TSTP Solution File: ITP015_2 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : ITP015_2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n014.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 : 300s
% DateTime : Sat May 4 08:06:27 EDT 2024
% Result : Theorem 203.89s 26.30s
% Output : CNFRefutation 203.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 58
% Syntax : Number of formulae : 131 ( 73 unt; 35 typ; 0 def)
% Number of atoms : 178 ( 77 equ)
% Maximal formula atoms : 19 ( 1 avg)
% Number of connectives : 133 ( 51 ~; 46 |; 17 &)
% ( 9 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 6 ( 4 usr)
% Number of type conns : 23 ( 18 >; 5 *; 0 +; 0 <<)
% Number of predicates : 5 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 13 con; 0-2 aty)
% Number of variables : 121 ( 0 sgn 121 !; 0 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
del: $tType ).
tff(decl_sort2,type,
tp__o: $tType ).
tff(decl_sort3,type,
tp__ty_2Einteger_2Eint: $tType ).
tff(decl_sort4,type,
tp__ty_2Enum_2Enum: $tType ).
tff(decl_22,type,
bool: del ).
tff(decl_24,type,
arr: ( del * del ) > del ).
tff(decl_25,type,
mem: ( $i * del ) > $o ).
tff(decl_26,type,
ap: ( $i * $i ) > $i ).
tff(decl_29,type,
p: $i > $o ).
tff(decl_30,type,
inj__o: tp__o > $i ).
tff(decl_35,type,
fo__c_2Ebool_2ET: tp__o ).
tff(decl_36,type,
c_2Ebool_2EF: $i ).
tff(decl_37,type,
fo__c_2Ebool_2EF: tp__o ).
tff(decl_42,type,
ty_2Einteger_2Eint: del ).
tff(decl_43,type,
inj__ty_2Einteger_2Eint: tp__ty_2Einteger_2Eint > $i ).
tff(decl_44,type,
surj__ty_2Einteger_2Eint: $i > tp__ty_2Einteger_2Eint ).
tff(decl_45,type,
c_2Einteger_2Eint__neg: $i ).
tff(decl_46,type,
fo__c_2Einteger_2Eint__neg: tp__ty_2Einteger_2Eint > tp__ty_2Einteger_2Eint ).
tff(decl_47,type,
ty_2Enum_2Enum: del ).
tff(decl_48,type,
inj__ty_2Enum_2Enum: tp__ty_2Enum_2Enum > $i ).
tff(decl_49,type,
surj__ty_2Enum_2Enum: $i > tp__ty_2Enum_2Enum ).
tff(decl_50,type,
c_2Einteger_2ENum: $i ).
tff(decl_51,type,
fo__c_2Einteger_2ENum: tp__ty_2Einteger_2Eint > tp__ty_2Enum_2Enum ).
tff(decl_52,type,
c_2Einteger_2Eint__of__num: $i ).
tff(decl_53,type,
fo__c_2Einteger_2Eint__of__num: tp__ty_2Enum_2Enum > tp__ty_2Einteger_2Eint ).
tff(decl_54,type,
c_2Einteger_2Eint__lt: $i ).
tff(decl_55,type,
fo__c_2Einteger_2Eint__lt: ( tp__ty_2Einteger_2Eint * tp__ty_2Einteger_2Eint ) > tp__o ).
tff(decl_56,type,
c_2Ebool_2ECOND: del > $i ).
tff(decl_57,type,
ty_2Efcp_2Ecart: ( del * del ) > del ).
tff(decl_58,type,
c_2Einteger__word_2Ei2w: del > $i ).
tff(decl_59,type,
c_2Eprim__rec_2E_3C: $i ).
tff(decl_70,type,
fo__c_2Enum_2E0: tp__ty_2Enum_2Enum ).
tff(decl_71,type,
c_2Ewords_2En2w: del > $i ).
tff(decl_72,type,
c_2Ewords_2Eword__2comp: del > $i ).
tff(decl_76,type,
esk3_0: del ).
fof(ax_false_p,axiom,
~ p(c_2Ebool_2EF),
file('/export/starexec/sandbox2/tmp/tmp.SUb1PjUPWi/E---3.1_7833.p',ax_false_p) ).
tff(boolext,axiom,
! [X5] :
( mem(X5,bool)
=> ! [X6] :
( mem(X6,bool)
=> ( ( p(X5)
<=> p(X6) )
=> ( X5 = X6 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.SUb1PjUPWi/E---3.1_7833.p',boolext) ).
tff(stp_inj_surj_ty_2Einteger_2Eint,axiom,
! [X13: tp__ty_2Einteger_2Eint] : ( surj__ty_2Einteger_2Eint(inj__ty_2Einteger_2Eint(X13)) = X13 ),
file('/export/starexec/sandbox2/tmp/tmp.SUb1PjUPWi/E---3.1_7833.p',stp_inj_surj_ty_2Einteger_2Eint) ).
tff(stp_eq_fo_c_2Einteger_2Eint__neg,axiom,
! [X15: tp__ty_2Einteger_2Eint] : ( inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__neg(X15)) = ap(c_2Einteger_2Eint__neg,inj__ty_2Einteger_2Eint(X15)) ),
file('/export/starexec/sandbox2/tmp/tmp.SUb1PjUPWi/E---3.1_7833.p',stp_eq_fo_c_2Einteger_2Eint__neg) ).
tff(stp_eq_fo_c_2Einteger_2Eint__of__num,axiom,
! [X19: tp__ty_2Enum_2Enum] : ( inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__of__num(X19)) = ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X19)) ),
file('/export/starexec/sandbox2/tmp/tmp.SUb1PjUPWi/E---3.1_7833.p',stp_eq_fo_c_2Einteger_2Eint__of__num) ).
tff(mem_c_2Ebool_2EF,axiom,
mem(c_2Ebool_2EF,bool),
file('/export/starexec/sandbox2/tmp/tmp.SUb1PjUPWi/E---3.1_7833.p',mem_c_2Ebool_2EF) ).
tff(stp_inj_mem_o,axiom,
! [X10: tp__o] : mem(inj__o(X10),bool),
file('/export/starexec/sandbox2/tmp/tmp.SUb1PjUPWi/E---3.1_7833.p',stp_inj_mem_o) ).
tff(stp_eq_fo_c_2Einteger_2Eint__lt,axiom,
! [X20: tp__ty_2Einteger_2Eint,X21: tp__ty_2Einteger_2Eint] : ( inj__o(fo__c_2Einteger_2Eint__lt(X20,X21)) = ap(ap(c_2Einteger_2Eint__lt,inj__ty_2Einteger_2Eint(X20)),inj__ty_2Einteger_2Eint(X21)) ),
file('/export/starexec/sandbox2/tmp/tmp.SUb1PjUPWi/E---3.1_7833.p',stp_eq_fo_c_2Einteger_2Eint__lt) ).
tff(conj_thm_2Einteger_2EINT__LT__CALCULATE,axiom,
! [X43: tp__ty_2Enum_2Enum,X44: tp__ty_2Enum_2Enum] :
( ( p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X43))),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X44))))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(X43)),inj__ty_2Enum_2Enum(X44))) )
& ( p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X43)))),ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X44)))))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(X44)),inj__ty_2Enum_2Enum(X43))) )
& ( p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X43)))),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X44))))
<=> ( ( X43 != fo__c_2Enum_2E0 )
| ( X44 != fo__c_2Enum_2E0 ) ) )
& ( p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X43))),ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X44)))))
<=> ~ $true ) ),
file('/export/starexec/sandbox2/tmp/tmp.SUb1PjUPWi/E---3.1_7833.p',conj_thm_2Einteger_2EINT__LT__CALCULATE) ).
tff(stp_inj_mem_ty_2Einteger_2Eint,axiom,
! [X14: tp__ty_2Einteger_2Eint] : mem(inj__ty_2Einteger_2Eint(X14),ty_2Einteger_2Eint),
file('/export/starexec/sandbox2/tmp/tmp.SUb1PjUPWi/E---3.1_7833.p',stp_inj_mem_ty_2Einteger_2Eint) ).
tff(stp_eq_fo_c_2Einteger_2ENum,axiom,
! [X18: tp__ty_2Einteger_2Eint] : ( inj__ty_2Enum_2Enum(fo__c_2Einteger_2ENum(X18)) = ap(c_2Einteger_2ENum,inj__ty_2Einteger_2Eint(X18)) ),
file('/export/starexec/sandbox2/tmp/tmp.SUb1PjUPWi/E---3.1_7833.p',stp_eq_fo_c_2Einteger_2ENum) ).
tff(stp_iso_mem_ty_2Einteger_2Eint,axiom,
! [X4] :
( mem(X4,ty_2Einteger_2Eint)
=> ( X4 = inj__ty_2Einteger_2Eint(surj__ty_2Einteger_2Eint(X4)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.SUb1PjUPWi/E---3.1_7833.p',stp_iso_mem_ty_2Einteger_2Eint) ).
tff(conj_thm_2Einteger_2EINT__NEG__0,axiom,
surj__ty_2Einteger_2Eint(ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) = surj__ty_2Einteger_2Eint(ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),
file('/export/starexec/sandbox2/tmp/tmp.SUb1PjUPWi/E---3.1_7833.p',conj_thm_2Einteger_2EINT__NEG__0) ).
tff(ax_thm_2Einteger__word_2Ei2w__def,axiom,
! [X22: del,X45: tp__ty_2Einteger_2Eint] : ( ap(c_2Einteger__word_2Ei2w(X22),inj__ty_2Einteger_2Eint(X45)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,X22)),ap(ap(c_2Einteger_2Eint__lt,inj__ty_2Einteger_2Eint(X45)),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))),ap(c_2Ewords_2Eword__2comp(X22),ap(c_2Ewords_2En2w(X22),ap(c_2Einteger_2ENum,ap(c_2Einteger_2Eint__neg,inj__ty_2Einteger_2Eint(X45)))))),ap(c_2Ewords_2En2w(X22),ap(c_2Einteger_2ENum,inj__ty_2Einteger_2Eint(X45)))) ),
file('/export/starexec/sandbox2/tmp/tmp.SUb1PjUPWi/E---3.1_7833.p',ax_thm_2Einteger__word_2Ei2w__def) ).
tff(stp_inj_surj_ty_2Enum_2Enum,axiom,
! [X16: tp__ty_2Enum_2Enum] : ( surj__ty_2Enum_2Enum(inj__ty_2Enum_2Enum(X16)) = X16 ),
file('/export/starexec/sandbox2/tmp/tmp.SUb1PjUPWi/E---3.1_7833.p',stp_inj_surj_ty_2Enum_2Enum) ).
tff(conj_thm_2Einteger_2ENUM__OF__INT,axiom,
! [X43: tp__ty_2Enum_2Enum] : ( surj__ty_2Enum_2Enum(ap(c_2Einteger_2ENum,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X43)))) = X43 ),
file('/export/starexec/sandbox2/tmp/tmp.SUb1PjUPWi/E---3.1_7833.p',conj_thm_2Einteger_2ENUM__OF__INT) ).
tff(conj_thm_2Ebool_2Ebool__case__thm,axiom,
! [X22: del] :
( ! [X39] :
( mem(X39,X22)
=> ! [X40] :
( mem(X40,X22)
=> ( ap(ap(ap(c_2Ebool_2ECOND(X22),inj__o(fo__c_2Ebool_2ET)),X39),X40) = X39 ) ) )
& ! [X41] :
( mem(X41,X22)
=> ! [X42] :
( mem(X42,X22)
=> ( ap(ap(ap(c_2Ebool_2ECOND(X22),inj__o(fo__c_2Ebool_2EF)),X41),X42) = X42 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.SUb1PjUPWi/E---3.1_7833.p',conj_thm_2Ebool_2Ebool__case__thm) ).
tff(conj_thm_2Ewords_2EWORD__NEG__0,axiom,
! [X22: del] : ( ap(c_2Ewords_2Eword__2comp(X22),ap(c_2Ewords_2En2w(X22),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = ap(c_2Ewords_2En2w(X22),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)) ),
file('/export/starexec/sandbox2/tmp/tmp.SUb1PjUPWi/E---3.1_7833.p',conj_thm_2Ewords_2EWORD__NEG__0) ).
tff(stp_eq_fo_c_2Ebool_2EF,axiom,
inj__o(fo__c_2Ebool_2EF) = c_2Ebool_2EF,
file('/export/starexec/sandbox2/tmp/tmp.SUb1PjUPWi/E---3.1_7833.p',stp_eq_fo_c_2Ebool_2EF) ).
tff(ap_tp,axiom,
! [X1: del,X2: del,X3] :
( mem(X3,arr(X1,X2))
=> ! [X4] :
( mem(X4,X1)
=> mem(ap(X3,X4),X2) ) ),
file('/export/starexec/sandbox2/tmp/tmp.SUb1PjUPWi/E---3.1_7833.p',ap_tp) ).
tff(mem_c_2Ewords_2En2w,axiom,
! [X22: del] : mem(c_2Ewords_2En2w(X22),arr(ty_2Enum_2Enum,ty_2Efcp_2Ecart(bool,X22))),
file('/export/starexec/sandbox2/tmp/tmp.SUb1PjUPWi/E---3.1_7833.p',mem_c_2Ewords_2En2w) ).
tff(conj_thm_2Einteger__word_2Ei2w__0,conjecture,
! [X22: del] : ( ap(c_2Einteger__word_2Ei2w(X22),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = ap(c_2Ewords_2En2w(X22),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)) ),
file('/export/starexec/sandbox2/tmp/tmp.SUb1PjUPWi/E---3.1_7833.p',conj_thm_2Einteger__word_2Ei2w__0) ).
tff(stp_inj_mem_ty_2Enum_2Enum,axiom,
! [X17: tp__ty_2Enum_2Enum] : mem(inj__ty_2Enum_2Enum(X17),ty_2Enum_2Enum),
file('/export/starexec/sandbox2/tmp/tmp.SUb1PjUPWi/E---3.1_7833.p',stp_inj_mem_ty_2Enum_2Enum) ).
fof(c_0_23,plain,
~ p(c_2Ebool_2EF),
inference(fof_simplification,[status(thm)],[ax_false_p]) ).
tff(c_0_24,plain,
! [X52,X53] :
( ( ~ p(X52)
| ~ p(X53)
| ( X52 = X53 )
| ~ mem(X53,bool)
| ~ mem(X52,bool) )
& ( p(X52)
| p(X53)
| ( X52 = X53 )
| ~ mem(X53,bool)
| ~ mem(X52,bool) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[boolext])])])])]) ).
fof(c_0_25,plain,
~ p(c_2Ebool_2EF),
inference(fof_nnf,[status(thm)],[c_0_23]) ).
tff(c_0_26,plain,
! [X79: tp__ty_2Einteger_2Eint] : ( surj__ty_2Einteger_2Eint(inj__ty_2Einteger_2Eint(X79)) = X79 ),
inference(variable_rename,[status(thm)],[stp_inj_surj_ty_2Einteger_2Eint]) ).
tff(c_0_27,plain,
! [X82: tp__ty_2Einteger_2Eint] : ( inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__neg(X82)) = ap(c_2Einteger_2Eint__neg,inj__ty_2Einteger_2Eint(X82)) ),
inference(variable_rename,[status(thm)],[stp_eq_fo_c_2Einteger_2Eint__neg]) ).
tff(c_0_28,plain,
! [X87: tp__ty_2Enum_2Enum] : ( inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__of__num(X87)) = ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X87)) ),
inference(variable_rename,[status(thm)],[stp_eq_fo_c_2Einteger_2Eint__of__num]) ).
tcf(c_0_29,plain,
! [X4,X3] :
( p(X3)
| p(X4)
| ( X3 = X4 )
| ~ mem(X4,bool)
| ~ mem(X3,bool) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
tcf(c_0_30,plain,
mem(c_2Ebool_2EF,bool),
inference(split_conjunct,[status(thm)],[mem_c_2Ebool_2EF]) ).
cnf(c_0_31,plain,
~ p(c_2Ebool_2EF),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
tff(c_0_32,plain,
! [X65: tp__o] : mem(inj__o(X65),bool),
inference(variable_rename,[status(thm)],[stp_inj_mem_o]) ).
tff(c_0_33,plain,
! [X88: tp__ty_2Einteger_2Eint,X89: tp__ty_2Einteger_2Eint] : ( inj__o(fo__c_2Einteger_2Eint__lt(X88,X89)) = ap(ap(c_2Einteger_2Eint__lt,inj__ty_2Einteger_2Eint(X88)),inj__ty_2Einteger_2Eint(X89)) ),
inference(variable_rename,[status(thm)],[stp_eq_fo_c_2Einteger_2Eint__lt]) ).
tcf(c_0_34,plain,
! [X13: tp__ty_2Einteger_2Eint] : surj__ty_2Einteger_2Eint(inj__ty_2Einteger_2Eint(X13)) = X13,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
tcf(c_0_35,plain,
! [X13: tp__ty_2Einteger_2Eint] : inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__neg(X13)) = ap(c_2Einteger_2Eint__neg,inj__ty_2Einteger_2Eint(X13)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
tff(c_0_36,plain,
! [X43: tp__ty_2Enum_2Enum,X44: tp__ty_2Enum_2Enum] :
( ( p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X43))),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X44))))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(X43)),inj__ty_2Enum_2Enum(X44))) )
& ( p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X43)))),ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X44)))))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(X44)),inj__ty_2Enum_2Enum(X43))) )
& ( p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X43)))),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X44))))
<=> ( ( X43 != fo__c_2Enum_2E0 )
| ( X44 != fo__c_2Enum_2E0 ) ) )
& ( p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X43))),ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X44)))))
<=> ~ $true ) ),
inference(fof_simplification,[status(thm)],[conj_thm_2Einteger_2EINT__LT__CALCULATE]) ).
tcf(c_0_37,plain,
! [X16: tp__ty_2Enum_2Enum] : inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__of__num(X16)) = ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X16)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
tff(c_0_38,plain,
! [X80: tp__ty_2Einteger_2Eint] : mem(inj__ty_2Einteger_2Eint(X80),ty_2Einteger_2Eint),
inference(variable_rename,[status(thm)],[stp_inj_mem_ty_2Einteger_2Eint]) ).
tff(c_0_39,plain,
! [X86: tp__ty_2Einteger_2Eint] : ( inj__ty_2Enum_2Enum(fo__c_2Einteger_2ENum(X86)) = ap(c_2Einteger_2ENum,inj__ty_2Einteger_2Eint(X86)) ),
inference(variable_rename,[status(thm)],[stp_eq_fo_c_2Einteger_2ENum]) ).
tcf(c_0_40,plain,
! [X3] :
( ( X3 = c_2Ebool_2EF )
| p(X3)
| ~ mem(X3,bool) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
tcf(c_0_41,plain,
! [X9: tp__o] : mem(inj__o(X9),bool),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
tcf(c_0_42,plain,
! [X13: tp__ty_2Einteger_2Eint,X14: tp__ty_2Einteger_2Eint] : inj__o(fo__c_2Einteger_2Eint__lt(X13,X14)) = ap(ap(c_2Einteger_2Eint__lt,inj__ty_2Einteger_2Eint(X13)),inj__ty_2Einteger_2Eint(X14)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
tcf(c_0_43,plain,
! [X13: tp__ty_2Einteger_2Eint] : surj__ty_2Einteger_2Eint(ap(c_2Einteger_2Eint__neg,inj__ty_2Einteger_2Eint(X13))) = fo__c_2Einteger_2Eint__neg(X13),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
tff(c_0_44,plain,
! [X134: tp__ty_2Enum_2Enum,X135: tp__ty_2Enum_2Enum] :
( ( ~ p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X134))),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X135))))
| p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(X134)),inj__ty_2Enum_2Enum(X135))) )
& ( ~ p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(X134)),inj__ty_2Enum_2Enum(X135)))
| p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X134))),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X135)))) )
& ( ~ p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X134)))),ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X135)))))
| p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(X135)),inj__ty_2Enum_2Enum(X134))) )
& ( ~ p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(X135)),inj__ty_2Enum_2Enum(X134)))
| p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X134)))),ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X135))))) )
& ( ~ p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X134)))),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X135))))
| ( X134 != fo__c_2Enum_2E0 )
| ( X135 != fo__c_2Enum_2E0 ) )
& ( ( X134 = fo__c_2Enum_2E0 )
| p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X134)))),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X135)))) )
& ( ( X135 = fo__c_2Enum_2E0 )
| p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X134)))),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X135)))) )
& ( ~ p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X134))),ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X135)))))
| ~ $true )
& ( $true
| p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X134))),ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X135))))) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])])]) ).
tff(c_0_45,plain,
! [X81] :
( ~ mem(X81,ty_2Einteger_2Eint)
| ( X81 = inj__ty_2Einteger_2Eint(surj__ty_2Einteger_2Eint(X81)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[stp_iso_mem_ty_2Einteger_2Eint])])]) ).
tcf(c_0_46,plain,
surj__ty_2Einteger_2Eint(ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) = surj__ty_2Einteger_2Eint(ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),
inference(split_conjunct,[status(thm)],[conj_thm_2Einteger_2EINT__NEG__0]) ).
tcf(c_0_47,plain,
! [X16: tp__ty_2Enum_2Enum] : surj__ty_2Einteger_2Eint(ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X16))) = fo__c_2Einteger_2Eint__of__num(X16),
inference(spm,[status(thm)],[c_0_34,c_0_37]) ).
tcf(c_0_48,plain,
! [X13: tp__ty_2Einteger_2Eint] : mem(inj__ty_2Einteger_2Eint(X13),ty_2Einteger_2Eint),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
tff(c_0_49,plain,
! [X137: del,X138: tp__ty_2Einteger_2Eint] : ( ap(c_2Einteger__word_2Ei2w(X137),inj__ty_2Einteger_2Eint(X138)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,X137)),ap(ap(c_2Einteger_2Eint__lt,inj__ty_2Einteger_2Eint(X138)),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))),ap(c_2Ewords_2Eword__2comp(X137),ap(c_2Ewords_2En2w(X137),ap(c_2Einteger_2ENum,ap(c_2Einteger_2Eint__neg,inj__ty_2Einteger_2Eint(X138)))))),ap(c_2Ewords_2En2w(X137),ap(c_2Einteger_2ENum,inj__ty_2Einteger_2Eint(X138)))) ),
inference(variable_rename,[status(thm)],[ax_thm_2Einteger__word_2Ei2w__def]) ).
tff(c_0_50,plain,
! [X83: tp__ty_2Enum_2Enum] : ( surj__ty_2Enum_2Enum(inj__ty_2Enum_2Enum(X83)) = X83 ),
inference(variable_rename,[status(thm)],[stp_inj_surj_ty_2Enum_2Enum]) ).
tcf(c_0_51,plain,
! [X13: tp__ty_2Einteger_2Eint] : inj__ty_2Enum_2Enum(fo__c_2Einteger_2ENum(X13)) = ap(c_2Einteger_2ENum,inj__ty_2Einteger_2Eint(X13)),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
tff(c_0_52,plain,
! [X136: tp__ty_2Enum_2Enum] : ( surj__ty_2Enum_2Enum(ap(c_2Einteger_2ENum,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X136)))) = X136 ),
inference(variable_rename,[status(thm)],[conj_thm_2Einteger_2ENUM__OF__INT]) ).
tcf(c_0_53,plain,
! [X9: tp__o] :
( ( inj__o(X9) = c_2Ebool_2EF )
| p(inj__o(X9)) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
tcf(c_0_54,plain,
! [X16: tp__ty_2Enum_2Enum,X13: tp__ty_2Einteger_2Eint] : inj__o(fo__c_2Einteger_2Eint__lt(fo__c_2Einteger_2Eint__of__num(X16),X13)) = ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X16))),inj__ty_2Einteger_2Eint(X13)),
inference(spm,[status(thm)],[c_0_42,c_0_37]) ).
tcf(c_0_55,plain,
! [X16: tp__ty_2Enum_2Enum] : fo__c_2Einteger_2Eint__neg(fo__c_2Einteger_2Eint__of__num(X16)) = surj__ty_2Einteger_2Eint(ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X16)))),
inference(spm,[status(thm)],[c_0_43,c_0_37]) ).
tcf(c_0_56,plain,
! [X16: tp__ty_2Enum_2Enum,X17: tp__ty_2Enum_2Enum] :
( ~ p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X16))),ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X17)))))
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
tcf(c_0_57,plain,
! [X3] :
( ( X3 = inj__ty_2Einteger_2Eint(surj__ty_2Einteger_2Eint(X3)) )
| ~ mem(X3,ty_2Einteger_2Eint) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
tcf(c_0_58,plain,
surj__ty_2Einteger_2Eint(ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) = fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0),
inference(rw,[status(thm)],[c_0_46,c_0_47]) ).
tcf(c_0_59,plain,
! [X13: tp__ty_2Einteger_2Eint] : mem(ap(c_2Einteger_2Eint__neg,inj__ty_2Einteger_2Eint(X13)),ty_2Einteger_2Eint),
inference(spm,[status(thm)],[c_0_48,c_0_35]) ).
tcf(c_0_60,plain,
! [X1: del,X13: tp__ty_2Einteger_2Eint] : ap(c_2Einteger__word_2Ei2w(X1),inj__ty_2Einteger_2Eint(X13)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,X1)),ap(ap(c_2Einteger_2Eint__lt,inj__ty_2Einteger_2Eint(X13)),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))),ap(c_2Ewords_2Eword__2comp(X1),ap(c_2Ewords_2En2w(X1),ap(c_2Einteger_2ENum,ap(c_2Einteger_2Eint__neg,inj__ty_2Einteger_2Eint(X13)))))),ap(c_2Ewords_2En2w(X1),ap(c_2Einteger_2ENum,inj__ty_2Einteger_2Eint(X13)))),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
tcf(c_0_61,plain,
! [X16: tp__ty_2Enum_2Enum] : surj__ty_2Enum_2Enum(inj__ty_2Enum_2Enum(X16)) = X16,
inference(split_conjunct,[status(thm)],[c_0_50]) ).
tcf(c_0_62,plain,
! [X16: tp__ty_2Enum_2Enum] : inj__ty_2Enum_2Enum(fo__c_2Einteger_2ENum(fo__c_2Einteger_2Eint__of__num(X16))) = ap(c_2Einteger_2ENum,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X16))),
inference(spm,[status(thm)],[c_0_51,c_0_37]) ).
tcf(c_0_63,plain,
! [X16: tp__ty_2Enum_2Enum] : surj__ty_2Enum_2Enum(ap(c_2Einteger_2ENum,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X16)))) = X16,
inference(split_conjunct,[status(thm)],[c_0_52]) ).
tcf(c_0_64,plain,
! [X16: tp__ty_2Enum_2Enum,X13: tp__ty_2Einteger_2Eint] :
( ( ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X16))),inj__ty_2Einteger_2Eint(X13)) = c_2Ebool_2EF )
| p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X16))),inj__ty_2Einteger_2Eint(X13))) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
tcf(c_0_65,plain,
! [X16: tp__ty_2Enum_2Enum] : inj__ty_2Einteger_2Eint(surj__ty_2Einteger_2Eint(ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X16))))) = ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X16))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_55]),c_0_37]) ).
tcf(c_0_66,plain,
! [X16: tp__ty_2Enum_2Enum,X17: tp__ty_2Enum_2Enum] : ~ p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X16))),ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X17))))),
inference(cn,[status(thm)],[c_0_56]) ).
tcf(c_0_67,plain,
( ( ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)) )
| ~ mem(ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ty_2Einteger_2Eint) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_37]) ).
tcf(c_0_68,plain,
! [X16: tp__ty_2Enum_2Enum] : mem(ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X16))),ty_2Einteger_2Eint),
inference(spm,[status(thm)],[c_0_59,c_0_37]) ).
tff(c_0_69,plain,
! [X129: del,X130,X131,X132,X133] :
( ( ~ mem(X130,X129)
| ~ mem(X131,X129)
| ( ap(ap(ap(c_2Ebool_2ECOND(X129),inj__o(fo__c_2Ebool_2ET)),X130),X131) = X130 ) )
& ( ~ mem(X132,X129)
| ~ mem(X133,X129)
| ( ap(ap(ap(c_2Ebool_2ECOND(X129),inj__o(fo__c_2Ebool_2EF)),X132),X133) = X133 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Ebool_2Ebool__case__thm])])])]) ).
tcf(c_0_70,plain,
! [X1: del,X13: tp__ty_2Einteger_2Eint] : ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,X1)),ap(ap(c_2Einteger_2Eint__lt,inj__ty_2Einteger_2Eint(X13)),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))),ap(c_2Ewords_2Eword__2comp(X1),ap(c_2Ewords_2En2w(X1),ap(c_2Einteger_2ENum,ap(c_2Einteger_2Eint__neg,inj__ty_2Einteger_2Eint(X13)))))),ap(c_2Ewords_2En2w(X1),inj__ty_2Enum_2Enum(fo__c_2Einteger_2ENum(X13)))) = ap(c_2Einteger__word_2Ei2w(X1),inj__ty_2Einteger_2Eint(X13)),
inference(rw,[status(thm)],[c_0_60,c_0_51]) ).
tcf(c_0_71,plain,
! [X16: tp__ty_2Enum_2Enum] : fo__c_2Einteger_2ENum(fo__c_2Einteger_2Eint__of__num(X16)) = X16,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]) ).
tff(c_0_72,plain,
! [X143: del] : ( ap(c_2Ewords_2Eword__2comp(X143),ap(c_2Ewords_2En2w(X143),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = ap(c_2Ewords_2En2w(X143),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)) ),
inference(variable_rename,[status(thm)],[conj_thm_2Ewords_2EWORD__NEG__0]) ).
tcf(c_0_73,plain,
! [X16: tp__ty_2Enum_2Enum,X17: tp__ty_2Enum_2Enum] : ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X16))),ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X17)))) = c_2Ebool_2EF,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66]) ).
tcf(c_0_74,plain,
ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68])]) ).
tcf(c_0_75,plain,
! [X4,X3,X1: del] :
( ( ap(ap(ap(c_2Ebool_2ECOND(X1),inj__o(fo__c_2Ebool_2EF)),X3),X4) = X4 )
| ~ mem(X3,X1)
| ~ mem(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
tcf(c_0_76,plain,
inj__o(fo__c_2Ebool_2EF) = c_2Ebool_2EF,
inference(split_conjunct,[status(thm)],[stp_eq_fo_c_2Ebool_2EF]) ).
tcf(c_0_77,plain,
! [X1: del,X16: tp__ty_2Enum_2Enum] : ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,X1)),ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X16))),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))),ap(c_2Ewords_2Eword__2comp(X1),ap(c_2Ewords_2En2w(X1),ap(c_2Einteger_2ENum,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X16))))))),ap(c_2Ewords_2En2w(X1),inj__ty_2Enum_2Enum(X16))) = ap(c_2Einteger__word_2Ei2w(X1),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X16))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_37]),c_0_37]),c_0_37]) ).
tcf(c_0_78,plain,
! [X16: tp__ty_2Enum_2Enum] : ap(c_2Einteger_2ENum,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X16))) = inj__ty_2Enum_2Enum(X16),
inference(rw,[status(thm)],[c_0_62,c_0_71]) ).
tcf(c_0_79,plain,
! [X1: del] : ap(c_2Ewords_2Eword__2comp(X1),ap(c_2Ewords_2En2w(X1),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = ap(c_2Ewords_2En2w(X1),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
tcf(c_0_80,plain,
! [X16: tp__ty_2Enum_2Enum] : ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X16))),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = c_2Ebool_2EF,
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
tff(c_0_81,plain,
! [X48: del,X49: del,X50,X51] :
( ~ mem(X50,arr(X48,X49))
| ~ mem(X51,X48)
| mem(ap(X50,X51),X49) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ap_tp])])])]) ).
tff(c_0_82,plain,
! [X105: del] : mem(c_2Ewords_2En2w(X105),arr(ty_2Enum_2Enum,ty_2Efcp_2Ecart(bool,X105))),
inference(variable_rename,[status(thm)],[mem_c_2Ewords_2En2w]) ).
tff(c_0_83,negated_conjecture,
~ ! [X22: del] : ( ap(c_2Einteger__word_2Ei2w(X22),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = ap(c_2Ewords_2En2w(X22),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)) ),
inference(assume_negation,[status(cth)],[conj_thm_2Einteger__word_2Ei2w__0]) ).
tcf(c_0_84,plain,
! [X4,X3,X1: del] :
( ( ap(ap(ap(c_2Ebool_2ECOND(X1),c_2Ebool_2EF),X3),X4) = X4 )
| ~ mem(X4,X1)
| ~ mem(X3,X1) ),
inference(rw,[status(thm)],[c_0_75,c_0_76]) ).
tcf(c_0_85,plain,
! [X1: del] : ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,X1)),c_2Ebool_2EF),ap(c_2Ewords_2En2w(X1),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Ewords_2En2w(X1),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = ap(c_2Einteger__word_2Ei2w(X1),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_74]),c_0_78]),c_0_79]),c_0_80]) ).
tcf(c_0_86,plain,
! [X2: del,X4,X3,X1: del] :
( mem(ap(X3,X4),X2)
| ~ mem(X3,arr(X1,X2))
| ~ mem(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
tcf(c_0_87,plain,
! [X1: del] : mem(c_2Ewords_2En2w(X1),arr(ty_2Enum_2Enum,ty_2Efcp_2Ecart(bool,X1))),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
tff(c_0_88,plain,
! [X84: tp__ty_2Enum_2Enum] : mem(inj__ty_2Enum_2Enum(X84),ty_2Enum_2Enum),
inference(variable_rename,[status(thm)],[stp_inj_mem_ty_2Enum_2Enum]) ).
tff(c_0_89,negated_conjecture,
ap(c_2Einteger__word_2Ei2w(esk3_0),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) != ap(c_2Ewords_2En2w(esk3_0),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_83])])])]) ).
tcf(c_0_90,plain,
! [X1: del] :
( ( ap(c_2Einteger__word_2Ei2w(X1),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = ap(c_2Ewords_2En2w(X1),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)) )
| ~ mem(ap(c_2Ewords_2En2w(X1),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),ty_2Efcp_2Ecart(bool,X1)) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
tcf(c_0_91,plain,
! [X1: del,X3] :
( mem(ap(c_2Ewords_2En2w(X1),X3),ty_2Efcp_2Ecart(bool,X1))
| ~ mem(X3,ty_2Enum_2Enum) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
tcf(c_0_92,plain,
! [X16: tp__ty_2Enum_2Enum] : mem(inj__ty_2Enum_2Enum(X16),ty_2Enum_2Enum),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
tcf(c_0_93,negated_conjecture,
ap(c_2Einteger__word_2Ei2w(esk3_0),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) != ap(c_2Ewords_2En2w(esk3_0),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
tcf(c_0_94,plain,
! [X1: del] : ap(c_2Einteger__word_2Ei2w(X1),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = ap(c_2Ewords_2En2w(X1),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92])]) ).
cnf(c_0_95,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_94])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.14 % Problem : ITP015_2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.11/0.15 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n014.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 11:58:32 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.21/0.51 Running first-order theorem proving
% 0.21/0.51 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.SUb1PjUPWi/E---3.1_7833.p
% 203.89/26.30 # Version: 3.1.0
% 203.89/26.30 # Preprocessing class: FSLSSMSMSSSNFFN.
% 203.89/26.30 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 203.89/26.30 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 203.89/26.30 # Starting new_bool_3 with 300s (1) cores
% 203.89/26.30 # Starting new_bool_1 with 300s (1) cores
% 203.89/26.30 # Starting sh5l with 300s (1) cores
% 203.89/26.30 # C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 7986 completed with status 0
% 203.89/26.30 # Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 203.89/26.30 # Preprocessing class: FSLSSMSMSSSNFFN.
% 203.89/26.30 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 203.89/26.30 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 203.89/26.30 # No SInE strategy applied
% 203.89/26.30 # Search class: FGHSM-FFMM31-DFFFFFNN
% 203.89/26.30 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 203.89/26.30 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 450s (1) cores
% 203.89/26.30 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 203.89/26.30 # Starting new_bool_3 with 226s (1) cores
% 203.89/26.30 # Starting new_bool_1 with 226s (1) cores
% 203.89/26.30 # Starting sh5l with 226s (1) cores
% 203.89/26.30 # C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 8002 completed with status 0
% 203.89/26.30 # Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 203.89/26.30 # Preprocessing class: FSLSSMSMSSSNFFN.
% 203.89/26.30 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 203.89/26.30 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 203.89/26.30 # No SInE strategy applied
% 203.89/26.30 # Search class: FGHSM-FFMM31-DFFFFFNN
% 203.89/26.30 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 203.89/26.30 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 450s (1) cores
% 203.89/26.30 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 203.89/26.30 # Preprocessing time : 0.005 s
% 203.89/26.30 # Presaturation interreduction done
% 203.89/26.30
% 203.89/26.30 # Proof found!
% 203.89/26.30 # SZS status Theorem
% 203.89/26.30 # SZS output start CNFRefutation
% See solution above
% 203.89/26.30 # Parsed axioms : 128
% 203.89/26.30 # Removed by relevancy pruning/SinE : 0
% 203.89/26.30 # Initial clauses : 171
% 203.89/26.30 # Removed in clause preprocessing : 81
% 203.89/26.30 # Initial clauses in saturation : 90
% 203.89/26.30 # Processed clauses : 49021
% 203.89/26.30 # ...of these trivial : 261
% 203.89/26.30 # ...subsumed : 44271
% 203.89/26.30 # ...remaining for further processing : 4489
% 203.89/26.30 # Other redundant clauses eliminated : 6977
% 203.89/26.30 # Clauses deleted for lack of memory : 0
% 203.89/26.30 # Backward-subsumed : 117
% 203.89/26.30 # Backward-rewritten : 73
% 203.89/26.30 # Generated clauses : 2441445
% 203.89/26.30 # ...of the previous two non-redundant : 2292350
% 203.89/26.30 # ...aggressively subsumed : 0
% 203.89/26.30 # Contextual simplify-reflections : 43
% 203.89/26.30 # Paramodulations : 2433762
% 203.89/26.30 # Factorizations : 692
% 203.89/26.30 # NegExts : 0
% 203.89/26.30 # Equation resolutions : 6994
% 203.89/26.30 # Disequality decompositions : 0
% 203.89/26.30 # Total rewrite steps : 1000617
% 203.89/26.30 # ...of those cached : 993485
% 203.89/26.30 # Propositional unsat checks : 0
% 203.89/26.30 # Propositional check models : 0
% 203.89/26.30 # Propositional check unsatisfiable : 0
% 203.89/26.30 # Propositional clauses : 0
% 203.89/26.30 # Propositional clauses after purity: 0
% 203.89/26.30 # Propositional unsat core size : 0
% 203.89/26.30 # Propositional preprocessing time : 0.000
% 203.89/26.30 # Propositional encoding time : 0.000
% 203.89/26.30 # Propositional solver time : 0.000
% 203.89/26.30 # Success case prop preproc time : 0.000
% 203.89/26.30 # Success case prop encoding time : 0.000
% 203.89/26.30 # Success case prop solver time : 0.000
% 203.89/26.30 # Current number of processed clauses : 4204
% 203.89/26.30 # Positive orientable unit clauses : 513
% 203.89/26.30 # Positive unorientable unit clauses: 0
% 203.89/26.30 # Negative unit clauses : 45
% 203.89/26.30 # Non-unit-clauses : 3646
% 203.89/26.30 # Current number of unprocessed clauses: 2241680
% 203.89/26.30 # ...number of literals in the above : 9079955
% 203.89/26.30 # Current number of archived formulas : 0
% 203.89/26.30 # Current number of archived clauses : 279
% 203.89/26.30 # Clause-clause subsumption calls (NU) : 1515748
% 203.89/26.30 # Rec. Clause-clause subsumption calls : 813205
% 203.89/26.30 # Non-unit clause-clause subsumptions : 20127
% 203.89/26.30 # Unit Clause-clause subsumption calls : 26441
% 203.89/26.30 # Rewrite failures with RHS unbound : 0
% 203.89/26.30 # BW rewrite match attempts : 5524
% 203.89/26.30 # BW rewrite match successes : 60
% 203.89/26.30 # Condensation attempts : 0
% 203.89/26.30 # Condensation successes : 0
% 203.89/26.30 # Termbank termtop insertions : 48403992
% 203.89/26.30 # Search garbage collected termcells : 1143
% 203.89/26.30
% 203.89/26.30 # -------------------------------------------------
% 203.89/26.30 # User time : 24.308 s
% 203.89/26.30 # System time : 0.896 s
% 203.89/26.30 # Total time : 25.204 s
% 203.89/26.30 # Maximum resident set size: 2148 pages
% 203.89/26.30
% 203.89/26.30 # -------------------------------------------------
% 203.89/26.30 # User time : 125.067 s
% 203.89/26.30 # System time : 1.895 s
% 203.89/26.30 # Total time : 126.962 s
% 203.89/26.30 # Maximum resident set size: 1840 pages
% 203.89/26.30 % E---3.1 exiting
% 203.89/26.30 % E exiting
%------------------------------------------------------------------------------