TSTP Solution File: SCT004-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SCT004-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n003.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 : Thu Aug 31 14:10:42 EDT 2023
% Result : Unsatisfiable 0.68s 0.85s
% Output : CNFRefutation 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 125
% Syntax : Number of formulae : 148 ( 5 unt; 117 typ; 0 def)
% Number of atoms : 99 ( 15 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 122 ( 54 ~; 68 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 25 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
c_Set_Oinsert: ( $i * $i * $i ) > $i ).
tff(decl_23,type,
tc_bool: $i ).
tff(decl_24,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_25,type,
c_Lattices_Olower__semilattice__class_Oinf: ( $i * $i * $i ) > $i ).
tff(decl_26,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(decl_27,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_28,type,
class_Orderings_Obot: $i > $o ).
tff(decl_29,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_30,type,
tc_prod: ( $i * $i ) > $i ).
tff(decl_31,type,
c_Relation_Orel__comp: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_32,type,
c_Lattices_Oupper__semilattice__class_Osup: ( $i * $i * $i ) > $i ).
tff(decl_33,type,
c_Transitive__Closure_Ortrancl: ( $i * $i ) > $i ).
tff(decl_34,type,
c_snd: ( $i * $i ) > $i ).
tff(decl_35,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_36,type,
c_fst: ( $i * $i ) > $i ).
tff(decl_37,type,
hBOOL: $i > $o ).
tff(decl_38,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1: ( $i * $i * $i ) > $i ).
tff(decl_39,type,
c_Wellfounded_Owf: ( $i * $i ) > $o ).
tff(decl_40,type,
c_Relation_ORange: ( $i * $i * $i ) > $i ).
tff(decl_41,type,
c_in: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
c_COMBK: ( $i * $i * $i ) > $i ).
tff(decl_43,type,
c_Product__Type_OSigma: ( $i * $i * $i * $i ) > $i ).
tff(decl_44,type,
c_Transitive__Closure_Otrancl: ( $i * $i ) > $i ).
tff(decl_45,type,
class_Lattices_Olattice: $i > $o ).
tff(decl_46,type,
t_a: $i ).
tff(decl_47,type,
v_x: $i ).
tff(decl_48,type,
c_Relation_ODomain: ( $i * $i * $i ) > $i ).
tff(decl_49,type,
class_Lattices_Odistrib__lattice: $i > $o ).
tff(decl_50,type,
c_Relation_OId__on: ( $i * $i ) > $i ).
tff(decl_51,type,
c_Relation_Orefl__on: ( $i * $i * $i ) > $o ).
tff(decl_52,type,
class_Lattices_Oupper__semilattice: $i > $o ).
tff(decl_53,type,
c_Relation_OImage: ( $i * $i * $i * $i ) > $i ).
tff(decl_54,type,
c_List_Osko__Recdef__Xtfl__wf__induct__1__1: ( $i * $i * $i ) > $i ).
tff(decl_55,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(decl_56,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_57,type,
c_Set_Oimage: ( $i * $i * $i * $i ) > $i ).
tff(decl_58,type,
class_Lattices_Olower__semilattice: $i > $o ).
tff(decl_59,type,
c_Relation_Osym: ( $i * $i ) > $o ).
tff(decl_60,type,
class_Lattices_Obounded__lattice: $i > $o ).
tff(decl_61,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1: ( $i * $i * $i ) > $i ).
tff(decl_62,type,
c_Wellfounded_Oacyclic: ( $i * $i ) > $o ).
tff(decl_63,type,
c_Relation_Oconverse: ( $i * $i * $i ) > $i ).
tff(decl_64,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_65,type,
c_split: ( $i * $i * $i * $i ) > $i ).
tff(decl_66,type,
c_Relation_Oantisym: ( $i * $i ) > $o ).
tff(decl_67,type,
c_Relation_OField: ( $i * $i ) > $i ).
tff(decl_68,type,
c_Relation_Ototal__on: ( $i * $i * $i ) > $o ).
tff(decl_69,type,
c_Order__Relation_Ostrict__linear__order__on: ( $i * $i * $i ) > $o ).
tff(decl_70,type,
class_HOL_Ominus: $i > $o ).
tff(decl_71,type,
v_r: $i ).
tff(decl_72,type,
c_Wellfounded_Oacc: ( $i * $i ) > $i ).
tff(decl_73,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1: ( $i * $i * $i ) > $i ).
tff(decl_74,type,
c_List_Osko__Recdef__Xcuts__eq__1__1: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_75,type,
c_Recdef_Ocut: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_76,type,
class_HOL_Oord: $i > $o ).
tff(decl_77,type,
c_Relation_Otrans: ( $i * $i ) > $o ).
tff(decl_78,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_79,type,
c_Relation_Osingle__valued: ( $i * $i * $i ) > $o ).
tff(decl_80,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_81,type,
c_Equiv__Relations_Oequiv: ( $i * $i * $i ) > $o ).
tff(decl_82,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_83,type,
c_Relation_Oirrefl: ( $i * $i ) > $o ).
tff(decl_84,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_85,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2: ( $i * $i * $i * $i ) > $i ).
tff(decl_86,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_87,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2: ( $i * $i * $i * $i ) > $i ).
tff(decl_88,type,
c_Equiv__Relations_Oquotient: ( $i * $i * $i ) > $i ).
tff(decl_89,type,
c_Relation_OId: $i > $i ).
tff(decl_90,type,
c_Relation_Oinv__image: ( $i * $i * $i * $i ) > $i ).
tff(decl_91,type,
c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_92,type,
c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_93,type,
c_Nitpick_Orefl_H: ( $i * $i ) > $o ).
tff(decl_94,type,
c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1: ( $i * $i ) > $i ).
tff(decl_95,type,
c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1: ( $i * $i ) > $i ).
tff(decl_96,type,
t_b: $i ).
tff(decl_97,type,
c_ATP__Linkup_Osko__Relation__XId__onE__1__1: ( $i * $i * $i ) > $i ).
tff(decl_98,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1: ( $i * $i ) > $i ).
tff(decl_99,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1: ( $i * $i ) > $i ).
tff(decl_100,type,
c_ATP__Linkup_Osko__Relation__XIdE__1__1: ( $i * $i ) > $i ).
tff(decl_101,type,
c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1: ( $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_102,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1: ( $i * $i ) > $i ).
tff(decl_103,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_104,type,
v_sko__Transitive__Closure__Xtrancl__Xcases__1: ( $i * $i * $i ) > $i ).
tff(decl_105,type,
c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_106,type,
c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_107,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_108,type,
v_sko__Transitive__Closure__Xrtrancl__Xcases__1: ( $i * $i * $i ) > $i ).
tff(decl_109,type,
c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_110,type,
c_FunDef_Oin__rel: ( $i * $i * $i ) > $i ).
tff(decl_111,type,
c_Wellfounded_OwfP: ( $i * $i ) > $o ).
tff(decl_112,type,
c_ATP__Linkup_Osko__Relation__XImageE__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_113,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1: ( $i * $i * $i ) > $i ).
tff(decl_114,type,
v_sko__Wellfounded__Xacc__Xinducts__1: ( $i * $i ) > $i ).
tff(decl_115,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1: ( $i * $i * $i ) > $i ).
tff(decl_116,type,
c_ATP__Linkup_Osko__Relation__XImage__iff__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_117,type,
c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1: ( $i * $i * $i ) > $i ).
tff(decl_118,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1: ( $i * $i * $i ) > $i ).
tff(decl_119,type,
v_sko__Wellfounded__Xacc__Xinduct__1: ( $i * $i ) > $i ).
tff(decl_120,type,
c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1: ( $i * $i * $i ) > $i ).
tff(decl_121,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1: ( $i * $i * $i ) > $i ).
tff(decl_122,type,
c_Equiv__Relations_Ocongruent: ( $i * $i * $i * $i ) > $o ).
tff(decl_123,type,
c_Equiv__Relations_Ocongruent2: ( $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_124,type,
c_ATP__Linkup_Osko__Relation__XRangeE__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_125,type,
c_ATP__Linkup_Osko__Relation__XDomainE__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_126,type,
c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_127,type,
c_ATP__Linkup_Osko__Relation__XRange__iff__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_128,type,
c_ATP__Linkup_Osko__Relation__XtransI__1__1: ( $i * $i ) > $i ).
tff(decl_129,type,
c_ATP__Linkup_Osko__Relation__XtransI__1__3: ( $i * $i ) > $i ).
tff(decl_130,type,
c_ATP__Linkup_Osko__Relation__XtransI__1__2: ( $i * $i ) > $i ).
tff(decl_131,type,
c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1: ( $i * $i ) > $i ).
tff(decl_132,type,
c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2: ( $i * $i ) > $i ).
tff(decl_133,type,
c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3: ( $i * $i ) > $i ).
tff(decl_134,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
tff(decl_135,type,
c_Arrow__Order__Mirabelle_OLin: $i ).
tff(decl_136,type,
v_L: $i ).
tff(decl_137,type,
v_xa: $i ).
tff(decl_138,type,
c_fequal: ( $i * $i * $i ) > $o ).
cnf(cls_conjecture_13,negated_conjecture,
( 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_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)))
| ~ 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)))
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_13) ).
cnf(cls_conjecture_15,negated_conjecture,
( 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_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)))
| ~ 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)))
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_15) ).
cnf(cls_conjecture_0,negated_conjecture,
( c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_8,negated_conjecture,
( 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_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_x != v_xa
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| v_x != v_xa
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_8) ).
cnf(cls_conjecture_17,negated_conjecture,
( hBOOL(c_in(c_Pair(X1,X2,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(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| X1 = X2
| hBOOL(c_in(c_Pair(X3,X4,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(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| X4 = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_17) ).
cnf(cls_conjecture_3,negated_conjecture,
( ~ hBOOL(c_in(c_Pair(X1,X1,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(X2,X2,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('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_irrefl__def_1,axiom,
( c_Relation_Oirrefl(X1,X2)
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X1,X2),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X1,X2),X2,X2),X1,tc_prod(X2,X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_irrefl__def_1) ).
cnf(cls_irrefl__def_0,axiom,
( ~ hBOOL(c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2)))
| ~ c_Relation_Oirrefl(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_irrefl__def_0) ).
cnf(c_0_8,negated_conjecture,
( 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)))
| ~ 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)))
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
inference(fof_simplification,[status(thm)],[cls_conjecture_13]) ).
cnf(c_0_9,negated_conjecture,
( 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)))
| ~ 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)))
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
inference(fof_simplification,[status(thm)],[cls_conjecture_15]) ).
cnf(c_0_10,negated_conjecture,
( 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)))
| ~ 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)))
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
c_0_8 ).
cnf(c_0_11,negated_conjecture,
c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt),
inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).
cnf(c_0_12,negated_conjecture,
( 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_x != v_xa
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| v_x != v_xa
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
inference(fof_simplification,[status(thm)],[cls_conjecture_8]) ).
cnf(c_0_13,negated_conjecture,
( 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)))
| ~ 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)))
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
c_0_9 ).
cnf(c_0_14,negated_conjecture,
( 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))) ),
inference(cn,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt),
c_0_11 ).
cnf(c_0_16,negated_conjecture,
( hBOOL(c_in(c_Pair(X1,X2,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(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| X1 = X2
| hBOOL(c_in(c_Pair(X3,X4,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(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| X4 = X3 ),
cls_conjecture_17 ).
cnf(c_0_17,negated_conjecture,
( ~ hBOOL(c_in(c_Pair(X1,X1,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(X2,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
cls_conjecture_3 ).
cnf(c_0_18,axiom,
( c_Relation_Oirrefl(X1,X2)
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X1,X2),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X1,X2),X2,X2),X1,tc_prod(X2,X2))) ),
cls_irrefl__def_1 ).
cnf(c_0_19,axiom,
( ~ hBOOL(c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2)))
| ~ c_Relation_Oirrefl(X3,X2) ),
cls_irrefl__def_0 ).
cnf(c_0_20,negated_conjecture,
( 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_x != v_xa
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| v_x != v_xa
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
c_0_12 ).
cnf(c_0_21,negated_conjecture,
( 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))) ),
inference(cn,[status(thm)],[c_0_13]) ).
cnf(c_0_22,negated_conjecture,
( 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(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]) ).
cnf(c_0_23,negated_conjecture,
( X1 = X2
| hBOOL(c_in(c_Pair(X2,X1,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(X1,X2,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(ef,[status(thm)],[c_0_16]) ).
cnf(c_0_24,negated_conjecture,
~ hBOOL(c_in(c_Pair(X1,X1,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(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_25,negated_conjecture,
( 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
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
inference(cn,[status(thm)],[c_0_20]) ).
cnf(c_0_26,negated_conjecture,
( 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(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_15])]) ).
cnf(c_0_27,negated_conjecture,
( 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(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_28,negated_conjecture,
( 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(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_15])]) ).
cnf(c_0_29,negated_conjecture,
v_xa = v_x,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_24]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SCT004-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 15:08:37 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.68/0.85 % Version : CSE_E---1.5
% 0.68/0.85 % Problem : theBenchmark.p
% 0.68/0.85 % Proof found
% 0.68/0.85 % SZS status Theorem for theBenchmark.p
% 0.68/0.85 % SZS output start Proof
% See solution above
% 0.68/0.86 % Total time : 0.247000 s
% 0.68/0.86 % SZS output end Proof
% 0.68/0.86 % Total time : 0.269000 s
%------------------------------------------------------------------------------