 = A
| ~ occurrence_of(sK2(sK3),A) ),
inference(resolve,[status(thm)],[c_1214,c_189]) ).
cnf(c_1267,plain,
( arboreal(A)
| occurrence_of(sK2(sK3),tptp1) ),
inference(resolve,[status(thm)],[c_387,c_229]) ).
cnf(c_1313,plain,
( tptp2 = tptp1
| arboreal(A) ),
inference(resolve,[status(thm)],[c_1267,c_1219]) ).
cnf(c_1309,plain,
arboreal(A),
inference(resolve,[status(thm)],[c_250,c_1313]) ).
cnf(c_1310,plain,
$false,
inference(resolve,[status(thm)],[c_1309,c_770]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PRO010+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n011.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 04:57:43 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 3812061 was started by sandbox on n011,
% 0.08/0.36 % Sat Sep 26 04:57:43 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.38
% 0.12/0.38 % From the command line: assign(max_seconds, 300).
% 0.59/0.48
% 0.59/0.48 % SZS status Theorem for theBenchmark
% 0.59/0.48
% 0.59/0.48 % Proof 1 at 0.07 (+ 0.02) seconds.
% 0.59/0.48 % Length of proof is 32.
% 0.59/0.48 % Level of proof is 9.
% 0.59/0.48 % Maximum clause weight is 27.000.
% 0.59/0.48 % Given clauses 259.
% 0.59/0.48
% 0.59/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------