TSTP Solution File: ANA045-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ANA045-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 17:21:13 EDT 2023
% Result : Unsatisfiable 234.11s 30.30s
% Output : Proof 234.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA045-1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.16/0.35 % Computer : n013.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Fri Aug 25 18:03:02 EDT 2023
% 0.16/0.35 % CPUTime :
% 234.11/30.30 Command-line arguments: --no-flatten-goal
% 234.11/30.30
% 234.11/30.30 % SZS status Unsatisfiable
% 234.11/30.30
% 234.11/30.30 % SZS output start Proof
% 234.11/30.30 Take the following subset of the input axioms:
% 234.11/30.32 fof(cls_Datatype_Ooption_Odistinct__1_0, axiom, ![T_a, V_a_H]: c_Datatype_Ooption_ONone!=c_Datatype_Ooption_OSome(V_a_H, T_a)).
% 234.11/30.32 fof(cls_Datatype_Ooption_Odistinct__2_0, axiom, ![T_a2, V_a_H2]: c_Datatype_Ooption_OSome(V_a_H2, T_a2)!=c_Datatype_Ooption_ONone).
% 234.11/30.32 fof(cls_Datatype__Universe_OAtom__not__Scons_0, axiom, ![V_a, T_b, V_M, V_N, T_a2]: c_Datatype__Universe_OAtom(V_a, T_a2, T_b)!=c_Datatype__Universe_OScons(V_M, V_N, T_a2, T_b)).
% 234.11/30.32 fof(cls_Datatype__Universe_OIn0__not__In1_0, axiom, ![T_a2, T_b2, V_M2, V_N2]: c_Datatype__Universe_OIn0(V_M2, T_a2, T_b2)!=c_Datatype__Universe_OIn1(V_N2, T_a2, T_b2)).
% 234.11/30.32 fof(cls_Datatype__Universe_OIn1__not__In0_0, axiom, ![T_a2, T_b2, V_M2, V_N2]: c_Datatype__Universe_OIn1(V_N2, T_a2, T_b2)!=c_Datatype__Universe_OIn0(V_M2, T_a2, T_b2)).
% 234.11/30.32 fof(cls_Datatype__Universe_OLeaf__not__Numb_0, axiom, ![V_k, T_a2, V_a2, T_b2]: c_Datatype__Universe_OLeaf(V_a2, T_a2, T_b2)!=c_Datatype__Universe_ONumb(V_k, T_a2, T_b2)).
% 234.11/30.32 fof(cls_Datatype__Universe_OLeaf__not__Scons_0, axiom, ![T_a2, V_a2, T_b2, V_M2, V_N2]: c_Datatype__Universe_OLeaf(V_a2, T_a2, T_b2)!=c_Datatype__Universe_OScons(V_M2, V_N2, T_a2, T_b2)).
% 234.11/30.32 fof(cls_Datatype__Universe_ONumb__not__Leaf_0, axiom, ![T_a2, V_a2, T_b2, V_k2]: c_Datatype__Universe_ONumb(V_k2, T_a2, T_b2)!=c_Datatype__Universe_OLeaf(V_a2, T_a2, T_b2)).
% 234.11/30.32 fof(cls_Datatype__Universe_ONumb__not__Scons_0, axiom, ![T_a2, T_b2, V_k2, V_M2, V_N2]: c_Datatype__Universe_ONumb(V_k2, T_a2, T_b2)!=c_Datatype__Universe_OScons(V_M2, V_N2, T_a2, T_b2)).
% 234.11/30.32 fof(cls_Datatype__Universe_OScons__not__Atom_0, axiom, ![T_a2, V_a2, T_b2, V_M2, V_N2]: c_Datatype__Universe_OScons(V_M2, V_N2, T_a2, T_b2)!=c_Datatype__Universe_OAtom(V_a2, T_a2, T_b2)).
% 234.11/30.32 fof(cls_Datatype__Universe_OScons__not__Leaf_0, axiom, ![T_a2, V_a2, T_b2, V_M2, V_N2]: c_Datatype__Universe_OScons(V_M2, V_N2, T_a2, T_b2)!=c_Datatype__Universe_OLeaf(V_a2, T_a2, T_b2)).
% 234.11/30.32 fof(cls_Datatype__Universe_OScons__not__Numb_0, axiom, ![T_a2, T_b2, V_k2, V_M2, V_N2]: c_Datatype__Universe_OScons(V_M2, V_N2, T_a2, T_b2)!=c_Datatype__Universe_ONumb(V_k2, T_a2, T_b2)).
% 234.11/30.32 fof(cls_IntArith_Oarith__special__14_0, axiom, ![V_y, T_a2]: (~class_Numeral_Onumber__ring(T_a2) | (~class_Ring__and__Field_Oordered__idom(T_a2) | (~c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(V_y, c_Numeral_Obin__minus(c_Numeral_OPls)), T_a2), T_a2) | ~c_lessequals(c_0, c_Numeral_Onumber__of(V_y, T_a2), T_a2))))).
% 234.11/30.32 fof(cls_IntArith_Oarith__special__15_0, axiom, ![T_a2, V_y2]: (~class_Numeral_Onumber__ring(T_a2) | (~class_Ring__and__Field_Oordered__idom(T_a2) | (~c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(V_y2, c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls, c_Numeral_Obit_OB1))), T_a2), T_a2) | ~c_lessequals(c_1, c_Numeral_Onumber__of(V_y2, T_a2), T_a2))))).
% 234.11/30.32 fof(cls_IntArith_Oarith__special__16_0, axiom, ![V_x, T_a2]: (~class_Numeral_Onumber__ring(T_a2) | (~class_Ring__and__Field_Oordered__idom(T_a2) | (~c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls, c_Numeral_Obin__minus(V_x)), T_a2), T_a2) | ~c_lessequals(c_Numeral_Onumber__of(V_x, T_a2), c_0, T_a2))))).
% 234.11/30.32 fof(cls_IntArith_Oarith__special__17_0, axiom, ![T_a2, V_x2]: (~class_Numeral_Onumber__ring(T_a2) | (~class_Ring__and__Field_Oordered__idom(T_a2) | (~c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls, c_Numeral_Obit_OB1), c_Numeral_Obin__minus(V_x2)), T_a2), T_a2) | ~c_lessequals(c_Numeral_Onumber__of(V_x2, T_a2), c_1, T_a2))))).
% 234.11/30.32 fof(cls_IntDef_Oint__less__0__conv_0, axiom, ![V_k2]: ~c_less(c_IntDef_Oint(V_k2), c_0, tc_IntDef_Oint)).
% 234.11/30.32 fof(cls_IntDef_Onot__int__zless__negative_0, axiom, ![V_n, V_m]: ~c_less(c_IntDef_Oint(V_n), c_uminus(c_IntDef_Oint(V_m), tc_IntDef_Oint), tc_IntDef_Oint)).
% 234.11/30.32 fof(cls_IntDef_Onot__neg__int_0, axiom, ![V_n2]: ~c_IntDef_Oneg(c_IntDef_Oint(V_n2), tc_IntDef_Oint)).
% 234.11/30.32 fof(cls_IntDef_Onot__zle__0__negative_0, axiom, ![V_n2]: ~c_lessequals(c_0, c_uminus(c_IntDef_Oint(c_Suc(V_n2)), tc_IntDef_Oint), tc_IntDef_Oint)).
% 234.11/30.32 fof(cls_List_ONil2__notin__lex_0, axiom, ![V_r, V_xs, T_a2]: ~c_in(c_Pair(V_xs, c_List_Olist_ONil, tc_List_Olist(T_a2), tc_List_Olist(T_a2)), c_List_Olex(V_r, T_a2), tc_prod(tc_List_Olist(T_a2), tc_List_Olist(T_a2)))).
% 234.11/30.32 fof(cls_List_ONil__notin__lex_0, axiom, ![V_ys, T_a2, V_r2]: ~c_in(c_Pair(c_List_Olist_ONil, V_ys, tc_List_Olist(T_a2), tc_List_Olist(T_a2)), c_List_Olex(V_r2, T_a2), tc_prod(tc_List_Olist(T_a2), tc_List_Olist(T_a2)))).
% 234.11/30.32 fof(cls_List_Odistinct_Osimps__2_0, axiom, ![T_a__1, V_x2, V_xs2]: (~c_List_Odistinct(c_List_Olist_OCons(V_x2, V_xs2, T_a__1), T_a__1) | ~c_in(V_x2, c_List_Oset(V_xs2, T_a__1), T_a__1))).
% 234.11/30.32 fof(cls_List_Olength__greater__0__conv_0, axiom, ![T_a2]: ~c_less(c_0, c_Nat_Osize(c_List_Olist_ONil, tc_List_Olist(T_a2)), tc_nat)).
% 234.11/30.32 fof(cls_List_Olexord__Nil__right_0, axiom, ![T_a2, V_r2, V_x2]: ~c_in(c_Pair(V_x2, c_List_Olist_ONil, tc_List_Olist(T_a2), tc_List_Olist(T_a2)), c_List_Olexord(V_r2, T_a2), tc_prod(tc_List_Olist(T_a2), tc_List_Olist(T_a2)))).
% 234.11/30.32 fof(cls_List_Olist_Odistinct__1_0, axiom, ![V_list_H, T_a2, V_a_H2]: c_List_Olist_ONil!=c_List_Olist_OCons(V_a_H2, V_list_H, T_a2)).
% 234.11/30.32 fof(cls_List_Olist_Odistinct__2_0, axiom, ![T_a2, V_a_H2, V_list_H2]: c_List_Olist_OCons(V_a_H2, V_list_H2, T_a2)!=c_List_Olist_ONil).
% 234.11/30.32 fof(cls_List_Onot__Cons__self_0, axiom, ![T_a2, V_x2, V_xs2]: V_xs2!=c_List_Olist_OCons(V_x2, V_xs2, T_a2)).
% 234.11/30.32 fof(cls_List_Onull_Osimps__2_0, axiom, ![V_x2, V_xs2, T_a__1_2]: ~c_List_Onull(c_List_Olist_OCons(V_x2, V_xs2, T_a__1_2), T_a__1_2)).
% 234.11/30.32 fof(cls_List_Oop_Amem_Osimps__1_0, axiom, ![V_x2, T_a__1_2]: ~c_List_Oop_Amem(V_x2, c_List_Olist_ONil, T_a__1_2)).
% 234.11/30.32 fof(cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0, axiom, ![V_t, T_a2, V_x2]: c_List_Olist_OCons(V_x2, V_t, T_a2)!=V_t).
% 234.11/30.32 fof(cls_Map_Omap__of__zip__is__None_0, axiom, ![T_a2, V_x2, T_b2, V_xs2, V_ys2]: (~c_in(V_x2, c_List_Oset(V_xs2, T_a2), T_a2) | (c_Map_Omap__of(c_List_Ozip(V_xs2, V_ys2, T_a2, T_b2), V_x2, T_a2, T_b2)!=c_Datatype_Ooption_ONone | c_Nat_Osize(V_xs2, tc_List_Olist(T_a2))!=c_Nat_Osize(V_ys2, tc_List_Olist(T_b2))))).
% 234.11/30.32 fof(cls_NatArith_Oof__nat__less__0__iff_0, axiom, ![T_a2, V_m2]: (~class_Ring__and__Field_Oordered__semidom(T_a2) | ~c_less(c_NatArith_Oof__nat(V_m2, T_a2), c_0, T_a2))).
% 234.11/30.32 fof(cls_Nat_OSuc__not__Zero_0, axiom, ![V_m2]: c_Suc(V_m2)!=c_0).
% 234.11/30.32 fof(cls_Nat_OZero__not__Suc_0, axiom, ![V_m2]: c_0!=c_Suc(V_m2)).
% 234.11/30.32 fof(cls_Nat_Oless__irrefl_0, axiom, ![V_n2]: ~c_less(V_n2, V_n2, tc_nat)).
% 234.11/30.32 fof(cls_Nat_Onot__add__less1_0, axiom, ![V_i, V_j]: ~c_less(c_plus(V_i, V_j, tc_nat), V_i, tc_nat)).
% 234.11/30.32 fof(cls_Nat_Onot__add__less2_0, axiom, ![V_i2, V_j2]: ~c_less(c_plus(V_j2, V_i2, tc_nat), V_i2, tc_nat)).
% 234.11/30.32 fof(cls_Nat_Onot__less0_0, axiom, ![V_n2]: ~c_less(V_n2, c_0, tc_nat)).
% 234.11/30.32 fof(cls_Numeral_Obin__rel__simps__10_0, axiom, ![T_a2]: (~class_Ring__and__Field_Ocomm__semiring__1__cancel(T_a2) | ~c_IntDef_Oiszero(c_1, T_a2))).
% 234.11/30.32 fof(cls_Numeral_Obin__rel__simps__13_0, axiom, ![T_a2, V_y2, V_x2]: (~class_Numeral_Onumber__ring(T_a2) | (~class_Ring__and__Field_Oordered__idom(T_a2) | (~c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(V_y2, c_Numeral_Obin__minus(V_x2)), T_a2), T_a2) | ~c_lessequals(c_Numeral_Onumber__of(V_x2, T_a2), c_Numeral_Onumber__of(V_y2, T_a2), T_a2))))).
% 234.11/30.32 fof(cls_Numeral_Obin__rel__simps__3_0, axiom, ![T_a2]: (~class_Numeral_Onumber__ring(T_a2) | ~c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin, T_a2), T_a2))).
% 234.11/30.32 fof(cls_Numeral_Obin__rel__simps__5_0, axiom, ![V_w, T_a2]: (~class_Numeral_Onumber__ring(T_a2) | (~class_Ring__and__Field_Oordered__idom(T_a2) | ~c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(V_w, c_Numeral_Obit_OB1), T_a2), T_a2)))).
% 234.11/30.32 fof(cls_Numeral_Obin__rel__simps__7_0, axiom, ![T_a2]: (~class_Numeral_Onumber__ring(T_a2) | (~class_Ring__and__Field_Oordered__idom(T_a2) | ~c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls, T_a2), T_a2)))).
% 234.11/30.32 fof(cls_Numeral_Obin__rel__simps__8_0, axiom, ![T_a2]: (~class_Ring__and__Field_Oordered__idom(T_a2) | ~c_IntDef_Oneg(c_0, T_a2))).
% 234.11/30.32 fof(cls_Numeral_Obin__rel__simps__9_0, axiom, ![T_a2]: (~class_Ring__and__Field_Oordered__idom(T_a2) | ~c_IntDef_Oneg(c_1, T_a2))).
% 234.11/30.32 fof(cls_OrderedGroup_Oabs__ge__zero_0, axiom, ![T_a2, V_a2]: (~class_OrderedGroup_Olordered__ab__group__abs(T_a2) | c_lessequals(c_0, c_HOL_Oabs(V_a2, T_a2), T_a2))).
% 234.11/30.32 fof(cls_OrderedGroup_Oabs__not__less__zero_0, axiom, ![T_a2, V_a2]: (~class_OrderedGroup_Olordered__ab__group__abs(T_a2) | ~c_less(c_HOL_Oabs(V_a2, T_a2), c_0, T_a2))).
% 234.11/30.32 fof(cls_OrderedGroup_Ozero__less__abs__iff_0, axiom, ![T_a2]: (~class_OrderedGroup_Olordered__ab__group__abs(T_a2) | ~c_less(c_0, c_HOL_Oabs(c_0, T_a2), T_a2))).
% 234.11/30.32 fof(cls_Orderings_Oorder__less__irrefl_0, axiom, ![T_a2, V_x2]: (~class_Orderings_Oorder(T_a2) | ~c_less(V_x2, V_x2, T_a2))).
% 234.11/30.32 fof(cls_Parity_Oeven__nat__Suc_0, axiom, ![V_x2]: (~c_Parity_Oeven(V_x2, tc_nat) | ~c_Parity_Oeven(c_Suc(V_x2), tc_nat))).
% 234.11/30.32 fof(cls_Parity_Oneq__one__mod__two_1, axiom, ![V_x2]: (c_Divides_Oop_Amod(V_x2, c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls, c_Numeral_Obit_OB1), c_Numeral_Obit_OB0), tc_IntDef_Oint), tc_IntDef_Oint)!=c_0 | c_Divides_Oop_Amod(V_x2, c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls, c_Numeral_Obit_OB1), c_Numeral_Obit_OB0), tc_IntDef_Oint), tc_IntDef_Oint)!=c_1)).
% 234.11/30.32 fof(cls_Parity_Opower__le__zero__eq__number__of_0, axiom, ![T_a2, V_x2, V_w2]: (~class_Power_Orecpower(T_a2) | (~class_Ring__and__Field_Oordered__idom(T_a2) | (~c_lessequals(c_Nat_Opower(V_x2, c_Numeral_Onumber__of(V_w2, tc_nat), T_a2), c_0, T_a2) | c_Numeral_Onumber__of(V_w2, tc_nat)!=c_0)))).
% 234.11/30.32 fof(cls_Parity_Opower__less__zero__eq__number__of_0, axiom, ![T_a2, V_x2, V_w2]: (~class_Power_Orecpower(T_a2) | (~class_Ring__and__Field_Oordered__idom(T_a2) | (~c_Parity_Oeven(c_Numeral_Onumber__of(V_w2, tc_nat), tc_nat) | ~c_less(c_Nat_Opower(V_x2, c_Numeral_Onumber__of(V_w2, tc_nat), T_a2), c_0, T_a2))))).
% 234.11/30.32 fof(cls_Ring__and__Field_Oaxclass__0__neq__1__class_Oaxioms_0, axiom, ![T_a2]: (~class_Ring__and__Field_Oaxclass__0__neq__1(T_a2) | c_0!=c_1)).
% 234.11/30.32 fof(cls_Ring__and__Field_Odivide__eq__eq__1_0, axiom, ![V_b, T_a2]: (~class_Ring__and__Field_Odivision__by__zero(T_a2) | (~class_Ring__and__Field_Oordered__field(T_a2) | c_divide(V_b, c_0, T_a2)!=c_1))).
% 234.11/30.32 fof(cls_Ring__and__Field_Oeq__divide__eq__1_0, axiom, ![T_a2, V_b2]: (~class_Ring__and__Field_Odivision__by__zero(T_a2) | (~class_Ring__and__Field_Oordered__field(T_a2) | c_1!=c_divide(V_b2, c_0, T_a2)))).
% 234.11/30.32 fof(cls_Ring__and__Field_Omult__cancel__right1_2, axiom, ![V_c, T_a2]: (~class_Ring__and__Field_Oordered__idom(T_a2) | V_c=c_times(c_1, V_c, T_a2))).
% 234.11/30.32 fof(cls_Ring__and__Field_Onot__one__le__zero_0, axiom, ![T_a2]: (~class_Ring__and__Field_Oordered__semidom(T_a2) | ~c_lessequals(c_1, c_0, T_a2))).
% 234.11/30.32 fof(cls_Ring__and__Field_Onot__one__less__zero_0, axiom, ![T_a2]: (~class_Ring__and__Field_Oordered__semidom(T_a2) | ~c_less(c_1, c_0, T_a2))).
% 234.11/30.32 fof(cls_Ring__and__Field_Oone__neq__zero_0, axiom, ![T_a2]: (~class_Ring__and__Field_Oaxclass__0__neq__1(T_a2) | c_1!=c_0)).
% 234.11/30.32 fof(cls_Set_OCompl__iff_0, axiom, ![V_A, T_a2, V_c2]: (~c_in(V_c2, V_A, T_a2) | ~c_in(V_c2, c_uminus(V_A, tc_set(T_a2)), T_a2))).
% 234.11/30.32 fof(cls_Set_ODiff__iff_1, axiom, ![V_B, T_a2, V_A2, V_c2]: (~c_in(V_c2, V_B, T_a2) | ~c_in(V_c2, c_minus(V_A2, V_B, tc_set(T_a2)), T_a2))).
% 234.11/30.32 fof(cls_Set_Odisjoint__insert__1_0, axiom, ![T_a2, V_a2, V_A2, V_B2]: (~c_in(V_a2, V_B2, T_a2) | c_inter(V_B2, c_insert(V_a2, V_A2, T_a2), T_a2)!=c_emptyset)).
% 234.11/30.32 fof(cls_Set_Odisjoint__insert__2_0, axiom, ![T_a2, V_b2, V_A2, V_B2]: (~c_in(V_b2, V_A2, T_a2) | c_emptyset!=c_inter(V_A2, c_insert(V_b2, V_B2, T_a2), T_a2))).
% 234.11/30.32 fof(cls_Set_Oempty__iff_0, axiom, ![T_a2, V_c2]: ~c_in(V_c2, c_emptyset, T_a2)).
% 234.11/30.32 fof(cls_Set_Oempty__not__insert_0, axiom, ![T_a2, V_a2, V_A2]: c_emptyset!=c_insert(V_a2, V_A2, T_a2)).
% 234.11/30.32 fof(cls_Set_Oinsert__disjoint__1_0, axiom, ![T_a2, V_a2, V_A2, V_B2]: (~c_in(V_a2, V_B2, T_a2) | c_inter(c_insert(V_a2, V_A2, T_a2), V_B2, T_a2)!=c_emptyset)).
% 234.11/30.32 fof(cls_Set_Oinsert__disjoint__2_0, axiom, ![T_a2, V_a2, V_A2, V_B2]: (~c_in(V_a2, V_B2, T_a2) | c_emptyset!=c_inter(c_insert(V_a2, V_A2, T_a2), V_B2, T_a2))).
% 234.11/30.32 fof(cls_Set_Oinsert__not__empty_0, axiom, ![T_a2, V_a2, V_A2]: c_insert(V_a2, V_A2, T_a2)!=c_emptyset).
% 234.11/30.32 fof(cls_Set_Onot__psubset__empty_0, axiom, ![T_a2, V_A2]: ~c_less(V_A2, c_emptyset, tc_set(T_a2))).
% 234.11/30.32 fof(cls_Set_OpsubsetE_0, axiom, ![T_a2, V_A2, V_B2]: (~c_less(V_A2, V_B2, tc_set(T_a2)) | ~c_lessequals(V_B2, V_A2, tc_set(T_a2)))).
% 234.11/30.32 fof(cls_Sum__Type_OInl__not__Inr_0, axiom, ![T_a2, V_a2, V_b2, T_b2]: c_Sum__Type_OInl(V_a2, T_a2, T_b2)!=c_Sum__Type_OInr(V_b2, T_b2, T_a2)).
% 234.11/30.32 fof(cls_Sum__Type_OInr__not__Inl_0, axiom, ![T_a2, V_a2, V_b2, T_b2]: c_Sum__Type_OInr(V_b2, T_b2, T_a2)!=c_Sum__Type_OInl(V_a2, T_a2, T_b2)).
% 234.11/30.32 fof(cls_Wellfounded__Recursion_Oacyclic__insert_1, axiom, ![T_a2, V_r2, V_y2, V_x2]: (~c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(V_y2, V_x2, T_a2, T_a2), V_r2, tc_prod(T_a2, T_a2)), T_a2) | ~c_in(c_Pair(V_x2, V_y2, T_a2, T_a2), c_Transitive__Closure_Ortrancl(V_r2, T_a2), tc_prod(T_a2, T_a2)))).
% 234.11/30.32 fof(cls_Wellfounded__Recursion_Owf__insert_1, axiom, ![T_a2, V_r2, V_y2, V_x2]: (~c_Wellfounded__Recursion_Owf(c_insert(c_Pair(V_y2, V_x2, T_a2, T_a2), V_r2, tc_prod(T_a2, T_a2)), T_a2) | ~c_in(c_Pair(V_x2, V_y2, T_a2, T_a2), c_Transitive__Closure_Ortrancl(V_r2, T_a2), tc_prod(T_a2, T_a2)))).
% 234.11/30.32 fof(cls_Wellfounded__Recursion_Owf__not__refl_0, axiom, ![T_a2, V_a2, V_r2]: (~c_Wellfounded__Recursion_Owf(V_r2, T_a2) | ~c_in(c_Pair(V_a2, V_a2, T_a2, T_a2), V_r2, tc_prod(T_a2, T_a2)))).
% 234.11/30.32 fof(cls_conjecture_0, negated_conjecture, ![V_U]: ~c_lessequals(c_0, c_times(V_U, c_HOL_Oabs(v_g(v_x(V_U)), t_b), t_b), t_b)).
% 234.11/30.32 fof(clsrel_Ring__and__Field_Oordered__idom_50, axiom, ![T]: (~class_Ring__and__Field_Oordered__idom(T) | class_OrderedGroup_Olordered__ab__group__abs(T))).
% 234.11/30.32 fof(tfree_tcs, negated_conjecture, class_Ring__and__Field_Oordered__idom(t_b)).
% 234.11/30.32
% 234.11/30.32 Now clausify the problem and encode Horn clauses using encoding 3 of
% 234.11/30.32 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 234.11/30.32 We repeatedly replace C & s=t => u=v by the two clauses:
% 234.11/30.32 fresh(y, y, x1...xn) = u
% 234.11/30.32 C => fresh(s, t, x1...xn) = v
% 234.11/30.32 where fresh is a fresh function symbol and x1..xn are the free
% 234.11/30.32 variables of u and v.
% 234.11/30.32 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 234.11/30.32 input problem has no model of domain size 1).
% 234.11/30.32
% 234.11/30.32 The encoding turns the above axioms into the following unit equations and goals:
% 234.11/30.32
% 234.11/30.32 Axiom 1 (tfree_tcs): class_Ring__and__Field_Oordered__idom(t_b) = true2.
% 234.11/30.32 Axiom 2 (clsrel_Ring__and__Field_Oordered__idom_50): fresh471(X, X, Y) = true2.
% 234.11/30.32 Axiom 3 (cls_OrderedGroup_Oabs__ge__zero_0): fresh1540(X, X, Y, Z) = true2.
% 234.11/30.32 Axiom 4 (clsrel_Ring__and__Field_Oordered__idom_50): fresh471(class_Ring__and__Field_Oordered__idom(X), true2, X) = class_OrderedGroup_Olordered__ab__group__abs(X).
% 234.11/30.32 Axiom 5 (cls_Ring__and__Field_Omult__cancel__right1_2): fresh60(X, X, Y, Z) = Z.
% 234.11/30.32 Axiom 6 (cls_Ring__and__Field_Omult__cancel__right1_2): fresh60(class_Ring__and__Field_Oordered__idom(X), true2, X, Y) = c_times(c_1, Y, X).
% 234.11/30.32 Axiom 7 (cls_OrderedGroup_Oabs__ge__zero_0): fresh1540(class_OrderedGroup_Olordered__ab__group__abs(X), true2, X, Y) = c_lessequals(c_0, c_HOL_Oabs(Y, X), X).
% 234.11/30.32
% 234.11/30.32 Goal 1 (cls_conjecture_0): c_lessequals(c_0, c_times(X, c_HOL_Oabs(v_g(v_x(X)), t_b), t_b), t_b) = true2.
% 234.11/30.32 The goal is true when:
% 234.11/30.32 X = c_1
% 234.11/30.32
% 234.11/30.32 Proof:
% 234.11/30.32 c_lessequals(c_0, c_times(c_1, c_HOL_Oabs(v_g(v_x(c_1)), t_b), t_b), t_b)
% 234.11/30.32 = { by axiom 6 (cls_Ring__and__Field_Omult__cancel__right1_2) R->L }
% 234.11/30.32 c_lessequals(c_0, fresh60(class_Ring__and__Field_Oordered__idom(t_b), true2, t_b, c_HOL_Oabs(v_g(v_x(c_1)), t_b)), t_b)
% 234.11/30.32 = { by axiom 1 (tfree_tcs) }
% 234.11/30.32 c_lessequals(c_0, fresh60(true2, true2, t_b, c_HOL_Oabs(v_g(v_x(c_1)), t_b)), t_b)
% 234.11/30.32 = { by axiom 5 (cls_Ring__and__Field_Omult__cancel__right1_2) }
% 234.11/30.32 c_lessequals(c_0, c_HOL_Oabs(v_g(v_x(c_1)), t_b), t_b)
% 234.11/30.32 = { by axiom 7 (cls_OrderedGroup_Oabs__ge__zero_0) R->L }
% 234.11/30.32 fresh1540(class_OrderedGroup_Olordered__ab__group__abs(t_b), true2, t_b, v_g(v_x(c_1)))
% 234.11/30.32 = { by axiom 4 (clsrel_Ring__and__Field_Oordered__idom_50) R->L }
% 234.11/30.32 fresh1540(fresh471(class_Ring__and__Field_Oordered__idom(t_b), true2, t_b), true2, t_b, v_g(v_x(c_1)))
% 234.11/30.33 = { by axiom 1 (tfree_tcs) }
% 234.11/30.33 fresh1540(fresh471(true2, true2, t_b), true2, t_b, v_g(v_x(c_1)))
% 234.11/30.33 = { by axiom 2 (clsrel_Ring__and__Field_Oordered__idom_50) }
% 234.11/30.33 fresh1540(true2, true2, t_b, v_g(v_x(c_1)))
% 234.11/30.33 = { by axiom 3 (cls_OrderedGroup_Oabs__ge__zero_0) }
% 234.11/30.33 true2
% 234.11/30.33 % SZS output end Proof
% 234.11/30.33
% 234.11/30.33 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------