%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : PRO010+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 17:50:16 EDT 2022
% Result : Theorem 9.61s 9.82s
% Output : CNFRefutation 9.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 12
% Syntax : Number of formulae : 105 ( 21 unt; 0 def)
% Number of atoms : 342 ( 36 equ)
% Maximal formula atoms : 27 ( 3 avg)
% Number of connectives : 367 ( 130 ~; 136 |; 82 &)
% ( 6 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-2 aty)
% Number of variables : 158 ( 4 sgn 78 !; 38 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_01,axiom,
! [X2] :
( activity_occurrence(X2)
=> ? [X3] :
( activity(X3)
& occurrence_of(X2,X3) ) ) ).
fof(sos_02,axiom,
! [X4,X5,X6] :
( ( occurrence_of(X4,X5)
& occurrence_of(X4,X6) )
=> X5 = X6 ) ).
fof(sos_21,axiom,
! [X56,X57] :
( leaf(X56,X57)
<=> ( ( root(X56,X57)
| ? [X58] : min_precedes(X58,X56,X57) )
& ~ ? [X59] : min_precedes(X56,X59,X57) ) ) ).
fof(sos_24,axiom,
! [X67,X68] :
( subactivity_occurrence(X67,X68)
=> ( activity_occurrence(X67)
& activity_occurrence(X68) ) ) ).
fof(sos_34,axiom,
! [X102,X103] :
( leaf_occ(X102,X103)
<=> ? [X104] :
( occurrence_of(X103,X104)
& subactivity_occurrence(X102,X103)
& leaf(X102,X104) ) ) ).
fof(sos_35,axiom,
! [X105] :
( occurrence_of(X105,tptp0)
=> ? [X106,X107,X108] :
( occurrence_of(X106,tptp3)
& root_occ(X106,X105)
& occurrence_of(X107,tptp4)
& next_subocc(X106,X107,tptp0)
& ( occurrence_of(X108,tptp1)
| occurrence_of(X108,tptp2) )
& next_subocc(X107,X108,tptp0)
& leaf_occ(X108,X105) ) ) ).
fof(sos_47,axiom,
tptp1 != tptp2 ).
fof(goals,conjecture,
! [X109] :
( occurrence_of(X109,tptp0)
=> ? [X110,X111] :
( leaf_occ(X111,X109)
& ( occurrence_of(X111,tptp1)
=> ~ ? [X112] :
( occurrence_of(X112,tptp2)
& min_precedes(X110,X112,tptp0) ) )
& ( occurrence_of(X111,tptp2)
=> ~ ? [X113] :
( occurrence_of(X113,tptp1)
& min_precedes(X110,X113,tptp0) ) ) ) ) ).
fof(subgoal_0,plain,
! [X109] :
( occurrence_of(X109,tptp0)
=> ? [X110,X111] :
( leaf_occ(X111,X109)
& ( occurrence_of(X111,tptp1)
=> ~ ? [X112] :
( occurrence_of(X112,tptp2)
& min_precedes(X110,X112,tptp0) ) )
& ( occurrence_of(X111,tptp2)
=> ~ ? [X113] :
( occurrence_of(X113,tptp1)
& min_precedes(X110,X113,tptp0) ) ) ) ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X109] :
( occurrence_of(X109,tptp0)
=> ? [X110,X111] :
( leaf_occ(X111,X109)
& ( occurrence_of(X111,tptp1)
=> ~ ? [X112] :
( occurrence_of(X112,tptp2)
& min_precedes(X110,X112,tptp0) ) )
& ( occurrence_of(X111,tptp2)
=> ~ ? [X113] :
( occurrence_of(X113,tptp1)
& min_precedes(X110,X113,tptp0) ) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X2] :
( ~ activity_occurrence(X2)
| ? [X3] :
( activity(X3)
& occurrence_of(X2,X3) ) ),
inference(canonicalize,[],[sos_01]) ).
fof(normalize_0_1,plain,
! [X2] :
( ~ activity_occurrence(X2)
| ? [X3] :
( activity(X3)
& occurrence_of(X2,X3) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X2] :
( ( ~ activity_occurrence(X2)
| activity(skolemFOFtoCNF_X3(X2)) )
& ( ~ activity_occurrence(X2)
| occurrence_of(X2,skolemFOFtoCNF_X3(X2)) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X2] :
( ~ activity_occurrence(X2)
| occurrence_of(X2,skolemFOFtoCNF_X3(X2)) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X67,X68] :
( ~ subactivity_occurrence(X67,X68)
| ( activity_occurrence(X67)
& activity_occurrence(X68) ) ),
inference(canonicalize,[],[sos_24]) ).
fof(normalize_0_5,plain,
! [X67,X68] :
( ~ subactivity_occurrence(X67,X68)
| ( activity_occurrence(X67)
& activity_occurrence(X68) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X67,X68] :
( ( ~ subactivity_occurrence(X67,X68)
| activity_occurrence(X67) )
& ( ~ subactivity_occurrence(X67,X68)
| activity_occurrence(X68) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X67,X68] :
( ~ subactivity_occurrence(X67,X68)
| activity_occurrence(X67) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
? [X109] :
( occurrence_of(X109,tptp0)
& ! [X110,X111] :
( ~ leaf_occ(X111,X109)
| ( occurrence_of(X111,tptp1)
& ? [X112] :
( min_precedes(X110,X112,tptp0)
& occurrence_of(X112,tptp2) ) )
| ( occurrence_of(X111,tptp2)
& ? [X113] :
( min_precedes(X110,X113,tptp0)
& occurrence_of(X113,tptp1) ) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_9,plain,
( occurrence_of(skolemFOFtoCNF_X109,tptp0)
& ! [X110,X111] :
( ~ leaf_occ(X111,skolemFOFtoCNF_X109)
| ( occurrence_of(X111,tptp1)
& ? [X112] :
( min_precedes(X110,X112,tptp0)
& occurrence_of(X112,tptp2) ) )
| ( occurrence_of(X111,tptp2)
& ? [X113] :
( min_precedes(X110,X113,tptp0)
& occurrence_of(X113,tptp1) ) ) ) ),
inference(skolemize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
occurrence_of(skolemFOFtoCNF_X109,tptp0),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X105] :
( ~ occurrence_of(X105,tptp0)
| ? [X106,X107,X108] :
( leaf_occ(X108,X105)
& next_subocc(X106,X107,tptp0)
& next_subocc(X107,X108,tptp0)
& occurrence_of(X106,tptp3)
& occurrence_of(X107,tptp4)
& root_occ(X106,X105)
& ( occurrence_of(X108,tptp1)
| occurrence_of(X108,tptp2) ) ) ),
inference(canonicalize,[],[sos_35]) ).
fof(normalize_0_12,plain,
! [X105] :
( ~ occurrence_of(X105,tptp0)
| ? [X106,X107,X108] :
( leaf_occ(X108,X105)
& next_subocc(X106,X107,tptp0)
& next_subocc(X107,X108,tptp0)
& occurrence_of(X106,tptp3)
& occurrence_of(X107,tptp4)
& root_occ(X106,X105)
& ( occurrence_of(X108,tptp1)
| occurrence_of(X108,tptp2) ) ) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X105] :
( ( ~ occurrence_of(X105,tptp0)
| leaf_occ(skolemFOFtoCNF_X108(X105),X105) )
& ( ~ occurrence_of(X105,tptp0)
| next_subocc(skolemFOFtoCNF_X106(X105),skolemFOFtoCNF_X107(X105),tptp0) )
& ( ~ occurrence_of(X105,tptp0)
| next_subocc(skolemFOFtoCNF_X107(X105),skolemFOFtoCNF_X108(X105),tptp0) )
& ( ~ occurrence_of(X105,tptp0)
| occurrence_of(skolemFOFtoCNF_X106(X105),tptp3) )
& ( ~ occurrence_of(X105,tptp0)
| occurrence_of(skolemFOFtoCNF_X107(X105),tptp4) )
& ( ~ occurrence_of(X105,tptp0)
| root_occ(skolemFOFtoCNF_X106(X105),X105) )
& ( ~ occurrence_of(X105,tptp0)
| occurrence_of(skolemFOFtoCNF_X108(X105),tptp1)
| occurrence_of(skolemFOFtoCNF_X108(X105),tptp2) ) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X105] :
( ~ occurrence_of(X105,tptp0)
| leaf_occ(skolemFOFtoCNF_X108(X105),X105) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [X102,X103] :
( ~ leaf_occ(X102,X103)
<=> ! [X104] :
( ~ leaf(X102,X104)
| ~ occurrence_of(X103,X104)
| ~ subactivity_occurrence(X102,X103) ) ),
inference(canonicalize,[],[sos_34]) ).
fof(normalize_0_16,plain,
! [X102,X103] :
( ~ leaf_occ(X102,X103)
<=> ! [X104] :
( ~ leaf(X102,X104)
| ~ occurrence_of(X103,X104)
| ~ subactivity_occurrence(X102,X103) ) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [X102,X103,X104] :
( ( ~ leaf_occ(X102,X103)
| leaf(X102,skolemFOFtoCNF_X104(X102,X103)) )
& ( ~ leaf_occ(X102,X103)
| occurrence_of(X103,skolemFOFtoCNF_X104(X102,X103)) )
& ( ~ leaf_occ(X102,X103)
| subactivity_occurrence(X102,X103) )
& ( ~ leaf(X102,X104)
| ~ occurrence_of(X103,X104)
| ~ subactivity_occurrence(X102,X103)
| leaf_occ(X102,X103) ) ),
inference(clausify,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [X102,X103] :
( ~ leaf_occ(X102,X103)
| subactivity_occurrence(X102,X103) ),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [X4,X5,X6] :
( ~ occurrence_of(X4,X5)
| ~ occurrence_of(X4,X6)
| X5 = X6 ),
inference(canonicalize,[],[sos_02]) ).
fof(normalize_0_20,plain,
! [X4,X5,X6] :
( ~ occurrence_of(X4,X5)
| ~ occurrence_of(X4,X6)
| X5 = X6 ),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [X102,X103] :
( ~ leaf_occ(X102,X103)
| leaf(X102,skolemFOFtoCNF_X104(X102,X103)) ),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_22,plain,
! [X102,X103] :
( ~ leaf_occ(X102,X103)
| occurrence_of(X103,skolemFOFtoCNF_X104(X102,X103)) ),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_23,plain,
! [X56,X57] :
( ~ leaf(X56,X57)
<=> ( ( ~ root(X56,X57)
& ! [X58] : ~ min_precedes(X58,X56,X57) )
| ? [X59] : min_precedes(X56,X59,X57) ) ),
inference(canonicalize,[],[sos_21]) ).
fof(normalize_0_24,plain,
! [X56,X57] :
( ~ leaf(X56,X57)
<=> ( ( ~ root(X56,X57)
& ! [X58] : ~ min_precedes(X58,X56,X57) )
| ? [X59] : min_precedes(X56,X59,X57) ) ),
inference(specialize,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [X56,X57,X58,X59] :
( ( ~ leaf(X56,X57)
| ~ min_precedes(X56,X59,X57) )
& ( ~ leaf(X56,X57)
| min_precedes(skolemFOFtoCNF_X58(X56,X57),X56,X57)
| root(X56,X57) )
& ( ~ min_precedes(X58,X56,X57)
| leaf(X56,X57)
| min_precedes(X56,skolemFOFtoCNF_X59(X56,X57),X57) )
& ( ~ root(X56,X57)
| leaf(X56,X57)
| min_precedes(X56,skolemFOFtoCNF_X59(X56,X57),X57) ) ),
inference(clausify,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [X56,X57,X59] :
( ~ leaf(X56,X57)
| ~ min_precedes(X56,X59,X57) ),
inference(conjunct,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
! [X110,X111] :
( ~ leaf_occ(X111,skolemFOFtoCNF_X109)
| ( occurrence_of(X111,tptp1)
& ? [X112] :
( min_precedes(X110,X112,tptp0)
& occurrence_of(X112,tptp2) ) )
| ( occurrence_of(X111,tptp2)
& ? [X113] :
( min_precedes(X110,X113,tptp0)
& occurrence_of(X113,tptp1) ) ) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_28,plain,
! [X110,X111] :
( ~ leaf_occ(X111,skolemFOFtoCNF_X109)
| ( occurrence_of(X111,tptp1)
& ? [X112] :
( min_precedes(X110,X112,tptp0)
& occurrence_of(X112,tptp2) ) )
| ( occurrence_of(X111,tptp2)
& ? [X113] :
( min_precedes(X110,X113,tptp0)
& occurrence_of(X113,tptp1) ) ) ),
inference(specialize,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
! [X110,X111] :
( ( ~ leaf_occ(X111,skolemFOFtoCNF_X109)
| min_precedes(X110,skolemFOFtoCNF_X112(X110),tptp0)
| min_precedes(X110,skolemFOFtoCNF_X113(X110),tptp0) )
& ( ~ leaf_occ(X111,skolemFOFtoCNF_X109)
| min_precedes(X110,skolemFOFtoCNF_X112(X110),tptp0)
| occurrence_of(X111,tptp2) )
& ( ~ leaf_occ(X111,skolemFOFtoCNF_X109)
| min_precedes(X110,skolemFOFtoCNF_X112(X110),tptp0)
| occurrence_of(skolemFOFtoCNF_X113(X110),tptp1) )
& ( ~ leaf_occ(X111,skolemFOFtoCNF_X109)
| min_precedes(X110,skolemFOFtoCNF_X113(X110),tptp0)
| occurrence_of(X111,tptp1) )
& ( ~ leaf_occ(X111,skolemFOFtoCNF_X109)
| min_precedes(X110,skolemFOFtoCNF_X113(X110),tptp0)
| occurrence_of(skolemFOFtoCNF_X112(X110),tptp2) )
& ( ~ leaf_occ(X111,skolemFOFtoCNF_X109)
| occurrence_of(X111,tptp1)
| occurrence_of(X111,tptp2) )
& ( ~ leaf_occ(X111,skolemFOFtoCNF_X109)
| occurrence_of(X111,tptp1)
| occurrence_of(skolemFOFtoCNF_X113(X110),tptp1) )
& ( ~ leaf_occ(X111,skolemFOFtoCNF_X109)
| occurrence_of(X111,tptp2)
| occurrence_of(skolemFOFtoCNF_X112(X110),tptp2) )
& ( ~ leaf_occ(X111,skolemFOFtoCNF_X109)
| occurrence_of(skolemFOFtoCNF_X112(X110),tptp2)
| occurrence_of(skolemFOFtoCNF_X113(X110),tptp1) ) ),
inference(clausify,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
! [X110,X111] :
( ~ leaf_occ(X111,skolemFOFtoCNF_X109)
| min_precedes(X110,skolemFOFtoCNF_X112(X110),tptp0)
| occurrence_of(X111,tptp2) ),
inference(conjunct,[],[normalize_0_29]) ).
fof(normalize_0_31,plain,
! [X110,X111] :
( ~ leaf_occ(X111,skolemFOFtoCNF_X109)
| min_precedes(X110,skolemFOFtoCNF_X113(X110),tptp0)
| occurrence_of(X111,tptp1) ),
inference(conjunct,[],[normalize_0_29]) ).
fof(normalize_0_32,plain,
tptp1 != tptp2,
inference(canonicalize,[],[sos_47]) ).
cnf(refute_0_0,plain,
( ~ activity_occurrence(X2)
| occurrence_of(X2,skolemFOFtoCNF_X3(X2)) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ activity_occurrence(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109))
| occurrence_of(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X3(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109))) ),
inference(subst,[],[refute_0_0:[bind(X2,$fot(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109)))]]) ).
cnf(refute_0_2,plain,
( ~ subactivity_occurrence(X67,X68)
| activity_occurrence(X67) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( ~ subactivity_occurrence(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109)
| activity_occurrence(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109)) ),
inference(subst,[],[refute_0_2:[bind(X67,$fot(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109))),bind(X68,$fot(skolemFOFtoCNF_X109))]]) ).
cnf(refute_0_4,plain,
occurrence_of(skolemFOFtoCNF_X109,tptp0),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_5,plain,
( ~ occurrence_of(X105,tptp0)
| leaf_occ(skolemFOFtoCNF_X108(X105),X105) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_6,plain,
( ~ occurrence_of(skolemFOFtoCNF_X109,tptp0)
| leaf_occ(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109) ),
inference(subst,[],[refute_0_5:[bind(X105,$fot(skolemFOFtoCNF_X109))]]) ).
cnf(refute_0_7,plain,
leaf_occ(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109),
inference(resolve,[$cnf( occurrence_of(skolemFOFtoCNF_X109,tptp0) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ leaf_occ(X102,X103)
| subactivity_occurrence(X102,X103) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_9,plain,
( ~ leaf_occ(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109)
| subactivity_occurrence(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109) ),
inference(subst,[],[refute_0_8:[bind(X102,$fot(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109))),bind(X103,$fot(skolemFOFtoCNF_X109))]]) ).
cnf(refute_0_10,plain,
subactivity_occurrence(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109),
inference(resolve,[$cnf( leaf_occ(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
activity_occurrence(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109)),
inference(resolve,[$cnf( subactivity_occurrence(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109) )],[refute_0_10,refute_0_3]) ).
cnf(refute_0_12,plain,
occurrence_of(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X3(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109))),
inference(resolve,[$cnf( activity_occurrence(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109)) )],[refute_0_11,refute_0_1]) ).
cnf(refute_0_13,plain,
( ~ occurrence_of(X4,X5)
| ~ occurrence_of(X4,X6)
| X5 = X6 ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_14,plain,
( ~ occurrence_of(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),X_154)
| ~ occurrence_of(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X3(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109)))
| skolemFOFtoCNF_X3(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109)) = X_154 ),
inference(subst,[],[refute_0_13:[bind(X4,$fot(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109))),bind(X5,$fot(skolemFOFtoCNF_X3(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109)))),bind(X6,$fot(X_154))]]) ).
cnf(refute_0_15,plain,
( ~ occurrence_of(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),X_154)
| skolemFOFtoCNF_X3(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109)) = X_154 ),
inference(resolve,[$cnf( occurrence_of(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X3(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109))) )],[refute_0_12,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ occurrence_of(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),tptp2)
| skolemFOFtoCNF_X3(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109)) = tptp2 ),
inference(subst,[],[refute_0_15:[bind(X_154,$fot(tptp2))]]) ).
cnf(refute_0_17,plain,
( ~ leaf_occ(X102,X103)
| leaf(X102,skolemFOFtoCNF_X104(X102,X103)) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_18,plain,
( ~ leaf_occ(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109)
| leaf(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109)) ),
inference(subst,[],[refute_0_17:[bind(X102,$fot(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109))),bind(X103,$fot(skolemFOFtoCNF_X109))]]) ).
cnf(refute_0_19,plain,
leaf(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109)),
inference(resolve,[$cnf( leaf_occ(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109) )],[refute_0_7,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ leaf_occ(X102,X103)
| occurrence_of(X103,skolemFOFtoCNF_X104(X102,X103)) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_21,plain,
( ~ leaf_occ(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109)
| occurrence_of(skolemFOFtoCNF_X109,skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109)) ),
inference(subst,[],[refute_0_20:[bind(X102,$fot(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109))),bind(X103,$fot(skolemFOFtoCNF_X109))]]) ).
cnf(refute_0_22,plain,
occurrence_of(skolemFOFtoCNF_X109,skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109)),
inference(resolve,[$cnf( leaf_occ(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109) )],[refute_0_7,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ occurrence_of(skolemFOFtoCNF_X109,X_154)
| ~ occurrence_of(skolemFOFtoCNF_X109,tptp0)
| tptp0 = X_154 ),
inference(subst,[],[refute_0_13:[bind(X4,$fot(skolemFOFtoCNF_X109)),bind(X5,$fot(tptp0)),bind(X6,$fot(X_154))]]) ).
cnf(refute_0_24,plain,
( ~ occurrence_of(skolemFOFtoCNF_X109,X_154)
| tptp0 = X_154 ),
inference(resolve,[$cnf( occurrence_of(skolemFOFtoCNF_X109,tptp0) )],[refute_0_4,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ occurrence_of(skolemFOFtoCNF_X109,skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109))
| tptp0 = skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109) ),
inference(subst,[],[refute_0_24:[bind(X_154,$fot(skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109)))]]) ).
cnf(refute_0_26,plain,
tptp0 = skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109),
inference(resolve,[$cnf( occurrence_of(skolemFOFtoCNF_X109,skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109)) )],[refute_0_22,refute_0_25]) ).
cnf(refute_0_27,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_28,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_29,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( tptp0 != skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109)
| skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109) = tptp0 ),
inference(subst,[],[refute_0_29:[bind(X,$fot(tptp0)),bind(Y,$fot(skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109)))]]) ).
cnf(refute_0_31,plain,
skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109) = tptp0,
inference(resolve,[$cnf( $equal(tptp0,skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109)) )],[refute_0_26,refute_0_30]) ).
cnf(refute_0_32,plain,
( skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109) != tptp0
| ~ leaf(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109))
| leaf(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),tptp0) ),
introduced(tautology,[equality,[$cnf( leaf(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109)) ),[1],$fot(tptp0)]]) ).
cnf(refute_0_33,plain,
( ~ leaf(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109))
| leaf(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),tptp0) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109),tptp0) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
leaf(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),tptp0),
inference(resolve,[$cnf( leaf(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109)) )],[refute_0_19,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ leaf(X56,X57)
| ~ min_precedes(X56,X59,X57) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_36,plain,
( ~ leaf(X_169,tptp0)
| ~ min_precedes(X_169,skolemFOFtoCNF_X112(X_169),tptp0) ),
inference(subst,[],[refute_0_35:[bind(X56,$fot(X_169)),bind(X57,$fot(tptp0)),bind(X59,$fot(skolemFOFtoCNF_X112(X_169)))]]) ).
cnf(refute_0_37,plain,
( ~ leaf_occ(X111,skolemFOFtoCNF_X109)
| min_precedes(X110,skolemFOFtoCNF_X112(X110),tptp0)
| occurrence_of(X111,tptp2) ),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_38,plain,
( ~ leaf_occ(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109)
| min_precedes(X_167,skolemFOFtoCNF_X112(X_167),tptp0)
| occurrence_of(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),tptp2) ),
inference(subst,[],[refute_0_37:[bind(X110,$fot(X_167)),bind(X111,$fot(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109)))]]) ).
cnf(refute_0_39,plain,
( min_precedes(X_167,skolemFOFtoCNF_X112(X_167),tptp0)
| occurrence_of(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),tptp2) ),
inference(resolve,[$cnf( leaf_occ(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109) )],[refute_0_7,refute_0_38]) ).
cnf(refute_0_40,plain,
( min_precedes(X_169,skolemFOFtoCNF_X112(X_169),tptp0)
| occurrence_of(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),tptp2) ),
inference(subst,[],[refute_0_39:[bind(X_167,$fot(X_169))]]) ).
cnf(refute_0_41,plain,
( ~ leaf(X_169,tptp0)
| occurrence_of(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),tptp2) ),
inference(resolve,[$cnf( min_precedes(X_169,skolemFOFtoCNF_X112(X_169),tptp0) )],[refute_0_40,refute_0_36]) ).
cnf(refute_0_42,plain,
( ~ leaf(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),tptp0)
| occurrence_of(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),tptp2) ),
inference(subst,[],[refute_0_41:[bind(X_169,$fot(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109)))]]) ).
cnf(refute_0_43,plain,
occurrence_of(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),tptp2),
inference(resolve,[$cnf( leaf(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),tptp0) )],[refute_0_34,refute_0_42]) ).
cnf(refute_0_44,plain,
skolemFOFtoCNF_X3(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109)) = tptp2,
inference(resolve,[$cnf( occurrence_of(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),tptp2) )],[refute_0_43,refute_0_16]) ).
cnf(refute_0_45,plain,
( skolemFOFtoCNF_X3(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109)) != X_154
| skolemFOFtoCNF_X3(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109)) != tptp2
| tptp2 = X_154 ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_X3(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109)),X_154) ),[0],$fot(tptp2)]]) ).
cnf(refute_0_46,plain,
( skolemFOFtoCNF_X3(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109)) != X_154
| tptp2 = X_154 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X3(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109)),tptp2) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
( ~ occurrence_of(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),X_154)
| tptp2 = X_154 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X3(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109)),X_154) )],[refute_0_15,refute_0_46]) ).
cnf(refute_0_48,plain,
( ~ occurrence_of(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),tptp1)
| tptp2 = tptp1 ),
inference(subst,[],[refute_0_47:[bind(X_154,$fot(tptp1))]]) ).
cnf(refute_0_49,plain,
( ~ leaf(X_185,tptp0)
| ~ min_precedes(X_185,skolemFOFtoCNF_X113(X_185),tptp0) ),
inference(subst,[],[refute_0_35:[bind(X56,$fot(X_185)),bind(X57,$fot(tptp0)),bind(X59,$fot(skolemFOFtoCNF_X113(X_185)))]]) ).
cnf(refute_0_50,plain,
( ~ leaf_occ(X111,skolemFOFtoCNF_X109)
| min_precedes(X110,skolemFOFtoCNF_X113(X110),tptp0)
| occurrence_of(X111,tptp1) ),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_51,plain,
( ~ leaf_occ(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109)
| min_precedes(X_183,skolemFOFtoCNF_X113(X_183),tptp0)
| occurrence_of(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),tptp1) ),
inference(subst,[],[refute_0_50:[bind(X110,$fot(X_183)),bind(X111,$fot(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109)))]]) ).
cnf(refute_0_52,plain,
( min_precedes(X_183,skolemFOFtoCNF_X113(X_183),tptp0)
| occurrence_of(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),tptp1) ),
inference(resolve,[$cnf( leaf_occ(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109) )],[refute_0_7,refute_0_51]) ).
cnf(refute_0_53,plain,
( min_precedes(X_185,skolemFOFtoCNF_X113(X_185),tptp0)
| occurrence_of(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),tptp1) ),
inference(subst,[],[refute_0_52:[bind(X_183,$fot(X_185))]]) ).
cnf(refute_0_54,plain,
( ~ leaf(X_185,tptp0)
| occurrence_of(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),tptp1) ),
inference(resolve,[$cnf( min_precedes(X_185,skolemFOFtoCNF_X113(X_185),tptp0) )],[refute_0_53,refute_0_49]) ).
cnf(refute_0_55,plain,
( ~ leaf(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),tptp0)
| occurrence_of(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),tptp1) ),
inference(subst,[],[refute_0_54:[bind(X_185,$fot(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109)))]]) ).
cnf(refute_0_56,plain,
occurrence_of(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),tptp1),
inference(resolve,[$cnf( leaf(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),tptp0) )],[refute_0_34,refute_0_55]) ).
cnf(refute_0_57,plain,
tptp2 = tptp1,
inference(resolve,[$cnf( occurrence_of(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),tptp1) )],[refute_0_56,refute_0_48]) ).
cnf(refute_0_58,plain,
tptp1 != tptp2,
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_59,plain,
( tptp2 != tptp1
| tptp1 = tptp2 ),
inference(subst,[],[refute_0_29:[bind(X,$fot(tptp2)),bind(Y,$fot(tptp1))]]) ).
cnf(refute_0_60,plain,
tptp2 != tptp1,
inference(resolve,[$cnf( $equal(tptp1,tptp2) )],[refute_0_59,refute_0_58]) ).
cnf(refute_0_61,plain,
$false,
inference(resolve,[$cnf( $equal(tptp2,tptp1) )],[refute_0_57,refute_0_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : PRO010+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 03:57:31 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 9.61/9.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.61/9.82
% 9.61/9.82 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.61/9.83
%------------------------------------------------------------------------------