TSTP Solution File: SCT124+1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SCT124+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n015.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 : Tue May 21 02:44:59 EDT 2024
% Result : Theorem 102.59s 13.55s
% Output : CNFRefutation 102.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 30
% Syntax : Number of formulae : 265 ( 99 unt; 0 def)
% Number of atoms : 540 ( 156 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 457 ( 182 ~; 224 |; 14 &)
% ( 4 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 28 ( 28 usr; 7 con; 0-4 aty)
% Number of variables : 760 ( 285 sgn 196 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Lin__irrefl,axiom,
! [X18,X19,X17] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X17),c_Arrow__Order__Mirabelle_OLin))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X19),X18)),X17))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X18),X19)),X17)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Lin__irrefl) ).
fof(fact_mem__def,axiom,
! [X8,X6,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X6),X8))
<=> hBOOL(hAPP(X8,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).
fof(fact_r__into__trancl_H,axiom,
! [X26,X50,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X50),X26))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X50),c_Transitive__Closure_Otrancl(X10,X26))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__into__trancl_H) ).
fof(fact_insertE,axiom,
! [X8,X18,X19,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X19),c_Set_Oinsert(X10,X18,X8)))
=> ( X19 != X18
=> hBOOL(hAPP(hAPP(c_member(X10),X19),X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertE) ).
fof(fact_insert__subset,axiom,
! [X7,X8,X6,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),c_Set_Oinsert(X10,X6,X8),X7)
<=> ( hBOOL(hAPP(hAPP(c_member(X10),X6),X7))
& c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X8,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__subset) ).
fof(fact_subset__insertI,axiom,
! [X19,X7,X10] : c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X7,c_Set_Oinsert(X10,X19,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI) ).
fof(fact_insert__code,axiom,
! [X6,X8,X16,X10] :
( hBOOL(hAPP(c_Set_Oinsert(X10,X16,X8),X6))
<=> ( X16 = X6
| hBOOL(hAPP(X8,X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__code) ).
fof(fact_split__paired__All,axiom,
! [X9,X10,X24] :
( ! [X47] : hBOOL(hAPP(X24,X47))
<=> ! [X14,X15] : hBOOL(hAPP(X24,hAPP(hAPP(c_Product__Type_OPair(X10,X9),X14),X15))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__paired__All) ).
fof(fact_rev__predicate1D,axiom,
! [X67,X10,X6,X24] :
( hBOOL(hAPP(X24,X6))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X24,X67)
=> hBOOL(hAPP(X67,X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate1D) ).
fof(fact_top1I,axiom,
! [X6,X10] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top1I) ).
fof(fact_UNIV__I,axiom,
! [X6,X10] : hBOOL(hAPP(hAPP(c_member(X10),X6),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__I) ).
fof(fact_linear__alt,axiom,
? [X42] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X42),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linear__alt) ).
fof(help_c__COMBK__1,axiom,
! [X92,X91,X9,X10] : hAPP(c_COMBK(X10,X9,X91),X92) = X91,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_equalityI,axiom,
! [X7,X8,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X8,X7)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X7,X8)
=> X8 = X7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityI) ).
fof(fact_subset__UNIV,axiom,
! [X8,X10] : c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X8,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__UNIV) ).
fof(fact_subrelI,axiom,
! [X25,X26,X9,X10] :
( ! [X3,X41] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X9)),hAPP(hAPP(c_Product__Type_OPair(X10,X9),X3),X41)),X26))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X9)),hAPP(hAPP(c_Product__Type_OPair(X10,X9),X3),X41)),X25)) )
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X9),tc_HOL_Obool),X26,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subrelI) ).
fof(fact_ext,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
fof(fact_r__into__rtrancl,axiom,
! [X26,X50,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X50),X26))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X50),c_Transitive__Closure_Ortrancl(X10,X26))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__into__rtrancl) ).
fof(fact_dictatorI,axiom,
! [X4,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X5),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
=> ! [X14,X15] :
( X14 != X15
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X14),X15)),hAPP(X3,X4)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X14),X15)),hAPP(X5,X3))) ) ) )
=> c_Arrow__Order__Mirabelle_Odictator(X5,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dictatorI) ).
fof(fact_rtrancl_Ortrancl__refl,axiom,
! [X26,X19,X10] : hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X19),X19)),c_Transitive__Closure_Ortrancl(X10,X26))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__refl) ).
fof(conj_0,conjecture,
? [X47] : c_Arrow__Order__Mirabelle_Odictator(v_F,X47),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_assms_I1_J,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms_I1_J) ).
fof(fact_subsetD,axiom,
! [X11,X7,X8,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X8,X7)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X11),X8))
=> hBOOL(hAPP(hAPP(c_member(X10),X11),X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subsetD) ).
fof(fact_insertI1,axiom,
! [X7,X19,X10] : hBOOL(hAPP(hAPP(c_member(X10),X19),c_Set_Oinsert(X10,X19,X7))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI1) ).
fof(fact_insert__absorb,axiom,
! [X8,X19,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X19),X8))
=> c_Set_Oinsert(X10,X19,X8) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb) ).
fof(fact_insert__absorb2,axiom,
! [X8,X6,X10] : c_Set_Oinsert(X10,X6,c_Set_Oinsert(X10,X6,X8)) = c_Set_Oinsert(X10,X6,X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb2) ).
fof(fact_insert__commute,axiom,
! [X8,X16,X6,X10] : c_Set_Oinsert(X10,X6,c_Set_Oinsert(X10,X16,X8)) = c_Set_Oinsert(X10,X16,c_Set_Oinsert(X10,X6,X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__commute) ).
fof(fact_complete__Lin,axiom,
! [X18,X19] :
( X19 != X18
=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X19),X18)),X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complete__Lin) ).
fof(fact_subset__refl,axiom,
! [X8,X10] : c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X8,X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__refl) ).
fof(fact_subset__insertI2,axiom,
! [X18,X7,X8,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X8,X7)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X8,c_Set_Oinsert(X10,X18,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI2) ).
fof(c_0_30,plain,
! [X18,X19,X17] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X17),c_Arrow__Order__Mirabelle_OLin))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X19),X18)),X17))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X18),X19)),X17)) ) ),
inference(fof_simplification,[status(thm)],[fact_Lin__irrefl]) ).
fof(c_0_31,plain,
! [X194,X195,X196] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X196),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X195),X194)),X196))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X194),X195)),X196)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])]) ).
fof(c_0_32,plain,
! [X112,X113,X114] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X114),X113),X112))
| hBOOL(hAPP(X112,X113)) )
& ( ~ hBOOL(hAPP(X112,X113))
| hBOOL(hAPP(hAPP(c_member(X114),X113),X112)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])])]) ).
cnf(c_0_33,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_34,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X2),X1))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_35,plain,
! [X594,X595,X596] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X596,X596)),X595),X594))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X596,X596)),X595),c_Transitive__Closure_Otrancl(X596,X594))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__into__trancl_H])])]) ).
cnf(c_0_36,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(X3,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1))) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Otrancl(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_39,plain,
! [X8,X18,X19,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X19),c_Set_Oinsert(X10,X18,X8)))
=> ( X19 != X18
=> hBOOL(hAPP(hAPP(c_member(X10),X19),X8)) ) ),
inference(fof_simplification,[status(thm)],[fact_insertE]) ).
fof(c_0_40,plain,
! [X693,X694,X695,X696] :
( ( hBOOL(hAPP(hAPP(c_member(X696),X695),X693))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X696,tc_HOL_Obool),c_Set_Oinsert(X696,X695,X694),X693) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X696,tc_HOL_Obool),X694,X693)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X696,tc_HOL_Obool),c_Set_Oinsert(X696,X695,X694),X693) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X696),X695),X693))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X696,tc_HOL_Obool),X694,X693)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X696,tc_HOL_Obool),c_Set_Oinsert(X696,X695,X694),X693) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__subset])])])]) ).
fof(c_0_41,plain,
! [X744,X745,X746] : c_Orderings_Oord__class_Oless__eq(tc_fun(X746,tc_HOL_Obool),X745,c_Set_Oinsert(X746,X744,X745)),
inference(variable_rename,[status(thm)],[fact_subset__insertI]) ).
cnf(c_0_42,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2))) ),
inference(spm,[status(thm)],[c_0_36,c_0_34]) ).
fof(c_0_43,plain,
! [X728,X729,X730,X731] :
( ( ~ hBOOL(hAPP(c_Set_Oinsert(X731,X730,X729),X728))
| X730 = X728
| hBOOL(hAPP(X729,X728)) )
& ( X730 != X728
| hBOOL(hAPP(c_Set_Oinsert(X731,X730,X729),X728)) )
& ( ~ hBOOL(hAPP(X729,X728))
| hBOOL(hAPP(c_Set_Oinsert(X731,X730,X729),X728)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__code])])])]) ).
fof(c_0_44,plain,
! [X207,X208,X209,X211,X212,X213,X214,X215,X218] :
( ( ~ hBOOL(hAPP(X209,esk10_3(X207,X208,X209)))
| hBOOL(hAPP(X209,hAPP(hAPP(c_Product__Type_OPair(X208,X207),X211),X212))) )
& ( ~ hBOOL(hAPP(X215,hAPP(hAPP(c_Product__Type_OPair(X214,X213),esk11_3(X213,X214,X215)),esk12_3(X213,X214,X215))))
| hBOOL(hAPP(X215,X218)) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__paired__All])])])])])]) ).
cnf(c_0_45,plain,
( hBOOL(hAPP(c_Transitive__Closure_Otrancl(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X3),X2)) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
fof(c_0_46,plain,
! [X663,X664,X665,X666] :
( ~ hBOOL(hAPP(hAPP(c_member(X666),X665),c_Set_Oinsert(X666,X664,X663)))
| X665 = X664
| hBOOL(hAPP(hAPP(c_member(X666),X665),X663)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])]) ).
fof(c_0_47,plain,
! [X152,X153,X154,X155] :
( ~ hBOOL(hAPP(X155,X154))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X153,tc_HOL_Obool),X155,X152)
| hBOOL(hAPP(X152,X154)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate1D])])]) ).
cnf(c_0_48,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X4,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_49,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oinsert(X1,X3,X2)),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_50,plain,
( ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)))
| ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,X1)) ),
inference(spm,[status(thm)],[c_0_42,c_0_34]) ).
cnf(c_0_51,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X4,X1),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_52,plain,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk11_3(X3,X2,X1)),esk12_3(X3,X2,X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_53,plain,
! [X324,X325] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X325,tc_HOL_Obool)),X324)),
inference(variable_rename,[status(thm)],[fact_top1I]) ).
cnf(c_0_54,plain,
( hBOOL(hAPP(c_Transitive__Closure_Otrancl(X1,X2),X3))
| ~ hBOOL(hAPP(X2,X3)) ),
inference(spm,[status(thm)],[c_0_45,c_0_34]) ).
fof(c_0_55,plain,
! [X326,X327] : hBOOL(hAPP(hAPP(c_member(X327),X326),c_Orderings_Otop__class_Otop(tc_fun(X327,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_UNIV__I]) ).
cnf(c_0_56,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X3,X4))) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_57,plain,
( hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_58,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oinsert(X1,X3,c_Set_Oinsert(X1,X4,X2))),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
fof(c_0_59,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk9_0),c_Arrow__Order__Mirabelle_OLin)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact_linear__alt])]) ).
cnf(c_0_60,plain,
( ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)))
| ~ hBOOL(hAPP(X3,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X5),X4)))
| ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Set_Oinsert(X1,X2,X3))) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
fof(c_0_61,plain,
! [X320,X321,X322,X323] : hAPP(c_COMBK(X323,X322,X321),X320) = X321,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
cnf(c_0_62,plain,
( hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4))
| ~ hBOOL(hAPP(X3,hAPP(hAPP(c_Product__Type_OPair(X5,X6),esk11_3(X6,X5,c_Set_Oinsert(X1,X2,X3))),esk12_3(X6,X5,c_Set_Oinsert(X1,X2,X3))))) ),
inference(spm,[status(thm)],[c_0_52,c_0_51]) ).
cnf(c_0_63,plain,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_64,plain,
( ~ hBOOL(hAPP(c_Transitive__Closure_Otrancl(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)))
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)))
| ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Transitive__Closure_Otrancl(X1,X2))) ),
inference(spm,[status(thm)],[c_0_50,c_0_54]) ).
cnf(c_0_65,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_66,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(X3),X1),X4))
| ~ hBOOL(hAPP(c_Set_Oinsert(X3,X2,X4),X1)) ),
inference(spm,[status(thm)],[c_0_56,c_0_34]) ).
cnf(c_0_67,plain,
( hBOOL(hAPP(c_Set_Oinsert(X1,X2,c_Set_Oinsert(X1,X3,X4)),X5))
| ~ hBOOL(hAPP(X4,X5)) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_68,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk9_0),c_Arrow__Order__Mirabelle_OLin)),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_69,plain,
( ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)))
| ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Set_Oinsert(X4,X5,X1))) ),
inference(spm,[status(thm)],[c_0_60,c_0_51]) ).
cnf(c_0_70,plain,
hAPP(c_COMBK(X1,X2,X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_71,plain,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),X4)),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_72,plain,
( ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)))
| ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Transitive__Closure_Otrancl(X4,X1))) ),
inference(spm,[status(thm)],[c_0_64,c_0_54]) ).
cnf(c_0_73,plain,
hBOOL(hAPP(c_Transitive__Closure_Otrancl(X1,c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))),X2)),
inference(spm,[status(thm)],[c_0_45,c_0_65]) ).
cnf(c_0_74,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(X3),X1),c_Set_Oinsert(X3,X4,X5)))
| ~ hBOOL(hAPP(X5,X1)) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_75,plain,
hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0)),
inference(spm,[status(thm)],[c_0_37,c_0_68]) ).
cnf(c_0_76,plain,
( ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Set_Oinsert(X1,X2,c_COMBK(X3,X4,X5))))
| ~ hBOOL(X5) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_70])]) ).
cnf(c_0_77,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(X3),X1),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))) ),
inference(spm,[status(thm)],[c_0_66,c_0_71]) ).
cnf(c_0_78,plain,
~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Transitive__Closure_Otrancl(X1,c_Transitive__Closure_Otrancl(X2,c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_73])]) ).
cnf(c_0_79,plain,
( esk9_0 = X1
| hBOOL(hAPP(hAPP(c_member(X2),esk9_0),c_Set_Oinsert(X2,X3,c_Arrow__Order__Mirabelle_OLin))) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_80,plain,
( hBOOL(hAPP(c_Set_Oinsert(X1,X2,c_COMBK(X3,X4,X5)),X6))
| ~ hBOOL(X5) ),
inference(spm,[status(thm)],[c_0_62,c_0_70]) ).
cnf(c_0_81,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))
| ~ hBOOL(X2)
| ~ hBOOL(X4) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_82,plain,
hBOOL(hAPP(hAPP(c_member(X1),esk9_0),c_Set_Oinsert(X1,X2,c_Arrow__Order__Mirabelle_OLin))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_75])]) ).
fof(c_0_83,plain,
! [X128,X129,X130] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X130,tc_HOL_Obool),X129,X128)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X130,tc_HOL_Obool),X128,X129)
| X129 = X128 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityI])])]) ).
fof(c_0_84,plain,
! [X334,X335] : c_Orderings_Oord__class_Oless__eq(tc_fun(X335,tc_HOL_Obool),X334,c_Orderings_Otop__class_Otop(tc_fun(X335,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_subset__UNIV]) ).
fof(c_0_85,plain,
! [X185,X186,X187,X188] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X188,X187)),hAPP(hAPP(c_Product__Type_OPair(X188,X187),esk6_4(X185,X186,X187,X188)),esk7_4(X185,X186,X187,X188))),X186))
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X188,X187),tc_HOL_Obool),X186,X185) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X188,X187)),hAPP(hAPP(c_Product__Type_OPair(X188,X187),esk6_4(X185,X186,X187,X188)),esk7_4(X185,X186,X187,X188))),X185))
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X188,X187),tc_HOL_Obool),X186,X185) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subrelI])])])])]) ).
cnf(c_0_86,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))
| ~ hBOOL(X4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_77]),c_0_81]) ).
cnf(c_0_87,plain,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,c_Arrow__Order__Mirabelle_OLin),esk9_0)),
inference(spm,[status(thm)],[c_0_37,c_0_82]) ).
cnf(c_0_88,plain,
( X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_89,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_90,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X4,X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk6_4(X3,X4,X2,X1)),esk7_4(X3,X4,X2,X1))),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_91,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_92,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(X3),X1),c_COMBK(X4,X5,X6)))
| ~ hBOOL(X6) ),
inference(spm,[status(thm)],[c_0_66,c_0_80]) ).
cnf(c_0_93,plain,
( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_94,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_95,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(X3),X1),c_COMBK(X4,X5,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0)))) ),
inference(spm,[status(thm)],[c_0_92,c_0_75]) ).
cnf(c_0_96,plain,
c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_97,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),c_COMBK(X3,X4,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0))))
| ~ hBOOL(X2)
| ~ hBOOL(X5) ),
inference(spm,[status(thm)],[c_0_76,c_0_95]) ).
cnf(c_0_98,plain,
c_Orderings_Otop__class_Otop(tc_fun(v_F,tc_HOL_Obool)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_96]),c_0_96]) ).
cnf(c_0_99,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),c_COMBK(X3,X4,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0))))
| ~ hBOOL(X5) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_95]),c_0_97]) ).
cnf(c_0_100,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),
inference(spm,[status(thm)],[c_0_98,c_0_98]) ).
cnf(c_0_101,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_COMBK(X3,X4,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0)))),
inference(spm,[status(thm)],[c_0_99,c_0_87]) ).
fof(c_0_102,plain,
! [X105,X106] :
( hAPP(X106,esk5_2(X105,X106)) != hAPP(X105,esk5_2(X105,X106))
| X106 = X105 ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])])]) ).
cnf(c_0_103,plain,
hBOOL(hAPP(c_Transitive__Closure_Otrancl(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))),X3)),
inference(spm,[status(thm)],[c_0_45,c_0_91]) ).
cnf(c_0_104,plain,
( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) ),
inference(spm,[status(thm)],[c_0_93,c_0_100]) ).
cnf(c_0_105,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X3,c_COMBK(X4,X5,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0))),
inference(spm,[status(thm)],[c_0_90,c_0_101]) ).
cnf(c_0_106,plain,
( X1 = X2
| hAPP(X1,esk5_2(X2,X1)) != hAPP(X2,esk5_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_107,plain,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,c_Transitive__Closure_Otrancl(X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))),X5)),
inference(spm,[status(thm)],[c_0_62,c_0_103]) ).
cnf(c_0_108,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = c_COMBK(X2,X3,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0)),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_109,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk6_4(X3,X4,X2,X1)),esk7_4(X3,X4,X2,X1))),X4))
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_110,plain,
( X1 = c_COMBK(X2,X3,X4)
| hAPP(X1,esk5_2(c_COMBK(X2,X3,X4),X1)) != X4 ),
inference(spm,[status(thm)],[c_0_106,c_0_70]) ).
cnf(c_0_111,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(X3),X1),c_Transitive__Closure_Otrancl(X4,c_COMBK(v_F,v_F,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0))))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_107]),c_0_108]) ).
cnf(c_0_112,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X3,X4)
| hBOOL(hAPP(X3,hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk6_4(X4,X3,X2,X1)),esk7_4(X4,X3,X2,X1)))) ),
inference(spm,[status(thm)],[c_0_37,c_0_109]) ).
cnf(c_0_113,plain,
( c_COMBK(v_F,v_F,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0)) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_COMBK(v_F,v_F,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0)),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_104,c_0_108]),c_0_108]) ).
cnf(c_0_114,plain,
c_COMBK(X1,X2,X3) = c_COMBK(X4,X5,X3),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_70])]) ).
cnf(c_0_115,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X3,X4)
| ~ hBOOL(hAPP(X4,hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk6_4(X4,X3,X2,X1)),esk7_4(X4,X3,X2,X1)))) ),
inference(spm,[status(thm)],[c_0_90,c_0_34]) ).
fof(c_0_116,plain,
! [X393,X394,X395] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X395,X395)),X394),X393))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X395,X395)),X394),c_Transitive__Closure_Ortrancl(X395,X393))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__into__rtrancl])])]) ).
cnf(c_0_117,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),c_Transitive__Closure_Otrancl(X3,c_COMBK(v_F,v_F,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0)))))
| ~ hBOOL(X2)
| ~ hBOOL(X4) ),
inference(spm,[status(thm)],[c_0_76,c_0_111]) ).
fof(c_0_118,plain,
! [X4,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X5),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
=> ! [X14,X15] :
( X14 != X15
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X14),X15)),hAPP(X3,X4)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X14),X15)),hAPP(X5,X3))) ) ) )
=> c_Arrow__Order__Mirabelle_Odictator(X5,X4) ) ),
inference(fof_simplification,[status(thm)],[fact_dictatorI]) ).
fof(c_0_119,plain,
! [X390,X391,X392] : hBOOL(hAPP(hAPP(c_member(tc_prod(X392,X392)),hAPP(hAPP(c_Product__Type_OPair(X392,X392),X391),X391)),c_Transitive__Closure_Ortrancl(X392,X390))),
inference(variable_rename,[status(thm)],[fact_rtrancl_Ortrancl__refl]) ).
cnf(c_0_120,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),c_COMBK(X3,X4,X5),X6)
| hBOOL(X5) ),
inference(spm,[status(thm)],[c_0_112,c_0_70]) ).
cnf(c_0_121,plain,
( c_COMBK(X1,X2,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0)) = X3
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_COMBK(X1,X2,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0)),X3) ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_122,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X3,c_COMBK(X4,X5,X6))
| ~ hBOOL(X6) ),
inference(spm,[status(thm)],[c_0_115,c_0_70]) ).
cnf(c_0_123,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_124,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),c_Transitive__Closure_Otrancl(X3,c_COMBK(v_F,v_F,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0)))))
| ~ hBOOL(X4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_111]),c_0_117]) ).
fof(c_0_125,plain,
! [X100,X101] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk2_2(X100,X101)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X101,X100)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X101),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) )
& ( esk3_2(X100,X101) != esk4_2(X100,X101)
| c_Arrow__Order__Mirabelle_Odictator(X101,X100)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X101),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk3_2(X100,X101)),esk4_2(X100,X101))),hAPP(esk2_2(X100,X101),X100)))
| c_Arrow__Order__Mirabelle_Odictator(X101,X100)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X101),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk3_2(X100,X101)),esk4_2(X100,X101))),hAPP(X101,esk2_2(X100,X101))))
| c_Arrow__Order__Mirabelle_Odictator(X101,X100)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X101),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_118])])])])]) ).
fof(c_0_126,negated_conjecture,
~ ? [X47] : c_Arrow__Order__Mirabelle_Odictator(v_F,X47),
inference(assume_negation,[status(cth)],[conj_0]) ).
cnf(c_0_127,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_Transitive__Closure_Ortrancl(X1,X3))),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_128,plain,
( X1 = c_COMBK(X2,X3,X4)
| hBOOL(X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X6),tc_HOL_Obool),X1,c_COMBK(X2,X3,X4)) ),
inference(spm,[status(thm)],[c_0_88,c_0_120]) ).
cnf(c_0_129,plain,
( c_COMBK(X1,X2,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0)) = c_COMBK(X3,X4,X5)
| ~ hBOOL(X5) ),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_130,plain,
( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X3),X2)) ),
inference(spm,[status(thm)],[c_0_37,c_0_123]) ).
cnf(c_0_131,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Transitive__Closure_Otrancl(X3,c_COMBK(v_F,v_F,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0))))),
inference(spm,[status(thm)],[c_0_124,c_0_87]) ).
cnf(c_0_132,plain,
( c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| esk3_2(X1,X2) != esk4_2(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) ),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_133,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))),
inference(split_conjunct,[status(thm)],[fact_assms_I1_J]) ).
fof(c_0_134,negated_conjecture,
! [X93] : ~ c_Arrow__Order__Mirabelle_Odictator(v_F,X93),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_126])])]) ).
cnf(c_0_135,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(tc_Arrow__Order__Mirabelle_Oalt,X1)),c_Arrow__Order__Mirabelle_OLin)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_127]),c_0_127])]) ).
cnf(c_0_136,plain,
( c_COMBK(X1,X2,X3) = c_COMBK(X4,X5,X6)
| hBOOL(X3)
| hBOOL(X6) ),
inference(spm,[status(thm)],[c_0_128,c_0_120]) ).
cnf(c_0_137,plain,
( c_COMBK(X1,X2,X3) = X4
| hAPP(X4,esk5_2(X4,c_COMBK(X1,X2,X3))) != X3 ),
inference(spm,[status(thm)],[c_0_106,c_0_70]) ).
cnf(c_0_138,plain,
( c_COMBK(X1,X2,X3) = c_COMBK(X4,X5,X6)
| ~ hBOOL(X6)
| ~ hBOOL(X3) ),
inference(spm,[status(thm)],[c_0_129,c_0_129]) ).
cnf(c_0_139,plain,
hBOOL(hAPP(c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Otrancl(X2,c_COMBK(v_F,v_F,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0)))),X3)),
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
fof(c_0_140,plain,
! [X131,X132,X133,X134] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X134,tc_HOL_Obool),X133,X132)
| ~ hBOOL(hAPP(hAPP(c_member(X134),X131),X133))
| hBOOL(hAPP(hAPP(c_member(X134),X131),X132)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subsetD])])]) ).
cnf(c_0_141,plain,
( c_Arrow__Order__Mirabelle_Odictator(X1,X2)
| esk4_2(X2,X1) != esk3_2(X2,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(v_F,v_F,c_Arrow__Order__Mirabelle_OLin)))) ),
inference(rw,[status(thm)],[c_0_132,c_0_114]) ).
cnf(c_0_142,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(v_F,v_F,c_Arrow__Order__Mirabelle_OLin)))),
inference(rw,[status(thm)],[c_0_133,c_0_114]) ).
cnf(c_0_143,negated_conjecture,
~ c_Arrow__Order__Mirabelle_Odictator(v_F,X1),
inference(split_conjunct,[status(thm)],[c_0_134]) ).
cnf(c_0_144,plain,
~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Transitive__Closure_Ortrancl(tc_Arrow__Order__Mirabelle_Oalt,X1))),
inference(spm,[status(thm)],[c_0_135,c_0_34]) ).
cnf(c_0_145,plain,
( X1 = X2
| hBOOL(X2)
| hBOOL(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_136]),c_0_70]) ).
cnf(c_0_146,plain,
( c_COMBK(X1,X2,X3) = X4
| ~ hBOOL(hAPP(X4,esk5_2(X4,c_COMBK(X1,X2,X3))))
| ~ hBOOL(X3) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138])]) ).
cnf(c_0_147,plain,
hBOOL(hAPP(c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Otrancl(X2,c_COMBK(X3,X4,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0)))),X5)),
inference(spm,[status(thm)],[c_0_139,c_0_114]) ).
cnf(c_0_148,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_140]) ).
cnf(c_0_149,plain,
esk4_2(X1,v_F) != esk3_2(X1,v_F),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_143]) ).
cnf(c_0_150,plain,
( hAPP(c_Arrow__Order__Mirabelle_OLin,c_Transitive__Closure_Ortrancl(tc_Arrow__Order__Mirabelle_Oalt,X1)) = X2
| hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_151,plain,
( c_COMBK(v_F,v_F,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0)) = X1
| ~ hBOOL(hAPP(X1,esk5_2(X1,c_COMBK(v_F,v_F,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0))))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_108]),c_0_108]),c_0_108]),c_0_75])]) ).
cnf(c_0_152,plain,
( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Otrancl(X2,c_COMBK(X3,X4,X5))),X6))
| ~ hBOOL(X5) ),
inference(spm,[status(thm)],[c_0_147,c_0_129]) ).
cnf(c_0_153,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk9_0),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X3,c_Arrow__Order__Mirabelle_OLin),X2) ),
inference(spm,[status(thm)],[c_0_148,c_0_82]) ).
cnf(c_0_154,plain,
( hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0) = X1
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_129]),c_0_70]) ).
cnf(c_0_155,plain,
( hBOOL(esk4_2(X1,v_F))
| hAPP(c_Arrow__Order__Mirabelle_OLin,c_Transitive__Closure_Ortrancl(tc_Arrow__Order__Mirabelle_Oalt,X2)) != esk3_2(X1,v_F) ),
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_156,plain,
( c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Otrancl(X2,c_COMBK(X3,X4,X5))) = c_COMBK(v_F,v_F,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0))
| ~ hBOOL(X5) ),
inference(spm,[status(thm)],[c_0_151,c_0_152]) ).
cnf(c_0_157,plain,
hBOOL(hAPP(hAPP(c_member(X1),esk9_0),c_Set_Oinsert(X1,X2,c_Set_Oinsert(X1,X3,c_Set_Oinsert(X1,X4,c_Arrow__Order__Mirabelle_OLin))))),
inference(spm,[status(thm)],[c_0_153,c_0_58]) ).
cnf(c_0_158,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
fof(c_0_159,plain,
! [X671,X672,X673] : hBOOL(hAPP(hAPP(c_member(X673),X672),c_Set_Oinsert(X673,X672,X671))),
inference(variable_rename,[status(thm)],[fact_insertI1]) ).
cnf(c_0_160,plain,
( hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0) = X1
| X1 = X2
| hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_154,c_0_145]) ).
cnf(c_0_161,plain,
( hBOOL(esk4_2(X1,v_F))
| esk3_2(X1,v_F) != hAPP(c_Arrow__Order__Mirabelle_OLin,c_COMBK(v_F,v_F,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0)))
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_155,c_0_156]) ).
cnf(c_0_162,plain,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,c_Set_Oinsert(X1,X3,c_Set_Oinsert(X1,X4,c_Arrow__Order__Mirabelle_OLin))),esk9_0)),
inference(spm,[status(thm)],[c_0_37,c_0_157]) ).
cnf(c_0_163,plain,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X2)),
inference(er,[status(thm)],[c_0_158]) ).
fof(c_0_164,plain,
! [X686,X687,X688] :
( ~ hBOOL(hAPP(hAPP(c_member(X688),X687),X686))
| c_Set_Oinsert(X688,X687,X686) = X686 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__absorb])])]) ).
cnf(c_0_165,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X2,X3))),
inference(split_conjunct,[status(thm)],[c_0_159]) ).
cnf(c_0_166,plain,
( hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0) = X1
| hBOOL(c_Transitive__Closure_Ortrancl(tc_Arrow__Order__Mirabelle_Oalt,X2))
| ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,X1)) ),
inference(spm,[status(thm)],[c_0_144,c_0_160]) ).
cnf(c_0_167,plain,
( hBOOL(esk4_2(X1,v_F))
| esk3_2(X1,v_F) != hAPP(c_Arrow__Order__Mirabelle_OLin,c_COMBK(v_F,v_F,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0))) ),
inference(spm,[status(thm)],[c_0_161,c_0_162]) ).
cnf(c_0_168,plain,
( ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Set_Oinsert(X1,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3),X4)))
| ~ hBOOL(hAPP(X4,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2))) ),
inference(spm,[status(thm)],[c_0_60,c_0_163]) ).
cnf(c_0_169,plain,
( c_Set_Oinsert(X1,X2,X3) = X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_164]) ).
cnf(c_0_170,plain,
( hBOOL(c_Transitive__Closure_Ortrancl(tc_Arrow__Order__Mirabelle_Oalt,X1))
| hBOOL(X2)
| ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,X2)) ),
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
fof(c_0_171,plain,
! [X721,X722,X723] : c_Set_Oinsert(X723,X722,c_Set_Oinsert(X723,X722,X721)) = c_Set_Oinsert(X723,X722,X721),
inference(variable_rename,[status(thm)],[fact_insert__absorb2]) ).
cnf(c_0_172,plain,
hBOOL(hAPP(c_Transitive__Closure_Ortrancl(X1,c_Set_Oinsert(tc_prod(X1,X1),X2,X3)),X2)),
inference(spm,[status(thm)],[c_0_130,c_0_165]) ).
cnf(c_0_173,plain,
( hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0) = esk9_0
| hBOOL(c_Transitive__Closure_Ortrancl(tc_Arrow__Order__Mirabelle_Oalt,X1)) ),
inference(spm,[status(thm)],[c_0_166,c_0_75]) ).
cnf(c_0_174,plain,
( esk4_2(X1,v_F) = hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0)
| esk3_2(X1,v_F) != hAPP(c_Arrow__Order__Mirabelle_OLin,c_COMBK(v_F,v_F,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0))) ),
inference(spm,[status(thm)],[c_0_154,c_0_167]) ).
cnf(c_0_175,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),X4))
| ~ hBOOL(hAPP(X4,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)))
| ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,X4)) ),
inference(spm,[status(thm)],[c_0_168,c_0_169]) ).
cnf(c_0_176,plain,
( hBOOL(c_Transitive__Closure_Ortrancl(tc_Arrow__Order__Mirabelle_Oalt,X1))
| hBOOL(esk9_0) ),
inference(spm,[status(thm)],[c_0_170,c_0_75]) ).
cnf(c_0_177,plain,
c_Set_Oinsert(X1,X2,c_Set_Oinsert(X1,X2,X3)) = c_Set_Oinsert(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_171]) ).
cnf(c_0_178,plain,
hAPP(c_Transitive__Closure_Ortrancl(X1,c_Set_Oinsert(tc_prod(X1,X1),X2,X3)),X2) = hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0),
inference(spm,[status(thm)],[c_0_154,c_0_172]) ).
cnf(c_0_179,plain,
( c_Transitive__Closure_Ortrancl(tc_Arrow__Order__Mirabelle_Oalt,X1) = hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0)
| hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0) = esk9_0 ),
inference(spm,[status(thm)],[c_0_154,c_0_173]) ).
cnf(c_0_180,plain,
( esk3_2(X1,v_F) != hAPP(c_Arrow__Order__Mirabelle_OLin,c_COMBK(v_F,v_F,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0)))
| esk3_2(X1,v_F) != hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0) ),
inference(spm,[status(thm)],[c_0_149,c_0_174]) ).
cnf(c_0_181,plain,
~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_COMBK(X1,X2,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_101]),c_0_70]),c_0_75])]) ).
cnf(c_0_182,plain,
( hBOOL(c_COMBK(v_F,v_F,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0)))
| hBOOL(esk9_0)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_176,c_0_156]) ).
cnf(c_0_183,plain,
( ~ hBOOL(hAPP(c_Set_Oinsert(X1,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3),X4),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)))
| ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Set_Oinsert(X1,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3),X4))) ),
inference(spm,[status(thm)],[c_0_168,c_0_177]) ).
cnf(c_0_184,plain,
hAPP(c_Set_Oinsert(X1,X2,X3),X2) = hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0),
inference(spm,[status(thm)],[c_0_154,c_0_163]) ).
cnf(c_0_185,plain,
( hAPP(hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0),X1) = hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0)
| hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0) = esk9_0 ),
inference(spm,[status(thm)],[c_0_178,c_0_179]) ).
cnf(c_0_186,plain,
( esk3_2(X1,v_F) = hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0)
| hAPP(c_Arrow__Order__Mirabelle_OLin,c_COMBK(v_F,v_F,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0))) != hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0) ),
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_160])]),c_0_181]) ).
cnf(c_0_187,plain,
( hBOOL(c_COMBK(v_F,v_F,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0)))
| hBOOL(esk9_0) ),
inference(spm,[status(thm)],[c_0_182,c_0_176]) ).
cnf(c_0_188,plain,
~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Set_Oinsert(X1,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X2),X3))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_184]),c_0_75])]) ).
cnf(c_0_189,plain,
( hAPP(X1,X2) = X1
| X1 = esk9_0
| X1 = X3
| hBOOL(X3) ),
inference(spm,[status(thm)],[c_0_185,c_0_160]) ).
cnf(c_0_190,plain,
hAPP(c_Arrow__Order__Mirabelle_OLin,c_COMBK(v_F,v_F,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0))) != hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0),
inference(spm,[status(thm)],[c_0_180,c_0_186]) ).
cnf(c_0_191,plain,
( c_COMBK(v_F,v_F,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0)) = hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0)
| hBOOL(esk9_0) ),
inference(spm,[status(thm)],[c_0_154,c_0_187]) ).
cnf(c_0_192,plain,
( esk9_0 = c_Arrow__Order__Mirabelle_OLin
| c_Arrow__Order__Mirabelle_OLin = X1
| hBOOL(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_189]),c_0_145]) ).
cnf(c_0_193,plain,
( hBOOL(esk9_0)
| hAPP(c_Arrow__Order__Mirabelle_OLin,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0)) != hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0) ),
inference(spm,[status(thm)],[c_0_190,c_0_191]) ).
cnf(c_0_194,plain,
( hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0) = X1
| esk9_0 = c_Arrow__Order__Mirabelle_OLin
| c_Arrow__Order__Mirabelle_OLin = X1 ),
inference(spm,[status(thm)],[c_0_154,c_0_192]) ).
cnf(c_0_195,plain,
( X1 = X2
| ~ hBOOL(X2)
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_138]),c_0_70]) ).
cnf(c_0_196,plain,
( esk9_0 = c_Arrow__Order__Mirabelle_OLin
| c_Arrow__Order__Mirabelle_OLin = X1
| hBOOL(esk9_0)
| hAPP(c_Arrow__Order__Mirabelle_OLin,X1) != X1 ),
inference(spm,[status(thm)],[c_0_193,c_0_194]) ).
fof(c_0_197,plain,
! [X724,X725,X726,X727] : c_Set_Oinsert(X727,X726,c_Set_Oinsert(X727,X725,X724)) = c_Set_Oinsert(X727,X725,c_Set_Oinsert(X727,X726,X724)),
inference(variable_rename,[status(thm)],[fact_insert__commute]) ).
cnf(c_0_198,plain,
( esk9_0 = c_Arrow__Order__Mirabelle_OLin
| c_Arrow__Order__Mirabelle_OLin = X1
| X2 = X1
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_195,c_0_192]) ).
cnf(c_0_199,plain,
( esk9_0 = c_Arrow__Order__Mirabelle_OLin
| hBOOL(esk9_0) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_194])]) ).
cnf(c_0_200,plain,
( esk9_0 = X1
| hBOOL(hAPP(hAPP(c_member(X2),esk9_0),c_Arrow__Order__Mirabelle_OLin)) ),
inference(spm,[status(thm)],[c_0_56,c_0_82]) ).
cnf(c_0_201,plain,
c_Set_Oinsert(X1,X2,c_Set_Oinsert(X1,X3,X4)) = c_Set_Oinsert(X1,X3,c_Set_Oinsert(X1,X2,X4)),
inference(split_conjunct,[status(thm)],[c_0_197]) ).
cnf(c_0_202,plain,
( esk9_0 = c_Arrow__Order__Mirabelle_OLin
| esk9_0 = X1
| c_Arrow__Order__Mirabelle_OLin = X1 ),
inference(spm,[status(thm)],[c_0_198,c_0_199]) ).
cnf(c_0_203,plain,
hBOOL(hAPP(hAPP(c_member(X1),esk9_0),c_Arrow__Order__Mirabelle_OLin)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_200]),c_0_75])]) ).
cnf(c_0_204,plain,
hBOOL(hAPP(c_Transitive__Closure_Ortrancl(X1,X2),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3))),
inference(spm,[status(thm)],[c_0_37,c_0_127]) ).
cnf(c_0_205,plain,
hBOOL(hAPP(c_Transitive__Closure_Ortrancl(X1,c_Set_Oinsert(tc_prod(X1,X1),X2,c_Set_Oinsert(tc_prod(X1,X1),X3,X4))),X3)),
inference(spm,[status(thm)],[c_0_172,c_0_201]) ).
cnf(c_0_206,plain,
( c_Transitive__Closure_Ortrancl(tc_Arrow__Order__Mirabelle_Oalt,X1) = c_Arrow__Order__Mirabelle_OLin
| esk9_0 = c_Arrow__Order__Mirabelle_OLin ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_202]),c_0_203])]) ).
cnf(c_0_207,plain,
~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Set_Oinsert(X1,X2,c_Transitive__Closure_Ortrancl(tc_Arrow__Order__Mirabelle_Oalt,X3)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_204]),c_0_204])]) ).
cnf(c_0_208,plain,
( esk9_0 = c_Arrow__Order__Mirabelle_OLin
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,X1)) ),
inference(spm,[status(thm)],[c_0_205,c_0_206]) ).
cnf(c_0_209,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X2,c_Transitive__Closure_Ortrancl(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk6_4(c_Transitive__Closure_Ortrancl(X1,X3),X2,X1,X1)),esk7_4(c_Transitive__Closure_Ortrancl(X1,X3),X2,X1,X1))),X3)) ),
inference(spm,[status(thm)],[c_0_90,c_0_123]) ).
cnf(c_0_210,plain,
esk9_0 = c_Arrow__Order__Mirabelle_OLin,
inference(spm,[status(thm)],[c_0_207,c_0_208]) ).
fof(c_0_211,plain,
! [X18,X19] :
( X19 != X18
=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X19),X18)),X3)) ) ),
inference(fof_simplification,[status(thm)],[fact_complete__Lin]) ).
cnf(c_0_212,plain,
( X1 = c_Transitive__Closure_Ortrancl(tc_Arrow__Order__Mirabelle_Oalt,X2)
| hBOOL(esk9_0)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_195,c_0_176]) ).
cnf(c_0_213,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X2,c_Transitive__Closure_Ortrancl(X1,X2)),
inference(spm,[status(thm)],[c_0_209,c_0_109]) ).
cnf(c_0_214,plain,
( hAPP(X1,X2) = X1
| X1 = c_Arrow__Order__Mirabelle_OLin
| X1 = X3
| hBOOL(X3) ),
inference(rw,[status(thm)],[c_0_189,c_0_210]) ).
fof(c_0_215,plain,
! [X197,X198] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk8_2(X197,X198)),c_Arrow__Order__Mirabelle_OLin))
| X198 = X197 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X198),X197)),esk8_2(X197,X198)))
| X198 = X197 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_211])])])]) ).
cnf(c_0_216,plain,
( c_Transitive__Closure_Ortrancl(tc_Arrow__Order__Mirabelle_Oalt,X1) = c_Transitive__Closure_Ortrancl(tc_Arrow__Order__Mirabelle_Oalt,X2)
| hBOOL(esk9_0) ),
inference(spm,[status(thm)],[c_0_212,c_0_176]) ).
cnf(c_0_217,plain,
( c_Transitive__Closure_Ortrancl(X1,X2) = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_88,c_0_213]) ).
cnf(c_0_218,plain,
( hAPP(X1,X2) = X1
| X1 = c_Arrow__Order__Mirabelle_OLin
| hBOOL(c_Arrow__Order__Mirabelle_OLin) ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_214])]) ).
cnf(c_0_219,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk8_2(X1,X2)),c_Arrow__Order__Mirabelle_OLin))
| X2 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_215]) ).
cnf(c_0_220,plain,
( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(tc_Arrow__Order__Mirabelle_Oalt,X1),X2))
| hBOOL(esk9_0) ),
inference(spm,[status(thm)],[c_0_205,c_0_216]) ).
cnf(c_0_221,plain,
( c_Transitive__Closure_Ortrancl(X1,c_COMBK(X2,X3,X4)) = c_COMBK(X2,X3,X4)
| ~ hBOOL(X4) ),
inference(spm,[status(thm)],[c_0_217,c_0_122]) ).
cnf(c_0_222,plain,
( c_COMBK(X1,X2,X3) = X3
| X3 = c_Arrow__Order__Mirabelle_OLin
| hBOOL(c_Arrow__Order__Mirabelle_OLin) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_218])]) ).
cnf(c_0_223,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk8_2(X1,X2)),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin,X3) ),
inference(spm,[status(thm)],[c_0_148,c_0_219]) ).
cnf(c_0_224,plain,
( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(tc_Arrow__Order__Mirabelle_Oalt,X1),X2))
| hBOOL(c_Arrow__Order__Mirabelle_OLin) ),
inference(rw,[status(thm)],[c_0_220,c_0_210]) ).
cnf(c_0_225,plain,
( c_Transitive__Closure_Ortrancl(X1,X2) = X2
| X2 = c_Arrow__Order__Mirabelle_OLin
| hBOOL(c_Arrow__Order__Mirabelle_OLin) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_222]),c_0_145]) ).
cnf(c_0_226,plain,
( X1 = X2
| hBOOL(hAPP(X3,esk8_2(X1,X2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin,X3) ),
inference(spm,[status(thm)],[c_0_37,c_0_223]) ).
cnf(c_0_227,plain,
( X1 = c_Arrow__Order__Mirabelle_OLin
| hBOOL(hAPP(X1,X2))
| hBOOL(c_Arrow__Order__Mirabelle_OLin) ),
inference(spm,[status(thm)],[c_0_224,c_0_225]) ).
fof(c_0_228,plain,
! [X159,X160] : c_Orderings_Oord__class_Oless__eq(tc_fun(X160,tc_HOL_Obool),X159,X159),
inference(variable_rename,[status(thm)],[fact_subset__refl]) ).
fof(c_0_229,plain,
! [X740,X741,X742,X743] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X743,tc_HOL_Obool),X742,X741)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X743,tc_HOL_Obool),X742,c_Set_Oinsert(X743,X740,X741)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__insertI2])])]) ).
cnf(c_0_230,plain,
( X1 = X2
| hBOOL(X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin,c_COMBK(X4,X5,X3)) ),
inference(spm,[status(thm)],[c_0_226,c_0_70]) ).
cnf(c_0_231,plain,
( c_COMBK(X1,X2,X3) = c_Arrow__Order__Mirabelle_OLin
| hBOOL(c_Arrow__Order__Mirabelle_OLin)
| hBOOL(X3) ),
inference(spm,[status(thm)],[c_0_227,c_0_70]) ).
cnf(c_0_232,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(split_conjunct,[status(thm)],[c_0_228]) ).
cnf(c_0_233,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oinsert(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_229]) ).
cnf(c_0_234,plain,
( X1 = X2
| hBOOL(c_Arrow__Order__Mirabelle_OLin)
| hBOOL(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_230,c_0_231]),c_0_232])]) ).
cnf(c_0_235,plain,
( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = c_Set_Oinsert(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3) ),
inference(spm,[status(thm)],[c_0_93,c_0_233]) ).
cnf(c_0_236,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),
inference(spm,[status(thm)],[c_0_89,c_0_100]) ).
cnf(c_0_237,plain,
( X1 = X2
| hBOOL(c_Arrow__Order__Mirabelle_OLin) ),
inference(ef,[status(thm)],[c_0_234]) ).
cnf(c_0_238,plain,
( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = c_Set_Oinsert(X2,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X4) ),
inference(spm,[status(thm)],[c_0_235,c_0_100]) ).
cnf(c_0_239,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_COMBK(v_F,v_F,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0))),
inference(rw,[status(thm)],[c_0_236,c_0_108]) ).
cnf(c_0_240,plain,
~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Set_Oinsert(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_63]),c_0_63])]) ).
cnf(c_0_241,plain,
( X1 = X2
| X3 = X1
| hBOOL(X2)
| ~ hBOOL(X3) ),
inference(spm,[status(thm)],[c_0_195,c_0_145]) ).
cnf(c_0_242,plain,
hBOOL(c_Arrow__Order__Mirabelle_OLin),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_237])]) ).
cnf(c_0_243,plain,
( c_COMBK(v_F,v_F,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0)) = c_Set_Oinsert(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_COMBK(v_F,v_F,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_238,c_0_108]),c_0_108]) ).
cnf(c_0_244,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_COMBK(X3,X4,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0))),
inference(spm,[status(thm)],[c_0_239,c_0_114]) ).
cnf(c_0_245,plain,
( hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_OLin) = X1
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[c_0_154,c_0_210]) ).
cnf(c_0_246,plain,
~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Set_Oinsert(X1,X2,c_COMBK(X3,X4,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0))))),
inference(spm,[status(thm)],[c_0_240,c_0_108]) ).
cnf(c_0_247,plain,
( c_Arrow__Order__Mirabelle_OLin = X1
| X1 = X2
| hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_241,c_0_242]) ).
cnf(c_0_248,plain,
c_Set_Oinsert(X1,X2,c_COMBK(X3,X4,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0))) = c_COMBK(v_F,v_F,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0)),
inference(spm,[status(thm)],[c_0_243,c_0_244]) ).
cnf(c_0_249,plain,
hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_OLin) = c_Arrow__Order__Mirabelle_OLin,
inference(spm,[status(thm)],[c_0_245,c_0_242]) ).
cnf(c_0_250,plain,
~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_COMBK(X1,X2,hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_OLin)))),
inference(spm,[status(thm)],[c_0_181,c_0_210]) ).
cnf(c_0_251,plain,
( c_COMBK(v_F,v_F,c_Arrow__Order__Mirabelle_OLin) = X1
| hBOOL(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_246,c_0_247]),c_0_248]),c_0_210]),c_0_249]),c_0_249]),c_0_242])]) ).
cnf(c_0_252,plain,
~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_COMBK(X1,X2,c_Arrow__Order__Mirabelle_OLin))),
inference(spm,[status(thm)],[c_0_250,c_0_249]) ).
cnf(c_0_253,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X3,c_Transitive__Closure_Otrancl(X4,c_COMBK(v_F,v_F,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0)))),
inference(spm,[status(thm)],[c_0_90,c_0_131]) ).
cnf(c_0_254,plain,
hAPP(c_Arrow__Order__Mirabelle_OLin,c_COMBK(X1,X2,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0))) != hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0),
inference(spm,[status(thm)],[c_0_190,c_0_114]) ).
cnf(c_0_255,plain,
( X1 = c_Arrow__Order__Mirabelle_OLin
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_195,c_0_242]) ).
cnf(c_0_256,plain,
hBOOL(c_member(X1)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_251]),c_0_70]),c_0_108]),c_0_210]),c_0_249]),c_0_252]) ).
cnf(c_0_257,plain,
c_Transitive__Closure_Otrancl(X1,c_COMBK(v_F,v_F,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0))) = c_COMBK(v_F,v_F,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0)),
inference(spm,[status(thm)],[c_0_113,c_0_253]) ).
cnf(c_0_258,plain,
hAPP(c_Arrow__Order__Mirabelle_OLin,c_COMBK(X1,X2,hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_OLin))) != hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_OLin),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_254,c_0_210]),c_0_210]) ).
cnf(c_0_259,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X1,c_COMBK(v_F,v_F,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0)))),c_Arrow__Order__Mirabelle_OLin)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_131]),c_0_131])]) ).
cnf(c_0_260,plain,
( c_COMBK(v_F,v_F,c_Arrow__Order__Mirabelle_OLin) = X1
| X1 = c_Arrow__Order__Mirabelle_OLin ),
inference(spm,[status(thm)],[c_0_255,c_0_251]) ).
cnf(c_0_261,plain,
c_member(X1) = c_Arrow__Order__Mirabelle_OLin,
inference(spm,[status(thm)],[c_0_255,c_0_256]) ).
cnf(c_0_262,plain,
c_Transitive__Closure_Otrancl(X1,c_COMBK(X2,X3,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0))) = c_COMBK(X2,X3,hAPP(c_Arrow__Order__Mirabelle_OLin,esk9_0)),
inference(spm,[status(thm)],[c_0_257,c_0_114]) ).
cnf(c_0_263,plain,
hAPP(c_Arrow__Order__Mirabelle_OLin,c_COMBK(X1,X2,c_Arrow__Order__Mirabelle_OLin)) != c_Arrow__Order__Mirabelle_OLin,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_258,c_0_249]),c_0_249]) ).
cnf(c_0_264,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_259,c_0_260]),c_0_261]),c_0_262]),c_0_210]),c_0_249]),c_0_70]),c_0_242])]),c_0_263]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SCT124+1 : TPTP v8.2.0. Released v5.2.0.
% 0.03/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 23:56:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.49 Running first-order theorem proving
% 0.21/0.49 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 102.59/13.55 # Version: 3.1.0
% 102.59/13.55 # Preprocessing class: FSLSSMSMSSSNFFN.
% 102.59/13.55 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 102.59/13.55 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 102.59/13.55 # Starting new_bool_3 with 300s (1) cores
% 102.59/13.55 # Starting new_bool_1 with 300s (1) cores
% 102.59/13.55 # Starting sh5l with 300s (1) cores
% 102.59/13.55 # new_bool_1 with pid 1820 completed with status 0
% 102.59/13.55 # Result found by new_bool_1
% 102.59/13.55 # Preprocessing class: FSLSSMSMSSSNFFN.
% 102.59/13.55 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 102.59/13.55 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 102.59/13.55 # Starting new_bool_3 with 300s (1) cores
% 102.59/13.55 # Starting new_bool_1 with 300s (1) cores
% 102.59/13.55 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 102.59/13.55 # Search class: FGHSM-FSLS33-DFFFFFNN
% 102.59/13.55 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 102.59/13.55 # Starting SAT001_MinMin_p005000_rr_RG with 100s (1) cores
% 102.59/13.55 # SAT001_MinMin_p005000_rr_RG with pid 1823 completed with status 0
% 102.59/13.55 # Result found by SAT001_MinMin_p005000_rr_RG
% 102.59/13.55 # Preprocessing class: FSLSSMSMSSSNFFN.
% 102.59/13.55 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 102.59/13.55 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 102.59/13.55 # Starting new_bool_3 with 300s (1) cores
% 102.59/13.55 # Starting new_bool_1 with 300s (1) cores
% 102.59/13.55 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 102.59/13.55 # Search class: FGHSM-FSLS33-DFFFFFNN
% 102.59/13.55 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 102.59/13.55 # Starting SAT001_MinMin_p005000_rr_RG with 100s (1) cores
% 102.59/13.55 # Preprocessing time : 0.006 s
% 102.59/13.55 # Presaturation interreduction done
% 102.59/13.55
% 102.59/13.55 # Proof found!
% 102.59/13.55 # SZS status Theorem
% 102.59/13.55 # SZS output start CNFRefutation
% See solution above
% 102.59/13.55 # Parsed axioms : 529
% 102.59/13.55 # Removed by relevancy pruning/SinE : 365
% 102.59/13.55 # Initial clauses : 242
% 102.59/13.55 # Removed in clause preprocessing : 14
% 102.59/13.55 # Initial clauses in saturation : 228
% 102.59/13.55 # Processed clauses : 21532
% 102.59/13.55 # ...of these trivial : 208
% 102.59/13.55 # ...subsumed : 17877
% 102.59/13.55 # ...remaining for further processing : 3447
% 102.59/13.55 # Other redundant clauses eliminated : 4985
% 102.59/13.55 # Clauses deleted for lack of memory : 0
% 102.59/13.55 # Backward-subsumed : 337
% 102.59/13.55 # Backward-rewritten : 604
% 102.59/13.55 # Generated clauses : 830382
% 102.59/13.55 # ...of the previous two non-redundant : 794263
% 102.59/13.55 # ...aggressively subsumed : 0
% 102.59/13.55 # Contextual simplify-reflections : 17
% 102.59/13.55 # Paramodulations : 825290
% 102.59/13.55 # Factorizations : 51
% 102.59/13.55 # NegExts : 0
% 102.59/13.55 # Equation resolutions : 5041
% 102.59/13.55 # Disequality decompositions : 0
% 102.59/13.55 # Total rewrite steps : 211429
% 102.59/13.55 # ...of those cached : 203460
% 102.59/13.55 # Propositional unsat checks : 0
% 102.59/13.55 # Propositional check models : 0
% 102.59/13.55 # Propositional check unsatisfiable : 0
% 102.59/13.55 # Propositional clauses : 0
% 102.59/13.55 # Propositional clauses after purity: 0
% 102.59/13.55 # Propositional unsat core size : 0
% 102.59/13.55 # Propositional preprocessing time : 0.000
% 102.59/13.55 # Propositional encoding time : 0.000
% 102.59/13.55 # Propositional solver time : 0.000
% 102.59/13.55 # Success case prop preproc time : 0.000
% 102.59/13.55 # Success case prop encoding time : 0.000
% 102.59/13.55 # Success case prop solver time : 0.000
% 102.59/13.55 # Current number of processed clauses : 2320
% 102.59/13.55 # Positive orientable unit clauses : 165
% 102.59/13.55 # Positive unorientable unit clauses: 10
% 102.59/13.55 # Negative unit clauses : 168
% 102.59/13.55 # Non-unit-clauses : 1977
% 102.59/13.55 # Current number of unprocessed clauses: 752013
% 102.59/13.55 # ...number of literals in the above : 2933640
% 102.59/13.55 # Current number of archived formulas : 0
% 102.59/13.55 # Current number of archived clauses : 1117
% 102.59/13.55 # Clause-clause subsumption calls (NU) : 794123
% 102.59/13.55 # Rec. Clause-clause subsumption calls : 474677
% 102.59/13.55 # Non-unit clause-clause subsumptions : 12716
% 102.59/13.55 # Unit Clause-clause subsumption calls : 25639
% 102.59/13.55 # Rewrite failures with RHS unbound : 0
% 102.59/13.55 # BW rewrite match attempts : 6056
% 102.59/13.55 # BW rewrite match successes : 300
% 102.59/13.55 # Condensation attempts : 0
% 102.59/13.55 # Condensation successes : 0
% 102.59/13.55 # Termbank termtop insertions : 19941336
% 102.59/13.55 # Search garbage collected termcells : 7366
% 102.59/13.55
% 102.59/13.55 # -------------------------------------------------
% 102.59/13.55 # User time : 12.312 s
% 102.59/13.55 # System time : 0.412 s
% 102.59/13.55 # Total time : 12.724 s
% 102.59/13.55 # Maximum resident set size: 3484 pages
% 102.59/13.55
% 102.59/13.55 # -------------------------------------------------
% 102.59/13.55 # User time : 12.334 s
% 102.59/13.55 # System time : 0.417 s
% 102.59/13.55 # Total time : 12.751 s
% 102.59/13.55 # Maximum resident set size: 2556 pages
% 102.59/13.55 % E---3.1 exiting
% 102.59/13.55 % E exiting
%------------------------------------------------------------------------------