%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ANA018-1 : 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 : n019.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 12:02:46 PM UTC 2026
% Result : Unsatisfiable 19.27s 3.45s
% Output : CNFRefutation 19.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 47
% Syntax : Number of clauses : 172 ( 92 unt; 8 nHn; 122 RR)
% Number of literals : 285 ( 78 equ; 128 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 31 ( 31 usr; 15 con; 0-3 aty)
% Number of variables : 210 ( 26 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(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_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_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_IntDef_Oint__0__neq__1_0,axiom,
c_0 != c_1,
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_IntDef_Oint__0__neq__1_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_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_IntDiv_Ozdiv__zmult__self1_0,axiom,
( c_div(c_times(X2,X1,tc_IntDef_Oint),X1,tc_IntDef_Oint) = X2
| X1 = c_0 ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_IntDiv_Ozdiv__zmult__self1_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_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(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_Numeral_Omult__minus1_0,axiom,
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1) = c_uminus(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_Numeral_Omult__minus1_0) ).
cnf(cls_IntDiv_Ozdiv__1_0,axiom,
c_div(X1,c_1,tc_IntDef_Oint) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_IntDiv_Ozdiv__1_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_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_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1,axiom,
( ~ c_lessequals(c_Orderings_Omax(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| c_lessequals(X3,X4,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1) ).
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(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_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_conjecture_2,negated_conjecture,
c_less(c_0,v_ca,t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_SetInterval_OlessThan__0_0,axiom,
c_SetInterval_OlessThan(c_0,tc_nat) = c_emptyset,
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_SetInterval_OlessThan__0_0) ).
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(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_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_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_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_SetInterval_Ocard__lessThan_0,axiom,
c_Finite__Set_Ocard(c_SetInterval_OlessThan(X1,tc_nat),tc_nat) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_SetInterval_Ocard__lessThan_0) ).
cnf(cls_conjecture_4,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
cnf(cls_conjecture_3,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_x(X1),t_b),c_times(v_ca,c_HOL_Oabs(v_f(X1),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_21,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Osemigroup__mult(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_21) ).
cnf(cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0,axiom,
( ~ c_lessequals(c_0,X4,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| c_lessequals(c_times(X4,X2,X1),c_times(X4,X3,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0) ).
cnf(cls_OrderedGroup_Omult__ac__1_0,axiom,
( ~ class_OrderedGroup_Osemigroup__mult(X1)
| c_times(c_times(X2,X3,X1),X4,X1) = c_times(X2,c_times(X3,X4,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__ac__1_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_42,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Opordered__semiring(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_42) ).
cnf(cls_conjecture_1,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_f(X1),t_b),c_times(v_c,c_HOL_Oabs(v_g(X1),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(c_0_47,axiom,
c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble) = c_0,
cls_List_Onibble_Osize__10_0 ).
cnf(c_0_48,axiom,
c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) = c_0,
cls_Datatype_Ounit_Osize_0 ).
cnf(c_0_49,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_50,axiom,
c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat) = c_0,
cls_NatBin_Onat__numeral__0__eq__0_0 ).
cnf(c_0_51,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_47,c_0_48]) ).
cnf(c_0_52,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_53,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_54,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_55,plain,
~ c_less(c_IntDef_Oint(X1),c_uminus(c_IntDef_Oint(X2),tc_IntDef_Oint),tc_IntDef_Oint),
c_0_49 ).
cnf(c_0_56,axiom,
c_IntDef_Oint(c_1) = c_1,
cls_IntDef_Oint__1_0 ).
cnf(c_0_57,axiom,
c_IntDef_Oint(c_0) = c_0,
cls_IntDef_Oint__eq__0__conv_1 ).
cnf(c_0_58,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_50,c_0_48]),c_0_51]) ).
cnf(c_0_59,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_60,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Oab__group__add(X1) ),
c_0_52 ).
cnf(c_0_61,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
tfree_tcs ).
cnf(c_0_62,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_63,plain,
c_0 != c_1,
inference(fof_simplification,[status(thm)],[cls_IntDef_Oint__0__neq__1_0]) ).
cnf(c_0_64,plain,
( ~ c_lessequals(X1,c_minus(X2,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(X1,X2,tc_IntDef_Oint) ),
c_0_53 ).
cnf(c_0_65,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_66,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_54 ).
cnf(c_0_67,plain,
~ c_less(c_IntDef_Oint(X1),c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_68,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_57,c_0_48]),c_0_48]),c_0_51]),c_0_58]),c_0_51]),c_0_58]) ).
cnf(c_0_69,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_70,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_uminus(X2,X1),X1) = X2 ),
c_0_59 ).
cnf(c_0_71,negated_conjecture,
class_OrderedGroup_Oab__group__add(t_b),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_72,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_62 ).
cnf(c_0_73,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_74,axiom,
( c_div(c_times(X2,X1,tc_IntDef_Oint),X1,tc_IntDef_Oint) = X2
| X1 = c_0 ),
cls_IntDiv_Ozdiv__zmult__self1_0 ).
cnf(c_0_75,plain,
c_0 != c_1,
c_0_63 ).
cnf(c_0_76,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_64,c_0_65]) ).
cnf(c_0_77,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_66,c_0_48]),c_0_51]),c_0_58]),c_0_48]),c_0_51]),c_0_58]) ).
cnf(c_0_78,axiom,
class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
clsarity_IntDef__Oint_48 ).
cnf(c_0_79,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_67,c_0_68]) ).
cnf(c_0_80,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_81,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_69 ).
cnf(c_0_82,negated_conjecture,
c_uminus(c_uminus(X1,t_b),t_b) = X1,
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_83,negated_conjecture,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(spm,[status(thm)],[c_0_72,c_0_61]) ).
cnf(c_0_84,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_85,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Oorder(X1) ),
c_0_73 ).
cnf(c_0_86,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_87,plain,
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1) = c_uminus(X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_Numeral_Omult__minus1_0]) ).
cnf(c_0_88,axiom,
c_div(X1,c_1,tc_IntDef_Oint) = X1,
cls_IntDiv_Ozdiv__1_0 ).
cnf(c_0_89,plain,
( X2 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat)
| c_div(c_times(X1,X2,tc_IntDef_Oint),X2,tc_IntDef_Oint) = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_48]),c_0_51]),c_0_58]) ).
cnf(c_0_90,plain,
c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat) != c_1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_48]),c_0_51]),c_0_58]) ).
cnf(c_0_91,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_76,c_0_77]),c_0_78])]),c_0_79]) ).
cnf(c_0_92,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_80,c_0_48]),c_0_51]),c_0_58]),c_0_48]),c_0_51]),c_0_58]) ).
cnf(c_0_93,axiom,
c_IntDef_Onat(c_0) = c_0,
cls_IntDef_Onat__zero_0 ).
cnf(c_0_94,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_95,plain,
( ~ c_lessequals(c_Orderings_Omax(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| c_lessequals(X3,X4,X1) ),
inference(fof_simplification,[status(thm)],[cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1]) ).
cnf(c_0_96,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_81,c_0_82]),c_0_83])]) ).
cnf(c_0_97,plain,
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X2,X2,X1) ),
c_0_84 ).
cnf(c_0_98,negated_conjecture,
class_Orderings_Oorder(t_b),
inference(spm,[status(thm)],[c_0_85,c_0_61]) ).
cnf(c_0_99,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Olinorder(X1) ),
c_0_86 ).
cnf(c_0_100,plain,
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1) = c_uminus(X2,X1) ),
c_0_87 ).
cnf(c_0_101,plain,
c_times(X1,c_1,tc_IntDef_Oint) = X1,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_90]) ).
cnf(c_0_102,axiom,
class_Numeral_Onumber__ring(tc_IntDef_Oint),
clsarity_IntDef__Oint_60 ).
cnf(c_0_103,axiom,
c_IntDef_Onat(c_IntDef_Oint(X1)) = X1,
cls_IntDef_Onat__int_0 ).
cnf(c_0_104,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_91,c_0_92]) ).
cnf(c_0_105,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_93,c_0_48]),c_0_48]),c_0_51]),c_0_58]),c_0_51]),c_0_58]) ).
cnf(c_0_106,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_94 ).
cnf(c_0_107,axiom,
class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
clsarity_IntDef__Oint_58 ).
cnf(c_0_108,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_109,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_110,plain,
( ~ c_lessequals(c_Orderings_Omax(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| c_lessequals(X3,X4,X1) ),
c_0_95 ).
cnf(c_0_111,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_96,c_0_97]),c_0_82]),c_0_98])]) ).
cnf(c_0_112,negated_conjecture,
class_Orderings_Olinorder(t_b),
inference(spm,[status(thm)],[c_0_99,c_0_61]) ).
cnf(c_0_113,negated_conjecture,
c_less(c_0,v_ca,t_b),
cls_conjecture_2 ).
cnf(c_0_114,axiom,
c_SetInterval_OlessThan(c_0,tc_nat) = c_emptyset,
cls_SetInterval_OlessThan__0_0 ).
cnf(c_0_115,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_116,plain,
c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_102])]) ).
cnf(c_0_117,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_103,c_0_104]),c_0_105]) ).
cnf(c_0_118,axiom,
c_Finite__Set_Ocard(c_emptyset,X1) = c_0,
cls_Finite__Set_Ocard__empty_0 ).
cnf(c_0_119,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_120,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_106,c_0_107]),c_0_102])]) ).
cnf(c_0_121,plain,
~ c_IntDef_Oneg(c_IntDef_Oint(X1),tc_IntDef_Oint),
c_0_108 ).
cnf(c_0_122,plain,
( ~ c_lessequals(X4,X2,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(X4,X3,X1) ),
c_0_109 ).
cnf(c_0_123,negated_conjecture,
c_lessequals(X1,c_Orderings_Omax(X2,X1,t_b),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_112])]) ).
cnf(c_0_124,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_125,negated_conjecture,
c_less(c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble),v_ca,t_b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_48]),c_0_51]) ).
cnf(c_0_126,plain,
c_SetInterval_OlessThan(c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),tc_nat) = c_emptyset,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_48]),c_0_51]),c_0_58]) ).
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_115,c_0_116]),c_0_117]) ).
cnf(c_0_128,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_129,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_118,c_0_48]),c_0_51]),c_0_58]) ).
cnf(c_0_130,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_68,c_0_119]),c_0_120]) ).
cnf(c_0_131,plain,
~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),tc_IntDef_Oint),
inference(spm,[status(thm)],[c_0_121,c_0_68]) ).
cnf(c_0_132,negated_conjecture,
( ~ c_lessequals(c_Orderings_Omax(X3,X1,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_122,c_0_123]),c_0_98])]) ).
cnf(c_0_133,plain,
( ~ c_less(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(X2,X3,X1) ),
c_0_124 ).
cnf(c_0_134,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_135,negated_conjecture,
c_less(c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),v_ca,t_b),
inference(rw,[status(thm)],[c_0_125,c_0_58]) ).
cnf(c_0_136,axiom,
c_Finite__Set_Ocard(c_SetInterval_OlessThan(X1,tc_nat),tc_nat) = X1,
cls_SetInterval_Ocard__lessThan_0 ).
cnf(c_0_137,plain,
c_SetInterval_OlessThan(c_Numeral_Onumber__of(c_Numeral_OMin,tc_nat),tc_nat) = c_emptyset,
inference(rw,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_138,plain,
( c_IntDef_Oint(X1) != c_IntDef_Oint(X2)
| X1 = X2 ),
c_0_128 ).
cnf(c_0_139,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_119,c_0_129]),c_0_130]),c_0_130]),c_0_131]) ).
cnf(c_0_140,negated_conjecture,
( ~ c_less(c_Orderings_Omax(X3,X1,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_132,c_0_133]),c_0_98])]) ).
cnf(c_0_141,plain,
( ~ class_Orderings_Olinorder(X1)
| c_Orderings_Omax(X2,X2,X1) = X2 ),
c_0_134 ).
cnf(c_0_142,negated_conjecture,
c_less(c_Numeral_Onumber__of(c_Numeral_OMin,tc_nat),v_ca,t_b),
inference(rw,[status(thm)],[c_0_135,c_0_127]) ).
cnf(c_0_143,plain,
c_Numeral_Onumber__of(c_Numeral_OMin,tc_nat) = c_Finite__Set_Ocard(c_emptyset,tc_nat),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_144,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_138,c_0_139]) ).
cnf(c_0_145,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),
inference(fof_simplification,[status(thm)],[cls_conjecture_4]) ).
cnf(c_0_146,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_x(X1),t_b),c_times(v_ca,c_HOL_Oabs(v_f(X1),t_b),t_b),t_b),
cls_conjecture_3 ).
cnf(c_0_147,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Osemigroup__mult(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_21]) ).
cnf(c_0_148,plain,
( ~ c_lessequals(c_0,X4,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| c_lessequals(c_times(X4,X2,X1),c_times(X4,X3,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0]) ).
cnf(c_0_149,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_140,c_0_141]),c_0_112])]) ).
cnf(c_0_150,negated_conjecture,
c_less(c_Finite__Set_Ocard(c_emptyset,tc_nat),v_ca,t_b),
inference(rw,[status(thm)],[c_0_142,c_0_143]) ).
cnf(c_0_151,plain,
c_Finite__Set_Ocard(c_emptyset,X1) = c_Finite__Set_Ocard(c_emptyset,X2),
inference(spm,[status(thm)],[c_0_144,c_0_139]) ).
cnf(c_0_152,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),
c_0_145 ).
cnf(c_0_153,negated_conjecture,
( ~ c_lessequals(c_times(v_ca,c_HOL_Oabs(v_f(X1),t_b),t_b),X2,t_b)
| c_lessequals(c_HOL_Oabs(v_x(X1),t_b),X2,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_146]),c_0_98])]) ).
cnf(c_0_154,plain,
( ~ class_OrderedGroup_Osemigroup__mult(X1)
| c_times(c_times(X2,X3,X1),X4,X1) = c_times(X2,c_times(X3,X4,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Omult__ac__1_0]) ).
cnf(c_0_155,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Osemigroup__mult(X1) ),
c_0_147 ).
cnf(c_0_156,plain,
( ~ c_lessequals(c_0,X4,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| c_lessequals(c_times(X4,X2,X1),c_times(X4,X3,X1),X1) ),
c_0_148 ).
cnf(c_0_157,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Opordered__semiring(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_42]) ).
cnf(c_0_158,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_122,c_0_149]),c_0_98])]) ).
cnf(c_0_159,negated_conjecture,
c_less(c_Finite__Set_Ocard(c_emptyset,X1),v_ca,t_b),
inference(spm,[status(thm)],[c_0_150,c_0_151]) ).
cnf(c_0_160,negated_conjecture,
~ c_lessequals(c_times(v_ca,c_HOL_Oabs(v_f(v_xa),t_b),t_b),c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),
inference(spm,[status(thm)],[c_0_152,c_0_153]) ).
cnf(c_0_161,plain,
( ~ class_OrderedGroup_Osemigroup__mult(X1)
| c_times(c_times(X2,X3,X1),X4,X1) = c_times(X2,c_times(X3,X4,X1),X1) ),
c_0_154 ).
cnf(c_0_162,negated_conjecture,
class_OrderedGroup_Osemigroup__mult(t_b),
inference(spm,[status(thm)],[c_0_155,c_0_61]) ).
cnf(c_0_163,plain,
( ~ c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),X1,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3)
| c_lessequals(c_times(X1,X2,X3),c_times(X1,X4,X3),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_156,c_0_48]),c_0_51]),c_0_58]) ).
cnf(c_0_164,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Opordered__semiring(X1) ),
c_0_157 ).
cnf(c_0_165,negated_conjecture,
( ~ c_lessequals(v_ca,X2,t_b)
| c_lessequals(c_Finite__Set_Ocard(c_emptyset,X1),X2,t_b) ),
inference(spm,[status(thm)],[c_0_158,c_0_159]) ).
cnf(c_0_166,negated_conjecture,
~ c_lessequals(c_times(v_ca,c_HOL_Oabs(v_f(v_xa),t_b),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_162])]) ).
cnf(c_0_167,plain,
( ~ c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_Finite__Set_Ocard(c_emptyset,tc_nat),X1,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3)
| c_lessequals(c_times(X1,X2,X3),c_times(X1,X4,X3),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_163,c_0_127]),c_0_143]) ).
cnf(c_0_168,negated_conjecture,
class_Ring__and__Field_Opordered__semiring(t_b),
inference(spm,[status(thm)],[c_0_164,c_0_61]) ).
cnf(c_0_169,negated_conjecture,
c_lessequals(c_Finite__Set_Ocard(c_emptyset,X1),v_ca,t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_97]),c_0_98])]) ).
cnf(c_0_170,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_f(X1),t_b),c_times(v_c,c_HOL_Oabs(v_g(X1),t_b),t_b),t_b),
cls_conjecture_1 ).
cnf(c_0_171,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_167]),c_0_168]),c_0_169]),c_0_170])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA018-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.36 % Computer : n019.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Mon Sep 21 13:23:51 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 19.27/3.45 % Version: 3.5.1
% 19.27/3.45 % Preprocessing class: FMLMSMSMSSSNFFN.
% 19.27/3.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 19.27/3.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 19.27/3.45 % Starting new_bool_3 with 300s (1) cores
% 19.27/3.45 % Starting new_bool_1 with 300s (1) cores
% 19.27/3.45 % Starting sh5l with 300s (1) cores
% 19.27/3.45 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2672006 completed with status 0
% 19.27/3.45 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 19.27/3.45 % Preprocessing class: FMLMSMSMSSSNFFN.
% 19.27/3.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 19.27/3.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 19.27/3.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 19.27/3.45 % No SInE strategy applied
% 19.27/3.45 % Search class: FGHSM-SMLM32-DFFFFFNN
% 19.27/3.45 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 19.27/3.45 % Starting SubtermCWHack with 136s (1) cores
% 19.27/3.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 19.27/3.45 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 113s (1) cores
% 19.27/3.45 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 19.27/3.45 % Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 19.27/3.45 % G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 2672033 completed with status 0
% 19.27/3.45 % Result found by G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 19.27/3.45 % Preprocessing class: FMLMSMSMSSSNFFN.
% 19.27/3.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 19.27/3.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 19.27/3.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 19.27/3.45 % No SInE strategy applied
% 19.27/3.45 % Search class: FGHSM-SMLM32-DFFFFFNN
% 19.27/3.45 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 19.27/3.45 % Starting SubtermCWHack with 136s (1) cores
% 19.27/3.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 19.27/3.45 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 113s (1) cores
% 19.27/3.45 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 19.27/3.45 % Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 19.27/3.45 % Preprocessing time : 0.050 s
% 19.27/3.45 % Presaturation interreduction done
% 19.27/3.45
% 19.27/3.45 % Proof found!
% 19.27/3.45 % SZS status Unsatisfiable
% 19.27/3.45 % SZS output start CNFRefutation
% See solution above
% 19.27/3.45 % Parsed axioms : 2794
% 19.27/3.45 % Removed by relevancy pruning/SinE : 0
% 19.27/3.45 % Initial clauses : 2794
% 19.27/3.45 % Removed in clause preprocessing : 9
% 19.27/3.45 % Initial clauses in saturation : 2785
% 19.27/3.45 % Processed clauses : 11754
% 19.27/3.45 % ...of these trivial : 86
% 19.27/3.45 % ...subsumed : 5186
% 19.27/3.45 % ...remaining for further processing : 6482
% 19.27/3.45 % Other redundant clauses eliminated : 145
% 19.27/3.45 % Clauses deleted for lack of memory : 0
% 19.27/3.45 % Backward-subsumed : 76
% 19.27/3.45 % Backward-rewritten : 666
% 19.27/3.45 % Generated clauses : 26869
% 19.27/3.45 % ...of the previous two non-redundant : 23464
% 19.27/3.45 % ...aggressively subsumed : 0
% 19.27/3.45 % Contextual simplify-reflections : 31
% 19.27/3.45 % Paramodulations : 26681
% 19.27/3.45 % Factorizations : 0
% 19.27/3.45 % NegExts : 0
% 19.27/3.45 % Equation resolutions : 188
% 19.27/3.45 % Disequality decompositions : 0
% 19.27/3.45 % Total rewrite steps : 13804
% 19.27/3.45 % ...of those cached : 12210
% 19.27/3.45 % Propositional unsat checks : 1
% 19.27/3.45 % Propositional check models : 1
% 19.27/3.45 % Propositional check unsatisfiable : 0
% 19.27/3.45 % Propositional clauses : 0
% 19.27/3.45 % Propositional clauses after purity: 0
% 19.27/3.45 % Propositional unsat core size : 0
% 19.27/3.45 % Propositional preprocessing time : 0.000
% 19.27/3.45 % Propositional encoding time : 0.020
% 19.27/3.45 % Propositional solver time : 0.024
% 19.27/3.45 % Success case prop preproc time : 0.000
% 19.27/3.45 % Success case prop encoding time : 0.000
% 19.27/3.45 % Success case prop solver time : 0.000
% 19.27/3.45 % Current number of processed clauses : 3082
% 19.27/3.45 % Positive orientable unit clauses : 732
% 19.27/3.45 % Positive unorientable unit clauses: 10
% 19.27/3.45 % Negative unit clauses : 449
% 19.27/3.45 % Non-unit-clauses : 1891
% 19.27/3.45 % Current number of unprocessed clauses: 15319
% 19.27/3.45 % ...number of literals in the above : 34561
% 19.27/3.45 % Current number of archived formulas : 0
% 19.27/3.45 % Current number of archived clauses : 3408
% 19.27/3.45 % Clause-clause subsumption calls (NU) : 3801785
% 19.27/3.45 % Rec. Clause-clause subsumption calls : 2816670
% 19.27/3.45 % Non-unit clause-clause subsumptions : 3328
% 19.27/3.45 % Unit Clause-clause subsumption calls : 135494
% 19.27/3.45 % Rewrite failures with RHS unbound : 0
% 19.27/3.45 % BW rewrite match attempts : 1463
% 19.27/3.45 % BW rewrite match successes : 142
% 19.27/3.45 % Condensation attempts : 0
% 19.27/3.45 % Condensation successes : 0
% 19.27/3.45 % Termbank termtop insertions : 447502
% 19.27/3.45 % Search garbage collected termcells : 4078
% 19.27/3.45
% 19.27/3.45 % -------------------------------------------------
% 19.27/3.45 % User time : 2.782 s
% 19.27/3.45 % System time : 0.088 s
% 19.27/3.45 % Total time : 2.870 s
% 19.27/3.45 % Maximum resident set size: 8508 pages
% 19.27/3.45
% 19.27/3.45 % -------------------------------------------------
% 19.27/3.45 % User time : 13.295 s
% 19.27/3.45 % System time : 0.432 s
% 19.27/3.45 % Total time : 13.727 s
% 19.27/3.45 % Maximum resident set size: 6400 pages
% 19.27/3.45 % E exiting
%------------------------------------------------------------------------------