%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ANA022-1 : 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 : n010.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 12:02:47 PM UTC 2026
% Result : Unsatisfiable 114.51s 15.10s
% Output : CNFRefutation 114.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 67
% Syntax : Number of clauses : 271 ( 106 unt; 11 nHn; 178 RR)
% Number of literals : 497 ( 111 equ; 250 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-3 aty)
% Number of functors : 32 ( 32 usr; 13 con; 0-3 aty)
% Number of variables : 430 ( 50 sgn)
% Comments :
%------------------------------------------------------------------------------
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_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_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_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_conjecture_2,negated_conjecture,
~ c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(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(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_OrderedGroup_Oneg__le__iff__le_0,axiom,
( ~ c_lessequals(c_uminus(X2,X1),c_uminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oneg__le__iff__le_0) ).
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_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(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_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(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_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_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(clsrel_Ring__and__Field_Oordered__idom_45,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Oord(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_45) ).
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(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0,axiom,
( ~ c_lessequals(c_Orderings_Omax(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) ).
cnf(cls_SetInterval_OatLeast__iff_0,axiom,
( ~ c_in(X2,c_SetInterval_OatLeast(X3,X1),X1)
| ~ class_Orderings_Oord(X1)
| c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_SetInterval_OatLeast__iff_0) ).
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_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_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_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_SetInterval_OCompl__lessThan_0,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_uminus(c_SetInterval_OlessThan(X2,X1),tc_set(X1)) = c_SetInterval_OatLeast(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_SetInterval_OCompl__lessThan_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_Orderings_Omin__max_Obelow__sup_Osup__idem_0,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_Orderings_Omax(X2,X2,X1) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0) ).
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(cls_SetInterval_OlessThan__iff_0,axiom,
( ~ c_in(X2,c_SetInterval_OlessThan(X3,X1),X1)
| ~ class_Orderings_Oord(X1)
| c_less(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_SetInterval_OlessThan__iff_0) ).
cnf(cls_Set_OCompl__iff_1,axiom,
( c_in(X1,c_uminus(X2,tc_set(X3)),X3)
| c_in(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_Set_OCompl__iff_1) ).
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_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(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_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_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_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_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(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_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__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_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_OrderedGroup_Ocompare__rls__9_0,axiom,
( ~ c_lessequals(X2,c_minus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(c_plus(X2,X4,X1),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_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_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_Oadd__le__cancel__right_0,axiom,
( ~ c_lessequals(c_plus(X2,X3,X1),c_plus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oadd__le__cancel__right_0) ).
cnf(cls_conjecture_1,negated_conjecture,
c_lessequals(v_k(X1),v_f(X1),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
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(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_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(c_0_67,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_68,axiom,
c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble) = c_0,
cls_List_Onibble_Osize__10_0 ).
cnf(c_0_69,axiom,
c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) = c_0,
cls_Datatype_Ounit_Osize_0 ).
cnf(c_0_70,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_71,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Oab__group__add(X1) ),
c_0_67 ).
cnf(c_0_72,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
tfree_tcs ).
cnf(c_0_73,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_74,negated_conjecture,
~ c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(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_75,axiom,
c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat) = c_0,
cls_NatBin_Onat__numeral__0__eq__0_0 ).
cnf(c_0_76,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_68,c_0_69]) ).
cnf(c_0_77,plain,
( ~ c_lessequals(c_uminus(X2,X1),c_uminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X3,X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Oneg__le__iff__le_0]) ).
cnf(c_0_78,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_uminus(X2,X1),X1) = X2 ),
c_0_70 ).
cnf(c_0_79,negated_conjecture,
class_OrderedGroup_Oab__group__add(t_b),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_80,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_73 ).
cnf(c_0_81,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_82,negated_conjecture,
~ c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(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_74 ).
cnf(c_0_83,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_75,c_0_69]),c_0_76]) ).
cnf(c_0_84,axiom,
c_Finite__Set_Ocard(c_emptyset,X1) = c_0,
cls_Finite__Set_Ocard__empty_0 ).
cnf(c_0_85,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_86,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_87,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_88,plain,
( ~ c_lessequals(c_uminus(X2,X1),c_uminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X3,X2,X1) ),
c_0_77 ).
cnf(c_0_89,negated_conjecture,
c_uminus(c_uminus(X1,t_b),t_b) = X1,
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_90,negated_conjecture,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(spm,[status(thm)],[c_0_80,c_0_72]) ).
cnf(c_0_91,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_92,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Oorder(X1) ),
c_0_81 ).
cnf(c_0_93,negated_conjecture,
~ c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(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_82,c_0_69]),c_0_76]),c_0_83]) ).
cnf(c_0_94,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_84,c_0_69]),c_0_76]),c_0_83]) ).
cnf(c_0_95,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_96,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Olinorder(X1) ),
c_0_85 ).
cnf(c_0_97,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Oord(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_45]) ).
cnf(c_0_98,plain,
( ~ c_less(c_HOL_Oabs(X2,X1),c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
c_0_86 ).
cnf(c_0_99,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_100,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Olordered__ab__group__abs(X1) ),
c_0_87 ).
cnf(c_0_101,plain,
( ~ c_lessequals(c_Orderings_Omax(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| c_lessequals(X2,X4,X1) ),
inference(fof_simplification,[status(thm)],[cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0]) ).
cnf(c_0_102,negated_conjecture,
( ~ c_lessequals(c_uminus(X2,t_b),X1,t_b)
| c_lessequals(c_uminus(X1,t_b),X2,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_90])]) ).
cnf(c_0_103,plain,
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X2,X2,X1) ),
c_0_91 ).
cnf(c_0_104,negated_conjecture,
class_Orderings_Oorder(t_b),
inference(spm,[status(thm)],[c_0_92,c_0_72]) ).
cnf(c_0_105,negated_conjecture,
~ c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),c_Finite__Set_Ocard(c_emptyset,X1),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_106,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_95 ).
cnf(c_0_107,negated_conjecture,
class_Orderings_Olinorder(t_b),
inference(spm,[status(thm)],[c_0_96,c_0_72]) ).
cnf(c_0_108,plain,
( ~ c_in(X2,c_SetInterval_OatLeast(X3,X1),X1)
| ~ class_Orderings_Oord(X1)
| c_lessequals(X3,X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_SetInterval_OatLeast__iff_0]) ).
cnf(c_0_109,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Oord(X1) ),
c_0_97 ).
cnf(c_0_110,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_111,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_98,c_0_69]),c_0_76]),c_0_83]) ).
cnf(c_0_112,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(c_uminus(X2,X1),X1) = c_HOL_Oabs(X2,X1) ),
c_0_99 ).
cnf(c_0_113,negated_conjecture,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(spm,[status(thm)],[c_0_100,c_0_72]) ).
cnf(c_0_114,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_115,plain,
( ~ c_lessequals(c_Orderings_Omax(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| c_lessequals(X2,X4,X1) ),
c_0_101 ).
cnf(c_0_116,negated_conjecture,
c_lessequals(X1,X1,t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_89]),c_0_104])]) ).
cnf(c_0_117,negated_conjecture,
( ~ c_lessequals(c_Finite__Set_Ocard(c_emptyset,X1),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_minus(v_k(v_x),v_g(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(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107])]) ).
cnf(c_0_118,plain,
( ~ c_in(X2,c_SetInterval_OatLeast(X3,X1),X1)
| ~ class_Orderings_Oord(X1)
| c_lessequals(X3,X2,X1) ),
c_0_108 ).
cnf(c_0_119,negated_conjecture,
class_Orderings_Oord(t_b),
inference(spm,[status(thm)],[c_0_109,c_0_72]) ).
cnf(c_0_120,plain,
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X3,X2,X1)
| c_less(X2,X3,X1) ),
c_0_110 ).
cnf(c_0_121,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_111,c_0_94]) ).
cnf(c_0_122,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_112,c_0_89]),c_0_113])]) ).
cnf(c_0_123,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_124,plain,
( ~ c_lessequals(X4,X2,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(X4,X3,X1) ),
c_0_114 ).
cnf(c_0_125,negated_conjecture,
c_lessequals(X1,c_Orderings_Omax(X1,X2,t_b),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_107])]) ).
cnf(c_0_126,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_127,negated_conjecture,
( ~ c_in(c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),c_SetInterval_OatLeast(c_minus(v_k(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_Finite__Set_Ocard(c_emptyset,X1),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(spm,[status(thm)],[c_0_117,c_0_118]),c_0_119])]) ).
cnf(c_0_128,negated_conjecture,
( c_lessequals(X2,X1,t_b)
| c_less(X1,X2,t_b) ),
inference(spm,[status(thm)],[c_0_120,c_0_107]) ).
cnf(c_0_129,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_121,c_0_122]),c_0_113])]) ).
cnf(c_0_130,plain,
( ~ class_Orderings_Olinorder(X1)
| c_uminus(c_SetInterval_OlessThan(X2,X1),tc_set(X1)) = c_SetInterval_OatLeast(X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_SetInterval_OCompl__lessThan_0]) ).
cnf(c_0_131,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_132,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_133,plain,
~ c_less(c_IntDef_Oint(X1),c_uminus(c_IntDef_Oint(X2),tc_IntDef_Oint),tc_IntDef_Oint),
c_0_123 ).
cnf(c_0_134,axiom,
c_IntDef_Oint(c_1) = c_1,
cls_IntDef_Oint__1_0 ).
cnf(c_0_135,axiom,
c_IntDef_Oint(c_0) = c_0,
cls_IntDef_Oint__eq__0__conv_1 ).
cnf(c_0_136,negated_conjecture,
( ~ c_lessequals(c_Orderings_Omax(X1,X3,t_b),X2,t_b)
| c_lessequals(X1,X2,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_104])]) ).
cnf(c_0_137,plain,
( ~ c_less(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(X2,X3,X1) ),
c_0_126 ).
cnf(c_0_138,plain,
( ~ class_Orderings_Olinorder(X1)
| c_Orderings_Omax(X2,X2,X1) = X2 ),
inference(fof_simplification,[status(thm)],[cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0]) ).
cnf(c_0_139,negated_conjecture,
~ c_in(c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),c_SetInterval_OatLeast(c_minus(v_k(v_x),v_g(v_x),t_b),t_b),t_b),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_129]) ).
cnf(c_0_140,plain,
( ~ class_Orderings_Olinorder(X1)
| c_uminus(c_SetInterval_OlessThan(X2,X1),tc_set(X1)) = c_SetInterval_OatLeast(X2,X1) ),
c_0_130 ).
cnf(c_0_141,plain,
( ~ c_lessequals(X1,c_minus(X2,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(X1,X2,tc_IntDef_Oint) ),
c_0_131 ).
cnf(c_0_142,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_143,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_132 ).
cnf(c_0_144,plain,
~ c_less(c_IntDef_Oint(X1),c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint),
inference(spm,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_145,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_135,c_0_69]),c_0_69]),c_0_76]),c_0_83]),c_0_76]),c_0_83]) ).
cnf(c_0_146,negated_conjecture,
( ~ c_less(c_Orderings_Omax(X1,X3,t_b),X2,t_b)
| c_lessequals(X1,X2,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_104])]) ).
cnf(c_0_147,plain,
( ~ class_Orderings_Olinorder(X1)
| c_Orderings_Omax(X2,X2,X1) = X2 ),
c_0_138 ).
cnf(c_0_148,plain,
( ~ c_in(X2,c_SetInterval_OlessThan(X3,X1),X1)
| ~ class_Orderings_Oord(X1)
| c_less(X2,X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_SetInterval_OlessThan__iff_0]) ).
cnf(c_0_149,negated_conjecture,
~ c_in(c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),c_uminus(c_SetInterval_OlessThan(c_minus(v_k(v_x),v_g(v_x),t_b),t_b),tc_set(t_b)),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_107])]) ).
cnf(c_0_150,axiom,
( c_in(X1,c_uminus(X2,tc_set(X3)),X3)
| c_in(X1,X2,X3) ),
cls_Set_OCompl__iff_1 ).
cnf(c_0_151,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_141,c_0_142]) ).
cnf(c_0_152,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_143,c_0_69]),c_0_76]),c_0_83]),c_0_69]),c_0_76]),c_0_83]) ).
cnf(c_0_153,axiom,
class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
clsarity_IntDef__Oint_48 ).
cnf(c_0_154,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_144,c_0_145]) ).
cnf(c_0_155,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_156,negated_conjecture,
( ~ c_less(X1,X2,t_b)
| c_lessequals(X1,X2,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_107])]) ).
cnf(c_0_157,plain,
( ~ c_in(X2,c_SetInterval_OlessThan(X3,X1),X1)
| ~ class_Orderings_Oord(X1)
| c_less(X2,X3,X1) ),
c_0_148 ).
cnf(c_0_158,negated_conjecture,
c_in(c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),c_SetInterval_OlessThan(c_minus(v_k(v_x),v_g(v_x),t_b),t_b),t_b),
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_159,axiom,
c_minus(X1,X1,tc_nat) = c_0,
cls_Nat_Odiff__self__eq__0_0 ).
cnf(c_0_160,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_161,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_162,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_151,c_0_152]),c_0_153])]),c_0_154]) ).
cnf(c_0_163,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_155,c_0_69]),c_0_76]),c_0_83]),c_0_69]),c_0_76]),c_0_83]) ).
cnf(c_0_164,axiom,
c_IntDef_Onat(c_0) = c_0,
cls_IntDef_Onat__zero_0 ).
cnf(c_0_165,negated_conjecture,
( ~ c_lessequals(X3,X2,t_b)
| ~ c_less(X1,X3,t_b)
| c_lessequals(X1,X2,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_156]),c_0_104])]) ).
cnf(c_0_166,negated_conjecture,
c_less(c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_119])]) ).
cnf(c_0_167,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_159,c_0_69]),c_0_76]),c_0_83]) ).
cnf(c_0_168,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_169,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_170,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_171,plain,
( ~ c_lessequals(c_IntDef_Oint(X1),c_IntDef_Oint(X2),tc_IntDef_Oint)
| c_lessequals(X1,X2,tc_nat) ),
c_0_160 ).
cnf(c_0_172,axiom,
class_Orderings_Oorder(tc_IntDef_Oint),
clsarity_IntDef__Oint_31 ).
cnf(c_0_173,plain,
( ~ class_Numeral_Onumber__ring(X1)
| c_uminus(c_1,X1) = c_Numeral_Onumber__of(c_Numeral_OMin,X1) ),
c_0_161 ).
cnf(c_0_174,axiom,
class_Numeral_Onumber__ring(tc_IntDef_Oint),
clsarity_IntDef__Oint_60 ).
cnf(c_0_175,axiom,
c_IntDef_Onat(c_IntDef_Oint(X1)) = X1,
cls_IntDef_Onat__int_0 ).
cnf(c_0_176,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_162,c_0_163]) ).
cnf(c_0_177,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_164,c_0_69]),c_0_69]),c_0_76]),c_0_83]),c_0_76]),c_0_83]) ).
cnf(c_0_178,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_179,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_180,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_181,negated_conjecture,
( ~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),X1,t_b)
| c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),X1,t_b) ),
inference(spm,[status(thm)],[c_0_165,c_0_166]) ).
cnf(c_0_182,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_183,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_184,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_167,c_0_168]) ).
cnf(c_0_185,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_169,c_0_168]) ).
cnf(c_0_186,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_SetInterval_OatLeastLessThan(X3,X2,X1) = c_emptyset ),
c_0_170 ).
cnf(c_0_187,plain,
c_lessequals(X1,X1,tc_nat),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_103]),c_0_172])]) ).
cnf(c_0_188,axiom,
class_Orderings_Oorder(tc_nat),
clsarity_nat_3 ).
cnf(c_0_189,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_190,plain,
c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint),
inference(spm,[status(thm)],[c_0_173,c_0_174]) ).
cnf(c_0_191,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_175,c_0_176]),c_0_177]) ).
cnf(c_0_192,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_178 ).
cnf(c_0_193,axiom,
class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
clsarity_IntDef__Oint_58 ).
cnf(c_0_194,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_195,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(c_HOL_Oabs(X2,X1),X1) = c_HOL_Oabs(X2,X1) ),
c_0_179 ).
cnf(c_0_196,plain,
( ~ c_lessequals(c_0,X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X2,X1) = X2 ),
c_0_180 ).
cnf(c_0_197,negated_conjecture,
( ~ c_lessequals(X2,X1,t_b)
| ~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),X2,t_b)
| c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),X1,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_181]),c_0_104])]) ).
cnf(c_0_198,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_182 ).
cnf(c_0_199,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_200,plain,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(X2,c_0,X1) = X2 ),
c_0_183 ).
cnf(c_0_201,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_184,c_0_185]) ).
cnf(c_0_202,plain,
c_SetInterval_OatLeastLessThan(X1,X1,tc_nat) = c_emptyset,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_186,c_0_187]),c_0_188])]) ).
cnf(c_0_203,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_189,c_0_190]),c_0_191]) ).
cnf(c_0_204,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_205,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_206,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_192,c_0_193]),c_0_174])]) ).
cnf(c_0_207,plain,
~ c_IntDef_Oneg(c_IntDef_Oint(X1),tc_IntDef_Oint),
c_0_194 ).
cnf(c_0_208,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_195,c_0_122]),c_0_113])]) ).
cnf(c_0_209,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_196,c_0_69]),c_0_76]),c_0_83]) ).
cnf(c_0_210,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_211,negated_conjecture,
( ~ c_lessequals(X2,X1,t_b)
| ~ c_lessequals(v_k(v_x),c_plus(X2,v_g(v_x),t_b),t_b)
| c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),X1,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_198]),c_0_90])]) ).
cnf(c_0_212,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| X2 = c_plus(c_minus(X2,X3,X1),X3,X1) ),
c_0_199 ).
cnf(c_0_213,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_200,c_0_69]),c_0_76]),c_0_83]) ).
cnf(c_0_214,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_201,c_0_202]),c_0_203]) ).
cnf(c_0_215,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_204 ).
cnf(c_0_216,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_217,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_145,c_0_205]),c_0_206]) ).
cnf(c_0_218,plain,
~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),tc_IntDef_Oint),
inference(spm,[status(thm)],[c_0_207,c_0_145]) ).
cnf(c_0_219,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_208,c_0_209]),c_0_113])]) ).
cnf(c_0_220,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1) ),
c_0_210 ).
cnf(c_0_221,plain,
( ~ c_lessequals(X2,c_minus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(c_plus(X2,X4,X1),X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Ocompare__rls__9_0]) ).
cnf(c_0_222,negated_conjecture,
( ~ c_lessequals(v_k(v_x),X2,t_b)
| ~ c_lessequals(c_minus(X2,v_g(v_x),t_b),X1,t_b)
| c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),X1,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_211,c_0_212]),c_0_79])]) ).
cnf(c_0_223,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_213,c_0_203]),c_0_214]) ).
cnf(c_0_224,negated_conjecture,
class_OrderedGroup_Ocomm__monoid__add(t_b),
inference(spm,[status(thm)],[c_0_215,c_0_72]) ).
cnf(c_0_225,plain,
( c_IntDef_Oint(X1) != c_IntDef_Oint(X2)
| X1 = X2 ),
c_0_216 ).
cnf(c_0_226,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_205,c_0_94]),c_0_217]),c_0_217]),c_0_218]) ).
cnf(c_0_227,negated_conjecture,
( ~ c_lessequals(c_Numeral_Onumber__of(c_Numeral_OMin,tc_nat),X1,t_b)
| c_HOL_Oabs(X1,t_b) = X1 ),
inference(rw,[status(thm)],[c_0_219,c_0_203]) ).
cnf(c_0_228,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_220,c_0_69]),c_0_76]),c_0_83]) ).
cnf(c_0_229,plain,
( ~ c_lessequals(X2,c_minus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(c_plus(X2,X4,X1),X3,X1) ),
c_0_221 ).
cnf(c_0_230,negated_conjecture,
( ~ c_lessequals(v_k(v_x),X1,t_b)
| c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),c_minus(X1,v_g(v_x),t_b),t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_222,c_0_103]),c_0_104])]) ).
cnf(c_0_231,negated_conjecture,
c_plus(X1,c_Finite__Set_Ocard(c_emptyset,tc_nat),t_b) = X1,
inference(spm,[status(thm)],[c_0_223,c_0_224]) ).
cnf(c_0_232,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_225,c_0_226]) ).
cnf(c_0_233,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_k(v_x),v_g(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_93,c_0_106]),c_0_107]),c_0_203]),c_0_214])]) ).
cnf(c_0_234,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)],[c_0_227,c_0_214]) ).
cnf(c_0_235,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_228,c_0_203]),c_0_214]) ).
cnf(c_0_236,negated_conjecture,
( ~ c_lessequals(v_k(v_x),X1,t_b)
| c_lessequals(c_plus(c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),v_g(v_x),t_b),X1,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_229,c_0_230]),c_0_90])]) ).
cnf(c_0_237,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_238,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_239,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_212,c_0_231]),c_0_79])]) ).
cnf(c_0_240,plain,
c_Finite__Set_Ocard(c_emptyset,X1) = c_Finite__Set_Ocard(c_emptyset,X2),
inference(spm,[status(thm)],[c_0_232,c_0_226]) ).
cnf(c_0_241,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_k(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b) ),
inference(spm,[status(thm)],[c_0_233,c_0_234]) ).
cnf(c_0_242,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_235,c_0_122]),c_0_113])]) ).
cnf(c_0_243,plain,
( ~ c_lessequals(c_plus(X2,X3,X1),c_plus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_lessequals(X2,X4,X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Oadd__le__cancel__right_0]) ).
cnf(c_0_244,negated_conjecture,
( ~ c_lessequals(X2,X1,t_b)
| ~ c_lessequals(v_k(v_x),X2,t_b)
| c_lessequals(c_plus(c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),v_g(v_x),t_b),X1,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_236]),c_0_104])]) ).
cnf(c_0_245,negated_conjecture,
c_lessequals(v_k(X1),v_f(X1),t_b),
cls_conjecture_1 ).
cnf(c_0_246,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_237 ).
cnf(c_0_247,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_248,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_minus(X2,X3,X1),X1) = c_minus(X3,X2,X1) ),
c_0_238 ).
cnf(c_0_249,negated_conjecture,
c_minus(X1,c_Finite__Set_Ocard(c_emptyset,X2),t_b) = X1,
inference(spm,[status(thm)],[c_0_239,c_0_240]) ).
cnf(c_0_250,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(v_k(v_x),c_plus(c_minus(v_f(v_x),v_g(v_x),t_b),v_g(v_x),t_b),t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_241,c_0_198]),c_0_90])]) ).
cnf(c_0_251,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_242,c_0_240]) ).
cnf(c_0_252,plain,
( ~ c_lessequals(c_plus(X2,X3,X1),c_plus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_lessequals(X2,X4,X1) ),
c_0_243 ).
cnf(c_0_253,negated_conjecture,
( ~ c_lessequals(v_f(v_x),X1,t_b)
| c_lessequals(c_plus(c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),v_g(v_x),t_b),X1,t_b) ),
inference(spm,[status(thm)],[c_0_244,c_0_245]) ).
cnf(c_0_254,negated_conjecture,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b),
inference(spm,[status(thm)],[c_0_246,c_0_72]) ).
cnf(c_0_255,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_256,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_247 ).
cnf(c_0_257,negated_conjecture,
c_plus(X1,c_Finite__Set_Ocard(c_emptyset,X2),t_b) = X1,
inference(spm,[status(thm)],[c_0_231,c_0_240]) ).
cnf(c_0_258,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_248,c_0_249]),c_0_79])]) ).
cnf(c_0_259,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),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_250,c_0_212]),c_0_245]),c_0_79])]) ).
cnf(c_0_260,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_261,negated_conjecture,
( ~ c_lessequals(c_HOL_Oabs(X3,t_b),X2,t_b)
| c_lessequals(c_Finite__Set_Ocard(c_emptyset,X1),X2,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_251]),c_0_104])]) ).
cnf(c_0_262,negated_conjecture,
( ~ c_lessequals(v_f(v_x),c_plus(X1,v_g(v_x),t_b),t_b)
| c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),X1,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_252,c_0_253]),c_0_254])]) ).
cnf(c_0_263,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_255 ).
cnf(c_0_264,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_256,c_0_257]),c_0_258]),c_0_79])]) ).
cnf(c_0_265,negated_conjecture,
~ c_lessequals(c_Finite__Set_Ocard(c_emptyset,X1),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
inference(spm,[status(thm)],[c_0_259,c_0_240]) ).
cnf(c_0_266,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_minus(X2,X3,X1) = c_plus(X2,c_uminus(X3,X1),X1) ),
c_0_260 ).
cnf(c_0_267,negated_conjecture,
( ~ c_lessequals(v_f(v_x),c_plus(X2,v_g(v_x),t_b),t_b)
| c_lessequals(c_Finite__Set_Ocard(c_emptyset,X1),X2,t_b) ),
inference(spm,[status(thm)],[c_0_261,c_0_262]) ).
cnf(c_0_268,negated_conjecture,
c_lessequals(X1,c_plus(c_plus(X1,c_uminus(X2,t_b),t_b),X2,t_b),t_b),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_263,c_0_116]),c_0_90])]),c_0_264]) ).
cnf(c_0_269,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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_265,c_0_266]),c_0_79])]) ).
cnf(c_0_270,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_267,c_0_268]),c_0_269]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA022-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n010.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 13:24:42 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 114.51/15.10 % Version: 3.5.1
% 114.51/15.10 % Preprocessing class: FMLMSMSMSSSNFFN.
% 114.51/15.10 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 114.51/15.10 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 114.51/15.10 % Starting new_bool_3 with 300s (1) cores
% 114.51/15.10 % Starting new_bool_1 with 300s (1) cores
% 114.51/15.10 % Starting sh5l with 300s (1) cores
% 114.51/15.10 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 961854 completed with status 0
% 114.51/15.10 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 114.51/15.10 % Preprocessing class: FMLMSMSMSSSNFFN.
% 114.51/15.10 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 114.51/15.10 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 114.51/15.10 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 114.51/15.10 % No SInE strategy applied
% 114.51/15.10 % Search class: FGHSM-SMLM32-DFFFFFNN
% 114.51/15.10 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 114.51/15.10 % Starting SubtermCWHack with 136s (1) cores
% 114.51/15.10 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 114.51/15.10 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 113s (1) cores
% 114.51/15.10 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 114.51/15.10 % Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 114.51/15.10 % G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 961865 completed with status 0
% 114.51/15.10 % Result found by G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 114.51/15.10 % Preprocessing class: FMLMSMSMSSSNFFN.
% 114.51/15.10 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 114.51/15.10 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 114.51/15.10 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 114.51/15.10 % No SInE strategy applied
% 114.51/15.10 % Search class: FGHSM-SMLM32-DFFFFFNN
% 114.51/15.10 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 114.51/15.10 % Starting SubtermCWHack with 136s (1) cores
% 114.51/15.10 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 114.51/15.10 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 113s (1) cores
% 114.51/15.10 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 114.51/15.10 % Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 114.51/15.10 % Preprocessing time : 0.031 s
% 114.51/15.10 % Presaturation interreduction done
% 114.51/15.10
% 114.51/15.10 % Proof found!
% 114.51/15.10 % SZS status Unsatisfiable
% 114.51/15.10 % SZS output start CNFRefutation
% See solution above
% 114.51/15.10 % Parsed axioms : 2808
% 114.51/15.10 % Removed by relevancy pruning/SinE : 0
% 114.51/15.10 % Initial clauses : 2808
% 114.51/15.10 % Removed in clause preprocessing : 9
% 114.51/15.10 % Initial clauses in saturation : 2799
% 114.51/15.10 % Processed clauses : 37506
% 114.51/15.10 % ...of these trivial : 709
% 114.51/15.10 % ...subsumed : 23802
% 114.51/15.10 % ...remaining for further processing : 12995
% 114.51/15.10 % Other redundant clauses eliminated : 520
% 114.51/15.10 % Clauses deleted for lack of memory : 0
% 114.51/15.10 % Backward-subsumed : 317
% 114.51/15.10 % Backward-rewritten : 1274
% 114.51/15.10 % Generated clauses : 190760
% 114.51/15.10 % ...of the previous two non-redundant : 171656
% 114.51/15.10 % ...aggressively subsumed : 0
% 114.51/15.10 % Contextual simplify-reflections : 76
% 114.51/15.10 % Paramodulations : 190167
% 114.51/15.10 % Factorizations : 5
% 114.51/15.10 % NegExts : 0
% 114.51/15.10 % Equation resolutions : 588
% 114.51/15.10 % Disequality decompositions : 0
% 114.51/15.10 % Total rewrite steps : 124872
% 114.51/15.10 % ...of those cached : 116297
% 114.51/15.10 % Propositional unsat checks : 2
% 114.51/15.10 % Propositional check models : 1
% 114.51/15.10 % Propositional check unsatisfiable : 0
% 114.51/15.10 % Propositional clauses : 0
% 114.51/15.10 % Propositional clauses after purity: 0
% 114.51/15.10 % Propositional unsat core size : 0
% 114.51/15.10 % Propositional preprocessing time : 0.000
% 114.51/15.10 % Propositional encoding time : 0.222
% 114.51/15.10 % Propositional solver time : 0.210
% 114.51/15.10 % Success case prop preproc time : 0.000
% 114.51/15.10 % Success case prop encoding time : 0.000
% 114.51/15.10 % Success case prop solver time : 0.000
% 114.51/15.10 % Current number of processed clauses : 8730
% 114.51/15.10 % Positive orientable unit clauses : 1526
% 114.51/15.10 % Positive unorientable unit clauses: 30
% 114.51/15.10 % Negative unit clauses : 1194
% 114.51/15.10 % Non-unit-clauses : 5980
% 114.51/15.10 % Current number of unprocessed clauses: 137612
% 114.51/15.10 % ...number of literals in the above : 340247
% 114.51/15.10 % Current number of archived formulas : 0
% 114.51/15.10 % Current number of archived clauses : 4273
% 114.51/15.10 % Clause-clause subsumption calls (NU) : 10147880
% 114.51/15.10 % Rec. Clause-clause subsumption calls : 7612177
% 114.51/15.10 % Non-unit clause-clause subsumptions : 10958
% 114.51/15.10 % Unit Clause-clause subsumption calls : 461762
% 114.51/15.10 % Rewrite failures with RHS unbound : 0
% 114.51/15.10 % BW rewrite match attempts : 5276
% 114.51/15.10 % BW rewrite match successes : 489
% 114.51/15.10 % Condensation attempts : 0
% 114.51/15.10 % Condensation successes : 0
% 114.51/15.10 % Termbank termtop insertions : 3771357
% 114.51/15.10 % Search garbage collected termcells : 4116
% 114.51/15.10
% 114.51/15.10 % -------------------------------------------------
% 114.51/15.10 % User time : 13.063 s
% 114.51/15.10 % System time : 0.267 s
% 114.51/15.10 % Total time : 13.330 s
% 114.51/15.10 % Maximum resident set size: 8776 pages
% 114.51/15.10
% 114.51/15.10 % -------------------------------------------------
% 114.51/15.10 % User time : 69.025 s
% 114.51/15.10 % System time : 1.633 s
% 114.51/15.10 % Total time : 70.659 s
% 114.51/15.10 % Maximum resident set size: 6656 pages
% 114.51/15.10 % E exiting
%------------------------------------------------------------------------------