%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : PRO009+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n026.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 : Fri Sep 25 02:31:35 PM UTC 2026
% Result : Theorem 3.74s 1.21s
% Output : CNFRefutation 3.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 9
% Syntax : Number of formulae : 105 ( 12 unt; 0 def)
% Number of atoms : 383 ( 32 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 488 ( 210 ~; 203 |; 63 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 195 ( 0 sgn 176 !; 19 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1,X2,X3] :
( ( ~ min_precedes(X2,X3,X0)
& arboreal(X2)
& leaf_occ(X3,X1)
& subactivity_occurrence(X2,X1)
& occurrence_of(X1,X0) )
=> X3 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_02) ).
fof(f9,axiom,
! [X0,X1,X2] :
( ( occurrence_of(X0,X2)
& occurrence_of(X0,X1) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_08) ).
fof(f10,axiom,
! [X0,X1,X2] :
( ( leaf_occ(X1,X0)
& occurrence_of(X0,X2) )
=> ~ ? [X3] : min_precedes(X1,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_09) ).
fof(f17,axiom,
! [X0,X1] :
( occurrence_of(X0,X1)
=> ( arboreal(X0)
<=> atomic(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_16) ).
fof(f20,axiom,
! [X0,X1] :
( root_occ(X0,X1)
<=> ? [X2] :
( root(X0,X2)
& subactivity_occurrence(X0,X1)
& occurrence_of(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_19) ).
fof(f27,axiom,
! [X0,X1,X2] :
( next_subocc(X0,X1,X2)
<=> ( ~ ? [X3] :
( min_precedes(X3,X1,X2)
& min_precedes(X0,X3,X2) )
& min_precedes(X0,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_26) ).
fof(f33,axiom,
! [X0] :
( occurrence_of(X0,tptp0)
=> ? [X1,X2,X3] :
( leaf_occ(X3,X0)
& next_subocc(X2,X3,tptp0)
& ( occurrence_of(X3,tptp1)
| occurrence_of(X3,tptp2) )
& next_subocc(X1,X2,tptp0)
& occurrence_of(X2,tptp4)
& root_occ(X1,X0)
& occurrence_of(X1,tptp3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_32) ).
fof(f39,axiom,
atomic(tptp3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_38) ).
fof(f46,conjecture,
! [X0] :
( occurrence_of(X0,tptp0)
=> ? [X1,X2] :
( leaf_occ(X2,X0)
& min_precedes(X1,X2,tptp0)
& ( occurrence_of(X2,tptp1)
| occurrence_of(X2,tptp2) )
& root_occ(X1,X0)
& occurrence_of(X1,tptp3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f47,negated_conjecture,
~ ! [X0] :
( occurrence_of(X0,tptp0)
=> ? [X1,X2] :
( leaf_occ(X2,X0)
& min_precedes(X1,X2,tptp0)
& ( occurrence_of(X2,tptp1)
| occurrence_of(X2,tptp2) )
& root_occ(X1,X0)
& occurrence_of(X1,tptp3) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f51,plain,
? [X0] :
( occurrence_of(X0,tptp0)
& ! [X1,X2] :
( ~ leaf_occ(X2,X0)
| ~ min_precedes(X1,X2,tptp0)
| ( ~ occurrence_of(X2,tptp1)
& ~ occurrence_of(X2,tptp2) )
| ~ root_occ(X1,X0)
| ~ occurrence_of(X1,tptp3) ) ),
inference(ennf_transformation,[],[f47]) ).
fof(f52,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| ? [X1,X2,X3] :
( leaf_occ(X3,X0)
& next_subocc(X2,X3,tptp0)
& ( occurrence_of(X3,tptp1)
| occurrence_of(X3,tptp2) )
& next_subocc(X1,X2,tptp0)
& occurrence_of(X2,tptp4)
& root_occ(X1,X0)
& occurrence_of(X1,tptp3) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ~ leaf_occ(X1,X0)
| ~ occurrence_of(X0,X2)
| ! [X3] : ~ min_precedes(X1,X3,X2) ),
inference(ennf_transformation,[],[f10]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ~ leaf_occ(X1,X0)
| ~ occurrence_of(X0,X2)
| ! [X3] : ~ min_precedes(X1,X3,X2) ),
inference(flattening,[],[f61]) ).
fof(f67,plain,
! [X0,X1,X2] :
( next_subocc(X0,X1,X2)
<=> ( ! [X3] :
( ~ min_precedes(X3,X1,X2)
| ~ min_precedes(X0,X3,X2) )
& min_precedes(X0,X1,X2) ) ),
inference(ennf_transformation,[],[f27]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ~ occurrence_of(X0,X2)
| ~ occurrence_of(X0,X1)
| X1 = X2 ),
inference(ennf_transformation,[],[f9]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ~ occurrence_of(X0,X2)
| ~ occurrence_of(X0,X1)
| X1 = X2 ),
inference(flattening,[],[f69]) ).
fof(f77,plain,
! [X0,X1] :
( ~ occurrence_of(X0,X1)
| ( arboreal(X0)
<=> atomic(X1) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f80,plain,
! [X0,X1,X2,X3] :
( min_precedes(X2,X3,X0)
| ~ arboreal(X2)
| ~ leaf_occ(X3,X1)
| ~ subactivity_occurrence(X2,X1)
| ~ occurrence_of(X1,X0)
| X3 = X2 ),
inference(ennf_transformation,[],[f3]) ).
fof(f81,plain,
! [X0,X1,X2,X3] :
( min_precedes(X2,X3,X0)
| ~ arboreal(X2)
| ~ leaf_occ(X3,X1)
| ~ subactivity_occurrence(X2,X1)
| ~ occurrence_of(X1,X0)
| X3 = X2 ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
( occurrence_of(sK0,tptp0)
& ! [X1,X2] :
( ~ leaf_occ(X2,sK0)
| ~ min_precedes(X1,X2,tptp0)
| ( ~ occurrence_of(X2,tptp1)
& ~ occurrence_of(X2,tptp2) )
| ~ root_occ(X1,sK0)
| ~ occurrence_of(X1,tptp3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f51]) ).
fof(f83,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| ( leaf_occ(sK3(X0),X0)
& next_subocc(sK2(X0),sK3(X0),tptp0)
& ( occurrence_of(sK3(X0),tptp1)
| occurrence_of(sK3(X0),tptp2) )
& next_subocc(sK1(X0),sK2(X0),tptp0)
& occurrence_of(sK2(X0),tptp4)
& root_occ(sK1(X0),X0)
& occurrence_of(sK1(X0),tptp3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X1,sK1(X0)),skolemize(X2,sK2(X0)),skolemize(X3,sK3(X0))],[f52]) ).
fof(f84,plain,
! [X0,X1] :
( ( ~ root_occ(X0,X1)
| ? [X2] :
( root(X0,X2)
& subactivity_occurrence(X0,X1)
& occurrence_of(X1,X2) ) )
& ( ! [X2] :
( ~ root(X0,X2)
| ~ subactivity_occurrence(X0,X1)
| ~ occurrence_of(X1,X2) )
| root_occ(X0,X1) ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f85,plain,
! [X0,X1] :
( ( ~ root_occ(X0,X1)
| ? [X3] :
( root(X0,X3)
& subactivity_occurrence(X0,X1)
& occurrence_of(X1,X3) ) )
& ( ! [X2] :
( ~ root(X0,X2)
| ~ subactivity_occurrence(X0,X1)
| ~ occurrence_of(X1,X2) )
| root_occ(X0,X1) ) ),
inference(rectify,[],[f84]) ).
fof(f86,plain,
! [X0,X1] :
( ( ~ root_occ(X0,X1)
| ( root(X0,sK4(X0,X1))
& subactivity_occurrence(X0,X1)
& occurrence_of(X1,sK4(X0,X1)) ) )
& ( ! [X2] :
( ~ root(X0,X2)
| ~ subactivity_occurrence(X0,X1)
| ~ occurrence_of(X1,X2) )
| root_occ(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1))],[f85]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ( ~ next_subocc(X0,X1,X2)
| ( ! [X3] :
( ~ min_precedes(X3,X1,X2)
| ~ min_precedes(X0,X3,X2) )
& min_precedes(X0,X1,X2) ) )
& ( ? [X3] :
( min_precedes(X3,X1,X2)
& min_precedes(X0,X3,X2) )
| ~ min_precedes(X0,X1,X2)
| next_subocc(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f67]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ( ~ next_subocc(X0,X1,X2)
| ( ! [X3] :
( ~ min_precedes(X3,X1,X2)
| ~ min_precedes(X0,X3,X2) )
& min_precedes(X0,X1,X2) ) )
& ( ? [X3] :
( min_precedes(X3,X1,X2)
& min_precedes(X0,X3,X2) )
| ~ min_precedes(X0,X1,X2)
| next_subocc(X0,X1,X2) ) ),
inference(flattening,[],[f89]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ( ~ next_subocc(X0,X1,X2)
| ( ! [X4] :
( ~ min_precedes(X4,X1,X2)
| ~ min_precedes(X0,X4,X2) )
& min_precedes(X0,X1,X2) ) )
& ( ? [X3] :
( min_precedes(X3,X1,X2)
& min_precedes(X0,X3,X2) )
| ~ min_precedes(X0,X1,X2)
| next_subocc(X0,X1,X2) ) ),
inference(rectify,[],[f90]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ( ~ next_subocc(X0,X1,X2)
| ( ! [X4] :
( ~ min_precedes(X4,X1,X2)
| ~ min_precedes(X0,X4,X2) )
& min_precedes(X0,X1,X2) ) )
& ( ( min_precedes(sK7(X0,X1,X2),X1,X2)
& min_precedes(X0,sK7(X0,X1,X2),X2) )
| ~ min_precedes(X0,X1,X2)
| next_subocc(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X3,sK7(X0,X1,X2))],[f91]) ).
fof(f95,plain,
! [X0,X1] :
( ~ occurrence_of(X0,X1)
| ( ( ~ arboreal(X0)
| atomic(X1) )
& ( ~ atomic(X1)
| arboreal(X0) ) ) ),
inference(nnf_transformation,[],[f77]) ).
fof(f96,plain,
occurrence_of(sK0,tptp0),
inference(cnf_transformation,[],[f82]) ).
fof(f97,plain,
! [X2,X1] :
( ~ leaf_occ(X2,sK0)
| ~ min_precedes(X1,X2,tptp0)
| ~ occurrence_of(X2,tptp1)
| ~ root_occ(X1,sK0)
| ~ occurrence_of(X1,tptp3) ),
inference(cnf_transformation,[],[f82]) ).
fof(f98,plain,
! [X2,X1] :
( ~ leaf_occ(X2,sK0)
| ~ min_precedes(X1,X2,tptp0)
| ~ occurrence_of(X2,tptp2)
| ~ root_occ(X1,sK0)
| ~ occurrence_of(X1,tptp3) ),
inference(cnf_transformation,[],[f82]) ).
fof(f100,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| leaf_occ(sK3(X0),X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f102,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| occurrence_of(sK3(X0),tptp1)
| occurrence_of(sK3(X0),tptp2) ),
inference(cnf_transformation,[],[f83]) ).
fof(f103,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| next_subocc(sK1(X0),sK2(X0),tptp0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f105,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| root_occ(sK1(X0),X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f106,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| occurrence_of(sK1(X0),tptp3) ),
inference(cnf_transformation,[],[f83]) ).
fof(f110,plain,
atomic(tptp3),
inference(cnf_transformation,[],[f39]) ).
fof(f117,plain,
! [X0,X1] :
( ~ root_occ(X0,X1)
| root(X0,sK4(X0,X1)) ),
inference(cnf_transformation,[],[f86]) ).
fof(f118,plain,
! [X0,X1] :
( ~ root_occ(X0,X1)
| subactivity_occurrence(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f119,plain,
! [X0,X1] :
( ~ root_occ(X0,X1)
| occurrence_of(X1,sK4(X0,X1)) ),
inference(cnf_transformation,[],[f86]) ).
fof(f120,plain,
! [X2,X0,X1] :
( ~ root(X0,X2)
| ~ subactivity_occurrence(X0,X1)
| ~ occurrence_of(X1,X2)
| root_occ(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f124,plain,
! [X2,X3,X0,X1] :
( ~ leaf_occ(X1,X0)
| ~ occurrence_of(X0,X2)
| ~ min_precedes(X1,X3,X2) ),
inference(cnf_transformation,[],[f62]) ).
fof(f131,plain,
! [X2,X0,X1] :
( ~ next_subocc(X0,X1,X2)
| min_precedes(X0,X1,X2) ),
inference(cnf_transformation,[],[f92]) ).
fof(f136,plain,
! [X2,X0,X1] :
( ~ occurrence_of(X0,X2)
| ~ occurrence_of(X0,X1)
| X1 = X2 ),
inference(cnf_transformation,[],[f70]) ).
fof(f147,plain,
! [X0,X1] :
( ~ occurrence_of(X0,X1)
| ~ atomic(X1)
| arboreal(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f149,plain,
! [X2,X3,X0,X1] :
( min_precedes(X2,X3,X0)
| ~ arboreal(X2)
| ~ leaf_occ(X3,X1)
| ~ subactivity_occurrence(X2,X1)
| ~ occurrence_of(X1,X0)
| X2 = X3 ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_49,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ leaf_occ(X1,sK0)
| ~ root_occ(X0,sK0)
| ~ occurrence_of(X1,tptp2)
| ~ occurrence_of(X0,tptp3)
| ~ min_precedes(X0,X1,tptp0) ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_50,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ leaf_occ(X1,sK0)
| ~ root_occ(X0,sK0)
| ~ occurrence_of(X1,tptp1)
| ~ occurrence_of(X0,tptp3)
| ~ min_precedes(X0,X1,tptp0) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_51,negated_conjecture,
occurrence_of(sK0,tptp0),
inference(cnf_transformation,[],[f96]) ).
tcf(c_53,plain,
! [X0: $i] :
( occurrence_of(sK1(X0),tptp3)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_54,plain,
! [X0: $i] :
( root_occ(sK1(X0),X0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_56,plain,
! [X0: $i] :
( next_subocc(sK1(X0),sK2(X0),tptp0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_57,plain,
! [X0: $i] :
( occurrence_of(sK3(X0),tptp1)
| occurrence_of(sK3(X0),tptp2)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_59,plain,
! [X0: $i] :
( leaf_occ(sK3(X0),X0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_63,plain,
atomic(tptp3),
inference(cnf_transformation,[],[f110]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( root_occ(X2,X0)
| ~ root(X2,X1)
| ~ subactivity_occurrence(X2,X0)
| ~ occurrence_of(X0,X1) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( occurrence_of(X1,sK4(X0,X1))
| ~ root_occ(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( subactivity_occurrence(X0,X1)
| ~ root_occ(X0,X1) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( root(X0,sK4(X0,X1))
| ~ root_occ(X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ leaf_occ(X0,X3)
| ~ occurrence_of(X3,X2)
| ~ min_precedes(X0,X1,X2) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] :
( min_precedes(X0,X1,X2)
| ~ next_subocc(X0,X1,X2) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ occurrence_of(X0,X2)
| ~ occurrence_of(X0,X1) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( arboreal(X0)
| ~ atomic(X1)
| ~ occurrence_of(X0,X1) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( min_precedes(X3,X2,X1)
| ( X2 = X3 )
| ~ arboreal(X3)
| ~ subactivity_occurrence(X3,X0)
| ~ leaf_occ(X2,X0)
| ~ occurrence_of(X0,X1) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_1958,plain,
! [X0: $i] :
( subactivity_occurrence(sK1(X0),X0)
| ~ occurrence_of(X0,tptp0) ),
inference(superposition,[status(thm)],[c_54,c_72]) ).
tcf(c_2019,plain,
! [X0: $i] :
( arboreal(sK1(X0))
| ~ atomic(tptp3)
| ~ occurrence_of(X0,tptp0) ),
inference(superposition,[status(thm)],[c_53,c_99]) ).
tcf(c_2029,plain,
! [X0: $i] :
( arboreal(sK1(X0))
| ~ occurrence_of(X0,tptp0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2019,c_63]) ).
tcf(c_2046,plain,
arboreal(sK1(sK0)),
inference(superposition,[status(thm)],[c_51,c_2029]) ).
tcf(c_2051,plain,
! [X0: $i] :
( min_precedes(sK1(X0),sK2(X0),tptp0)
| ~ occurrence_of(X0,tptp0) ),
inference(superposition,[status(thm)],[c_56,c_85]) ).
tcf(c_2399,plain,
! [X0: $i] :
( ( X0 = tptp0 )
| ~ occurrence_of(sK0,X0) ),
inference(superposition,[status(thm)],[c_51,c_89]) ).
tcf(c_2432,plain,
( occurrence_of(sK1(sK0),tptp3)
| ~ occurrence_of(sK0,tptp0) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_2434,plain,
( root_occ(sK1(sK0),sK0)
| ~ occurrence_of(sK0,tptp0) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_2460,plain,
! [X0: $i,X1: $i] :
( ~ occurrence_of(X1,tptp0)
| ~ occurrence_of(X0,tptp0)
| ~ leaf_occ(sK1(X0),X1) ),
inference(superposition,[status(thm)],[c_2051,c_77]) ).
tcf(c_2482,plain,
! [X0: $i] :
( ( sK4(X0,sK0) = tptp0 )
| ~ root_occ(X0,sK0) ),
inference(superposition,[status(thm)],[c_71,c_2399]) ).
tcf(c_2503,plain,
( ( sK4(sK1(sK0),sK0) = tptp0 )
| ~ occurrence_of(sK0,tptp0) ),
inference(superposition,[status(thm)],[c_54,c_2482]) ).
tcf(c_2504,plain,
sK4(sK1(sK0),sK0) = tptp0,
inference(forward_subsumption_resolution,[status(thm)],[c_2503,c_51]) ).
tcf(c_2506,plain,
( root(sK1(sK0),tptp0)
| ~ root_occ(sK1(sK0),sK0) ),
inference(superposition,[status(thm)],[c_2504,c_73]) ).
tcf(c_2530,plain,
root(sK1(sK0),tptp0),
inference(global_subsumption_just,[status(thm)],[c_2506,c_51,c_2434,c_2506]) ).
tcf(c_2594,plain,
! [X0: $i] :
( root_occ(X0,sK0)
| ~ root(X0,tptp0)
| ~ subactivity_occurrence(X0,sK0) ),
inference(superposition,[status(thm)],[c_51,c_70]) ).
tcf(c_2829,plain,
( root_occ(sK1(sK0),sK0)
| ~ occurrence_of(sK0,tptp0)
| ~ root(sK1(sK0),tptp0) ),
inference(superposition,[status(thm)],[c_1958,c_2594]) ).
tcf(c_2830,plain,
root_occ(sK1(sK0),sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_2829,c_51,c_2530]) ).
tcf(c_3059,plain,
! [X0: $i,X1: $i] :
( min_precedes(X1,X0,tptp0)
| ( X0 = X1 )
| ~ arboreal(X1)
| ~ subactivity_occurrence(X1,sK0)
| ~ leaf_occ(X0,sK0) ),
inference(superposition,[status(thm)],[c_51,c_102]) ).
tcf(c_3142,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ arboreal(X1)
| ~ subactivity_occurrence(X1,sK0)
| ~ leaf_occ(X0,sK0)
| ~ root_occ(X1,sK0)
| ~ occurrence_of(X1,tptp3)
| ~ occurrence_of(X0,tptp1) ),
inference(superposition,[status(thm)],[c_3059,c_50]) ).
tcf(c_3143,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ arboreal(X1)
| ~ subactivity_occurrence(X1,sK0)
| ~ leaf_occ(X0,sK0)
| ~ root_occ(X1,sK0)
| ~ occurrence_of(X1,tptp3)
| ~ occurrence_of(X0,tptp2) ),
inference(superposition,[status(thm)],[c_3059,c_49]) ).
tcf(c_3230,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ arboreal(X1)
| ~ leaf_occ(X0,sK0)
| ~ root_occ(X1,sK0)
| ~ occurrence_of(X1,tptp3)
| ~ occurrence_of(X0,tptp1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3142,c_72]) ).
tcf(c_3250,plain,
! [X0: $i] :
( ( sK1(sK0) = X0 )
| ~ arboreal(sK1(sK0))
| ~ leaf_occ(X0,sK0)
| ~ occurrence_of(X0,tptp1)
| ~ occurrence_of(sK1(sK0),tptp3) ),
inference(superposition,[status(thm)],[c_2830,c_3230]) ).
tcf(c_3251,plain,
! [X0: $i] :
( ( sK1(sK0) = X0 )
| ~ leaf_occ(X0,sK0)
| ~ occurrence_of(X0,tptp1)
| ~ occurrence_of(sK1(sK0),tptp3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3250,c_2046]) ).
tcf(c_3265,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ arboreal(X1)
| ~ leaf_occ(X0,sK0)
| ~ root_occ(X1,sK0)
| ~ occurrence_of(X1,tptp3)
| ~ occurrence_of(X0,tptp2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3143,c_72]) ).
tcf(c_3285,plain,
! [X0: $i] :
( ( sK1(sK0) = X0 )
| ~ arboreal(sK1(sK0))
| ~ leaf_occ(X0,sK0)
| ~ occurrence_of(X0,tptp2)
| ~ occurrence_of(sK1(sK0),tptp3) ),
inference(superposition,[status(thm)],[c_2830,c_3265]) ).
tcf(c_3286,plain,
! [X0: $i] :
( ( sK1(sK0) = X0 )
| ~ leaf_occ(X0,sK0)
| ~ occurrence_of(X0,tptp2)
| ~ occurrence_of(sK1(sK0),tptp3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3285,c_2046]) ).
tcf(c_4478,plain,
! [X0: $i] :
( ( sK1(sK0) = X0 )
| ~ leaf_occ(X0,sK0)
| ~ occurrence_of(X0,tptp1) ),
inference(global_subsumption_just,[status(thm)],[c_3251,c_51,c_2432,c_3251]) ).
tcf(c_4487,plain,
( ( sK1(sK0) = sK3(sK0) )
| ~ occurrence_of(sK0,tptp0)
| ~ occurrence_of(sK3(sK0),tptp1) ),
inference(superposition,[status(thm)],[c_59,c_4478]) ).
tcf(c_4488,plain,
( ( sK1(sK0) = sK3(sK0) )
| ~ occurrence_of(sK3(sK0),tptp1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4487,c_51]) ).
tcf(c_4495,plain,
( occurrence_of(sK3(sK0),tptp2)
| ( sK1(sK0) = sK3(sK0) )
| ~ occurrence_of(sK0,tptp0) ),
inference(superposition,[status(thm)],[c_57,c_4488]) ).
tcf(c_4496,plain,
( occurrence_of(sK3(sK0),tptp2)
| ( sK1(sK0) = sK3(sK0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4495,c_51]) ).
tcf(c_4714,plain,
! [X0: $i] :
( ( sK1(sK0) = X0 )
| ~ leaf_occ(X0,sK0)
| ~ occurrence_of(X0,tptp2) ),
inference(global_subsumption_just,[status(thm)],[c_3286,c_51,c_2432,c_3286]) ).
tcf(c_4723,plain,
( ( sK1(sK0) = sK3(sK0) )
| ~ occurrence_of(sK0,tptp0)
| ~ occurrence_of(sK3(sK0),tptp2) ),
inference(superposition,[status(thm)],[c_59,c_4714]) ).
tcf(c_4724,plain,
( ( sK1(sK0) = sK3(sK0) )
| ~ occurrence_of(sK3(sK0),tptp2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4723,c_51]) ).
tcf(c_4727,plain,
sK1(sK0) = sK3(sK0),
inference(global_subsumption_just,[status(thm)],[c_4724,c_4496,c_4724]) ).
tcf(c_4756,plain,
! [X0: $i] :
( ~ occurrence_of(sK0,tptp0)
| ~ occurrence_of(X0,tptp0)
| ~ leaf_occ(sK3(sK0),X0) ),
inference(superposition,[status(thm)],[c_4727,c_2460]) ).
tcf(c_4765,plain,
! [X0: $i] :
( ~ occurrence_of(X0,tptp0)
| ~ leaf_occ(sK3(sK0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4756,c_51]) ).
tcf(c_4832,plain,
~ occurrence_of(sK0,tptp0),
inference(superposition,[status(thm)],[c_59,c_4765]) ).
tcf(c_4833,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4832,c_51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PRO009+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 06:30:40 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.43
% 0.09/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.43
% 0.09/0.43 % Detected problem language: tptp
% 0.09/0.44 % Proving...
% 3.74/1.21 % SZS status Started for theBenchmark.p
% 3.74/1.21 % SZS status Theorem for theBenchmark.p
% 3.74/1.21
% 3.74/1.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.74/1.21
% 3.74/1.21 % ------ iProver source info
% 3.74/1.21
% 3.74/1.21 % git: date: 2026-07-19 20:42:38 +0200
% 3.74/1.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.74/1.21 % git: non_committed_changes: false
% 3.74/1.21
% 3.74/1.21 % ------ Parsing...
% 3.74/1.21 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.74/1.21
% 3.74/1.21 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.74/1.21
% 3.74/1.21 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.74/1.21
% 3.74/1.21 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.74/1.21 % ------ Proving...
% 3.74/1.21 % ------ Problem Properties
% 3.74/1.21
% 3.74/1.21 %
% 3.74/1.21 % clauses 54
% 3.74/1.21 % conjectures 3
% 3.74/1.21 % EPR 35
% 3.74/1.21 % Horn 45
% 3.74/1.21 % unary 12
% 3.74/1.21 % binary 22
% 3.74/1.21 % lits 137
% 3.74/1.21 % lits eq 12
% 3.74/1.21 % fd_pure 0
% 3.74/1.21 % fd_pseudo 0
% 3.74/1.21 % fd_cond 0
% 3.74/1.21 % fd_pseudo_cond 6
% 3.74/1.21 % AC symbols 0
% 3.74/1.21
% 3.74/1.21 % ------ Schedule dynamic 5 is on
% 3.74/1.21
% 3.74/1.21 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.74/1.21
% 3.74/1.21
% 3.74/1.21 % ------
% 3.74/1.21 % Current options:
% 3.74/1.21 % ------
% 3.74/1.21
% 3.74/1.21
% 3.74/1.21 %
% 3.74/1.21
% 3.74/1.21 % ------ Proving...
% 3.74/1.21 %
% 3.74/1.21
% 3.74/1.21 % SZS status Theorem for theBenchmark.p
% 3.74/1.21
% 3.74/1.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.74/1.21
% 3.74/1.21
%------------------------------------------------------------------------------