%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PRO006+2 : 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 : n012.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 23.82s 3.49s
% Output : CNFRefutation 23.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 15
% Syntax : Number of formulae : 129 ( 40 unt; 0 def)
% Number of atoms : 362 ( 30 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 380 ( 147 ~; 170 |; 51 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 183 ( 9 sgn 70 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_02,axiom,
! [X7,X8,X9,X10] :
( ( root_occ(X8,X9)
& root_occ(X7,X9)
& occurrence_of(X9,X10) )
=> X7 = X8 ),
file('theBenchmark.p',sos_02) ).
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_05,axiom,
! [X19,X20,X21] :
( next_subocc(X19,X20,X21)
=> ( arboreal(X20)
& arboreal(X19) ) ),
file('theBenchmark.p',sos_05) ).
fof(sos_10,axiom,
! [X32,X33] :
( root_occ(X32,X33)
<=> ? [X34] :
( root(X32,X34)
& subactivity_occurrence(X32,X33)
& occurrence_of(X33,X34) ) ),
file('theBenchmark.p',sos_10) ).
fof(sos_11,axiom,
! [X35,X36] :
( leaf_occ(X35,X36)
<=> ? [X37] :
( leaf(X35,X37)
& subactivity_occurrence(X35,X36)
& occurrence_of(X36,X37) ) ),
file('theBenchmark.p',sos_11) ).
fof(sos_21,axiom,
! [X60,X61,X62] :
( ( leaf_occ(X61,X60)
& occurrence_of(X60,X62) )
=> ~ ? [X63] : min_precedes(X61,X63,X62) ),
file('theBenchmark.p',sos_21) ).
fof(sos_22,axiom,
! [X64,X65,X66] :
( ( occurrence_of(X64,X66)
& occurrence_of(X64,X65) )
=> X65 = X66 ),
file('theBenchmark.p',sos_22) ).
fof(sos_24,axiom,
! [X70,X71,X72] :
( min_precedes(X71,X72,X70)
=> ? [X73] :
( subactivity_occurrence(X72,X73)
& subactivity_occurrence(X71,X73)
& occurrence_of(X73,X70) ) ),
file('theBenchmark.p',sos_24) ).
fof(sos_28,axiom,
! [X85,X86,X87,X88] :
( ( subactivity_occurrence(X88,X86)
& subactivity_occurrence(X87,X86)
& arboreal(X88)
& arboreal(X87)
& occurrence_of(X86,X85) )
=> ( X87 = X88
| min_precedes(X88,X87,X85)
| min_precedes(X87,X88,X85) ) ),
file('theBenchmark.p',sos_28) ).
fof(sos_30,axiom,
! [X91,X92] :
( ( ~ atomic(X91)
& occurrence_of(X92,X91) )
=> ? [X93] :
( subactivity_occurrence(X93,X92)
& root(X93,X91) ) ),
file('theBenchmark.p',sos_30) ).
fof(sos_32,axiom,
! [X95] :
( occurrence_of(X95,tptp0)
=> ? [X96,X97] :
( next_subocc(X96,X97,tptp0)
& leaf_occ(X97,X95)
& occurrence_of(X97,tptp3)
& root_occ(X96,X95)
& occurrence_of(X96,tptp4) ) ),
file('theBenchmark.p',sos_32) ).
fof(sos_45,axiom,
! [X98,X99] :
( ( ~ leaf_occ(X98,X99)
& arboreal(X98)
& subactivity_occurrence(X98,X99)
& occurrence_of(X99,tptp0) )
=> ? [X100] :
( next_subocc(X98,X100,tptp0)
& occurrence_of(X100,tptp1) ) ),
file('theBenchmark.p',sos_45) ).
fof(goals,conjecture,
~ ? [X101] : occurrence_of(X101,tptp0),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ~ ? [X101] : occurrence_of(X101,tptp0),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_37,plain,
( ~ min_precedes(D,B,C)
| ~ min_precedes(A,D,C)
| ~ next_subocc(A,B,C) ),
inference(clausify,[status(thm)],[sos_04]) ).
cnf(c_38,plain,
( min_precedes(A,B,C)
| ~ next_subocc(A,B,C) ),
inference(clausify,[status(thm)],[sos_04]) ).
cnf(c_40,plain,
( arboreal(A)
| ~ next_subocc(A,B,C) ),
inference(clausify,[status(thm)],[sos_05]) ).
cnf(c_41,plain,
( arboreal(B)
| ~ next_subocc(A,B,C) ),
inference(clausify,[status(thm)],[sos_05]) ).
fof(nnf_33,plain,
! [X95] :
( ? [X96,X97] :
( next_subocc(X96,X97,tptp0)
& leaf_occ(X97,X95)
& occurrence_of(X97,tptp3)
& root_occ(X96,X95)
& occurrence_of(X96,tptp4) )
| ~ occurrence_of(X95,tptp0) ),
inference(fof_nnf,[status(thm)],[sos_32]) ).
fof(sk_sos_32_sk,plain,
! [X95] :
( ( next_subocc(sK0(X95),sK1(X95),tptp0)
& leaf_occ(sK1(X95),X95)
& occurrence_of(sK1(X95),tptp3)
& root_occ(sK0(X95),X95)
& occurrence_of(sK0(X95),tptp4) )
| ~ occurrence_of(X95,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X96,sK0(X95)),skolemize(X97,sK1(X95))],[nnf_33]) ).
fof(sk_sos_32,plain,
( ! [VAR_0] :
( next_subocc(sK0(VAR_0),sK1(VAR_0),tptp0)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( leaf_occ(sK1(VAR_0),VAR_0)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( occurrence_of(sK1(VAR_0),tptp3)
| ~ 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),tptp4)
| ~ occurrence_of(VAR_0,tptp0) ) ),
inference(cnf_transformation,[status(thm)],[sk_sos_32_sk]) ).
cnf(c_42,plain,
( next_subocc(sK0(A),sK1(A),tptp0)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
fof(nnf_34,plain,
! [X98,X99] :
( ? [X100] :
( next_subocc(X98,X100,tptp0)
& occurrence_of(X100,tptp1) )
| leaf_occ(X98,X99)
| ~ arboreal(X98)
| ~ subactivity_occurrence(X98,X99)
| ~ occurrence_of(X99,tptp0) ),
inference(fof_nnf,[status(thm)],[sos_45]) ).
fof(sk_sos_45_sk,plain,
! [X98,X99] :
( ( next_subocc(X98,sK2(X98,X99),tptp0)
& occurrence_of(sK2(X98,X99),tptp1) )
| leaf_occ(X98,X99)
| ~ arboreal(X98)
| ~ subactivity_occurrence(X98,X99)
| ~ occurrence_of(X99,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X100,sK2(X98,X99))],[nnf_34]) ).
fof(sk_sos_45,plain,
( ! [VAR_0,VAR_1] :
( next_subocc(VAR_1,sK2(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(sK2(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_43,plain,
( next_subocc(B,sK2(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_50,plain,
( ~ root(A,C)
| ~ subactivity_occurrence(A,B)
| ~ occurrence_of(B,C)
| root_occ(A,B) ),
inference(clausify,[status(thm)],[sos_10]) ).
fof(nnf_31,plain,
! [X91,X92] :
( ? [X93] :
( subactivity_occurrence(X93,X92)
& root(X93,X91) )
| atomic(X91)
| ~ occurrence_of(X92,X91) ),
inference(fof_nnf,[status(thm)],[sos_30]) ).
fof(sk_sos_30_sk,plain,
! [X91,X92] :
( ( subactivity_occurrence(sK3(X91,X92),X92)
& root(sK3(X91,X92),X91) )
| atomic(X91)
| ~ occurrence_of(X92,X91) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X93,sK3(X91,X92))],[nnf_31]) ).
fof(sk_sos_30,plain,
( ! [VAR_0,VAR_1] :
( subactivity_occurrence(sK3(VAR_1,VAR_0),VAR_0)
| atomic(VAR_1)
| ~ occurrence_of(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( root(sK3(VAR_1,VAR_0),VAR_1)
| atomic(VAR_1)
| ~ occurrence_of(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_sos_30_sk]) ).
cnf(c_57,plain,
( root(sK3(B,A),B)
| atomic(B)
| ~ occurrence_of(A,B) ),
inference(split_conjunct,[status(thm)],[sk_sos_30]) ).
cnf(c_103,plain,
( ~ subactivity_occurrence(sK3(B,A),C)
| ~ occurrence_of(C,B)
| root_occ(sK3(B,A),C)
| atomic(B)
| ~ occurrence_of(A,B) ),
inference(resolve,[status(thm)],[c_57,c_50]) ).
cnf(c_113,plain,
( min_precedes(B,sK2(B,A),tptp0)
| leaf_occ(B,A)
| ~ arboreal(B)
| ~ subactivity_occurrence(B,A)
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_43,c_38]) ).
cnf(c_115,plain,
( arboreal(sK2(B,A))
| leaf_occ(B,A)
| ~ arboreal(B)
| ~ subactivity_occurrence(B,A)
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_43,c_41]) ).
cnf(c_116,plain,
( min_precedes(sK0(A),sK1(A),tptp0)
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_42,c_38]) ).
cnf(c_117,plain,
( ~ min_precedes(B,sK1(A),tptp0)
| ~ min_precedes(sK0(A),B,tptp0)
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_42,c_37]) ).
cnf(c_118,plain,
( arboreal(sK0(A))
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_42,c_40]) ).
cnf(c_119,plain,
( arboreal(sK1(A))
| ~ occurrence_of(A,tptp0) ),
inference(resolve,[status(thm)],[c_42,c_41]) ).
fof(nnf_35,plain,
? [X101] : occurrence_of(X101,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(X101,sK4)],[nnf_35]) ).
cnf(c_126,negated_conjecture,
occurrence_of(sK4,tptp0),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_127,plain,
( occurrence_of(sK2(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_132,plain,
tptp1 != tptp3,
inference(clausify,[status(thm)],[sos_42]) ).
cnf(c_133,plain,
tptp3 != tptp1,
inference(copy,[status(thm)],[c_132]) ).
fof(sos_34,axiom,
~ atomic(tptp0),
file('theBenchmark.p',sos_34) ).
cnf(c_142,plain,
~ atomic(tptp0),
inference(clausify,[status(thm)],[sos_34]) ).
cnf(c_143,plain,
( leaf_occ(sK1(A),A)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_144,plain,
( occurrence_of(sK1(A),tptp3)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_145,plain,
( root_occ(sK0(A),A)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_147,plain,
( subactivity_occurrence(sK3(B,A),A)
| atomic(B)
| ~ occurrence_of(A,B) ),
inference(split_conjunct,[status(thm)],[sk_sos_30]) ).
cnf(c_148,plain,
( D = C
| min_precedes(D,C,B)
| min_precedes(C,D,B)
| ~ subactivity_occurrence(D,A)
| ~ subactivity_occurrence(C,A)
| ~ arboreal(D)
| ~ arboreal(C)
| ~ occurrence_of(A,B) ),
inference(clausify,[status(thm)],[sos_28]) ).
fof(nnf_25,plain,
! [X70,X71,X72] :
( ? [X73] :
( subactivity_occurrence(X72,X73)
& subactivity_occurrence(X71,X73)
& occurrence_of(X73,X70) )
| ~ min_precedes(X71,X72,X70) ),
inference(fof_nnf,[status(thm)],[sos_24]) ).
fof(sk_sos_24_sk,plain,
! [X70,X71,X72] :
( ( subactivity_occurrence(X72,sK5(X70,X71,X72))
& subactivity_occurrence(X71,sK5(X70,X71,X72))
& occurrence_of(sK5(X70,X71,X72),X70) )
| ~ min_precedes(X71,X72,X70) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X73,sK5(X70,X71,X72))],[nnf_25]) ).
fof(sk_sos_24,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_24_sk]) ).
cnf(c_153,plain,
( subactivity_occurrence(B,sK5(C,A,B))
| ~ min_precedes(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_sos_24]) ).
cnf(c_154,plain,
( subactivity_occurrence(A,sK5(C,A,B))
| ~ min_precedes(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_sos_24]) ).
cnf(c_155,plain,
( occurrence_of(sK5(C,A,B),C)
| ~ min_precedes(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_sos_24]) ).
cnf(c_158,plain,
( C = B
| ~ occurrence_of(A,C)
| ~ occurrence_of(A,B) ),
inference(clausify,[status(thm)],[sos_22]) ).
cnf(c_159,plain,
( ~ min_precedes(C,D,B)
| ~ leaf_occ(C,A)
| ~ occurrence_of(A,B) ),
inference(clausify,[status(thm)],[sos_21]) ).
cnf(c_169,plain,
( subactivity_occurrence(A,B)
| ~ leaf_occ(A,B) ),
inference(clausify,[status(thm)],[sos_11]) ).
cnf(c_171,plain,
( subactivity_occurrence(A,B)
| ~ root_occ(A,B) ),
inference(clausify,[status(thm)],[sos_10]) ).
cnf(c_175,plain,
( D = C
| ~ root_occ(D,A)
| ~ root_occ(C,A)
| ~ occurrence_of(A,B) ),
inference(clausify,[status(thm)],[sos_02]) ).
cnf(c_203,plain,
( ~ subactivity_occurrence(sK3(B,A),A)
| root_occ(sK3(B,A),A)
| atomic(B)
| ~ occurrence_of(A,B) ),
inference(factor,[status(thm)],[c_103]) ).
cnf(c_213,plain,
arboreal(sK0(sK4)),
inference(resolve,[status(thm)],[c_126,c_118]) ).
cnf(c_215,plain,
min_precedes(sK0(sK4),sK1(sK4),tptp0),
inference(resolve,[status(thm)],[c_126,c_116]) ).
cnf(c_216,plain,
( arboreal(sK2(A,sK4))
| leaf_occ(A,sK4)
| ~ arboreal(A)
| ~ subactivity_occurrence(A,sK4) ),
inference(resolve,[status(thm)],[c_126,c_115]) ).
cnf(c_15380,negated_conjecture,
( ~ subactivity_occurrence(sK3(tptp0,sK4),A)
| ~ occurrence_of(A,tptp0)
| root_occ(sK3(tptp0,sK4),A)
| atomic(tptp0) ),
inference(resolve,[status(thm)],[c_126,c_103]) ).
cnf(c_223,negated_conjecture,
( ~ subactivity_occurrence(sK3(tptp0,sK4),A)
| ~ occurrence_of(A,tptp0)
| root_occ(sK3(tptp0,sK4),A) ),
inference(resolve,[status(thm)],[c_142,c_15380]) ).
cnf(c_257,plain,
root_occ(sK0(sK4),sK4),
inference(resolve,[status(thm)],[c_145,c_126]) ).
cnf(c_15381,negated_conjecture,
( subactivity_occurrence(sK3(tptp0,sK4),sK4)
| atomic(tptp0) ),
inference(resolve,[status(thm)],[c_147,c_126]) ).
cnf(c_259,negated_conjecture,
subactivity_occurrence(sK3(tptp0,sK4),sK4),
inference(resolve,[status(thm)],[c_142,c_15381]) ).
cnf(c_262,plain,
( ~ min_precedes(A,B,tptp0)
| ~ leaf_occ(A,sK4) ),
inference(resolve,[status(thm)],[c_159,c_126]) ).
cnf(c_271,plain,
( B = A
| ~ root_occ(B,sK4)
| ~ root_occ(A,sK4) ),
inference(resolve,[status(thm)],[c_175,c_126]) ).
cnf(c_15382,negated_conjecture,
( ~ subactivity_occurrence(sK3(tptp0,sK4),sK4)
| root_occ(sK3(tptp0,sK4),sK4)
| atomic(tptp0) ),
inference(resolve,[status(thm)],[c_203,c_126]) ).
cnf(c_15383,negated_conjecture,
( ~ subactivity_occurrence(sK3(tptp0,sK4),sK4)
| root_occ(sK3(tptp0,sK4),sK4) ),
inference(resolve,[status(thm)],[c_142,c_15382]) ).
cnf(c_285,negated_conjecture,
root_occ(sK3(tptp0,sK4),sK4),
inference(resolve,[status(thm)],[c_259,c_15383]) ).
cnf(c_331,plain,
subactivity_occurrence(sK0(sK4),sK4),
inference(resolve,[status(thm)],[c_257,c_171]) ).
cnf(c_340,plain,
~ leaf_occ(sK0(sK4),sK4),
inference(resolve,[status(thm)],[c_215,c_262]) ).
cnf(c_15384,plain,
( A = sK0(sK4)
| ~ root_occ(A,sK4) ),
inference(resolve,[status(thm)],[c_271,c_257]) ).
cnf(c_378,plain,
( sK0(sK4) = A
| ~ root_occ(A,sK4) ),
inference(copy,[status(thm)],[c_15384]) ).
cnf(c_15385,plain,
( arboreal(sK2(sK0(sK4),sK4))
| leaf_occ(sK0(sK4),sK4)
| ~ subactivity_occurrence(sK0(sK4),sK4) ),
inference(resolve,[status(thm)],[c_216,c_213]) ).
cnf(c_15386,plain,
( arboreal(sK2(sK0(sK4),sK4))
| leaf_occ(sK0(sK4),sK4) ),
inference(resolve,[status(thm)],[c_331,c_15385]) ).
cnf(c_387,plain,
arboreal(sK2(sK0(sK4),sK4)),
inference(resolve,[status(thm)],[c_340,c_15386]) ).
cnf(c_15387,plain,
( occurrence_of(sK2(sK0(sK4),sK4),tptp1)
| leaf_occ(sK0(sK4),sK4)
| ~ arboreal(sK0(sK4))
| ~ occurrence_of(sK4,tptp0) ),
inference(resolve,[status(thm)],[c_331,c_127]) ).
cnf(c_15388,negated_conjecture,
( occurrence_of(sK2(sK0(sK4),sK4),tptp1)
| leaf_occ(sK0(sK4),sK4)
| ~ arboreal(sK0(sK4)) ),
inference(resolve,[status(thm)],[c_126,c_15387]) ).
cnf(c_15389,negated_conjecture,
( occurrence_of(sK2(sK0(sK4),sK4),tptp1)
| leaf_occ(sK0(sK4),sK4) ),
inference(resolve,[status(thm)],[c_213,c_15388]) ).
cnf(c_412,negated_conjecture,
occurrence_of(sK2(sK0(sK4),sK4),tptp1),
inference(resolve,[status(thm)],[c_340,c_15389]) ).
cnf(c_15390,plain,
( min_precedes(sK0(sK4),sK2(sK0(sK4),sK4),tptp0)
| leaf_occ(sK0(sK4),sK4)
| ~ arboreal(sK0(sK4))
| ~ occurrence_of(sK4,tptp0) ),
inference(resolve,[status(thm)],[c_331,c_113]) ).
cnf(c_15391,negated_conjecture,
( min_precedes(sK0(sK4),sK2(sK0(sK4),sK4),tptp0)
| leaf_occ(sK0(sK4),sK4)
| ~ arboreal(sK0(sK4)) ),
inference(resolve,[status(thm)],[c_126,c_15390]) ).
cnf(c_15392,negated_conjecture,
( min_precedes(sK0(sK4),sK2(sK0(sK4),sK4),tptp0)
| leaf_occ(sK0(sK4),sK4) ),
inference(resolve,[status(thm)],[c_213,c_15391]) ).
cnf(c_414,negated_conjecture,
min_precedes(sK0(sK4),sK2(sK0(sK4),sK4),tptp0),
inference(resolve,[status(thm)],[c_340,c_15392]) ).
cnf(c_15393,plain,
sK0(sK4) = sK3(tptp0,sK4),
inference(resolve,[status(thm)],[c_378,c_285]) ).
cnf(c_453,plain,
sK3(tptp0,sK4) = sK0(sK4),
inference(copy,[status(thm)],[c_15393]) ).
cnf(c_15394,negated_conjecture,
( ~ subactivity_occurrence(sK3(tptp0,sK4),A)
| ~ occurrence_of(A,tptp0)
| root_occ(sK0(sK4),A) ),
inference(paramod,[status(thm)],[c_453,c_223]) ).
cnf(c_454,negated_conjecture,
( ~ subactivity_occurrence(sK0(sK4),A)
| ~ occurrence_of(A,tptp0)
| root_occ(sK0(sK4),A) ),
inference(paramod,[status(thm)],[c_453,c_15394]) ).
cnf(c_464,plain,
( sK2(sK0(sK4),sK4) = C
| min_precedes(sK2(sK0(sK4),sK4),C,B)
| min_precedes(C,sK2(sK0(sK4),sK4),B)
| ~ subactivity_occurrence(sK2(sK0(sK4),sK4),A)
| ~ subactivity_occurrence(C,A)
| ~ arboreal(C)
| ~ occurrence_of(A,B) ),
inference(resolve,[status(thm)],[c_387,c_148]) ).
cnf(c_512,plain,
( tptp1 = A
| ~ occurrence_of(sK2(sK0(sK4),sK4),A) ),
inference(resolve,[status(thm)],[c_412,c_158]) ).
cnf(c_795,plain,
occurrence_of(sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4)),tptp0),
inference(resolve,[status(thm)],[c_414,c_155]) ).
cnf(c_796,plain,
subactivity_occurrence(sK0(sK4),sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))),
inference(resolve,[status(thm)],[c_414,c_154]) ).
cnf(c_797,plain,
subactivity_occurrence(sK2(sK0(sK4),sK4),sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))),
inference(resolve,[status(thm)],[c_414,c_153]) ).
cnf(c_15395,plain,
( ~ subactivity_occurrence(sK0(sK4),sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4)))
| root_occ(sK0(sK4),sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))) ),
inference(resolve,[status(thm)],[c_795,c_454]) ).
cnf(c_1854,plain,
root_occ(sK0(sK4),sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))),
inference(resolve,[status(thm)],[c_796,c_15395]) ).
cnf(c_1884,plain,
( B = A
| ~ root_occ(B,sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4)))
| ~ root_occ(A,sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))) ),
inference(resolve,[status(thm)],[c_795,c_175]) ).
cnf(c_1889,plain,
( ~ min_precedes(A,B,tptp0)
| ~ leaf_occ(A,sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))) ),
inference(resolve,[status(thm)],[c_795,c_159]) ).
cnf(c_1894,plain,
root_occ(sK0(sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))),sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))),
inference(resolve,[status(thm)],[c_795,c_145]) ).
cnf(c_1895,plain,
occurrence_of(sK1(sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))),tptp3),
inference(resolve,[status(thm)],[c_795,c_144]) ).
cnf(c_1896,plain,
leaf_occ(sK1(sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))),sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))),
inference(resolve,[status(thm)],[c_795,c_143]) ).
cnf(c_1898,plain,
arboreal(sK1(sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4)))),
inference(resolve,[status(thm)],[c_795,c_119]) ).
cnf(c_1900,plain,
( ~ min_precedes(A,sK1(sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))),tptp0)
| ~ min_precedes(sK0(sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))),A,tptp0) ),
inference(resolve,[status(thm)],[c_795,c_117]) ).
cnf(c_15396,plain,
( sK2(sK0(sK4),sK4) = A
| min_precedes(sK2(sK0(sK4),sK4),A,tptp0)
| min_precedes(A,sK2(sK0(sK4),sK4),tptp0)
| ~ subactivity_occurrence(sK2(sK0(sK4),sK4),sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4)))
| ~ subactivity_occurrence(A,sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4)))
| ~ arboreal(A) ),
inference(resolve,[status(thm)],[c_464,c_795]) ).
cnf(c_1913,plain,
( sK2(sK0(sK4),sK4) = A
| min_precedes(sK2(sK0(sK4),sK4),A,tptp0)
| min_precedes(A,sK2(sK0(sK4),sK4),tptp0)
| ~ subactivity_occurrence(A,sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4)))
| ~ arboreal(A) ),
inference(resolve,[status(thm)],[c_797,c_15396]) ).
cnf(c_15397,plain,
( A = sK0(sK4)
| ~ root_occ(A,sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))) ),
inference(resolve,[status(thm)],[c_1884,c_1854]) ).
cnf(c_11637,plain,
( sK0(sK4) = A
| ~ root_occ(A,sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))) ),
inference(copy,[status(thm)],[c_15397]) ).
cnf(c_15398,plain,
sK0(sK4) = sK0(sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))),
inference(resolve,[status(thm)],[c_1894,c_11637]) ).
cnf(c_11641,plain,
sK0(sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))) = sK0(sK4),
inference(copy,[status(thm)],[c_15398]) ).
cnf(c_11643,plain,
( ~ min_precedes(A,sK1(sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))),tptp0)
| ~ min_precedes(sK0(sK4),A,tptp0) ),
inference(paramod,[status(thm)],[c_11641,c_1900]) ).
cnf(c_11673,plain,
~ min_precedes(sK2(sK0(sK4),sK4),sK1(sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))),tptp0),
inference(resolve,[status(thm)],[c_11643,c_414]) ).
cnf(c_11800,plain,
~ min_precedes(sK1(sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))),A,tptp0),
inference(resolve,[status(thm)],[c_1896,c_1889]) ).
cnf(c_11803,plain,
subactivity_occurrence(sK1(sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))),sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))),
inference(resolve,[status(thm)],[c_1896,c_169]) ).
cnf(c_15399,plain,
( sK2(sK0(sK4),sK4) = sK1(sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4)))
| min_precedes(sK2(sK0(sK4),sK4),sK1(sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))),tptp0)
| min_precedes(sK1(sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))),sK2(sK0(sK4),sK4),tptp0)
| ~ subactivity_occurrence(sK1(sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))),sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))) ),
inference(resolve,[status(thm)],[c_1913,c_1898]) ).
cnf(c_15400,plain,
( sK1(sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))) = sK2(sK0(sK4),sK4)
| min_precedes(sK2(sK0(sK4),sK4),sK1(sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))),tptp0)
| min_precedes(sK1(sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))),sK2(sK0(sK4),sK4),tptp0)
| ~ subactivity_occurrence(sK1(sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))),sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))) ),
inference(copy,[status(thm)],[c_15399]) ).
cnf(c_15401,plain,
( sK1(sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))) = sK2(sK0(sK4),sK4)
| min_precedes(sK2(sK0(sK4),sK4),sK1(sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))),tptp0)
| min_precedes(sK1(sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))),sK2(sK0(sK4),sK4),tptp0) ),
inference(resolve,[status(thm)],[c_11803,c_15400]) ).
cnf(c_15402,plain,
( sK1(sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))) = sK2(sK0(sK4),sK4)
| min_precedes(sK2(sK0(sK4),sK4),sK1(sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))),tptp0) ),
inference(resolve,[status(thm)],[c_11800,c_15401]) ).
cnf(c_14761,plain,
sK1(sK5(tptp0,sK0(sK4),sK2(sK0(sK4),sK4))) = sK2(sK0(sK4),sK4),
inference(resolve,[status(thm)],[c_11673,c_15402]) ).
cnf(c_15218,plain,
occurrence_of(sK2(sK0(sK4),sK4),tptp3),
inference(paramod,[status(thm)],[c_14761,c_1895]) ).
cnf(c_15403,plain,
tptp1 = tptp3,
inference(resolve,[status(thm)],[c_15218,c_512]) ).
cnf(c_15404,plain,
tptp3 = tptp1,
inference(copy,[status(thm)],[c_15403]) ).
cnf(c_15379,plain,
$false,
inference(resolve,[status(thm)],[c_133,c_15404]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : PRO006+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sat Sep 26 04:56:19 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.30 % Process 3941376 was started by sandbox2 on n012,
% 0.03/0.30 % Sat Sep 26 04:56:19 2026
% 0.03/0.30 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.03/0.31
% 0.03/0.31 % From the command line: assign(max_seconds, 300).
% 23.82/3.49
% 23.82/3.49 % given #500 (F,wt=27): 1537 -leaf_occ(f15(f8(f16(c1),tptp0)),c1). [resolve(1532,a,262,b)].
% 23.82/3.49
% 23.82/3.49 % given #1000 (W,wt=36): 922 occurrence_of(f9(tptp0,f15(c1),f16(c1)),f3(f16(c1),f9(tptp0,f15(c1),f16(c1)))). [resolve(710,a,170,a)].
% 23.82/3.49
% 23.82/3.49 % given #1500 (F,wt=38): 6620 -earlier(f5(f15(f10(f16(c1),tptp0)),tptp0),f15(f10(f16(c1),tptp0))). [resolve(6548,a,173,b)].
% 23.82/3.49
% 23.82/3.49 % given #2000 (T,wt=41): 5445 -occurrence_of(f17(f15(c1),f9(tptp0,f15(c1),f5(f15(c1),tptp0))),A) | tptp1 = A. [resolve(1952,a,158,b)].
% 23.82/3.49
% 23.82/3.49 % given #2500 (T,wt=42): 12092 -subactivity_occurrence(f4(f16(c1),tptp0),f16(c1)) | -subactivity_occurrence(f16(c1),f16(c1)) | min_precedes(f16(c1),f4(f16(c1),tptp0),tptp3) | f4(f16(c1),tptp0) = f16(c1). [resolve(12025,a,1162,a),flip(d)].
% 23.82/3.49
% 23.82/3.49 % SZS status Theorem for theBenchmark
% 23.82/3.49
% 23.82/3.49 % Proof 1 at 2.37 (+ 0.35) seconds.
% 23.82/3.49 % Length of proof is 87.
% 23.82/3.49 % Level of proof is 14.
% 23.82/3.49 % Maximum clause weight is 52.000.
% 23.82/3.49 % Given clauses 2842.
% 23.82/3.49
% 23.82/3.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------