%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PRO003+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 : n020.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 08:20:53 AM UTC 2026
% Result : Theorem 9.21s 1.79s
% Output : CNFRefutation 9.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 13
% Syntax : Number of formulae : 104 ( 33 unt; 0 def)
% Number of atoms : 276 ( 29 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 285 ( 113 ~; 116 |; 46 &)
% ( 2 <=>; 8 =>; 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 : 159 ( 3 sgn 65 !; 15 ?)
% 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_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] :
( ( root_occ(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]) ).
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) )
| ~ root_occ(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) )
| ~ root_occ(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)
| ~ root_occ(VAR_1,VAR_0)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0,VAR_1] :
( occurrence_of(sK3(VAR_1,VAR_0),tptp1)
| ~ root_occ(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)
| ~ root_occ(B,A)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_45]) ).
cnf(c_89,plain,
( arboreal(sK3(B,A))
| ~ root_occ(B,A)
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_87,c_83]) ).
cnf(c_90,plain,
( min_precedes(B,sK3(B,A),tptp0)
| ~ root_occ(B,A)
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_87,c_82]) ).
cnf(c_95,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_146,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_150,negated_conjecture,
occurrence_of(sK4,tptp0),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_151,plain,
( occurrence_of(sK3(B,A),tptp1)
| ~ root_occ(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_156,plain,
tptp1 != tptp3,
inference(clausify,[status(thm)],[sos_42]) ).
cnf(c_157,plain,
tptp3 != tptp1,
inference(copy,[status(thm)],[c_156]) ).
fof(sos_34,axiom,
~ atomic(tptp0),
file('theBenchmark.p',sos_34) ).
cnf(c_166,plain,
~ atomic(tptp0),
inference(clausify,[status(thm)],[sos_34]) ).
cnf(c_167,plain,
( leaf_occ(sK2(A),A)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_168,plain,
( occurrence_of(sK2(A),tptp3)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_169,plain,
( root_occ(sK1(A),A)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_173,plain,
( D = C
| ~ root_occ(D,A)
| ~ root_occ(C,A)
| ~ occurrence_of(A,B) ),
inference(clausify,[status(thm)],[sos_29]) ).
cnf(c_190,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_191,plain,
( subactivity_occurrence(B,sK5(C,A,B))
| ~ min_precedes(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_sos_06]) ).
cnf(c_192,plain,
( subactivity_occurrence(A,sK5(C,A,B))
| ~ min_precedes(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_sos_06]) ).
cnf(c_193,plain,
( occurrence_of(sK5(C,A,B),C)
| ~ min_precedes(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_sos_06]) ).
cnf(c_195,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_197,plain,
( subactivity_occurrence(sK0(B,A),A)
| atomic(B)
| ~ occurrence_of(A,B) ),
inference(split_conjunct,[status(thm)],[sk_sos]) ).
cnf(c_222,plain,
( atomic(A)
| ~ subactivity_occurrence(sK0(A,B),B)
| ~ occurrence_of(B,A)
| root_occ(sK0(A,B),B) ),
inference(factor,[status(thm)],[c_146]) ).
cnf(c_5390,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_150,c_146]) ).
cnf(c_226,negated_conjecture,
( ~ subactivity_occurrence(sK0(tptp0,sK4),A)
| ~ occurrence_of(A,tptp0)
| root_occ(sK0(tptp0,sK4),A) ),
inference(resolve,[status(thm)],[c_166,c_5390]) ).
cnf(c_248,plain,
root_occ(sK1(sK4),sK4),
inference(resolve,[status(thm)],[c_169,c_150]) ).
cnf(c_250,plain,
( B = A
| ~ root_occ(B,sK4)
| ~ root_occ(A,sK4) ),
inference(resolve,[status(thm)],[c_173,c_150]) ).
cnf(c_5391,negated_conjecture,
( subactivity_occurrence(sK0(tptp0,sK4),sK4)
| atomic(tptp0) ),
inference(resolve,[status(thm)],[c_197,c_150]) ).
cnf(c_264,negated_conjecture,
subactivity_occurrence(sK0(tptp0,sK4),sK4),
inference(resolve,[status(thm)],[c_166,c_5391]) ).
cnf(c_5392,negated_conjecture,
( atomic(tptp0)
| ~ subactivity_occurrence(sK0(tptp0,sK4),sK4)
| root_occ(sK0(tptp0,sK4),sK4) ),
inference(resolve,[status(thm)],[c_222,c_150]) ).
cnf(c_5393,negated_conjecture,
( atomic(tptp0)
| root_occ(sK0(tptp0,sK4),sK4) ),
inference(resolve,[status(thm)],[c_264,c_5392]) ).
cnf(c_272,negated_conjecture,
root_occ(sK0(tptp0,sK4),sK4),
inference(resolve,[status(thm)],[c_166,c_5393]) ).
cnf(c_5394,plain,
( occurrence_of(sK3(sK1(sK4),sK4),tptp1)
| ~ occurrence_of(sK4,tptp0) ),
inference(resolve,[status(thm)],[c_248,c_151]) ).
cnf(c_322,negated_conjecture,
occurrence_of(sK3(sK1(sK4),sK4),tptp1),
inference(resolve,[status(thm)],[c_150,c_5394]) ).
cnf(c_5395,plain,
( min_precedes(sK1(sK4),sK3(sK1(sK4),sK4),tptp0)
| ~ occurrence_of(sK4,tptp0) ),
inference(resolve,[status(thm)],[c_248,c_90]) ).
cnf(c_330,negated_conjecture,
min_precedes(sK1(sK4),sK3(sK1(sK4),sK4),tptp0),
inference(resolve,[status(thm)],[c_150,c_5395]) ).
cnf(c_5396,plain,
( arboreal(sK3(sK1(sK4),sK4))
| ~ occurrence_of(sK4,tptp0) ),
inference(resolve,[status(thm)],[c_248,c_89]) ).
cnf(c_331,negated_conjecture,
arboreal(sK3(sK1(sK4),sK4)),
inference(resolve,[status(thm)],[c_150,c_5396]) ).
cnf(c_5397,plain,
( A = sK1(sK4)
| ~ root_occ(A,sK4) ),
inference(resolve,[status(thm)],[c_250,c_248]) ).
cnf(c_345,plain,
( sK1(sK4) = A
| ~ root_occ(A,sK4) ),
inference(copy,[status(thm)],[c_5397]) ).
cnf(c_5398,plain,
sK1(sK4) = sK0(tptp0,sK4),
inference(resolve,[status(thm)],[c_345,c_272]) ).
cnf(c_420,plain,
sK0(tptp0,sK4) = sK1(sK4),
inference(copy,[status(thm)],[c_5398]) ).
cnf(c_5399,negated_conjecture,
( ~ subactivity_occurrence(sK0(tptp0,sK4),A)
| ~ occurrence_of(A,tptp0)
| root_occ(sK1(sK4),A) ),
inference(paramod,[status(thm)],[c_420,c_226]) ).
cnf(c_425,negated_conjecture,
( ~ subactivity_occurrence(sK1(sK4),A)
| ~ occurrence_of(A,tptp0)
| root_occ(sK1(sK4),A) ),
inference(paramod,[status(thm)],[c_420,c_5399]) ).
cnf(c_5400,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_331,c_195]) ).
cnf(c_433,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_5400]) ).
cnf(c_447,plain,
( tptp1 = A
| ~ occurrence_of(sK3(sK1(sK4),sK4),A) ),
inference(resolve,[status(thm)],[c_322,c_190]) ).
cnf(c_566,plain,
occurrence_of(sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4)),tptp0),
inference(resolve,[status(thm)],[c_330,c_193]) ).
cnf(c_567,plain,
subactivity_occurrence(sK1(sK4),sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))),
inference(resolve,[status(thm)],[c_330,c_192]) ).
cnf(c_568,plain,
subactivity_occurrence(sK3(sK1(sK4),sK4),sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))),
inference(resolve,[status(thm)],[c_330,c_191]) ).
cnf(c_5401,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_566,c_425]) ).
cnf(c_1200,plain,
root_occ(sK1(sK4),sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))),
inference(resolve,[status(thm)],[c_567,c_5401]) ).
cnf(c_1224,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_566,c_173]) ).
cnf(c_1226,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_566,c_169]) ).
cnf(c_1227,plain,
occurrence_of(sK2(sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))),tptp3),
inference(resolve,[status(thm)],[c_566,c_168]) ).
cnf(c_1228,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_566,c_167]) ).
cnf(c_1243,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_566,c_95]) ).
cnf(c_5402,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_433,c_566]) ).
cnf(c_1441,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_568,c_5402]) ).
cnf(c_5403,plain,
( A = sK1(sK4)
| ~ root_occ(A,sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))) ),
inference(resolve,[status(thm)],[c_1224,c_1200]) ).
cnf(c_4838,plain,
( sK1(sK4) = A
| ~ root_occ(A,sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))) ),
inference(copy,[status(thm)],[c_5403]) ).
cnf(c_5404,plain,
sK1(sK4) = sK1(sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))),
inference(resolve,[status(thm)],[c_1226,c_4838]) ).
cnf(c_4839,plain,
sK1(sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))) = sK1(sK4),
inference(copy,[status(thm)],[c_5404]) ).
cnf(c_4841,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_4839,c_1243]) ).
cnf(c_4946,plain,
~ min_precedes(sK3(sK1(sK4),sK4),sK2(sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))),tptp0),
inference(resolve,[status(thm)],[c_4841,c_330]) ).
cnf(c_5405,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_1441,c_1228]) ).
cnf(c_5406,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_5405]) ).
cnf(c_5260,plain,
sK2(sK5(tptp0,sK1(sK4),sK3(sK1(sK4),sK4))) = sK3(sK1(sK4),sK4),
inference(resolve,[status(thm)],[c_4946,c_5406]) ).
cnf(c_5314,plain,
occurrence_of(sK3(sK1(sK4),sK4),tptp3),
inference(paramod,[status(thm)],[c_5260,c_1227]) ).
cnf(c_5407,plain,
tptp1 = tptp3,
inference(resolve,[status(thm)],[c_5314,c_447]) ).
cnf(c_5408,plain,
tptp3 = tptp1,
inference(copy,[status(thm)],[c_5407]) ).
cnf(c_5389,plain,
$false,
inference(resolve,[status(thm)],[c_157,c_5408]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PRO003+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n020.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
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sat Sep 26 04:56:04 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 653407 was started by sandbox2 on n020,
% 0.08/0.37 % Sat Sep 26 04:56:04 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.38
% 0.08/0.38 % From the command line: assign(max_seconds, 300).
% 9.21/1.79
% 9.21/1.79 % given #500 (W,wt=32): 528 -min_precedes(A,f14(c1),B) | -occurrence_of(f4(f14(c1),tptp0),B) | subactivity_occurrence(A,f4(f14(c1),tptp0)). [resolve(514,a,175,c)].
% 9.21/1.79
% 9.21/1.79 % given #1000 (T,wt=40): 2666 -occurrence_of(f15(f13(c1),f3(tptp0,f13(c1),f15(f13(c1),c1))),A) | atomic(A). [resolve(1602,a,185,b)].
% 9.21/1.79
% 9.21/1.79 % SZS status Theorem for theBenchmark
% 9.21/1.79
% 9.21/1.79 % Proof 1 at 1.05 (+ 0.27) seconds.
% 9.21/1.79 % Length of proof is 68.
% 9.21/1.79 % Level of proof is 14.
% 9.21/1.79 % Maximum clause weight is 49.000.
% 9.21/1.79 % Given clauses 1325.
% 9.21/1.79
% 9.21/1.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------