TSTP Solution File: SCT004-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SCT004-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n006.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 Aug 22 10:55:07 EDT 2023
% Result : Unsatisfiable 128.72s 100.89s
% Output : CNFRefutation 128.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 130
% Syntax : Number of formulae : 180 ( 29 unt; 117 typ; 0 def)
% Number of atoms : 124 ( 23 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 108 ( 47 ~; 61 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 301 ( 108 >; 193 *; 0 +; 0 <<)
% Number of predicates : 33 ( 31 usr; 1 prp; 0-6 aty)
% Number of functors : 86 ( 86 usr; 9 con; 0-7 aty)
% Number of variables : 80 (; 80 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_Equiv__Relations_Ocongruent2 > c_Equiv__Relations_Ocongruent > c_lessequals > c_fequal > c_Relation_Ototal__on > c_Relation_Osingle__valued > c_Relation_Orefl__on > c_Order__Relation_Ostrict__linear__order__on > c_Equiv__Relations_Oequiv > c_Wellfounded_OwfP > c_Wellfounded_Owf > c_Wellfounded_Oacyclic > c_Relation_Otrans > c_Relation_Osym > c_Relation_Oirrefl > c_Relation_Oantisym > c_Nitpick_Orefl_H > hBOOL > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Olinorder > class_Orderings_Obot > class_OrderedGroup_Opordered__ab__group__add > class_OrderedGroup_Oab__group__add > class_Lattices_Oupper__semilattice > class_Lattices_Olower__semilattice > class_Lattices_Olattice > class_Lattices_Odistrib__lattice > class_Lattices_Obounded__lattice > class_HOL_Oord > class_HOL_Ominus > c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 > c_List_Osko__Recdef__Xcuts__eq__1__1 > c_Relation_Orel__comp > c_Recdef_Ocut > c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 > c_ATP__Linkup_Osko__Relation__XImageE__1__1 > c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1 > c_split > c_Set_Oimage > c_Relation_Oinv__image > c_Relation_OImage > c_Product__Type_OSigma > c_Pair > c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 > c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 > c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 > c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 > c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 > c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 > c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 > c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 > c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 > c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 > c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 > c_ATP__Linkup_Osko__Relation__XRangeE__1__1 > c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 > c_ATP__Linkup_Osko__Relation__XDomainE__1__1 > v_sko__Transitive__Closure__Xtrancl__Xcases__1 > v_sko__Transitive__Closure__Xrtrancl__Xcases__1 > c_in > c_Set_Oinsert > c_Relation_Oconverse > c_Relation_ORange > c_Relation_ODomain > c_List_Osko__Recdef__Xtfl__wf__induct__1__1 > c_Lattices_Oupper__semilattice__class_Osup > c_Lattices_Olower__semilattice__class_Oinf > c_HOL_Ominus__class_Ominus > c_FunDef_Oin__rel > c_Equiv__Relations_Oquotient > c_COMBK > c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 > c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 > c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 > c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 > c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 > c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 > c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 > c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 > c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 > c_ATP__Linkup_Osko__Relation__XId__onE__1__1 > v_sko__Wellfounded__Xacc__Xinducts__1 > v_sko__Wellfounded__Xacc__Xinduct__1 > tc_prod > tc_fun > hAPP > c_snd > c_fst > c_Wellfounded_Oacc > c_Transitive__Closure_Otrancl > c_Transitive__Closure_Ortrancl > c_Relation_OId__on > c_Relation_OField > c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 > c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 > c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 > c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 > c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3 > c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2 > c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1 > c_ATP__Linkup_Osko__Relation__XtransI__1__3 > c_ATP__Linkup_Osko__Relation__XtransI__1__2 > c_ATP__Linkup_Osko__Relation__XtransI__1__1 > c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 > c_ATP__Linkup_Osko__Relation__XIdE__1__1 > #nlpp > c_Relation_OId > c_Orderings_Obot__class_Obot > v_xa > v_x > v_r > v_L > tc_bool > tc_Arrow__Order__Mirabelle_Oalt > t_b > t_a > c_Arrow__Order__Mirabelle_OLin
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(v_x,type,
v_x: $i ).
tff(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1,type,
c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1: ( $i * $i ) > $i ).
tff(c_Set_Oinsert,type,
c_Set_Oinsert: ( $i * $i * $i ) > $i ).
tff(c_Relation_Oirrefl,type,
c_Relation_Oirrefl: ( $i * $i ) > $o ).
tff(class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
tff(c_Transitive__Closure_Ortrancl,type,
c_Transitive__Closure_Ortrancl: ( $i * $i ) > $i ).
tff(c_Relation_Oantisym,type,
c_Relation_Oantisym: ( $i * $i ) > $o ).
tff(c_COMBK,type,
c_COMBK: ( $i * $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Relation__XIdE__1__1,type,
c_ATP__Linkup_Osko__Relation__XIdE__1__1: ( $i * $i ) > $i ).
tff(class_HOL_Ominus,type,
class_HOL_Ominus: $i > $o ).
tff(c_Relation_Oinv__image,type,
c_Relation_Oinv__image: ( $i * $i * $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1,type,
c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1: ( $i * $i * $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2,type,
c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2: ( $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Relation__XImageE__1__1,type,
c_ATP__Linkup_Osko__Relation__XImageE__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1,type,
c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1: ( $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(c_Relation_Oconverse,type,
c_Relation_Oconverse: ( $i * $i * $i ) > $i ).
tff(v_xa,type,
v_xa: $i ).
tff(c_Relation_Otrans,type,
c_Relation_Otrans: ( $i * $i ) > $o ).
tff(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1: ( $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1: ( $i * $i * $i ) > $i ).
tff(c_Recdef_Ocut,type,
c_Recdef_Ocut: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1,type,
c_ATP__Linkup_Osko__Relation__XRange__iff__1__1: ( $i * $i * $i * $i ) > $i ).
tff(class_Lattices_Obounded__lattice,type,
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tff(c_Relation_Osingle__valued,type,
c_Relation_Osingle__valued: ( $i * $i * $i ) > $o ).
tff(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1: ( $i * $i ) > $i ).
tff(class_Lattices_Olattice,type,
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tff(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1: ( $i * $i * $i * $i ) > $i ).
tff(c_Wellfounded_Oacc,type,
c_Wellfounded_Oacc: ( $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Relation__XRangeE__1__1,type,
c_ATP__Linkup_Osko__Relation__XRangeE__1__1: ( $i * $i * $i * $i ) > $i ).
tff(c_Relation_Ototal__on,type,
c_Relation_Ototal__on: ( $i * $i * $i ) > $o ).
tff(c_ATP__Linkup_Osko__Relation__XtransI__1__3,type,
c_ATP__Linkup_Osko__Relation__XtransI__1__3: ( $i * $i ) > $i ).
tff(t_a,type,
t_a: $i ).
tff(c_ATP__Linkup_Osko__Relation__XtransI__1__2,type,
c_ATP__Linkup_Osko__Relation__XtransI__1__2: ( $i * $i ) > $i ).
tff(class_Orderings_Oorder,type,
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tff(class_Orderings_Opreorder,type,
class_Orderings_Opreorder: $i > $o ).
tff(c_ATP__Linkup_Osko__Relation__XId__onE__1__1,type,
c_ATP__Linkup_Osko__Relation__XId__onE__1__1: ( $i * $i * $i ) > $i ).
tff(c_Relation_ORange,type,
c_Relation_ORange: ( $i * $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1: ( $i * $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1: ( $i * $i * $i ) > $i ).
tff(c_List_Osko__Recdef__Xtfl__wf__induct__1__1,type,
c_List_Osko__Recdef__Xtfl__wf__induct__1__1: ( $i * $i * $i ) > $i ).
tff(c_snd,type,
c_snd: ( $i * $i ) > $i ).
tff(c_Orderings_Obot__class_Obot,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(c_Lattices_Oupper__semilattice__class_Osup,type,
c_Lattices_Oupper__semilattice__class_Osup: ( $i * $i * $i ) > $i ).
tff(tc_prod,type,
tc_prod: ( $i * $i ) > $i ).
tff(c_split,type,
c_split: ( $i * $i * $i * $i ) > $i ).
tff(c_in,type,
c_in: ( $i * $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1: ( $i * $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1: ( $i * $i ) > $i ).
tff(c_Equiv__Relations_Oquotient,type,
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tff(c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1,type,
c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1: ( $i * $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1: ( $i * $i * $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1: ( $i * $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1: ( $i * $i * $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1,type,
c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1: ( $i * $i ) > $i ).
tff(c_Nitpick_Orefl_H,type,
c_Nitpick_Orefl_H: ( $i * $i ) > $o ).
tff(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1,type,
c_ATP__Linkup_Osko__Relation__XImage__iff__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_Relation_Osym,type,
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tff(v_L,type,
v_L: $i ).
tff(c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3,type,
c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3: ( $i * $i ) > $i ).
tff(c_lessequals,type,
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tff(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1,type,
c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1: ( $i * $i * $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Relation__XDomainE__1__1,type,
c_ATP__Linkup_Osko__Relation__XDomainE__1__1: ( $i * $i * $i * $i ) > $i ).
tff(c_Wellfounded_Oacyclic,type,
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tff(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1: ( $i * $i * $i ) > $i ).
tff(c_Relation_OField,type,
c_Relation_OField: ( $i * $i ) > $i ).
tff(c_Relation_Orefl__on,type,
c_Relation_Orefl__on: ( $i * $i * $i ) > $o ).
tff(tc_fun,type,
tc_fun: ( $i * $i ) > $i ).
tff(tc_bool,type,
tc_bool: $i ).
tff(c_Wellfounded_Owf,type,
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tff(c_List_Osko__Recdef__Xcuts__eq__1__1,type,
c_List_Osko__Recdef__Xcuts__eq__1__1: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Relation__XtransI__1__1,type,
c_ATP__Linkup_Osko__Relation__XtransI__1__1: ( $i * $i ) > $i ).
tff(c_Relation_Orel__comp,type,
c_Relation_Orel__comp: ( $i * $i * $i * $i * $i ) > $i ).
tff(v_r,type,
v_r: $i ).
tff(c_Product__Type_OSigma,type,
c_Product__Type_OSigma: ( $i * $i * $i * $i ) > $i ).
tff(class_Lattices_Oupper__semilattice,type,
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tff(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1,type,
c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1: ( $i * $i * $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2: ( $i * $i * $i * $i ) > $i ).
tff(c_fequal,type,
c_fequal: ( $i * $i * $i ) > $o ).
tff(c_Equiv__Relations_Ocongruent2,type,
c_Equiv__Relations_Ocongruent2: ( $i * $i * $i * $i * $i * $i ) > $o ).
tff(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1: ( $i * $i * $i * $i ) > $i ).
tff(class_HOL_Oord,type,
class_HOL_Oord: $i > $o ).
tff(c_Relation_OImage,type,
c_Relation_OImage: ( $i * $i * $i * $i ) > $i ).
tff(c_Order__Relation_Ostrict__linear__order__on,type,
c_Order__Relation_Ostrict__linear__order__on: ( $i * $i * $i ) > $o ).
tff(c_Arrow__Order__Mirabelle_OLin,type,
c_Arrow__Order__Mirabelle_OLin: $i ).
tff(class_OrderedGroup_Oab__group__add,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(hAPP,type,
hAPP: ( $i * $i ) > $i ).
tff(class_Lattices_Odistrib__lattice,type,
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tff(c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1,type,
c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1: ( $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2,type,
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tff(c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1,type,
c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1: ( $i * $i * $i * $i ) > $i ).
tff(c_Pair,type,
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tff(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1,type,
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tff(c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1: ( $i * $i * $i ) > $i ).
tff(hBOOL,type,
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tff(c_Equiv__Relations_Oequiv,type,
c_Equiv__Relations_Oequiv: ( $i * $i * $i ) > $o ).
tff(c_Relation_OId,type,
c_Relation_OId: $i > $i ).
tff(c_FunDef_Oin__rel,type,
c_FunDef_Oin__rel: ( $i * $i * $i ) > $i ).
tff(class_Lattices_Olower__semilattice,type,
class_Lattices_Olower__semilattice: $i > $o ).
tff(c_Wellfounded_OwfP,type,
c_Wellfounded_OwfP: ( $i * $i ) > $o ).
tff(v_sko__Transitive__Closure__Xtrancl__Xcases__1,type,
v_sko__Transitive__Closure__Xtrancl__Xcases__1: ( $i * $i * $i ) > $i ).
tff(v_sko__Wellfounded__Xacc__Xinducts__1,type,
v_sko__Wellfounded__Xacc__Xinducts__1: ( $i * $i ) > $i ).
tff(c_fst,type,
c_fst: ( $i * $i ) > $i ).
tff(tc_Arrow__Order__Mirabelle_Oalt,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
tff(v_sko__Transitive__Closure__Xrtrancl__Xcases__1,type,
v_sko__Transitive__Closure__Xrtrancl__Xcases__1: ( $i * $i * $i ) > $i ).
tff(c_HOL_Ominus__class_Ominus,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(class_Orderings_Obot,type,
class_Orderings_Obot: $i > $o ).
tff(class_OrderedGroup_Opordered__ab__group__add,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(t_b,type,
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tff(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1,type,
c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1: ( $i * $i * $i * $i ) > $i ).
tff(v_sko__Wellfounded__Xacc__Xinduct__1,type,
v_sko__Wellfounded__Xacc__Xinduct__1: ( $i * $i ) > $i ).
tff(c_Transitive__Closure_Otrancl,type,
c_Transitive__Closure_Otrancl: ( $i * $i ) > $i ).
tff(c_Relation_OId__on,type,
c_Relation_OId__on: ( $i * $i ) > $i ).
tff(c_Equiv__Relations_Ocongruent,type,
c_Equiv__Relations_Ocongruent: ( $i * $i * $i * $i ) > $o ).
tff(c_Set_Oimage,type,
c_Set_Oimage: ( $i * $i * $i * $i ) > $i ).
tff(c_Relation_ODomain,type,
c_Relation_ODomain: ( $i * $i * $i ) > $i ).
tff(c_Lattices_Olower__semilattice__class_Oinf,type,
c_Lattices_Olower__semilattice__class_Oinf: ( $i * $i * $i ) > $i ).
tff(f_3602,axiom,
! [V_xg,V_xc] :
( ~ hBOOL(c_in(c_Pair(V_xg,V_xg,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(V_xc,V_xc,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file(unknown,unknown) ).
tff(f_3586,axiom,
( c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
file(unknown,unknown) ).
tff(f_3756,axiom,
( ~ hBOOL(c_in(c_Pair(v_x,v_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(c_Pair(v_x,v_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
file(unknown,unknown) ).
tff(f_3651,axiom,
( ( v_x != v_xa )
| hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| ( v_x != v_xa )
| hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
file(unknown,unknown) ).
tff(f_3783,axiom,
! [V_xh,V_yc,V_y,V_xb] :
( hBOOL(c_in(c_Pair(V_xh,V_yc,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(V_yc,V_xh,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ( V_xh = V_yc )
| hBOOL(c_in(c_Pair(V_y,V_xb,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(V_xb,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ( V_xb = V_y ) ),
file(unknown,unknown) ).
tff(f_3726,axiom,
( ~ hBOOL(c_in(c_Pair(v_xa,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(c_Pair(v_xa,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
file(unknown,unknown) ).
tff(f_3583,axiom,
! [V_S,V_x,T_a] :
( hBOOL(hAPP(V_S,V_x))
| ~ hBOOL(c_in(V_x,V_S,T_a)) ),
file(unknown,unknown) ).
tff(f_3578,axiom,
! [V_x,V_S,T_a] :
( hBOOL(c_in(V_x,V_S,T_a))
| ~ hBOOL(hAPP(V_S,V_x)) ),
file(unknown,unknown) ).
tff(f_1329,axiom,
! [V_a,V_A,T_a] :
( ( c_Set_Oinsert(V_a,V_A,T_a) = V_A )
| ~ hBOOL(c_in(V_a,V_A,T_a)) ),
file(unknown,unknown) ).
tff(f_857,axiom,
! [V_x,V_A,T_a] : hBOOL(hAPP(c_Set_Oinsert(V_x,V_A,T_a),V_x)),
file(unknown,unknown) ).
tff(f_1291,axiom,
! [V_x,V_B,T_a] : hBOOL(c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a)),
file(unknown,unknown) ).
tff(f_3218,axiom,
! [V_x,T_a,V_r] :
( ~ hBOOL(c_in(c_Pair(V_x,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ c_Relation_Oirrefl(V_r,T_a) ),
file(unknown,unknown) ).
tff(f_2127,axiom,
! [V_r,T_a] :
( c_Relation_Oirrefl(V_r,T_a)
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(V_r,T_a),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(V_r,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a))) ),
file(unknown,unknown) ).
tff(c_1322,plain,
! [V_xc_2399,V_xg_2398] :
( ~ hBOOL(c_in(c_Pair(V_xc_2399,V_xc_2399,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(V_xg_2398,V_xg_2398,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(cnfTransformation,[status(thm)],[f_3602]) ).
tff(c_114796,plain,
! [V_xg_2398] : ~ hBOOL(c_in(c_Pair(V_xg_2398,V_xg_2398,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(splitLeft,[status(thm)],[c_1322]) ).
tff(c_1316,plain,
c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt),
inference(cnfTransformation,[status(thm)],[f_3586]) ).
tff(c_1346,plain,
( ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(v_x,v_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(cnfTransformation,[status(thm)],[f_3756]) ).
tff(c_1396,plain,
( hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(v_x,v_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(demodulation,[status(thm),theory(equality)],[c_1316,c_1346]) ).
tff(c_126751,plain,
~ hBOOL(c_in(c_Pair(v_x,v_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(negUnitSimplification,[status(thm)],[c_114796,c_1396]) ).
tff(c_1332,plain,
( ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ( v_xa != v_x ) ),
inference(cnfTransformation,[status(thm)],[f_3651]) ).
tff(c_1400,plain,
( hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ( v_xa != v_x ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1316,c_1332]) ).
tff(c_24455,plain,
v_xa != v_x,
inference(splitLeft,[status(thm)],[c_1400]) ).
tff(c_1350,plain,
! [V_y_2412,V_xb_2413,V_yc_2411,V_xh_2410] :
( ( V_y_2412 = V_xb_2413 )
| hBOOL(c_in(c_Pair(V_xb_2413,V_y_2412,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(V_y_2412,V_xb_2413,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ( V_yc_2411 = V_xh_2410 )
| hBOOL(c_in(c_Pair(V_yc_2411,V_xh_2410,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(V_xh_2410,V_yc_2411,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(cnfTransformation,[status(thm)],[f_3783]) ).
tff(c_223820,plain,
! [V_yc_6066,V_xh_6067] :
( ( V_yc_6066 = V_xh_6067 )
| hBOOL(c_in(c_Pair(V_yc_6066,V_xh_6067,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(V_xh_6067,V_yc_6066,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(splitLeft,[status(thm)],[c_1350]) ).
tff(c_1342,plain,
( ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(v_xa,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(cnfTransformation,[status(thm)],[f_3726]) ).
tff(c_1398,plain,
( hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(v_xa,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(demodulation,[status(thm),theory(equality)],[c_1316,c_1342]) ).
tff(c_127330,plain,
~ hBOOL(c_in(c_Pair(v_xa,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(negUnitSimplification,[status(thm)],[c_114796,c_1398]) ).
tff(c_223876,plain,
( ( v_xa = v_x )
| hBOOL(c_in(c_Pair(v_x,v_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(resolution,[status(thm)],[c_223820,c_127330]) ).
tff(c_224044,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_126751,c_24455,c_223876]) ).
tff(c_224258,plain,
! [V_y_6073,V_xb_6074] :
( ( V_y_6073 = V_xb_6074 )
| hBOOL(c_in(c_Pair(V_xb_6074,V_y_6073,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(V_y_6073,V_xb_6074,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(splitRight,[status(thm)],[c_1350]) ).
tff(c_224314,plain,
( ( v_xa = v_x )
| hBOOL(c_in(c_Pair(v_x,v_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(resolution,[status(thm)],[c_224258,c_127330]) ).
tff(c_224482,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_126751,c_24455,c_224314]) ).
tff(c_224483,plain,
! [V_xc_2399] : ~ hBOOL(c_in(c_Pair(V_xc_2399,V_xc_2399,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(splitRight,[status(thm)],[c_1322]) ).
tff(c_235484,plain,
~ hBOOL(c_in(c_Pair(v_x,v_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(negUnitSimplification,[status(thm)],[c_224483,c_1396]) ).
tff(c_335661,plain,
! [V_yc_7543,V_xh_7544] :
( ( V_yc_7543 = V_xh_7544 )
| hBOOL(c_in(c_Pair(V_yc_7543,V_xh_7544,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(V_xh_7544,V_yc_7543,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(splitLeft,[status(thm)],[c_1350]) ).
tff(c_235299,plain,
~ hBOOL(c_in(c_Pair(v_xa,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(negUnitSimplification,[status(thm)],[c_224483,c_1398]) ).
tff(c_335718,plain,
( ( v_xa = v_x )
| hBOOL(c_in(c_Pair(v_x,v_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(resolution,[status(thm)],[c_335661,c_235299]) ).
tff(c_335885,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_235484,c_24455,c_335718]) ).
tff(c_336133,plain,
! [V_y_7553,V_xb_7554] :
( ( V_y_7553 = V_xb_7554 )
| hBOOL(c_in(c_Pair(V_xb_7554,V_y_7553,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(V_y_7553,V_xb_7554,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(splitRight,[status(thm)],[c_1350]) ).
tff(c_336190,plain,
( ( v_xa = v_x )
| hBOOL(c_in(c_Pair(v_x,v_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(resolution,[status(thm)],[c_336133,c_235299]) ).
tff(c_336357,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_235484,c_24455,c_336190]) ).
tff(c_336358,plain,
hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(splitRight,[status(thm)],[c_1400]) ).
tff(c_1314,plain,
! [V_x_2394,V_S_2393,T_a_2395] :
( ~ hBOOL(c_in(V_x_2394,V_S_2393,T_a_2395))
| hBOOL(hAPP(V_S_2393,V_x_2394)) ),
inference(cnfTransformation,[status(thm)],[f_3583]) ).
tff(c_336480,plain,
hBOOL(hAPP(v_L,c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(resolution,[status(thm)],[c_336358,c_1314]) ).
tff(c_1312,plain,
! [V_S_2391,V_x_2390,T_a_2392] :
( ~ hBOOL(hAPP(V_S_2391,V_x_2390))
| hBOOL(c_in(V_x_2390,V_S_2391,T_a_2392)) ),
inference(cnfTransformation,[status(thm)],[f_3578]) ).
tff(c_3799,plain,
! [V_a_2733,V_A_2734,T_a_2735] :
( ~ hBOOL(c_in(V_a_2733,V_A_2734,T_a_2735))
| ( c_Set_Oinsert(V_a_2733,V_A_2734,T_a_2735) = V_A_2734 ) ),
inference(cnfTransformation,[status(thm)],[f_1329]) ).
tff(c_3806,plain,
! [V_x_2390,V_S_2391,T_a_2392] :
( ( c_Set_Oinsert(V_x_2390,V_S_2391,T_a_2392) = V_S_2391 )
| ~ hBOOL(hAPP(V_S_2391,V_x_2390)) ),
inference(resolution,[status(thm)],[c_1312,c_3799]) ).
tff(c_336484,plain,
! [T_a_7560] : ( c_Set_Oinsert(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,T_a_7560) = v_L ),
inference(resolution,[status(thm)],[c_336480,c_3806]) ).
tff(c_342,plain,
! [V_x_619,V_A_620,T_a_621] : hBOOL(hAPP(c_Set_Oinsert(V_x_619,V_A_620,T_a_621),V_x_619)),
inference(cnfTransformation,[status(thm)],[f_857]) ).
tff(c_3946,plain,
! [V_x_2746,V_S_2747,T_a_2748] :
( ( c_Set_Oinsert(V_x_2746,V_S_2747,T_a_2748) = V_S_2747 )
| ~ hBOOL(hAPP(V_S_2747,V_x_2746)) ),
inference(resolution,[status(thm)],[c_1312,c_3799]) ).
tff(c_7102,plain,
! [V_x_2903,V_A_2904,T_a_2905,T_a_2906] : ( c_Set_Oinsert(V_x_2903,c_Set_Oinsert(V_x_2903,V_A_2904,T_a_2905),T_a_2906) = c_Set_Oinsert(V_x_2903,V_A_2904,T_a_2905) ),
inference(resolution,[status(thm)],[c_342,c_3946]) ).
tff(c_522,plain,
! [V_x_943,V_B_944,T_a_945] : hBOOL(c_in(V_x_943,c_Set_Oinsert(V_x_943,V_B_944,T_a_945),T_a_945)),
inference(cnfTransformation,[status(thm)],[f_1291]) ).
tff(c_7120,plain,
! [V_x_2903,V_A_2904,T_a_2905,T_a_2906] : hBOOL(c_in(V_x_2903,c_Set_Oinsert(V_x_2903,V_A_2904,T_a_2905),T_a_2906)),
inference(superposition,[status(thm),theory(equality)],[c_7102,c_522]) ).
tff(c_336501,plain,
! [T_a_2906] : hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,T_a_2906)),
inference(superposition,[status(thm),theory(equality)],[c_336484,c_7120]) ).
tff(c_339649,plain,
! [V_r_7629,T_a_7630,V_x_7631] :
( ~ c_Relation_Oirrefl(V_r_7629,T_a_7630)
| ~ hBOOL(c_in(c_Pair(V_x_7631,V_x_7631,T_a_7630,T_a_7630),V_r_7629,tc_prod(T_a_7630,T_a_7630))) ),
inference(cnfTransformation,[status(thm)],[f_3218]) ).
tff(c_339677,plain,
~ c_Relation_Oirrefl(v_L,tc_Arrow__Order__Mirabelle_Oalt),
inference(resolution,[status(thm)],[c_336501,c_339649]) ).
tff(c_806,plain,
! [V_r_1444,T_a_1445] :
( hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(V_r_1444,T_a_1445),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(V_r_1444,T_a_1445),T_a_1445,T_a_1445),V_r_1444,tc_prod(T_a_1445,T_a_1445)))
| c_Relation_Oirrefl(V_r_1444,T_a_1445) ),
inference(cnfTransformation,[status(thm)],[f_2127]) ).
tff(c_413435,plain,
! [V_xg_8869] : ~ hBOOL(c_in(c_Pair(V_xg_8869,V_xg_8869,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(splitLeft,[status(thm)],[c_1322]) ).
tff(c_413443,plain,
c_Relation_Oirrefl(v_L,tc_Arrow__Order__Mirabelle_Oalt),
inference(resolution,[status(thm)],[c_806,c_413435]) ).
tff(c_413458,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_339677,c_413443]) ).
tff(c_413460,plain,
! [V_xc_8870] : ~ hBOOL(c_in(c_Pair(V_xc_8870,V_xc_8870,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(splitRight,[status(thm)],[c_1322]) ).
tff(c_413468,plain,
c_Relation_Oirrefl(v_L,tc_Arrow__Order__Mirabelle_Oalt),
inference(resolution,[status(thm)],[c_806,c_413460]) ).
tff(c_413483,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_339677,c_413468]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SCT004-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.35 % Computer : n006.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 : Thu Aug 3 13:10:59 EDT 2023
% 0.14/0.35 % CPUTime :
% 128.72/100.89 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 128.72/100.90
% 128.72/100.90 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 128.90/100.94
% 128.90/100.94 Inference rules
% 128.90/100.94 ----------------------
% 128.90/100.94 #Ref : 44
% 128.90/100.94 #Sup : 95190
% 128.90/100.94 #Fact : 10
% 128.90/100.94 #Define : 0
% 128.90/100.94 #Split : 27
% 128.90/100.94 #Chain : 0
% 128.90/100.94 #Close : 0
% 128.90/100.94
% 128.90/100.94 Ordering : KBO
% 128.90/100.94
% 128.90/100.94 Simplification rules
% 128.90/100.94 ----------------------
% 128.90/100.94 #Subsume : 19077
% 128.90/100.94 #Demod : 71112
% 128.90/100.94 #Tautology : 27562
% 128.90/100.94 #SimpNegUnit : 767
% 128.90/100.94 #BackRed : 96
% 128.90/100.94
% 128.90/100.94 #Partial instantiations: 0
% 128.90/100.94 #Strategies tried : 1
% 128.90/100.94
% 128.90/100.94 Timing (in seconds)
% 128.90/100.94 ----------------------
% 128.90/100.94 Preprocessing : 1.51
% 128.90/100.94 Parsing : 0.86
% 128.90/100.94 CNF conversion : 0.12
% 128.90/100.94 Main loop : 98.36
% 128.90/100.94 Inferencing : 10.80
% 128.90/100.94 Reduction : 53.61
% 128.90/100.94 Demodulation : 46.55
% 128.90/100.94 BG Simplification : 0.98
% 128.90/100.94 Subsumption : 26.80
% 128.90/100.94 Abstraction : 1.51
% 128.90/100.94 MUC search : 0.00
% 128.90/100.94 Cooper : 0.00
% 128.90/100.94 Total : 99.93
% 128.90/100.94 Index Insertion : 0.00
% 128.90/100.94 Index Deletion : 0.00
% 128.90/100.94 Index Matching : 0.00
% 128.90/100.94 BG Taut test : 0.00
%------------------------------------------------------------------------------