%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ANA026-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:03:06 PM UTC 2026
% Result : Unsatisfiable 158.15s 24.15s
% Output : CNFRefutation 158.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 62
% Syntax : Number of clauses : 251 ( 109 unt; 10 nHn; 153 RR)
% Number of literals : 442 ( 117 equ; 222 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 29 ( 29 usr; 13 con; 0-3 aty)
% Number of variables : 377 ( 41 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_List_Onibble_Osize__10_0,axiom,
c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble) = c_0,
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_List_Onibble_Osize__10_0) ).
cnf(cls_Datatype_Ounit_Osize_0,axiom,
c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) = c_0,
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_Datatype_Ounit_Osize_0) ).
cnf(cls_IntDef_Onot__int__zless__negative_0,axiom,
~ c_less(c_IntDef_Oint(X1),c_uminus(c_IntDef_Oint(X2),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_IntDef_Onot__int__zless__negative_0) ).
cnf(cls_NatBin_Onat__numeral__0__eq__0_0,axiom,
c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat) = c_0,
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_NatBin_Onat__numeral__0__eq__0_0) ).
cnf(cls_IntArith_Ozle__diff1__eq_0,axiom,
( ~ c_lessequals(X1,c_minus(X2,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(X1,X2,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_IntArith_Ozle__diff1__eq_0) ).
cnf(cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1,axiom,
( ~ c_lessequals(c_0,X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(c_0,c_plus(X2,X2,X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1) ).
cnf(cls_IntDef_Oint__1_0,axiom,
c_IntDef_Oint(c_1) = c_1,
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_IntDef_Oint__1_0) ).
cnf(cls_IntDef_Oint__eq__0__conv_1,axiom,
c_IntDef_Oint(c_0) = c_0,
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_IntDef_Oint__eq__0__conv_1) ).
cnf(cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0,axiom,
c_plus(X1,c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X1,X2,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0) ).
cnf(clsarity_IntDef__Oint_48,axiom,
class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsarity_IntDef__Oint_48) ).
cnf(cls_IntDef_Oint__nat__eq_1,axiom,
( c_IntDef_Oint(c_IntDef_Onat(X1)) = c_0
| c_lessequals(c_0,X1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_IntDef_Oint__nat__eq_1) ).
cnf(cls_Nat_Odiff__self__eq__0_0,axiom,
c_minus(X1,X1,tc_nat) = c_0,
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_Nat_Odiff__self__eq__0_0) ).
cnf(cls_IntDef_Ozle__int_0,axiom,
( ~ c_lessequals(c_IntDef_Oint(X1),c_IntDef_Oint(X2),tc_IntDef_Oint)
| c_lessequals(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_IntDef_Ozle__int_0) ).
cnf(cls_Orderings_Oorder__class_Oaxioms__1_0,axiom,
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X2,X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
cnf(cls_Numeral_Obin__arith__extra__simps__3_0,axiom,
( ~ class_Numeral_Onumber__ring(X1)
| c_uminus(c_1,X1) = c_Numeral_Onumber__of(c_Numeral_OMin,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_Numeral_Obin__arith__extra__simps__3_0) ).
cnf(cls_IntDef_Onat__zero_0,axiom,
c_IntDef_Onat(c_0) = c_0,
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_IntDef_Onat__zero_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_4,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_4) ).
cnf(cls_List_Olength__upt_0,axiom,
c_Nat_Osize(c_List_Oupt(X1,X2),tc_List_Olist(tc_nat)) = c_minus(X2,X1,tc_nat),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_List_Olength__upt_0) ).
cnf(cls_SetInterval_Ocard__atLeastLessThan_0,axiom,
c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X1,X2,tc_nat),tc_nat) = c_minus(X2,X1,tc_nat),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_SetInterval_Ocard__atLeastLessThan_0) ).
cnf(cls_SetInterval_OatLeastLessThan__empty_0,axiom,
( ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_SetInterval_OatLeastLessThan(X3,X2,X1) = c_emptyset ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_SetInterval_OatLeastLessThan__empty_0) ).
cnf(clsarity_IntDef__Oint_31,axiom,
class_Orderings_Oorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsarity_IntDef__Oint_31) ).
cnf(clsarity_IntDef__Oint_60,axiom,
class_Numeral_Onumber__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsarity_IntDef__Oint_60) ).
cnf(cls_IntDef_Onat__int_0,axiom,
c_IntDef_Onat(c_IntDef_Oint(X1)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_IntDef_Onat__int_0) ).
cnf(cls_Numeral_Obin__rel__simps__7_0,axiom,
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Numeral_Onumber__ring(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_Numeral_Obin__rel__simps__7_0) ).
cnf(cls_OrderedGroup_Ominus__minus_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_uminus(X2,X1),X1) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Ominus__minus_0) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_50,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Olordered__ab__group__abs(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_50) ).
cnf(cls_OrderedGroup_Oadd__0__right_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(X2,c_0,X1) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oadd__0__right_0) ).
cnf(clsarity_nat_3,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsarity_nat_3) ).
cnf(cls_NatBin_Onat__number__of_0,axiom,
c_IntDef_Onat(c_Numeral_Onumber__of(X1,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X1,tc_nat),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_NatBin_Onat__number__of_0) ).
cnf(clsarity_IntDef__Oint_58,axiom,
class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsarity_IntDef__Oint_58) ).
cnf(cls_IntDef_Onot__neg__int_0,axiom,
~ c_IntDef_Oneg(c_IntDef_Oint(X1),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_IntDef_Onot__neg__int_0) ).
cnf(cls_OrderedGroup_Oabs__minus__cancel_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(c_uminus(X2,X1),X1) = c_HOL_Oabs(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oabs__minus__cancel_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_23,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_23) ).
cnf(cls_Finite__Set_Ocard__empty_0,axiom,
c_Finite__Set_Ocard(c_emptyset,X1) = c_0,
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_Finite__Set_Ocard__empty_0) ).
cnf(cls_NatBin_Oint__nat__number__of_1,axiom,
( c_IntDef_Oint(c_Numeral_Onumber__of(X1,tc_nat)) = c_Numeral_Onumber__of(X1,tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_NatBin_Oint__nat__number__of_1) ).
cnf(cls_OrderedGroup_Oabs__idempotent_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(c_HOL_Oabs(X2,X1),X1) = c_HOL_Oabs(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oabs__idempotent_0) ).
cnf(cls_OrderedGroup_Oabs__of__nonneg_0,axiom,
( ~ c_lessequals(c_0,X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X2,X1) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oabs__of__nonneg_0) ).
cnf(cls_IntDef_Oint__int__eq_0,axiom,
( c_IntDef_Oint(X1) != c_IntDef_Oint(X2)
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_IntDef_Oint__int__eq_0) ).
cnf(cls_conjecture_2,negated_conjecture,
~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_33,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_33) ).
cnf(cls_OrderedGroup_Ocompare__rls__10_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| X2 = c_plus(c_minus(X2,X3,X1),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__10_0) ).
cnf(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2,axiom,
( ~ c_lessequals(X4,X3,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| c_lessequals(c_Orderings_Omax(X4,X2,X1),X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
cnf(cls_OrderedGroup_Ominus__diff__eq_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_minus(X2,X3,X1),X1) = c_minus(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Ominus__diff__eq_0) ).
cnf(cls_OrderedGroup_Oab__group__add__class_Odiff__minus_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_minus(X2,X3,X1) = c_plus(X2,c_uminus(X3,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oab__group__add__class_Odiff__minus_0) ).
cnf(cls_OrderedGroup_Ocompare__rls__2_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_plus(X2,c_minus(X3,X4,X1),X1) = c_minus(c_plus(X2,X3,X1),X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__2_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_54,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Opordered__ab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_54) ).
cnf(cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(c_0,X2,X1) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_37,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_37) ).
cnf(cls_OrderedGroup_Oneg__le__iff__le_1,axiom,
( ~ c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(c_uminus(X3,X1),c_uminus(X2,X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oneg__le__iff__le_1) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_44,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Oorder(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_44) ).
cnf(cls_OrderedGroup_Oadd__le__cancel__left_1,axiom,
( ~ c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_lessequals(c_plus(X4,X2,X1),c_plus(X4,X3,X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oadd__le__cancel__left_1) ).
cnf(cls_conjecture_1,negated_conjecture,
c_lessequals(v_g(X1),v_k(X1),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_Orderings_Olinorder__not__le_0,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X3,X2,X1)
| c_less(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Olinorder__not__le_0) ).
cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oabs__ge__zero_0) ).
cnf(cls_Orderings_Oorder__class_Oorder__trans_0,axiom,
( ~ c_lessequals(X4,X2,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(X4,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
cnf(cls_OrderedGroup_Ocompare__rls__8_0,axiom,
( ~ c_lessequals(c_minus(X2,X3,X1),X4,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X2,c_plus(X4,X3,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__8_0) ).
cnf(cls_Orderings_Olinorder__not__le_1,axiom,
( ~ c_lessequals(X3,X2,X1)
| ~ c_less(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Olinorder__not__le_1) ).
cnf(cls_OrderedGroup_Ocompare__rls__8_1,axiom,
( ~ c_lessequals(X2,c_plus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(c_minus(X2,X4,X1),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__8_1) ).
cnf(cls_Orderings_Oorder__less__imp__le_0,axiom,
( ~ c_less(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
cnf(cls_OrderedGroup_Oabs__not__less__zero_0,axiom,
( ~ c_less(c_HOL_Oabs(X2,X1),c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oabs__not__less__zero_0) ).
cnf(cls_OrderedGroup_Ocompare__rls__11_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| X2 = c_minus(c_plus(X2,X3,X1),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__11_1) ).
cnf(c_0_62,axiom,
c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble) = c_0,
cls_List_Onibble_Osize__10_0 ).
cnf(c_0_63,axiom,
c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) = c_0,
cls_Datatype_Ounit_Osize_0 ).
cnf(c_0_64,plain,
~ c_less(c_IntDef_Oint(X1),c_uminus(c_IntDef_Oint(X2),tc_IntDef_Oint),tc_IntDef_Oint),
inference(fof_simplification,[status(thm)],[cls_IntDef_Onot__int__zless__negative_0]) ).
cnf(c_0_65,axiom,
c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat) = c_0,
cls_NatBin_Onat__numeral__0__eq__0_0 ).
cnf(c_0_66,plain,
c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) = c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble),
inference(rw,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_67,plain,
( ~ c_lessequals(X1,c_minus(X2,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(X1,X2,tc_IntDef_Oint) ),
inference(fof_simplification,[status(thm)],[cls_IntArith_Ozle__diff1__eq_0]) ).
cnf(c_0_68,plain,
( ~ c_lessequals(c_0,X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(c_0,c_plus(X2,X2,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1]) ).
cnf(c_0_69,plain,
~ c_less(c_IntDef_Oint(X1),c_uminus(c_IntDef_Oint(X2),tc_IntDef_Oint),tc_IntDef_Oint),
c_0_64 ).
cnf(c_0_70,axiom,
c_IntDef_Oint(c_1) = c_1,
cls_IntDef_Oint__1_0 ).
cnf(c_0_71,axiom,
c_IntDef_Oint(c_0) = c_0,
cls_IntDef_Oint__eq__0__conv_1 ).
cnf(c_0_72,plain,
c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble) = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_63]),c_0_66]) ).
cnf(c_0_73,plain,
( ~ c_lessequals(X1,c_minus(X2,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(X1,X2,tc_IntDef_Oint) ),
c_0_67 ).
cnf(c_0_74,axiom,
c_plus(X1,c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X1,X2,tc_IntDef_Oint),
cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0 ).
cnf(c_0_75,plain,
( ~ c_lessequals(c_0,X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(c_0,c_plus(X2,X2,X1),X1) ),
c_0_68 ).
cnf(c_0_76,plain,
~ c_less(c_IntDef_Oint(X1),c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_77,plain,
c_IntDef_Oint(c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat)) = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_63]),c_0_63]),c_0_66]),c_0_72]),c_0_66]),c_0_72]) ).
cnf(c_0_78,plain,
( ~ c_lessequals(X1,c_plus(X2,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(X1,X2,tc_IntDef_Oint) ),
inference(rw,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_79,plain,
( ~ c_lessequals(c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),X1,X2)
| ~ class_OrderedGroup_Olordered__ab__group(X2)
| c_lessequals(c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),c_plus(X1,X1,X2),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_63]),c_0_66]),c_0_72]),c_0_63]),c_0_66]),c_0_72]) ).
cnf(c_0_80,axiom,
class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
clsarity_IntDef__Oint_48 ).
cnf(c_0_81,plain,
~ c_less(c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_82,axiom,
( c_IntDef_Oint(c_IntDef_Onat(X1)) = c_0
| c_lessequals(c_0,X1,tc_IntDef_Oint) ),
cls_IntDef_Oint__nat__eq_1 ).
cnf(c_0_83,axiom,
c_minus(X1,X1,tc_nat) = c_0,
cls_Nat_Odiff__self__eq__0_0 ).
cnf(c_0_84,plain,
( ~ c_lessequals(c_IntDef_Oint(X1),c_IntDef_Oint(X2),tc_IntDef_Oint)
| c_lessequals(X1,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[cls_IntDef_Ozle__int_0]) ).
cnf(c_0_85,plain,
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X2,X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_Orderings_Oorder__class_Oaxioms__1_0]) ).
cnf(c_0_86,plain,
( ~ class_Numeral_Onumber__ring(X1)
| c_uminus(c_1,X1) = c_Numeral_Onumber__of(c_Numeral_OMin,X1) ),
inference(fof_simplification,[status(thm)],[cls_Numeral_Obin__arith__extra__simps__3_0]) ).
cnf(c_0_87,plain,
~ c_lessequals(c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80])]),c_0_81]) ).
cnf(c_0_88,plain,
( c_lessequals(c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),X1,tc_IntDef_Oint)
| c_IntDef_Oint(c_IntDef_Onat(X1)) = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_63]),c_0_66]),c_0_72]),c_0_63]),c_0_66]),c_0_72]) ).
cnf(c_0_89,axiom,
c_IntDef_Onat(c_0) = c_0,
cls_IntDef_Onat__zero_0 ).
cnf(c_0_90,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Oab__group__add(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_4]) ).
cnf(c_0_91,plain,
c_minus(X1,X1,tc_nat) = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_63]),c_0_66]),c_0_72]) ).
cnf(c_0_92,axiom,
c_Nat_Osize(c_List_Oupt(X1,X2),tc_List_Olist(tc_nat)) = c_minus(X2,X1,tc_nat),
cls_List_Olength__upt_0 ).
cnf(c_0_93,axiom,
c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X1,X2,tc_nat),tc_nat) = c_minus(X2,X1,tc_nat),
cls_SetInterval_Ocard__atLeastLessThan_0 ).
cnf(c_0_94,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_SetInterval_OatLeastLessThan(X3,X2,X1) = c_emptyset ),
inference(fof_simplification,[status(thm)],[cls_SetInterval_OatLeastLessThan__empty_0]) ).
cnf(c_0_95,plain,
( ~ c_lessequals(c_IntDef_Oint(X1),c_IntDef_Oint(X2),tc_IntDef_Oint)
| c_lessequals(X1,X2,tc_nat) ),
c_0_84 ).
cnf(c_0_96,plain,
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X2,X2,X1) ),
c_0_85 ).
cnf(c_0_97,axiom,
class_Orderings_Oorder(tc_IntDef_Oint),
clsarity_IntDef__Oint_31 ).
cnf(c_0_98,plain,
( ~ class_Numeral_Onumber__ring(X1)
| c_uminus(c_1,X1) = c_Numeral_Onumber__of(c_Numeral_OMin,X1) ),
c_0_86 ).
cnf(c_0_99,axiom,
class_Numeral_Onumber__ring(tc_IntDef_Oint),
clsarity_IntDef__Oint_60 ).
cnf(c_0_100,axiom,
c_IntDef_Onat(c_IntDef_Oint(X1)) = X1,
cls_IntDef_Onat__int_0 ).
cnf(c_0_101,plain,
c_IntDef_Oint(c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint))) = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_102,plain,
c_IntDef_Onat(c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat)) = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_63]),c_0_63]),c_0_66]),c_0_72]),c_0_66]),c_0_72]) ).
cnf(c_0_103,plain,
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Numeral_Onumber__ring(X1) ),
inference(fof_simplification,[status(thm)],[cls_Numeral_Obin__rel__simps__7_0]) ).
cnf(c_0_104,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_uminus(X2,X1),X1) = X2 ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Ominus__minus_0]) ).
cnf(c_0_105,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Oab__group__add(X1) ),
c_0_90 ).
cnf(c_0_106,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
tfree_tcs ).
cnf(c_0_107,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Olordered__ab__group__abs(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_50]) ).
cnf(c_0_108,plain,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(X2,c_0,X1) = X2 ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Oadd__0__right_0]) ).
cnf(c_0_109,plain,
c_Nat_Osize(c_List_Oupt(X1,X1),tc_List_Olist(tc_nat)) = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),
inference(rw,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_110,plain,
c_Nat_Osize(c_List_Oupt(X1,X2),tc_List_Olist(tc_nat)) = c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X1,X2,tc_nat),tc_nat),
inference(rw,[status(thm)],[c_0_93,c_0_92]) ).
cnf(c_0_111,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_SetInterval_OatLeastLessThan(X3,X2,X1) = c_emptyset ),
c_0_94 ).
cnf(c_0_112,plain,
c_lessequals(X1,X1,tc_nat),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97])]) ).
cnf(c_0_113,axiom,
class_Orderings_Oorder(tc_nat),
clsarity_nat_3 ).
cnf(c_0_114,axiom,
c_IntDef_Onat(c_Numeral_Onumber__of(X1,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X1,tc_nat),
cls_NatBin_Onat__number__of_0 ).
cnf(c_0_115,plain,
c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_116,plain,
c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint)) = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_102]) ).
cnf(c_0_117,plain,
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Numeral_Onumber__ring(X1) ),
c_0_103 ).
cnf(c_0_118,axiom,
class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
clsarity_IntDef__Oint_58 ).
cnf(c_0_119,plain,
~ c_IntDef_Oneg(c_IntDef_Oint(X1),tc_IntDef_Oint),
inference(fof_simplification,[status(thm)],[cls_IntDef_Onot__neg__int_0]) ).
cnf(c_0_120,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(c_uminus(X2,X1),X1) = c_HOL_Oabs(X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Oabs__minus__cancel_0]) ).
cnf(c_0_121,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_uminus(X2,X1),X1) = X2 ),
c_0_104 ).
cnf(c_0_122,negated_conjecture,
class_OrderedGroup_Oab__group__add(t_b),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_123,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Olordered__ab__group__abs(X1) ),
c_0_107 ).
cnf(c_0_124,plain,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(X2,c_0,X1) = X2 ),
c_0_108 ).
cnf(c_0_125,plain,
c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X1,X1,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),
inference(rw,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_126,plain,
c_SetInterval_OatLeastLessThan(X1,X1,tc_nat) = c_emptyset,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_113])]) ).
cnf(c_0_127,plain,
c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat) = c_Numeral_Onumber__of(c_Numeral_OMin,tc_nat),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_116]) ).
cnf(c_0_128,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_23]) ).
cnf(c_0_129,axiom,
c_Finite__Set_Ocard(c_emptyset,X1) = c_0,
cls_Finite__Set_Ocard__empty_0 ).
cnf(c_0_130,axiom,
( c_IntDef_Oint(c_Numeral_Onumber__of(X1,tc_nat)) = c_Numeral_Onumber__of(X1,tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
cls_NatBin_Oint__nat__number__of_1 ).
cnf(c_0_131,plain,
~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint),tc_IntDef_Oint),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_99])]) ).
cnf(c_0_132,plain,
~ c_IntDef_Oneg(c_IntDef_Oint(X1),tc_IntDef_Oint),
c_0_119 ).
cnf(c_0_133,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(c_HOL_Oabs(X2,X1),X1) = c_HOL_Oabs(X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Oabs__idempotent_0]) ).
cnf(c_0_134,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(c_uminus(X2,X1),X1) = c_HOL_Oabs(X2,X1) ),
c_0_120 ).
cnf(c_0_135,negated_conjecture,
c_uminus(c_uminus(X1,t_b),t_b) = X1,
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_136,negated_conjecture,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(spm,[status(thm)],[c_0_123,c_0_106]) ).
cnf(c_0_137,plain,
( ~ c_lessequals(c_0,X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X2,X1) = X2 ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Oabs__of__nonneg_0]) ).
cnf(c_0_138,plain,
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| c_plus(X1,c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),X2) = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_124,c_0_63]),c_0_66]),c_0_72]) ).
cnf(c_0_139,plain,
c_Numeral_Onumber__of(c_Numeral_OMin,tc_nat) = c_Finite__Set_Ocard(c_emptyset,tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_125,c_0_126]),c_0_127]) ).
cnf(c_0_140,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_128 ).
cnf(c_0_141,plain,
( c_IntDef_Oint(X1) != c_IntDef_Oint(X2)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[cls_IntDef_Oint__int__eq_0]) ).
cnf(c_0_142,plain,
c_Finite__Set_Ocard(c_emptyset,X1) = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_129,c_0_63]),c_0_66]),c_0_72]) ).
cnf(c_0_143,plain,
c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_130]),c_0_131]) ).
cnf(c_0_144,plain,
~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),tc_IntDef_Oint),
inference(spm,[status(thm)],[c_0_132,c_0_77]) ).
cnf(c_0_145,negated_conjecture,
~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(fof_simplification,[status(thm)],[cls_conjecture_2]) ).
cnf(c_0_146,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Olinorder(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_33]) ).
cnf(c_0_147,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(c_HOL_Oabs(X2,X1),X1) = c_HOL_Oabs(X2,X1) ),
c_0_133 ).
cnf(c_0_148,negated_conjecture,
c_HOL_Oabs(c_uminus(X1,t_b),t_b) = c_HOL_Oabs(X1,t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_136])]) ).
cnf(c_0_149,plain,
( ~ c_lessequals(c_0,X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X2,X1) = X2 ),
c_0_137 ).
cnf(c_0_150,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| X2 = c_plus(c_minus(X2,X3,X1),X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Ocompare__rls__10_0]) ).
cnf(c_0_151,plain,
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| c_plus(X1,c_Finite__Set_Ocard(c_emptyset,tc_nat),X2) = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_138,c_0_127]),c_0_139]) ).
cnf(c_0_152,negated_conjecture,
class_OrderedGroup_Ocomm__monoid__add(t_b),
inference(spm,[status(thm)],[c_0_140,c_0_106]) ).
cnf(c_0_153,plain,
( c_IntDef_Oint(X1) != c_IntDef_Oint(X2)
| X1 = X2 ),
c_0_141 ).
cnf(c_0_154,plain,
c_IntDef_Oint(c_Finite__Set_Ocard(c_emptyset,X1)) = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_142]),c_0_143]),c_0_143]),c_0_144]) ).
cnf(c_0_155,negated_conjecture,
~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
c_0_145 ).
cnf(c_0_156,plain,
( ~ c_lessequals(X4,X3,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| c_lessequals(c_Orderings_Omax(X4,X2,X1),X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2]) ).
cnf(c_0_157,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Olinorder(X1) ),
c_0_146 ).
cnf(c_0_158,negated_conjecture,
c_HOL_Oabs(c_HOL_Oabs(X1,t_b),t_b) = c_HOL_Oabs(X1,t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_136])]) ).
cnf(c_0_159,plain,
( ~ c_lessequals(c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),X1,X2)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X2)
| c_HOL_Oabs(X1,X2) = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_149,c_0_63]),c_0_66]),c_0_72]) ).
cnf(c_0_160,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| X2 = c_plus(c_minus(X2,X3,X1),X3,X1) ),
c_0_150 ).
cnf(c_0_161,negated_conjecture,
c_plus(X1,c_Finite__Set_Ocard(c_emptyset,tc_nat),t_b) = X1,
inference(spm,[status(thm)],[c_0_151,c_0_152]) ).
cnf(c_0_162,plain,
( c_IntDef_Oint(X2) != c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat)
| c_Finite__Set_Ocard(c_emptyset,X1) = X2 ),
inference(spm,[status(thm)],[c_0_153,c_0_154]) ).
cnf(c_0_163,negated_conjecture,
~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_155,c_0_63]),c_0_66]),c_0_72]) ).
cnf(c_0_164,plain,
( ~ c_lessequals(X4,X3,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| c_lessequals(c_Orderings_Omax(X4,X2,X1),X3,X1) ),
c_0_156 ).
cnf(c_0_165,negated_conjecture,
class_Orderings_Olinorder(t_b),
inference(spm,[status(thm)],[c_0_157,c_0_106]) ).
cnf(c_0_166,negated_conjecture,
( ~ c_lessequals(c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),X1,t_b)
| c_HOL_Oabs(X1,t_b) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_159]),c_0_136])]) ).
cnf(c_0_167,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_minus(X2,X3,X1),X1) = c_minus(X3,X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Ominus__diff__eq_0]) ).
cnf(c_0_168,negated_conjecture,
c_minus(X1,c_Finite__Set_Ocard(c_emptyset,tc_nat),t_b) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_122])]) ).
cnf(c_0_169,plain,
c_Finite__Set_Ocard(c_emptyset,X1) = c_Finite__Set_Ocard(c_emptyset,X2),
inference(spm,[status(thm)],[c_0_162,c_0_154]) ).
cnf(c_0_170,negated_conjecture,
( ~ c_lessequals(c_Finite__Set_Ocard(c_emptyset,tc_nat),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_164]),c_0_165]),c_0_127]),c_0_139])]) ).
cnf(c_0_171,negated_conjecture,
( ~ c_lessequals(c_Finite__Set_Ocard(c_emptyset,tc_nat),X1,t_b)
| c_HOL_Oabs(X1,t_b) = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_166,c_0_127]),c_0_139]) ).
cnf(c_0_172,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_minus(X2,X3,X1) = c_plus(X2,c_uminus(X3,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Oab__group__add__class_Odiff__minus_0]) ).
cnf(c_0_173,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_plus(X2,c_minus(X3,X4,X1),X1) = c_minus(c_plus(X2,X3,X1),X4,X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Ocompare__rls__2_0]) ).
cnf(c_0_174,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_minus(X2,X3,X1),X1) = c_minus(X3,X2,X1) ),
c_0_167 ).
cnf(c_0_175,negated_conjecture,
c_minus(X1,c_Finite__Set_Ocard(c_emptyset,X2),t_b) = X1,
inference(spm,[status(thm)],[c_0_168,c_0_169]) ).
cnf(c_0_176,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_54]) ).
cnf(c_0_177,plain,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(c_0,X2,X1) = X2 ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0]) ).
cnf(c_0_178,negated_conjecture,
( ~ c_lessequals(c_Finite__Set_Ocard(c_emptyset,tc_nat),c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
| ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b) ),
inference(spm,[status(thm)],[c_0_170,c_0_171]) ).
cnf(c_0_179,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_minus(X2,X3,X1) = c_plus(X2,c_uminus(X3,X1),X1) ),
c_0_172 ).
cnf(c_0_180,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_plus(X2,c_minus(X3,X4,X1),X1) = c_minus(c_plus(X2,X3,X1),X4,X1) ),
c_0_173 ).
cnf(c_0_181,negated_conjecture,
c_plus(X1,c_Finite__Set_Ocard(c_emptyset,X2),t_b) = X1,
inference(spm,[status(thm)],[c_0_161,c_0_169]) ).
cnf(c_0_182,negated_conjecture,
c_minus(c_Finite__Set_Ocard(c_emptyset,X1),X2,t_b) = c_uminus(X2,t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_175]),c_0_122])]) ).
cnf(c_0_183,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_37]) ).
cnf(c_0_184,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(c_uminus(X3,X1),c_uminus(X2,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Oneg__le__iff__le_1]) ).
cnf(c_0_185,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_176 ).
cnf(c_0_186,plain,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(c_0,X2,X1) = X2 ),
c_0_177 ).
cnf(c_0_187,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Oorder(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_44]) ).
cnf(c_0_188,negated_conjecture,
( ~ c_lessequals(c_Finite__Set_Ocard(c_emptyset,tc_nat),c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
| ~ c_lessequals(c_plus(v_f(v_x),c_uminus(v_k(v_x),t_b),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_179]),c_0_122])]) ).
cnf(c_0_189,negated_conjecture,
c_minus(X1,X2,t_b) = c_plus(X1,c_uminus(X2,t_b),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_181]),c_0_182]),c_0_122])]) ).
cnf(c_0_190,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_lessequals(c_plus(X4,X2,X1),c_plus(X4,X3,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Oadd__le__cancel__left_1]) ).
cnf(c_0_191,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_183 ).
cnf(c_0_192,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(c_uminus(X3,X1),c_uminus(X2,X1),X1) ),
c_0_184 ).
cnf(c_0_193,negated_conjecture,
c_lessequals(v_g(X1),v_k(X1),t_b),
cls_conjecture_1 ).
cnf(c_0_194,negated_conjecture,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(spm,[status(thm)],[c_0_185,c_0_106]) ).
cnf(c_0_195,plain,
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X3,X2,X1)
| c_less(X2,X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_Orderings_Olinorder__not__le_0]) ).
cnf(c_0_196,plain,
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| c_plus(c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),X1,X2) = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_186,c_0_63]),c_0_66]),c_0_72]) ).
cnf(c_0_197,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Oabs__ge__zero_0]) ).
cnf(c_0_198,plain,
( ~ c_lessequals(X4,X2,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(X4,X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_Orderings_Oorder__class_Oorder__trans_0]) ).
cnf(c_0_199,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Oorder(X1) ),
c_0_187 ).
cnf(c_0_200,negated_conjecture,
( ~ c_lessequals(c_Finite__Set_Ocard(c_emptyset,tc_nat),c_plus(v_f(v_x),c_uminus(v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_plus(v_f(v_x),c_uminus(v_k(v_x),t_b),t_b),c_plus(v_f(v_x),c_uminus(v_g(v_x),t_b),t_b),t_b) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_188,c_0_189]),c_0_189]) ).
cnf(c_0_201,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_lessequals(c_plus(X4,X2,X1),c_plus(X4,X3,X1),X1) ),
c_0_190 ).
cnf(c_0_202,negated_conjecture,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b),
inference(spm,[status(thm)],[c_0_191,c_0_106]) ).
cnf(c_0_203,negated_conjecture,
c_lessequals(c_uminus(v_k(X1),t_b),c_uminus(v_g(X1),t_b),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_193]),c_0_194])]) ).
cnf(c_0_204,plain,
( ~ c_lessequals(c_minus(X2,X3,X1),X4,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X2,c_plus(X4,X3,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Ocompare__rls__8_0]) ).
cnf(c_0_205,plain,
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X3,X2,X1)
| c_less(X2,X3,X1) ),
c_0_195 ).
cnf(c_0_206,plain,
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| c_plus(c_Finite__Set_Ocard(c_emptyset,tc_nat),X1,X2) = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_196,c_0_127]),c_0_139]) ).
cnf(c_0_207,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1) ),
c_0_197 ).
cnf(c_0_208,plain,
( ~ c_lessequals(X3,X2,X1)
| ~ c_less(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(fof_simplification,[status(thm)],[cls_Orderings_Olinorder__not__le_1]) ).
cnf(c_0_209,plain,
( ~ c_lessequals(X4,X2,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(X4,X3,X1) ),
c_0_198 ).
cnf(c_0_210,negated_conjecture,
class_Orderings_Oorder(t_b),
inference(spm,[status(thm)],[c_0_199,c_0_106]) ).
cnf(c_0_211,negated_conjecture,
~ c_lessequals(c_Finite__Set_Ocard(c_emptyset,tc_nat),c_plus(v_f(v_x),c_uminus(v_g(v_x),t_b),t_b),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_200,c_0_201]),c_0_202]),c_0_203])]) ).
cnf(c_0_212,plain,
( ~ c_lessequals(c_minus(X2,X3,X1),X4,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X2,c_plus(X4,X3,X1),X1) ),
c_0_204 ).
cnf(c_0_213,negated_conjecture,
( c_lessequals(X2,X1,t_b)
| c_less(X1,X2,t_b) ),
inference(spm,[status(thm)],[c_0_205,c_0_165]) ).
cnf(c_0_214,negated_conjecture,
c_plus(c_Finite__Set_Ocard(c_emptyset,tc_nat),X1,t_b) = X1,
inference(spm,[status(thm)],[c_0_206,c_0_152]) ).
cnf(c_0_215,negated_conjecture,
~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),t_b),c_HOL_Oabs(c_minus(v_g(v_x),v_f(v_x),t_b),t_b),t_b),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_174]),c_0_122])]),c_0_148]) ).
cnf(c_0_216,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X2)
| c_lessequals(c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),c_HOL_Oabs(X1,X2),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_207,c_0_63]),c_0_66]),c_0_72]) ).
cnf(c_0_217,plain,
( ~ c_lessequals(X3,X2,X1)
| ~ c_less(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
c_0_208 ).
cnf(c_0_218,negated_conjecture,
( ~ c_lessequals(v_k(X1),X2,t_b)
| c_lessequals(v_g(X1),X2,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_193]),c_0_210])]) ).
cnf(c_0_219,negated_conjecture,
~ c_lessequals(c_Finite__Set_Ocard(c_emptyset,X1),c_plus(v_f(v_x),c_uminus(v_g(v_x),t_b),t_b),t_b),
inference(spm,[status(thm)],[c_0_211,c_0_169]) ).
cnf(c_0_220,negated_conjecture,
( c_lessequals(X2,c_plus(X1,X3,t_b),t_b)
| c_less(X1,c_plus(X2,c_uminus(X3,t_b),t_b),t_b) ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_213]),c_0_194])]),c_0_189]) ).
cnf(c_0_221,negated_conjecture,
c_plus(c_Finite__Set_Ocard(c_emptyset,X1),X2,t_b) = X2,
inference(spm,[status(thm)],[c_0_214,c_0_169]) ).
cnf(c_0_222,negated_conjecture,
~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_Finite__Set_Ocard(c_emptyset,X1),t_b),c_HOL_Oabs(c_minus(v_g(v_x),v_f(v_x),t_b),t_b),t_b),
inference(spm,[status(thm)],[c_0_215,c_0_142]) ).
cnf(c_0_223,plain,
( ~ c_lessequals(X2,c_plus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(c_minus(X2,X4,X1),X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Ocompare__rls__8_1]) ).
cnf(c_0_224,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X2)
| c_lessequals(c_Finite__Set_Ocard(c_emptyset,tc_nat),c_HOL_Oabs(X1,X2),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_216,c_0_127]),c_0_139]) ).
cnf(c_0_225,plain,
( ~ c_less(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(X2,X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_Orderings_Oorder__less__imp__le_0]) ).
cnf(c_0_226,negated_conjecture,
( ~ c_lessequals(v_k(X2),X1,t_b)
| ~ c_less(X1,v_g(X2),t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_217,c_0_218]),c_0_165])]) ).
cnf(c_0_227,negated_conjecture,
c_less(v_f(v_x),v_g(v_x),t_b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_219,c_0_220]),c_0_135]),c_0_221]) ).
cnf(c_0_228,plain,
( ~ c_less(c_HOL_Oabs(X2,X1),c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Oabs__not__less__zero_0]) ).
cnf(c_0_229,negated_conjecture,
( ~ c_lessequals(c_Finite__Set_Ocard(c_emptyset,X1),c_HOL_Oabs(c_minus(v_g(v_x),v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_g(v_x),v_f(v_x),t_b),t_b),t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_222,c_0_164]),c_0_165])]) ).
cnf(c_0_230,plain,
( ~ c_lessequals(X2,c_plus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(c_minus(X2,X4,X1),X3,X1) ),
c_0_223 ).
cnf(c_0_231,negated_conjecture,
c_lessequals(c_Finite__Set_Ocard(c_emptyset,tc_nat),c_HOL_Oabs(X1,t_b),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_224,c_0_148]),c_0_136])]) ).
cnf(c_0_232,plain,
( ~ c_less(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(X2,X3,X1) ),
c_0_225 ).
cnf(c_0_233,negated_conjecture,
~ c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(spm,[status(thm)],[c_0_226,c_0_227]) ).
cnf(c_0_234,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| X2 = c_minus(c_plus(X2,X3,X1),X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Ocompare__rls__11_1]) ).
cnf(c_0_235,plain,
( ~ c_less(c_HOL_Oabs(X2,X1),c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
c_0_228 ).
cnf(c_0_236,negated_conjecture,
( ~ c_lessequals(c_Finite__Set_Ocard(c_emptyset,X1),c_HOL_Oabs(c_minus(v_g(v_x),v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(v_f(v_x),c_plus(c_HOL_Oabs(c_minus(v_g(v_x),v_f(v_x),t_b),t_b),v_k(v_x),t_b),t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_229,c_0_230]),c_0_194])]) ).
cnf(c_0_237,negated_conjecture,
c_HOL_Oabs(c_plus(X1,c_uminus(X2,t_b),t_b),t_b) = c_HOL_Oabs(c_plus(X2,c_uminus(X1,t_b),t_b),t_b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_174]),c_0_122])]),c_0_189]),c_0_189]) ).
cnf(c_0_238,negated_conjecture,
c_lessequals(c_Finite__Set_Ocard(c_emptyset,X1),c_HOL_Oabs(X2,t_b),t_b),
inference(spm,[status(thm)],[c_0_231,c_0_169]) ).
cnf(c_0_239,plain,
( ~ c_lessequals(X4,X2,X3)
| ~ c_less(X1,X4,X3)
| ~ class_Orderings_Oorder(X3)
| c_lessequals(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_209,c_0_232]) ).
cnf(c_0_240,negated_conjecture,
c_less(v_f(v_x),v_k(v_x),t_b),
inference(spm,[status(thm)],[c_0_233,c_0_213]) ).
cnf(c_0_241,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| X2 = c_minus(c_plus(X2,X3,X1),X3,X1) ),
c_0_234 ).
cnf(c_0_242,plain,
( ~ c_less(c_HOL_Oabs(X2,X1),c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_235,c_0_63]),c_0_66]),c_0_72]) ).
cnf(c_0_243,negated_conjecture,
~ c_lessequals(v_f(v_x),c_plus(c_HOL_Oabs(c_plus(v_f(v_x),c_uminus(v_g(v_x),t_b),t_b),t_b),v_k(v_x),t_b),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_236,c_0_189]),c_0_237]),c_0_238])]) ).
cnf(c_0_244,negated_conjecture,
( ~ c_lessequals(v_k(v_x),X1,t_b)
| c_lessequals(v_f(v_x),X1,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_239,c_0_240]),c_0_210])]) ).
cnf(c_0_245,negated_conjecture,
c_minus(X1,X1,t_b) = c_Finite__Set_Ocard(c_emptyset,tc_nat),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_241,c_0_214]),c_0_122])]) ).
cnf(c_0_246,plain,
( ~ c_less(c_HOL_Oabs(X2,X1),c_Finite__Set_Ocard(c_emptyset,X3),X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
inference(spm,[status(thm)],[c_0_242,c_0_142]) ).
cnf(c_0_247,negated_conjecture,
~ c_lessequals(v_k(v_x),c_plus(c_HOL_Oabs(c_plus(v_f(v_x),c_uminus(v_g(v_x),t_b),t_b),t_b),v_k(v_x),t_b),t_b),
inference(spm,[status(thm)],[c_0_243,c_0_244]) ).
cnf(c_0_248,negated_conjecture,
c_plus(X1,c_uminus(X1,t_b),t_b) = c_Finite__Set_Ocard(c_emptyset,tc_nat),
inference(rw,[status(thm)],[c_0_245,c_0_189]) ).
cnf(c_0_249,negated_conjecture,
~ c_less(c_HOL_Oabs(X1,t_b),c_Finite__Set_Ocard(c_emptyset,X2),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_246,c_0_148]),c_0_136])]) ).
cnf(c_0_250,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_247,c_0_220]),c_0_248]),c_0_249]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA026-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.77 % Computer : n016.cluster.edu
% 0.11/0.77 % Model : x86_64 x86_64
% 0.11/0.77 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.77 % Memory : 8046.5625MB
% 0.11/0.77 % OS : Linux 6.8.0-71-generic
% 0.11/0.77 % CPULimit : 300
% 0.11/0.77 % WCLimit : 300
% 0.11/0.77 % DateTime : Mon Sep 21 13:29:25 UTC 2026
% 0.11/0.77 % CPUTime :
% 0.11/0.77 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.82 Running first-order theorem proving
% 0.14/0.82 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
% 158.15/24.14 % Version: 3.5.1
% 158.15/24.14 % Preprocessing class: FMLMSMSMSSSNFFN.
% 158.15/24.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 158.15/24.14 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 158.15/24.14 % Starting new_bool_3 with 300s (1) cores
% 158.15/24.14 % Starting new_bool_1 with 300s (1) cores
% 158.15/24.14 % Starting sh5l with 300s (1) cores
% 158.15/24.14 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2519379 completed with status 0
% 158.15/24.14 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 158.15/24.14 % Preprocessing class: FMLMSMSMSSSNFFN.
% 158.15/24.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 158.15/24.14 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 158.15/24.14 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 158.15/24.14 % No SInE strategy applied
% 158.15/24.14 % Search class: FGHSM-SMLM32-DFFFFFNN
% 158.15/24.14 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 158.15/24.14 % Starting SubtermCWHack with 136s (1) cores
% 158.15/24.14 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 158.15/24.14 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 113s (1) cores
% 158.15/24.15 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 158.15/24.15 % Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 158.15/24.15 % G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 2519390 completed with status 0
% 158.15/24.15 % Result found by G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 158.15/24.15 % Preprocessing class: FMLMSMSMSSSNFFN.
% 158.15/24.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 158.15/24.15 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 158.15/24.15 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 158.15/24.15 % No SInE strategy applied
% 158.15/24.15 % Search class: FGHSM-SMLM32-DFFFFFNN
% 158.15/24.15 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 158.15/24.15 % Starting SubtermCWHack with 136s (1) cores
% 158.15/24.15 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 158.15/24.15 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 113s (1) cores
% 158.15/24.15 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 158.15/24.15 % Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 158.15/24.15 % Preprocessing time : 0.032 s
% 158.15/24.15 % Presaturation interreduction done
% 158.15/24.15
% 158.15/24.15 % Proof found!
% 158.15/24.15 % SZS status Unsatisfiable
% 158.15/24.15 % SZS output start CNFRefutation
% See solution above
% 158.15/24.15 % Parsed axioms : 2808
% 158.15/24.15 % Removed by relevancy pruning/SinE : 0
% 158.15/24.15 % Initial clauses : 2808
% 158.15/24.15 % Removed in clause preprocessing : 9
% 158.15/24.15 % Initial clauses in saturation : 2799
% 158.15/24.15 % Processed clauses : 59248
% 158.15/24.15 % ...of these trivial : 1155
% 158.15/24.15 % ...subsumed : 41024
% 158.15/24.15 % ...remaining for further processing : 17069
% 158.15/24.15 % Other redundant clauses eliminated : 2202
% 158.15/24.15 % Clauses deleted for lack of memory : 0
% 158.15/24.15 % Backward-subsumed : 790
% 158.15/24.15 % Backward-rewritten : 1666
% 158.15/24.15 % Generated clauses : 561834
% 158.15/24.15 % ...of the previous two non-redundant : 516122
% 158.15/24.15 % ...aggressively subsumed : 0
% 158.15/24.15 % Contextual simplify-reflections : 213
% 158.15/24.15 % Paramodulations : 559540
% 158.15/24.15 % Factorizations : 11
% 158.15/24.15 % NegExts : 0
% 158.15/24.15 % Equation resolutions : 2281
% 158.15/24.15 % Disequality decompositions : 0
% 158.15/24.15 % Total rewrite steps : 375118
% 158.15/24.15 % ...of those cached : 354281
% 158.15/24.15 % Propositional unsat checks : 3
% 158.15/24.15 % Propositional check models : 1
% 158.15/24.15 % Propositional check unsatisfiable : 0
% 158.15/24.15 % Propositional clauses : 0
% 158.15/24.15 % Propositional clauses after purity: 0
% 158.15/24.15 % Propositional unsat core size : 0
% 158.15/24.15 % Propositional preprocessing time : 0.000
% 158.15/24.15 % Propositional encoding time : 0.866
% 158.15/24.15 % Propositional solver time : 0.641
% 158.15/24.15 % Success case prop preproc time : 0.000
% 158.15/24.15 % Success case prop encoding time : 0.000
% 158.15/24.15 % Success case prop solver time : 0.000
% 158.15/24.15 % Current number of processed clauses : 11937
% 158.15/24.15 % Positive orientable unit clauses : 1918
% 158.15/24.15 % Positive unorientable unit clauses: 90
% 158.15/24.15 % Negative unit clauses : 1674
% 158.15/24.15 % Non-unit-clauses : 8255
% 158.15/24.15 % Current number of unprocessed clauses: 454728
% 158.15/24.15 % ...number of literals in the above : 1152147
% 158.15/24.15 % Current number of archived formulas : 0
% 158.15/24.15 % Current number of archived clauses : 5140
% 158.15/24.15 % Clause-clause subsumption calls (NU) : 15043428
% 158.15/24.15 % Rec. Clause-clause subsumption calls : 11311952
% 158.15/24.15 % Non-unit clause-clause subsumptions : 17568
% 158.15/24.15 % Unit Clause-clause subsumption calls : 869174
% 158.15/24.15 % Rewrite failures with RHS unbound : 0
% 158.15/24.15 % BW rewrite match attempts : 6742
% 158.15/24.15 % BW rewrite match successes : 712
% 158.15/24.15 % Condensation attempts : 0
% 158.15/24.15 % Condensation successes : 0
% 158.15/24.15 % Termbank termtop insertions : 12583074
% 158.15/24.15 % Search garbage collected termcells : 4116
% 158.15/24.15
% 158.15/24.15 % -------------------------------------------------
% 158.15/24.15 % User time : 21.800 s
% 158.15/24.15 % System time : 0.633 s
% 158.15/24.15 % Total time : 22.433 s
% 158.15/24.15 % Maximum resident set size: 8728 pages
% 158.15/24.15
% 158.15/24.15 % -------------------------------------------------
% 158.15/24.15 % User time : 109.741 s
% 158.15/24.15 % System time : 3.296 s
% 158.15/24.15 % Total time : 113.037 s
% 158.15/24.15 % Maximum resident set size: 6400 pages
% 158.15/24.15 % E exiting
%------------------------------------------------------------------------------