%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PRO006+4 : 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 : n013.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 08:20:55 AM UTC 2026
% Result : Theorem 9.92s 1.96s
% Output : CNFRefutation 9.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 14
% Syntax : Number of formulae : 121 ( 37 unt; 0 def)
% Number of atoms : 335 ( 29 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 353 ( 139 ~; 154 |; 49 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 176 ( 7 sgn 68 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos,axiom,
! [X0,X1] :
( ( ~ atomic(X0)
& occurrence_of(X1,X0) )
=> ? [X2] :
( subactivity_occurrence(X2,X1)
& root(X2,X0) ) ),
file('theBenchmark.p',sos) ).
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_06,axiom,
! [X21,X22,X23] :
( min_precedes(X22,X23,X21)
=> ? [X24] :
( subactivity_occurrence(X23,X24)
& subactivity_occurrence(X22,X24)
& occurrence_of(X24,X21) ) ),
file('theBenchmark.p',sos_06) ).
fof(sos_08,axiom,
! [X28,X29,X30] :
( ( occurrence_of(X28,X30)
& occurrence_of(X28,X29) )
=> X29 = X30 ),
file('theBenchmark.p',sos_08) ).
fof(sos_09,axiom,
! [X31,X32,X33] :
( ( leaf_occ(X32,X31)
& occurrence_of(X31,X33) )
=> ~ ? [X34] : min_precedes(X32,X34,X33) ),
file('theBenchmark.p',sos_09) ).
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_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_29,axiom,
! [X90,X91,X92,X93] :
( ( root_occ(X91,X92)
& root_occ(X90,X92)
& occurrence_of(X92,X93) )
=> X90 = X91 ),
file('theBenchmark.p',sos_29) ).
fof(sos_32,axiom,
! [X101] :
( occurrence_of(X101,tptp0)
=> ? [X102,X103] :
( next_subocc(X102,X103,tptp0)
& leaf_occ(X103,X101)
& occurrence_of(X103,tptp3)
& root_occ(X102,X101)
& occurrence_of(X102,tptp4) ) ),
file('theBenchmark.p',sos_32) ).
fof(sos_45,axiom,
! [X104,X105] :
( ( ~ leaf_occ(X104,X105)
& arboreal(X104)
& subactivity_occurrence(X104,X105)
& occurrence_of(X105,tptp0) )
=> ? [X106] :
( next_subocc(X104,X106,tptp0)
& occurrence_of(X106,tptp1) ) ),
file('theBenchmark.p',sos_45) ).
fof(goals,conjecture,
~ ? [X107] : occurrence_of(X107,tptp0),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ~ ? [X107] : occurrence_of(X107,tptp0),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_1,plain,
! [X0,X1] :
( ? [X2] :
( subactivity_occurrence(X2,X1)
& root(X2,X0) )
| atomic(X0)
| ~ occurrence_of(X1,X0) ),
inference(fof_nnf,[status(thm)],[sos]) ).
fof(sk_sos_sk,plain,
! [X0,X1] :
( ( subactivity_occurrence(sK0(X0,X1),X1)
& root(sK0(X0,X1),X0) )
| atomic(X0)
| ~ occurrence_of(X1,X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[nnf_1]) ).
fof(sk_sos,plain,
( ! [VAR_0,VAR_1] :
( subactivity_occurrence(sK0(VAR_1,VAR_0),VAR_0)
| atomic(VAR_1)
| ~ occurrence_of(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( root(sK0(VAR_1,VAR_0),VAR_1)
| atomic(VAR_1)
| ~ occurrence_of(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_sos_sk]) ).
cnf(c_37,plain,
( root(sK0(B,A),B)
| atomic(B)
| ~ occurrence_of(A,B) ),
inference(split_conjunct,[status(thm)],[sk_sos]) ).
cnf(c_43,plain,
( ~ root(A,C)
| ~ subactivity_occurrence(A,B)
| ~ occurrence_of(B,C)
| root_occ(A,B) ),
inference(clausify,[status(thm)],[sos_19]) ).
cnf(c_81,plain,
( ~ min_precedes(D,B,C)
| ~ min_precedes(A,D,C)
| ~ next_subocc(A,B,C) ),
inference(clausify,[status(thm)],[sos_26]) ).
cnf(c_82,plain,
( min_precedes(A,B,C)
| ~ next_subocc(A,B,C) ),
inference(clausify,[status(thm)],[sos_26]) ).
cnf(c_83,plain,
( arboreal(B)
| ~ next_subocc(A,B,C) ),
inference(clausify,[status(thm)],[sos_25]) ).
cnf(c_84,plain,
( arboreal(A)
| ~ next_subocc(A,B,C) ),
inference(clausify,[status(thm)],[sos_25]) ).
fof(nnf_33,plain,
! [X101] :
( ? [X102,X103] :
( next_subocc(X102,X103,tptp0)
& leaf_occ(X103,X101)
& occurrence_of(X103,tptp3)
& root_occ(X102,X101)
& occurrence_of(X102,tptp4) )
| ~ occurrence_of(X101,tptp0) ),
inference(fof_nnf,[status(thm)],[sos_32]) ).
fof(sk_sos_32_sk,plain,
! [X101] :
( ( next_subocc(sK1(X101),sK2(X101),tptp0)
& leaf_occ(sK2(X101),X101)
& occurrence_of(sK2(X101),tptp3)
& root_occ(sK1(X101),X101)
& occurrence_of(sK1(X101),tptp4) )
| ~ occurrence_of(X101,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X102,sK1(X101)),skolemize(X103,sK2(X101))],[nnf_33]) ).
fof(sk_sos_32,plain,
( ! [VAR_0] :
( next_subocc(sK1(VAR_0),sK2(VAR_0),tptp0)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( leaf_occ(sK2(VAR_0),VAR_0)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( occurrence_of(sK2(VAR_0),tptp3)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( root_occ(sK1(VAR_0),VAR_0)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( occurrence_of(sK1(VAR_0),tptp4)
| ~ occurrence_of(VAR_0,tptp0) ) ),
inference(cnf_transformation,[status(thm)],[sk_sos_32_sk]) ).
cnf(c_86,plain,
( next_subocc(sK1(A),sK2(A),tptp0)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
fof(nnf_34,plain,
! [X104,X105] :
( ? [X106] :
( next_subocc(X104,X106,tptp0)
& occurrence_of(X106,tptp1) )
| leaf_occ(X104,X105)
| ~ arboreal(X104)
| ~ subactivity_occurrence(X104,X105)
| ~ occurrence_of(X105,tptp0) ),
inference(fof_nnf,[status(thm)],[sos_45]) ).
fof(sk_sos_45_sk,plain,
! [X104,X105] :
( ( next_subocc(X104,sK3(X104,X105),tptp0)
& occurrence_of(sK3(X104,X105),tptp1) )
| leaf_occ(X104,X105)
| ~ arboreal(X104)
| ~ subactivity_occurrence(X104,X105)
| ~ occurrence_of(X105,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X106,sK3(X104,X105))],[nnf_34]) ).
fof(sk_sos_45,plain,
( ! [VAR_0,VAR_1] :
( next_subocc(VAR_1,sK3(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(sK3(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_45_sk]) ).
cnf(c_87,plain,
( next_subocc(B,sK3(B,A),tptp0)
| leaf_occ(B,A)
| ~ arboreal(B)
| ~ subactivity_occurrence(B,A)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_45]) ).
cnf(c_88,plain,
( arboreal(sK3(B,A))
| leaf_occ(B,A)
| ~ arboreal(B)
| ~ subactivity_occurrence(B,A)
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_87,c_83]) ).
cnf(c_89,plain,
( min_precedes(B,sK3(B,A),tptp0)
| leaf_occ(B,A)
| ~ arboreal(B)
| ~ subactivity_occurrence(B,A)
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_87,c_82]) ).
cnf(c_91,plain,
( arboreal(sK1(A))
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_86,c_84]) ).
cnf(c_93,plain,
( min_precedes(sK1(A),sK2(A),tptp0)
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_86,c_82]) ).
cnf(c_94,plain,
( ~ min_precedes(B,sK2(A),tptp0)
| ~ min_precedes(sK1(A),B,tptp0)
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_86,c_81]) ).
cnf(c_145,plain,
( atomic(A)
| ~ occurrence_of(B,A)
| ~ subactivity_occurrence(sK0(A,B),C)
| ~ occurrence_of(C,A)
| root_occ(sK0(A,B),C) ),
inference(resolve,[status(thm)],[c_43,c_37]) ).
fof(nnf_35,plain,
? [X107] : occurrence_of(X107,tptp0),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
occurrence_of(sK4,tptp0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X107,sK4)],[nnf_35]) ).
cnf(c_149,negated_conjecture,
occurrence_of(sK4,tptp0),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_150,plain,
( occurrence_of(sK3(B,A),tptp1)
| leaf_occ(B,A)
| ~ arboreal(B)
| ~ subactivity_occurrence(B,A)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_45]) ).
fof(sos_42,axiom,
tptp1 != tptp3,
file('theBenchmark.p',sos_42) ).
cnf(c_155,plain,
tptp1 != tptp3,
inference(clausify,[status(thm)],[sos_42]) ).
cnf(c_156,plain,
tptp3 != tptp1,
inference(copy,[status(thm)],[c_155]) ).
fof(sos_34,axiom,
~ atomic(tptp0),
file('theBenchmark.p',sos_34) ).
cnf(c_165,plain,
~ atomic(tptp0),
inference(clausify,[status(thm)],[sos_34]) ).
cnf(c_166,plain,
( leaf_occ(sK2(A),A)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_167,plain,
( occurrence_of(sK2(A),tptp3)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_168,plain,
( root_occ(sK1(A),A)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_172,plain,
( D = C
| ~ root_occ(D,A)
| ~ root_occ(C,A)
| ~ occurrence_of(A,B) ),
inference(clausify,[status(thm)],[sos_29]) ).
cnf(c_179,plain,
( subactivity_occurrence(A,B)
| ~ root_occ(A,B) ),
inference(clausify,[status(thm)],[sos_19]) ).
cnf(c_188,plain,
( ~ min_precedes(C,D,B)
| ~ leaf_occ(C,A)
| ~ occurrence_of(A,B) ),
inference(clausify,[status(thm)],[sos_09]) ).
cnf(c_189,plain,
( C = B
| ~ occurrence_of(A,C)
| ~ occurrence_of(A,B) ),
inference(clausify,[status(thm)],[sos_08]) ).
fof(nnf_7,plain,
! [X21,X22,X23] :
( ? [X24] :
( subactivity_occurrence(X23,X24)
& subactivity_occurrence(X22,X24)
& occurrence_of(X24,X21) )
| ~ min_precedes(X22,X23,X21) ),
inference(fof_nnf,[status(thm)],[sos_06]) ).
fof(sk_sos_06_sk,plain,
! [X21,X22,X23] :
( ( subactivity_occurrence(X23,sK5(X21,X22,X23))
& subactivity_occurrence(X22,sK5(X21,X22,X23))
& occurrence_of(sK5(X21,X22,X23),X21) )
| ~ min_precedes(X22,X23,X21) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X24,sK5(X21,X22,X23))],[nnf_7]) ).
fof(sk_sos_06,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( subactivity_occurrence(VAR_1,sK5(VAR_2,VAR_0,VAR_1))
| ~ min_precedes(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1,VAR_2] :
( subactivity_occurrence(VAR_0,sK5(VAR_2,VAR_0,VAR_1))
| ~ min_precedes(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1,VAR_2] :
( occurrence_of(sK5(VAR_2,VAR_0,VAR_1),VAR_2)
| ~ min_precedes(VAR_0,VAR_1,VAR_2) ) ),
inference(cnf_transformation,[status(thm)],[sk_sos_06_sk]) ).
cnf(c_190,plain,
( subactivity_occurrence(B,sK5(C,A,B))
| ~ min_precedes(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_sos_06]) ).
cnf(c_191,plain,
( subactivity_occurrence(A,sK5(C,A,B))
| ~ min_precedes(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_sos_06]) ).
cnf(c_192,plain,
( occurrence_of(sK5(C,A,B),C)
| ~ min_precedes(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_sos_06]) ).
cnf(c_194,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_196,plain,
( subactivity_occurrence(sK0(B,A),A)
| atomic(B)
| ~ occurrence_of(A,B) ),
inference(split_conjunct,[status(thm)],[sk_sos]) ).
cnf(c_221,plain,
( atomic(A)
| ~ subactivity_occurrence(sK0(A,B),B)
| ~ occurrence_of(B,A)
| root_occ(sK0(A,B),B) ),
inference(factor,[status(thm)],[c_145]) ).
cnf(c_5808,negated_conjecture,
( atomic(tptp0)
| ~ subactivity_occurrence(sK0(tptp0,sK4),A)
| ~ occurrence_of(A,tptp0)
| root_occ(sK0(tptp0,sK4),A) ),
inference(resolve,[status(thm)],[c_149,c_145]) ).
cnf(c_225,negated_conjecture,
( ~ subactivity_occurrence(sK0(tptp0,sK4),A)
| ~ occurrence_of(A,tptp0)
| root_occ(sK0(tptp0,sK4),A) ),
inference(resolve,[status(thm)],[c_165,c_5808]) ).
cnf(c_238,plain,
min_precedes(sK1(sK4),sK2(sK4),tptp0),
inference(resolve,[status(thm)],[c_149,c_93]) ).
cnf(c_240,plain,
arboreal(sK1(sK4)),
inference(resolve,[status(thm)],[c_149,c_91]) ).
cnf(c_247,plain,
root_occ(sK1(sK4),sK4),
inference(resolve,[status(thm)],[c_168,c_149]) ).
cnf(c_249,plain,
( B = A
| ~ root_occ(B,sK4)
| ~ root_occ(A,sK4) ),
inference(resolve,[status(thm)],[c_172,c_149]) ).
cnf(c_258,plain,
( ~ min_precedes(A,B,tptp0)
| ~ leaf_occ(A,sK4) ),
inference(resolve,[status(thm)],[c_188,c_149]) ).
cnf(c_5809,negated_conjecture,
( subactivity_occurrence(sK0(tptp0,sK4),sK4)
| atomic(tptp0) ),
inference(resolve,[status(thm)],[c_196,c_149]) ).
cnf(c_263,negated_conjecture,
subactivity_occurrence(sK0(tptp0,sK4),sK4),
inference(resolve,[status(thm)],[c_165,c_5809]) ).
cnf(c_5810,negated_conjecture,
( atomic(tptp0)
| ~ subactivity_occurrence(sK0(tptp0,sK4),sK4)
| root_occ(sK0(tptp0,sK4),sK4) ),
inference(resolve,[status(thm)],[c_221,c_149]) ).
cnf(c_5811,negated_conjecture,
( atomic(tptp0)
| root_occ(sK0(tptp0,sK4),sK4) ),
inference(resolve,[status(thm)],[c_263,c_5810]) ).
cnf(c_271,negated_conjecture,
root_occ(sK0(tptp0,sK4),sK4),
inference(resolve,[status(thm)],[c_165,c_5811]) ).
cnf(c_327,plain,
subactivity_occurrence(sK1(sK4),sK4),
inference(resolve,[status(thm)],[c_247,c_179]) ).
cnf(c_5812,plain,
( A = sK1(sK4)
| ~ root_occ(A,sK4) ),
inference(resolve,[status(thm)],[c_249,c_247]) ).
cnf(c_349,plain,
( sK1(sK4) = A
| ~ root_occ(A,sK4) ),
inference(copy,[status(thm)],[c_5812]) ).
cnf(c_5813,plain,
( occurrence_of(sK3(sK1(sK4),sK4),tptp1)
| leaf_occ(sK1(sK4),sK4)
| ~ arboreal(sK1(sK4))
| ~ occurrence_of(sK4,tptp0) ),
inference(resolve,[status(thm)],[c_327,c_150]) ).
cnf(c_5814,negated_conjecture,
( occurrence_of(sK3(sK1(sK4),sK4),tptp1)
| leaf_occ(sK1(sK4),sK4)
| ~ arboreal(sK1(sK4)) ),
inference(resolve,[status(thm)],[c_149,c_5813]) ).
cnf(c_363,negated_conjecture,
( occurrence_of(sK3(sK1(sK4),sK4),tptp1)
| leaf_occ(sK1(sK4),sK4) ),
inference(resolve,[status(thm)],[c_240,c_5814]) ).
cnf(c_5815,plain,
( min_precedes(sK1(sK4),sK3(sK1(sK4),sK4),tptp0)
| leaf_occ(sK1(sK4),sK4)
| ~ arboreal(sK1(sK4))
| ~ occurrence_of(sK4,tptp0) ),
inference(resolve,[status(thm)],[c_327,c_89]) ).
cnf(c_5816,negated_conjecture,
( min_precedes(sK1(sK4),sK3(sK1(sK4),sK4),tptp0)
| leaf_occ(sK1(sK4),sK4)
| ~ arboreal(sK1(sK4)) ),
inference(resolve,[status(thm)],[c_149,c_5815]) ).
cnf(c_367,negated_conjecture,
( min_precedes(sK1(sK4),sK3(sK1(sK4),sK4),tptp0)
| leaf_occ(sK1(sK4),sK4) ),
inference(resolve,[status(thm)],[c_240,c_5816]) ).
cnf(c_5817,plain,
( arboreal(sK3(sK1(sK4),sK4))
| leaf_occ(sK1(sK4),sK4)
| ~ arboreal(sK1(sK4))
| ~ occurrence_of(sK4,tptp0) ),
inference(resolve,[status(thm)],[c_327,c_88]) ).
cnf(c_5818,negated_conjecture,
( arboreal(sK3(sK1(sK4),sK4))
| leaf_occ(sK1(sK4),sK4)
| ~ arboreal(sK1(sK4)) ),
inference(resolve,[status(thm)],[c_149,c_5817]) ).
cnf(c_368,negated_conjecture,
( arboreal(sK3(sK1(sK4),sK4))
| leaf_occ(sK1(sK4),sK4) ),
inference(resolve,[status(thm)],[c_240,c_5818]) ).
cnf(c_394,plain,
~ leaf_occ(sK1(sK4),sK4),
inference(resolve,[status(thm)],[c_238,c_258]) ).
cnf(c_421,negated_conjecture,
arboreal(sK3(sK1(sK4),sK4)),
inference(resolve,[status(thm)],[c_394,c_368]) ).
cnf(c_422,negated_conjecture,
min_precedes(sK1(sK4),sK3(sK1(sK4),sK4),tptp0),
inference(resolve,[status(thm)],[c_394,c_367]) ).
cnf(c_426,negated_conjecture,
occurrence_of(sK3(sK1(sK4),sK4),tptp1),
inference(resolve,[status(thm)],[c_394,c_363]) ).
cnf(c_5819,plain,
sK1(sK4) = sK0(tptp0,sK4),
inference(resolve,[status(thm)],[c_349,c_271]) ).
cnf(c_435,plain,
sK0(tptp0,sK4) = sK1(sK4),
inference(copy,[status(thm)],[c_5819]) ).
cnf(c_5820,negated_conjecture,
( ~ subactivity_occurrence(sK0(tptp0,sK4),A)
| ~ occurrence_of(A,tptp0)
| root_occ(sK1(sK4),A) ),
inference(paramod,[status(thm)],[c_435,c_225]) ).
cnf(c_440,negated_conjecture,
( ~ subactivity_occurrence(sK1(sK4),A)
| ~ occurrence_of(A,tptp0)
| root_occ(sK1(sK4),A) ),
inference(paramod,[status(thm)],[c_435,c_5820]) ).
cnf(c_5821,plain,
( C = sK3(sK1(sK4),sK4)
| min_precedes(sK3(sK1(sK4),sK4),C,B)
| ~ leaf_occ(C,A)
| ~ subactivity_occurrence(sK3(sK1(sK4),sK4),A)
| ~ occurrence_of(A,B) ),
inference(resolve,[status(thm)],[c_421,c_194]) ).
cnf(c_446,plain,
( sK3(sK1(sK4),sK4) = C
| min_precedes(sK3(sK1(sK4),sK4),C,B)
| ~ leaf_occ(C,A)
| ~ subactivity_occurrence(sK3(sK1(sK4),sK4),A)
| ~ occurrence_of(A,B) ),
inference(copy,[status(thm)],[c_5821]) ).
cnf(c_513,plain,
( tptp1 = A
| ~ occurrence_of(sK3(sK1(sK4),sK4),A) ),
inference(resolve,[status(thm)],[c_426,c_189]) ).
cnf(c_702,plain,
occurrence_of(sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4)),tptp0),
inference(resolve,[status(thm)],[c_422,c_192]) ).
cnf(c_703,plain,
subactivity_occurrence(sK1(sK4),sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))),
inference(resolve,[status(thm)],[c_422,c_191]) ).
cnf(c_704,plain,
subactivity_occurrence(sK3(sK1(sK4),sK4),sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))),
inference(resolve,[status(thm)],[c_422,c_190]) ).
cnf(c_5822,plain,
( ~ subactivity_occurrence(sK1(sK4),sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4)))
| root_occ(sK1(sK4),sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))) ),
inference(resolve,[status(thm)],[c_702,c_440]) ).
cnf(c_1403,plain,
root_occ(sK1(sK4),sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))),
inference(resolve,[status(thm)],[c_703,c_5822]) ).
cnf(c_1431,plain,
( B = A
| ~ root_occ(B,sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4)))
| ~ root_occ(A,sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))) ),
inference(resolve,[status(thm)],[c_702,c_172]) ).
cnf(c_1433,plain,
root_occ(sK1(sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))),sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))),
inference(resolve,[status(thm)],[c_702,c_168]) ).
cnf(c_1434,plain,
occurrence_of(sK2(sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))),tptp3),
inference(resolve,[status(thm)],[c_702,c_167]) ).
cnf(c_1435,plain,
leaf_occ(sK2(sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))),sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))),
inference(resolve,[status(thm)],[c_702,c_166]) ).
cnf(c_1450,plain,
( ~ min_precedes(A,sK2(sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))),tptp0)
| ~ min_precedes(sK1(sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))),A,tptp0) ),
inference(resolve,[status(thm)],[c_702,c_94]) ).
cnf(c_5823,plain,
( sK3(sK1(sK4),sK4) = A
| min_precedes(sK3(sK1(sK4),sK4),A,tptp0)
| ~ leaf_occ(A,sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4)))
| ~ subactivity_occurrence(sK3(sK1(sK4),sK4),sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))) ),
inference(resolve,[status(thm)],[c_446,c_702]) ).
cnf(c_1769,plain,
( sK3(sK1(sK4),sK4) = A
| min_precedes(sK3(sK1(sK4),sK4),A,tptp0)
| ~ leaf_occ(A,sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))) ),
inference(resolve,[status(thm)],[c_704,c_5823]) ).
cnf(c_5824,plain,
( A = sK1(sK4)
| ~ root_occ(A,sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))) ),
inference(resolve,[status(thm)],[c_1431,c_1403]) ).
cnf(c_5315,plain,
( sK1(sK4) = A
| ~ root_occ(A,sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))) ),
inference(copy,[status(thm)],[c_5824]) ).
cnf(c_5825,plain,
sK1(sK4) = sK1(sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))),
inference(resolve,[status(thm)],[c_1433,c_5315]) ).
cnf(c_5316,plain,
sK1(sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))) = sK1(sK4),
inference(copy,[status(thm)],[c_5825]) ).
cnf(c_5318,plain,
( ~ min_precedes(A,sK2(sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))),tptp0)
| ~ min_precedes(sK1(sK4),A,tptp0) ),
inference(paramod,[status(thm)],[c_5316,c_1450]) ).
cnf(c_5327,plain,
~ min_precedes(sK3(sK1(sK4),sK4),sK2(sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))),tptp0),
inference(resolve,[status(thm)],[c_5318,c_422]) ).
cnf(c_5826,plain,
( sK3(sK1(sK4),sK4) = sK2(sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4)))
| min_precedes(sK3(sK1(sK4),sK4),sK2(sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))),tptp0) ),
inference(resolve,[status(thm)],[c_1769,c_1435]) ).
cnf(c_5827,plain,
( sK2(sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))) = sK3(sK1(sK4),sK4)
| min_precedes(sK3(sK1(sK4),sK4),sK2(sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))),tptp0) ),
inference(copy,[status(thm)],[c_5826]) ).
cnf(c_5678,plain,
sK2(sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))) = sK3(sK1(sK4),sK4),
inference(resolve,[status(thm)],[c_5327,c_5827]) ).
cnf(c_5732,plain,
occurrence_of(sK3(sK1(sK4),sK4),tptp3),
inference(paramod,[status(thm)],[c_5678,c_1434]) ).
cnf(c_5828,plain,
tptp1 = tptp3,
inference(resolve,[status(thm)],[c_5732,c_513]) ).
cnf(c_5829,plain,
tptp3 = tptp1,
inference(copy,[status(thm)],[c_5828]) ).
cnf(c_5807,plain,
$false,
inference(resolve,[status(thm)],[c_156,c_5829]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PRO006+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 04:55:56 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 1959715 was started by sandbox2 on n013,
% 0.10/0.37 % Sat Sep 26 04:55:56 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 9.92/1.96
% 9.92/1.96 % given #500 (T,wt=32): 539 occurrence_of(f4(f14(c1),tptp0),f9(f14(c1),f4(f14(c1),tptp0))). [resolve(415,a,182,a)].
% 9.92/1.96
% 9.92/1.96 % given #1000 (W,wt=40): 2756 arboreal(f7(f14(c1),tptp0)) | -min_precedes(f12(f7(f14(c1),tptp0),f14(c1),tptp0),A,tptp0) | -precedes(f14(c1),A). [resolve(616,a,170,a),unit_del(d,291)].
% 9.92/1.96
% 9.92/1.96 % SZS status Theorem for theBenchmark
% 9.92/1.96
% 9.92/1.96 % Proof 1 at 0.90 (+ 0.25) seconds.
% 9.92/1.96 % Length of proof is 82.
% 9.92/1.96 % Level of proof is 14.
% 9.92/1.96 % Maximum clause weight is 49.000.
% 9.92/1.96 % Given clauses 1335.
% 9.92/1.96
% 9.92/1.96 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------