%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : PRO011+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 17:50:17 EDT 2022
% Result : Theorem 0.78s 0.97s
% Output : CNFRefutation 0.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 72 ( 13 unt; 1 def)
% Number of atoms : 289 ( 18 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 324 ( 107 ~; 105 |; 93 &)
% ( 8 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 135 ( 2 sgn 71 !; 37 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_11,axiom,
! [X35,X36] :
( leaf_occ(X35,X36)
<=> ? [X37] :
( occurrence_of(X36,X37)
& subactivity_occurrence(X35,X36)
& leaf(X35,X37) ) ) ).
fof(sos_14,axiom,
! [X42,X43] :
( leaf(X42,X43)
<=> ( ( root(X42,X43)
| ? [X44] : min_precedes(X44,X42,X43) )
& ~ ? [X45] : min_precedes(X42,X45,X43) ) ) ).
fof(sos_22,axiom,
! [X64,X65,X66] :
( ( occurrence_of(X64,X65)
& occurrence_of(X64,X66) )
=> X65 = X66 ) ).
fof(sos_32,axiom,
! [X95] :
( occurrence_of(X95,tptp0)
=> ? [X96,X97,X98] :
( occurrence_of(X96,tptp3)
& root_occ(X96,X95)
& occurrence_of(X97,tptp4)
& next_subocc(X96,X97,tptp0)
& ( occurrence_of(X98,tptp1)
| occurrence_of(X98,tptp2) )
& next_subocc(X97,X98,tptp0)
& leaf_occ(X98,X95) ) ) ).
fof(goals,conjecture,
! [X99] :
( occurrence_of(X99,tptp0)
=> ? [X100,X101] :
( leaf_occ(X101,X99)
& ( occurrence_of(X101,tptp1)
=> ~ ? [X102] :
( occurrence_of(X102,tptp2)
& subactivity_occurrence(X102,X99)
& min_precedes(X100,X102,tptp0) ) )
& ( occurrence_of(X101,tptp2)
=> ~ ? [X103] :
( occurrence_of(X103,tptp1)
& subactivity_occurrence(X103,X99)
& min_precedes(X100,X103,tptp0) ) ) ) ) ).
fof(definition_0,definition,
! [X100,X101] :
( definitionFOFtoCNF_0(X100,X101)
<=> ( occurrence_of(X101,tptp1)
& ? [X102] :
( min_precedes(X100,X102,tptp0)
& occurrence_of(X102,tptp2)
& subactivity_occurrence(X102,skolemFOFtoCNF_X99) ) ) ) ).
fof(subgoal_0,plain,
! [X99] :
( occurrence_of(X99,tptp0)
=> ? [X100,X101] :
( leaf_occ(X101,X99)
& ( occurrence_of(X101,tptp1)
=> ~ ? [X102] :
( occurrence_of(X102,tptp2)
& subactivity_occurrence(X102,X99)
& min_precedes(X100,X102,tptp0) ) )
& ( occurrence_of(X101,tptp2)
=> ~ ? [X103] :
( occurrence_of(X103,tptp1)
& subactivity_occurrence(X103,X99)
& min_precedes(X100,X103,tptp0) ) ) ) ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X99] :
( occurrence_of(X99,tptp0)
=> ? [X100,X101] :
( leaf_occ(X101,X99)
& ( occurrence_of(X101,tptp1)
=> ~ ? [X102] :
( occurrence_of(X102,tptp2)
& subactivity_occurrence(X102,X99)
& min_precedes(X100,X102,tptp0) ) )
& ( occurrence_of(X101,tptp2)
=> ~ ? [X103] :
( occurrence_of(X103,tptp1)
& subactivity_occurrence(X103,X99)
& min_precedes(X100,X103,tptp0) ) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X42,X43] :
( ~ leaf(X42,X43)
<=> ( ( ~ root(X42,X43)
& ! [X44] : ~ min_precedes(X44,X42,X43) )
| ? [X45] : min_precedes(X42,X45,X43) ) ),
inference(canonicalize,[],[sos_14]) ).
fof(normalize_0_1,plain,
! [X42,X43] :
( ~ leaf(X42,X43)
<=> ( ( ~ root(X42,X43)
& ! [X44] : ~ min_precedes(X44,X42,X43) )
| ? [X45] : min_precedes(X42,X45,X43) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X42,X43,X44,X45] :
( ( ~ leaf(X42,X43)
| ~ min_precedes(X42,X45,X43) )
& ( ~ leaf(X42,X43)
| min_precedes(skolemFOFtoCNF_X44(X42,X43),X42,X43)
| root(X42,X43) )
& ( ~ min_precedes(X44,X42,X43)
| leaf(X42,X43)
| min_precedes(X42,skolemFOFtoCNF_X45(X42,X43),X43) )
& ( ~ root(X42,X43)
| leaf(X42,X43)
| min_precedes(X42,skolemFOFtoCNF_X45(X42,X43),X43) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X42,X43,X45] :
( ~ leaf(X42,X43)
| ~ min_precedes(X42,X45,X43) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X100,X101] :
( ~ definitionFOFtoCNF_0(X100,X101)
<=> ( ~ occurrence_of(X101,tptp1)
| ! [X102] :
( ~ min_precedes(X100,X102,tptp0)
| ~ occurrence_of(X102,tptp2)
| ~ subactivity_occurrence(X102,skolemFOFtoCNF_X99) ) ) ),
inference(canonicalize,[],[definition_0]) ).
fof(normalize_0_5,plain,
! [X100,X101,X102] :
( ( ~ definitionFOFtoCNF_0(X100,X101)
| min_precedes(X100,skolemFOFtoCNF_X102(X100),tptp0) )
& ( ~ definitionFOFtoCNF_0(X100,X101)
| occurrence_of(X101,tptp1) )
& ( ~ definitionFOFtoCNF_0(X100,X101)
| occurrence_of(skolemFOFtoCNF_X102(X100),tptp2) )
& ( ~ definitionFOFtoCNF_0(X100,X101)
| subactivity_occurrence(skolemFOFtoCNF_X102(X100),skolemFOFtoCNF_X99) )
& ( ~ min_precedes(X100,X102,tptp0)
| ~ occurrence_of(X101,tptp1)
| ~ occurrence_of(X102,tptp2)
| ~ subactivity_occurrence(X102,skolemFOFtoCNF_X99)
| definitionFOFtoCNF_0(X100,X101) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X100,X101] :
( ~ definitionFOFtoCNF_0(X100,X101)
| min_precedes(X100,skolemFOFtoCNF_X102(X100),tptp0) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
? [X99] :
( occurrence_of(X99,tptp0)
& ! [X100,X101] :
( ~ leaf_occ(X101,X99)
| ( occurrence_of(X101,tptp1)
& ? [X102] :
( min_precedes(X100,X102,tptp0)
& occurrence_of(X102,tptp2)
& subactivity_occurrence(X102,X99) ) )
| ( occurrence_of(X101,tptp2)
& ? [X103] :
( min_precedes(X100,X103,tptp0)
& occurrence_of(X103,tptp1)
& subactivity_occurrence(X103,X99) ) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_8,plain,
( occurrence_of(skolemFOFtoCNF_X99,tptp0)
& ! [X100,X101] :
( ~ leaf_occ(X101,skolemFOFtoCNF_X99)
| ( occurrence_of(X101,tptp1)
& ? [X102] :
( min_precedes(X100,X102,tptp0)
& occurrence_of(X102,tptp2)
& subactivity_occurrence(X102,skolemFOFtoCNF_X99) ) )
| ( occurrence_of(X101,tptp2)
& ? [X103] :
( min_precedes(X100,X103,tptp0)
& occurrence_of(X103,tptp1)
& subactivity_occurrence(X103,skolemFOFtoCNF_X99) ) ) ) ),
inference(skolemize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
occurrence_of(skolemFOFtoCNF_X99,tptp0),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X95] :
( ~ occurrence_of(X95,tptp0)
| ? [X96,X97,X98] :
( leaf_occ(X98,X95)
& next_subocc(X96,X97,tptp0)
& next_subocc(X97,X98,tptp0)
& occurrence_of(X96,tptp3)
& occurrence_of(X97,tptp4)
& root_occ(X96,X95)
& ( occurrence_of(X98,tptp1)
| occurrence_of(X98,tptp2) ) ) ),
inference(canonicalize,[],[sos_32]) ).
fof(normalize_0_11,plain,
! [X95] :
( ~ occurrence_of(X95,tptp0)
| ? [X96,X97,X98] :
( leaf_occ(X98,X95)
& next_subocc(X96,X97,tptp0)
& next_subocc(X97,X98,tptp0)
& occurrence_of(X96,tptp3)
& occurrence_of(X97,tptp4)
& root_occ(X96,X95)
& ( occurrence_of(X98,tptp1)
| occurrence_of(X98,tptp2) ) ) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X95] :
( ( ~ occurrence_of(X95,tptp0)
| leaf_occ(skolemFOFtoCNF_X98(X95),X95) )
& ( ~ occurrence_of(X95,tptp0)
| next_subocc(skolemFOFtoCNF_X96(X95),skolemFOFtoCNF_X97(X95),tptp0) )
& ( ~ occurrence_of(X95,tptp0)
| next_subocc(skolemFOFtoCNF_X97(X95),skolemFOFtoCNF_X98(X95),tptp0) )
& ( ~ occurrence_of(X95,tptp0)
| occurrence_of(skolemFOFtoCNF_X96(X95),tptp3) )
& ( ~ occurrence_of(X95,tptp0)
| occurrence_of(skolemFOFtoCNF_X97(X95),tptp4) )
& ( ~ occurrence_of(X95,tptp0)
| root_occ(skolemFOFtoCNF_X96(X95),X95) )
& ( ~ occurrence_of(X95,tptp0)
| occurrence_of(skolemFOFtoCNF_X98(X95),tptp1)
| occurrence_of(skolemFOFtoCNF_X98(X95),tptp2) ) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X95] :
( ~ occurrence_of(X95,tptp0)
| leaf_occ(skolemFOFtoCNF_X98(X95),X95) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X100,X101] :
( ~ leaf_occ(X101,skolemFOFtoCNF_X99)
| ( occurrence_of(X101,tptp1)
& ? [X102] :
( min_precedes(X100,X102,tptp0)
& occurrence_of(X102,tptp2)
& subactivity_occurrence(X102,skolemFOFtoCNF_X99) ) )
| ( occurrence_of(X101,tptp2)
& ? [X103] :
( min_precedes(X100,X103,tptp0)
& occurrence_of(X103,tptp1)
& subactivity_occurrence(X103,skolemFOFtoCNF_X99) ) ) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_15,plain,
! [X100,X101] :
( ~ leaf_occ(X101,skolemFOFtoCNF_X99)
| ( occurrence_of(X101,tptp1)
& ? [X102] :
( min_precedes(X100,X102,tptp0)
& occurrence_of(X102,tptp2)
& subactivity_occurrence(X102,skolemFOFtoCNF_X99) ) )
| ( occurrence_of(X101,tptp2)
& ? [X103] :
( min_precedes(X100,X103,tptp0)
& occurrence_of(X103,tptp1)
& subactivity_occurrence(X103,skolemFOFtoCNF_X99) ) ) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [X100,X101] :
( ~ leaf_occ(X101,skolemFOFtoCNF_X99)
| definitionFOFtoCNF_0(X100,X101)
| ( occurrence_of(X101,tptp2)
& ? [X103] :
( min_precedes(X100,X103,tptp0)
& occurrence_of(X103,tptp1)
& subactivity_occurrence(X103,skolemFOFtoCNF_X99) ) ) ),
inference(simplify,[],[normalize_0_15,normalize_0_4]) ).
fof(normalize_0_17,plain,
! [X100,X101] :
( ( ~ leaf_occ(X101,skolemFOFtoCNF_X99)
| definitionFOFtoCNF_0(X100,X101)
| min_precedes(X100,skolemFOFtoCNF_X103(X100),tptp0) )
& ( ~ leaf_occ(X101,skolemFOFtoCNF_X99)
| definitionFOFtoCNF_0(X100,X101)
| occurrence_of(X101,tptp2) )
& ( ~ leaf_occ(X101,skolemFOFtoCNF_X99)
| definitionFOFtoCNF_0(X100,X101)
| occurrence_of(skolemFOFtoCNF_X103(X100),tptp1) )
& ( ~ leaf_occ(X101,skolemFOFtoCNF_X99)
| definitionFOFtoCNF_0(X100,X101)
| subactivity_occurrence(skolemFOFtoCNF_X103(X100),skolemFOFtoCNF_X99) ) ),
inference(clausify,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [X100,X101] :
( ~ leaf_occ(X101,skolemFOFtoCNF_X99)
| definitionFOFtoCNF_0(X100,X101)
| min_precedes(X100,skolemFOFtoCNF_X103(X100),tptp0) ),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [X35,X36] :
( ~ leaf_occ(X35,X36)
<=> ! [X37] :
( ~ leaf(X35,X37)
| ~ occurrence_of(X36,X37)
| ~ subactivity_occurrence(X35,X36) ) ),
inference(canonicalize,[],[sos_11]) ).
fof(normalize_0_20,plain,
! [X35,X36] :
( ~ leaf_occ(X35,X36)
<=> ! [X37] :
( ~ leaf(X35,X37)
| ~ occurrence_of(X36,X37)
| ~ subactivity_occurrence(X35,X36) ) ),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [X35,X36,X37] :
( ( ~ leaf_occ(X35,X36)
| leaf(X35,skolemFOFtoCNF_X37(X35,X36)) )
& ( ~ leaf_occ(X35,X36)
| occurrence_of(X36,skolemFOFtoCNF_X37(X35,X36)) )
& ( ~ leaf_occ(X35,X36)
| subactivity_occurrence(X35,X36) )
& ( ~ leaf(X35,X37)
| ~ occurrence_of(X36,X37)
| ~ subactivity_occurrence(X35,X36)
| leaf_occ(X35,X36) ) ),
inference(clausify,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [X35,X36] :
( ~ leaf_occ(X35,X36)
| leaf(X35,skolemFOFtoCNF_X37(X35,X36)) ),
inference(conjunct,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [X35,X36] :
( ~ leaf_occ(X35,X36)
| occurrence_of(X36,skolemFOFtoCNF_X37(X35,X36)) ),
inference(conjunct,[],[normalize_0_21]) ).
fof(normalize_0_24,plain,
! [X64,X65,X66] :
( ~ occurrence_of(X64,X65)
| ~ occurrence_of(X64,X66)
| X65 = X66 ),
inference(canonicalize,[],[sos_22]) ).
fof(normalize_0_25,plain,
! [X64,X65,X66] :
( ~ occurrence_of(X64,X65)
| ~ occurrence_of(X64,X66)
| X65 = X66 ),
inference(specialize,[],[normalize_0_24]) ).
cnf(refute_0_0,plain,
( ~ leaf(X42,X43)
| ~ min_precedes(X42,X45,X43) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ leaf(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),tptp0)
| ~ min_precedes(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X102(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99)),tptp0) ),
inference(subst,[],[refute_0_0:[bind(X42,$fot(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99))),bind(X43,$fot(tptp0)),bind(X45,$fot(skolemFOFtoCNF_X102(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99))))]]) ).
cnf(refute_0_2,plain,
( ~ definitionFOFtoCNF_0(X100,X101)
| min_precedes(X100,skolemFOFtoCNF_X102(X100),tptp0) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( ~ definitionFOFtoCNF_0(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X98(skolemFOFtoCNF_X99))
| min_precedes(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X102(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99)),tptp0) ),
inference(subst,[],[refute_0_2:[bind(X100,$fot(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99))),bind(X101,$fot(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99)))]]) ).
cnf(refute_0_4,plain,
( ~ leaf(X_232,tptp0)
| ~ min_precedes(X_232,skolemFOFtoCNF_X103(X_232),tptp0) ),
inference(subst,[],[refute_0_0:[bind(X42,$fot(X_232)),bind(X43,$fot(tptp0)),bind(X45,$fot(skolemFOFtoCNF_X103(X_232)))]]) ).
cnf(refute_0_5,plain,
occurrence_of(skolemFOFtoCNF_X99,tptp0),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_6,plain,
( ~ occurrence_of(X95,tptp0)
| leaf_occ(skolemFOFtoCNF_X98(X95),X95) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_7,plain,
( ~ occurrence_of(skolemFOFtoCNF_X99,tptp0)
| leaf_occ(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X99) ),
inference(subst,[],[refute_0_6:[bind(X95,$fot(skolemFOFtoCNF_X99))]]) ).
cnf(refute_0_8,plain,
leaf_occ(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X99),
inference(resolve,[$cnf( occurrence_of(skolemFOFtoCNF_X99,tptp0) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ leaf_occ(X101,skolemFOFtoCNF_X99)
| definitionFOFtoCNF_0(X100,X101)
| min_precedes(X100,skolemFOFtoCNF_X103(X100),tptp0) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_10,plain,
( ~ leaf_occ(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X99)
| definitionFOFtoCNF_0(X_230,skolemFOFtoCNF_X98(skolemFOFtoCNF_X99))
| min_precedes(X_230,skolemFOFtoCNF_X103(X_230),tptp0) ),
inference(subst,[],[refute_0_9:[bind(X100,$fot(X_230)),bind(X101,$fot(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99)))]]) ).
cnf(refute_0_11,plain,
( definitionFOFtoCNF_0(X_230,skolemFOFtoCNF_X98(skolemFOFtoCNF_X99))
| min_precedes(X_230,skolemFOFtoCNF_X103(X_230),tptp0) ),
inference(resolve,[$cnf( leaf_occ(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X99) )],[refute_0_8,refute_0_10]) ).
cnf(refute_0_12,plain,
( definitionFOFtoCNF_0(X_232,skolemFOFtoCNF_X98(skolemFOFtoCNF_X99))
| min_precedes(X_232,skolemFOFtoCNF_X103(X_232),tptp0) ),
inference(subst,[],[refute_0_11:[bind(X_230,$fot(X_232))]]) ).
cnf(refute_0_13,plain,
( ~ leaf(X_232,tptp0)
| definitionFOFtoCNF_0(X_232,skolemFOFtoCNF_X98(skolemFOFtoCNF_X99)) ),
inference(resolve,[$cnf( min_precedes(X_232,skolemFOFtoCNF_X103(X_232),tptp0) )],[refute_0_12,refute_0_4]) ).
cnf(refute_0_14,plain,
( ~ leaf(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),tptp0)
| definitionFOFtoCNF_0(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X98(skolemFOFtoCNF_X99)) ),
inference(subst,[],[refute_0_13:[bind(X_232,$fot(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99)))]]) ).
cnf(refute_0_15,plain,
( ~ leaf_occ(X35,X36)
| leaf(X35,skolemFOFtoCNF_X37(X35,X36)) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_16,plain,
( ~ leaf_occ(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X99)
| leaf(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X37(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X99)) ),
inference(subst,[],[refute_0_15:[bind(X35,$fot(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99))),bind(X36,$fot(skolemFOFtoCNF_X99))]]) ).
cnf(refute_0_17,plain,
leaf(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X37(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X99)),
inference(resolve,[$cnf( leaf_occ(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X99) )],[refute_0_8,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ leaf_occ(X35,X36)
| occurrence_of(X36,skolemFOFtoCNF_X37(X35,X36)) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_19,plain,
( ~ leaf_occ(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X99)
| occurrence_of(skolemFOFtoCNF_X99,skolemFOFtoCNF_X37(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X99)) ),
inference(subst,[],[refute_0_18:[bind(X35,$fot(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99))),bind(X36,$fot(skolemFOFtoCNF_X99))]]) ).
cnf(refute_0_20,plain,
occurrence_of(skolemFOFtoCNF_X99,skolemFOFtoCNF_X37(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X99)),
inference(resolve,[$cnf( leaf_occ(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X99) )],[refute_0_8,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ occurrence_of(X64,X65)
| ~ occurrence_of(X64,X66)
| X65 = X66 ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_22,plain,
( ~ occurrence_of(skolemFOFtoCNF_X99,X_340)
| ~ occurrence_of(skolemFOFtoCNF_X99,tptp0)
| tptp0 = X_340 ),
inference(subst,[],[refute_0_21:[bind(X64,$fot(skolemFOFtoCNF_X99)),bind(X65,$fot(tptp0)),bind(X66,$fot(X_340))]]) ).
cnf(refute_0_23,plain,
( ~ occurrence_of(skolemFOFtoCNF_X99,X_340)
| tptp0 = X_340 ),
inference(resolve,[$cnf( occurrence_of(skolemFOFtoCNF_X99,tptp0) )],[refute_0_5,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ occurrence_of(skolemFOFtoCNF_X99,skolemFOFtoCNF_X37(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X99))
| tptp0 = skolemFOFtoCNF_X37(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X99) ),
inference(subst,[],[refute_0_23:[bind(X_340,$fot(skolemFOFtoCNF_X37(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X99)))]]) ).
cnf(refute_0_25,plain,
tptp0 = skolemFOFtoCNF_X37(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X99),
inference(resolve,[$cnf( occurrence_of(skolemFOFtoCNF_X99,skolemFOFtoCNF_X37(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X99)) )],[refute_0_20,refute_0_24]) ).
cnf(refute_0_26,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_27,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_28,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( tptp0 != skolemFOFtoCNF_X37(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X99)
| skolemFOFtoCNF_X37(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X99) = tptp0 ),
inference(subst,[],[refute_0_28:[bind(X,$fot(tptp0)),bind(Y,$fot(skolemFOFtoCNF_X37(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X99)))]]) ).
cnf(refute_0_30,plain,
skolemFOFtoCNF_X37(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X99) = tptp0,
inference(resolve,[$cnf( $equal(tptp0,skolemFOFtoCNF_X37(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X99)) )],[refute_0_25,refute_0_29]) ).
cnf(refute_0_31,plain,
( skolemFOFtoCNF_X37(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X99) != tptp0
| ~ leaf(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X37(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X99))
| leaf(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),tptp0) ),
introduced(tautology,[equality,[$cnf( leaf(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X37(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X99)) ),[1],$fot(tptp0)]]) ).
cnf(refute_0_32,plain,
( ~ leaf(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X37(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X99))
| leaf(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),tptp0) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X37(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X99),tptp0) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
leaf(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),tptp0),
inference(resolve,[$cnf( leaf(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X37(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X99)) )],[refute_0_17,refute_0_32]) ).
cnf(refute_0_34,plain,
definitionFOFtoCNF_0(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X98(skolemFOFtoCNF_X99)),
inference(resolve,[$cnf( leaf(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),tptp0) )],[refute_0_33,refute_0_14]) ).
cnf(refute_0_35,plain,
min_precedes(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X102(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99)),tptp0),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X98(skolemFOFtoCNF_X99)) )],[refute_0_34,refute_0_3]) ).
cnf(refute_0_36,plain,
~ leaf(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),tptp0),
inference(resolve,[$cnf( min_precedes(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),skolemFOFtoCNF_X102(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99)),tptp0) )],[refute_0_35,refute_0_1]) ).
cnf(refute_0_37,plain,
$false,
inference(resolve,[$cnf( leaf(skolemFOFtoCNF_X98(skolemFOFtoCNF_X99),tptp0) )],[refute_0_33,refute_0_36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : PRO011+2 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 02:04:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.78/0.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.78/0.97
% 0.78/0.97 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.78/0.97
%------------------------------------------------------------------------------