%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ANA015-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 12:02:45 PM UTC 2026
% Result : Unsatisfiable 67.85s 15.51s
% Output : CNFRefutation 67.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 31
% Syntax : Number of clauses : 112 ( 62 unt; 6 nHn; 72 RR)
% Number of literals : 172 ( 60 equ; 71 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 28 ( 28 usr; 14 con; 0-3 aty)
% Number of variables : 131 ( 19 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/sandbox2/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/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_Datatype_Ounit_Osize_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/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_NatBin_Onat__numeral__0__eq__0_0) ).
cnf(cls_IntDef_Oint__0__neq__1_0,axiom,
c_0 != c_1,
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_IntDef_Oint__0__neq__1_0) ).
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/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_IntDiv_Ozdiv__zmult__self1_0) ).
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/sandbox2/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/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_IntDiv_Ozdiv__1_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/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_IntDef_Onot__int__zless__negative_0) ).
cnf(cls_IntDef_Ozless__nat__conj_0,axiom,
( ~ c_less(c_IntDef_Onat(X1),c_IntDef_Onat(X2),tc_nat)
| c_less(c_0,X2,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_IntDef_Ozless__nat__conj_0) ).
cnf(clsarity_IntDef__Oint_60,axiom,
class_Numeral_Onumber__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsarity_IntDef__Oint_60) ).
cnf(cls_IntDef_Oint__1_0,axiom,
c_IntDef_Oint(c_1) = c_1,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_IntDef_Oint__eq__0__conv_1) ).
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/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_NatBin_Onat__number__of_0) ).
cnf(cls_IntDef_Onat__int_0,axiom,
c_IntDef_Onat(c_IntDef_Oint(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_IntDef_Onat__int_0) ).
cnf(cls_Nat_Onot__gr0_0,axiom,
( X1 = c_0
| c_less(c_0,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_Nat_Onot__gr0_0) ).
cnf(cls_SetInterval_OlessThan__0_0,axiom,
c_SetInterval_OlessThan(c_0,tc_nat) = c_emptyset,
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_SetInterval_OlessThan__0_0) ).
cnf(clsrel_Ring__and__Field_Oordered__field_7,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_7) ).
cnf(clsrel_Ring__and__Field_Oordered__field_34,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_34) ).
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/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oabs__ge__zero_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/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Ominus__minus_0) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
cnf(clsrel_Ring__and__Field_Oordered__field_47,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_OrderedGroup_Olordered__ab__group__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_47) ).
cnf(cls_conjecture_2,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(X1)),t_a),t_a),c_times(X1,c_HOL_Oabs(v_f(v_x(X1)),t_a),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_Ring__and__Field_Oabs__mult_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oabs(c_times(X2,X3,X1),X1) = c_times(c_HOL_Oabs(X2,X1),c_HOL_Oabs(X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
cnf(clsrel_Ring__and__Field_Oordered__field_24,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_OrderedGroup_Osemigroup__mult(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_24) ).
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/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0) ).
cnf(cls_SetInterval_Ocard__lessThan_0,axiom,
c_Finite__Set_Ocard(c_SetInterval_OlessThan(X1,tc_nat),tc_nat) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_SetInterval_Ocard__lessThan_0) ).
cnf(cls_OrderedGroup_Oabs__minus__cancel_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(c_uminus(X2,X1),X1) = c_HOL_Oabs(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oabs__minus__cancel_0) ).
cnf(cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0) ).
cnf(clsrel_Ring__and__Field_Oordered__field_46,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_Ring__and__Field_Opordered__semiring(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_46) ).
cnf(cls_conjecture_1,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_g(X1),t_a),c_times(v_d,c_HOL_Oabs(v_f(X1),t_a),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(c_0_31,axiom,
c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble) = c_0,
cls_List_Onibble_Osize__10_0 ).
cnf(c_0_32,axiom,
c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) = c_0,
cls_Datatype_Ounit_Osize_0 ).
cnf(c_0_33,axiom,
c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat) = c_0,
cls_NatBin_Onat__numeral__0__eq__0_0 ).
cnf(c_0_34,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_31,c_0_32]) ).
cnf(c_0_35,plain,
c_0 != c_1,
inference(fof_simplification,[status(thm)],[cls_IntDef_Oint__0__neq__1_0]) ).
cnf(c_0_36,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_37,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_33,c_0_32]),c_0_34]) ).
cnf(c_0_38,plain,
c_0 != c_1,
c_0_35 ).
cnf(c_0_39,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_40,axiom,
c_div(X1,c_1,tc_IntDef_Oint) = X1,
cls_IntDiv_Ozdiv__1_0 ).
cnf(c_0_41,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_36,c_0_32]),c_0_34]),c_0_37]) ).
cnf(c_0_42,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_38,c_0_32]),c_0_34]),c_0_37]) ).
cnf(c_0_43,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_44,plain,
( ~ c_less(c_IntDef_Onat(X1),c_IntDef_Onat(X2),tc_nat)
| c_less(c_0,X2,tc_IntDef_Oint) ),
inference(fof_simplification,[status(thm)],[cls_IntDef_Ozless__nat__conj_0]) ).
cnf(c_0_45,plain,
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1) = c_uminus(X2,X1) ),
c_0_39 ).
cnf(c_0_46,plain,
c_times(X1,c_1,tc_IntDef_Oint) = X1,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_47,axiom,
class_Numeral_Onumber__ring(tc_IntDef_Oint),
clsarity_IntDef__Oint_60 ).
cnf(c_0_48,plain,
~ c_less(c_IntDef_Oint(X1),c_uminus(c_IntDef_Oint(X2),tc_IntDef_Oint),tc_IntDef_Oint),
c_0_43 ).
cnf(c_0_49,axiom,
c_IntDef_Oint(c_1) = c_1,
cls_IntDef_Oint__1_0 ).
cnf(c_0_50,axiom,
c_IntDef_Oint(c_0) = c_0,
cls_IntDef_Oint__eq__0__conv_1 ).
cnf(c_0_51,plain,
( ~ c_less(c_IntDef_Onat(X1),c_IntDef_Onat(X2),tc_nat)
| c_less(c_0,X2,tc_IntDef_Oint) ),
c_0_44 ).
cnf(c_0_52,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_53,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_45,c_0_46]),c_0_47])]) ).
cnf(c_0_54,plain,
~ c_less(c_IntDef_Oint(X1),c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_55,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_50,c_0_32]),c_0_32]),c_0_34]),c_0_37]),c_0_34]),c_0_37]) ).
cnf(c_0_56,plain,
( ~ c_less(c_IntDef_Onat(X2),c_IntDef_Onat(X1),tc_nat)
| c_less(c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),X1,tc_IntDef_Oint) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_32]),c_0_34]),c_0_37]) ).
cnf(c_0_57,plain,
c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint)) = c_Numeral_Onumber__of(c_Numeral_OMin,tc_nat),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_58,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_54,c_0_55]) ).
cnf(c_0_59,plain,
~ c_less(c_IntDef_Onat(X1),c_Numeral_Onumber__of(c_Numeral_OMin,tc_nat),tc_nat),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]) ).
cnf(c_0_60,axiom,
c_IntDef_Onat(c_IntDef_Oint(X1)) = X1,
cls_IntDef_Onat__int_0 ).
cnf(c_0_61,axiom,
( X1 = c_0
| c_less(c_0,X1,tc_nat) ),
cls_Nat_Onot__gr0_0 ).
cnf(c_0_62,axiom,
c_SetInterval_OlessThan(c_0,tc_nat) = c_emptyset,
cls_SetInterval_OlessThan__0_0 ).
cnf(c_0_63,plain,
~ c_less(X1,c_Numeral_Onumber__of(c_Numeral_OMin,tc_nat),tc_nat),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_64,plain,
( c_less(c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),X1,tc_nat)
| 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_61,c_0_32]),c_0_34]),c_0_37]),c_0_32]),c_0_34]),c_0_37]) ).
cnf(c_0_65,plain,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_OrderedGroup_Oab__group__add(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__field_7]) ).
cnf(c_0_66,plain,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_Ring__and__Field_Oordered__idom(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__field_34]) ).
cnf(c_0_67,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_68,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_62,c_0_32]),c_0_34]),c_0_37]) ).
cnf(c_0_69,plain,
c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat) = c_Numeral_Onumber__of(c_Numeral_OMin,tc_nat),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
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__field(X1)
| class_OrderedGroup_Oab__group__add(X1) ),
c_0_65 ).
cnf(c_0_72,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a),
tfree_tcs ).
cnf(c_0_73,plain,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_OrderedGroup_Olordered__ab__group__abs(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__field_47]) ).
cnf(c_0_74,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(X1)),t_a),t_a),c_times(X1,c_HOL_Oabs(v_f(v_x(X1)),t_a),t_a),t_a),
inference(fof_simplification,[status(thm)],[cls_conjecture_2]) ).
cnf(c_0_75,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oabs(c_times(X2,X3,X1),X1) = c_times(c_HOL_Oabs(X2,X1),c_HOL_Oabs(X3,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_Ring__and__Field_Oabs__mult_0]) ).
cnf(c_0_76,plain,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_Ring__and__Field_Oordered__idom(X1) ),
c_0_66 ).
cnf(c_0_77,plain,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_OrderedGroup_Osemigroup__mult(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__field_24]) ).
cnf(c_0_78,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_79,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1) ),
c_0_67 ).
cnf(c_0_80,axiom,
c_Finite__Set_Ocard(c_SetInterval_OlessThan(X1,tc_nat),tc_nat) = X1,
cls_SetInterval_Ocard__lessThan_0 ).
cnf(c_0_81,plain,
c_SetInterval_OlessThan(c_Numeral_Onumber__of(c_Numeral_OMin,tc_nat),tc_nat) = c_emptyset,
inference(rw,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_82,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_83,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_uminus(X2,X1),X1) = X2 ),
c_0_70 ).
cnf(c_0_84,negated_conjecture,
class_OrderedGroup_Oab__group__add(t_a),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_85,plain,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_OrderedGroup_Olordered__ab__group__abs(X1) ),
c_0_73 ).
cnf(c_0_86,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(X1)),t_a),t_a),c_times(X1,c_HOL_Oabs(v_f(v_x(X1)),t_a),t_a),t_a),
c_0_74 ).
cnf(c_0_87,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oabs(c_times(X2,X3,X1),X1) = c_times(c_HOL_Oabs(X2,X1),c_HOL_Oabs(X3,X1),X1) ),
c_0_75 ).
cnf(c_0_88,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_a),
inference(spm,[status(thm)],[c_0_76,c_0_72]) ).
cnf(c_0_89,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_Osemigroup__mult__class_Omult__assoc_0]) ).
cnf(c_0_90,plain,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_OrderedGroup_Osemigroup__mult(X1) ),
c_0_77 ).
cnf(c_0_91,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_78 ).
cnf(c_0_92,plain,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_Ring__and__Field_Opordered__semiring(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__field_46]) ).
cnf(c_0_93,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_79,c_0_32]),c_0_34]),c_0_37]) ).
cnf(c_0_94,plain,
c_Numeral_Onumber__of(c_Numeral_OMin,tc_nat) = c_Finite__Set_Ocard(c_emptyset,tc_nat),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_95,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(c_uminus(X2,X1),X1) = c_HOL_Oabs(X2,X1) ),
c_0_82 ).
cnf(c_0_96,negated_conjecture,
c_uminus(c_uminus(X1,t_a),t_a) = X1,
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_97,negated_conjecture,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(spm,[status(thm)],[c_0_85,c_0_72]) ).
cnf(c_0_98,negated_conjecture,
~ c_lessequals(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),c_HOL_Oabs(v_g(v_x(X1)),t_a),t_a),c_times(X1,c_HOL_Oabs(v_f(v_x(X1)),t_a),t_a),t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_88])]) ).
cnf(c_0_99,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_89 ).
cnf(c_0_100,negated_conjecture,
class_OrderedGroup_Osemigroup__mult(t_a),
inference(spm,[status(thm)],[c_0_90,c_0_72]) ).
cnf(c_0_101,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_91,c_0_32]),c_0_34]),c_0_37]) ).
cnf(c_0_102,plain,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_Ring__and__Field_Opordered__semiring(X1) ),
c_0_92 ).
cnf(c_0_103,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_93,c_0_69]),c_0_94]) ).
cnf(c_0_104,negated_conjecture,
c_HOL_Oabs(c_uminus(X1,t_a),t_a) = c_HOL_Oabs(X1,t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97])]) ).
cnf(c_0_105,negated_conjecture,
~ c_lessequals(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),c_HOL_Oabs(v_g(v_x(c_times(X1,X2,t_a))),t_a),t_a),c_times(X1,c_times(X2,c_HOL_Oabs(v_f(v_x(c_times(X1,X2,t_a))),t_a),t_a),t_a),t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_100])]) ).
cnf(c_0_106,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_101,c_0_69]),c_0_94]) ).
cnf(c_0_107,negated_conjecture,
class_Ring__and__Field_Opordered__semiring(t_a),
inference(spm,[status(thm)],[c_0_102,c_0_72]) ).
cnf(c_0_108,negated_conjecture,
c_lessequals(c_Finite__Set_Ocard(c_emptyset,tc_nat),c_HOL_Oabs(X1,t_a),t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_97])]) ).
cnf(c_0_109,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),X1,t_a))),t_a),c_times(X1,c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),X1,t_a))),t_a),t_a),t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107]),c_0_108])]) ).
cnf(c_0_110,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_g(X1),t_a),c_times(v_d,c_HOL_Oabs(v_f(X1),t_a),t_a),t_a),
cls_conjecture_1 ).
cnf(c_0_111,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_109,c_0_110]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA015-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/5.52 % Computer : n007.cluster.edu
% 0.13/5.52 % Model : x86_64 x86_64
% 0.13/5.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.52 % Memory : 8046.5625MB
% 0.13/5.52 % OS : Linux 6.8.0-71-generic
% 0.13/5.52 % CPULimit : 300
% 0.13/5.52 % WCLimit : 300
% 0.13/5.52 % DateTime : Mon Sep 21 13:21:57 UTC 2026
% 0.13/5.53 % CPUTime :
% 0.13/5.53 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/5.56 Running first-order theorem proving
% 0.13/5.56 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 67.85/15.51 % Version: 3.5.1
% 67.85/15.51 % Preprocessing class: FMLMSMSMSSSNFFN.
% 67.85/15.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 67.85/15.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 67.85/15.51 % Starting new_bool_3 with 300s (1) cores
% 67.85/15.51 % Starting new_bool_1 with 300s (1) cores
% 67.85/15.51 % Starting sh5l with 300s (1) cores
% 67.85/15.51 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1180193 completed with status 0
% 67.85/15.51 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 67.85/15.51 % Preprocessing class: FMLMSMSMSSSNFFN.
% 67.85/15.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 67.85/15.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 67.85/15.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 67.85/15.51 % No SInE strategy applied
% 67.85/15.51 % Search class: FGHSM-SMLM32-DFFFFFNN
% 67.85/15.51 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 67.85/15.51 % Starting SubtermCWHack with 136s (1) cores
% 67.85/15.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 67.85/15.51 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 113s (1) cores
% 67.85/15.51 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 67.85/15.51 % Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 67.85/15.51 % G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 1180204 completed with status 0
% 67.85/15.51 % Result found by G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 67.85/15.51 % Preprocessing class: FMLMSMSMSSSNFFN.
% 67.85/15.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 67.85/15.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 67.85/15.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 67.85/15.51 % No SInE strategy applied
% 67.85/15.51 % Search class: FGHSM-SMLM32-DFFFFFNN
% 67.85/15.51 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 67.85/15.51 % Starting SubtermCWHack with 136s (1) cores
% 67.85/15.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 67.85/15.51 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 113s (1) cores
% 67.85/15.51 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 67.85/15.51 % Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 67.85/15.51 % Preprocessing time : 0.030 s
% 67.85/15.51 % Presaturation interreduction done
% 67.85/15.51
% 67.85/15.51 % Proof found!
% 67.85/15.51 % SZS status Unsatisfiable
% 67.85/15.51 % SZS output start CNFRefutation
% See solution above
% 67.85/15.51 % Parsed axioms : 2789
% 67.85/15.51 % Removed by relevancy pruning/SinE : 0
% 67.85/15.51 % Initial clauses : 2789
% 67.85/15.51 % Removed in clause preprocessing : 9
% 67.85/15.51 % Initial clauses in saturation : 2780
% 67.85/15.51 % Processed clauses : 43433
% 67.85/15.51 % ...of these trivial : 773
% 67.85/15.51 % ...subsumed : 31413
% 67.85/15.51 % ...remaining for further processing : 11247
% 67.85/15.51 % Other redundant clauses eliminated : 1044
% 67.85/15.51 % Clauses deleted for lack of memory : 0
% 67.85/15.51 % Backward-subsumed : 366
% 67.85/15.51 % Backward-rewritten : 1137
% 67.85/15.51 % Generated clauses : 261618
% 67.85/15.51 % ...of the previous two non-redundant : 233869
% 67.85/15.51 % ...aggressively subsumed : 0
% 67.85/15.51 % Contextual simplify-reflections : 171
% 67.85/15.51 % Paramodulations : 260502
% 67.85/15.51 % Factorizations : 5
% 67.85/15.51 % NegExts : 0
% 67.85/15.51 % Equation resolutions : 1111
% 67.85/15.51 % Disequality decompositions : 0
% 67.85/15.51 % Total rewrite steps : 214701
% 67.85/15.51 % ...of those cached : 202070
% 67.85/15.51 % Propositional unsat checks : 2
% 67.85/15.51 % Propositional check models : 1
% 67.85/15.51 % Propositional check unsatisfiable : 0
% 67.85/15.51 % Propositional clauses : 0
% 67.85/15.51 % Propositional clauses after purity: 0
% 67.85/15.51 % Propositional unsat core size : 0
% 67.85/15.51 % Propositional preprocessing time : 0.000
% 67.85/15.51 % Propositional encoding time : 0.293
% 67.85/15.51 % Propositional solver time : 0.241
% 67.85/15.51 % Success case prop preproc time : 0.000
% 67.85/15.51 % Success case prop encoding time : 0.000
% 67.85/15.51 % Success case prop solver time : 0.000
% 67.85/15.51 % Current number of processed clauses : 7091
% 67.85/15.51 % Positive orientable unit clauses : 1335
% 67.85/15.51 % Positive unorientable unit clauses: 50
% 67.85/15.51 % Negative unit clauses : 753
% 67.85/15.51 % Non-unit-clauses : 4953
% 67.85/15.51 % Current number of unprocessed clauses: 189370
% 67.85/15.51 % ...number of literals in the above : 507524
% 67.85/15.51 % Current number of archived formulas : 0
% 67.85/15.51 % Current number of archived clauses : 4164
% 67.85/15.51 % Clause-clause subsumption calls (NU) : 8022083
% 67.85/15.51 % Rec. Clause-clause subsumption calls : 5711364
% 67.85/15.51 % Non-unit clause-clause subsumptions : 20069
% 67.85/15.51 % Unit Clause-clause subsumption calls : 307812
% 67.85/15.51 % Rewrite failures with RHS unbound : 0
% 67.85/15.51 % BW rewrite match attempts : 4896
% 67.85/15.51 % BW rewrite match successes : 508
% 67.85/15.51 % Condensation attempts : 0
% 67.85/15.51 % Condensation successes : 0
% 67.85/15.51 % Termbank termtop insertions : 5904651
% 67.85/15.51 % Search garbage collected termcells : 4075
% 67.85/15.51
% 67.85/15.51 % -------------------------------------------------
% 67.85/15.51 % User time : 9.387 s
% 67.85/15.51 % System time : 0.272 s
% 67.85/15.51 % Total time : 9.659 s
% 67.85/15.51 % Maximum resident set size: 8508 pages
% 67.85/15.51
% 67.85/15.51 % -------------------------------------------------
% 67.85/15.51 % User time : 47.165 s
% 67.85/15.51 % System time : 1.226 s
% 67.85/15.51 % Total time : 48.391 s
% 67.85/15.51 % Maximum resident set size: 6400 pages
% 67.85/15.51 % E exiting
%------------------------------------------------------------------------------