TSTP Solution File: ANA034-10 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ANA034-10 : TPTP v8.1.2. Released v7.3.0.
% 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 : n027.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 17:21:09 EDT 2023
% Result : Unsatisfiable 3.81s 0.90s
% Output : Proof 4.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA034-10 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 18:40:49 EDT 2023
% 0.13/0.35 % CPUTime :
% 3.81/0.90 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 3.81/0.90
% 3.81/0.90 % SZS status Unsatisfiable
% 3.81/0.90
% 4.17/0.91 % SZS output start Proof
% 4.17/0.91 Axiom 1 (tfree_tcs): class_Ring__and__Field_Oordered__idom(t_b) = true.
% 4.17/0.91 Axiom 2 (cls_conjecture_0): c_less(c_0, v_c, t_b) = true.
% 4.17/0.91 Axiom 3 (ifeq_axiom_001): ifeq(X, X, Y, Z) = Y.
% 4.17/0.91 Axiom 4 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 4.17/0.91 Axiom 5 (clsrel_Ring__and__Field_Oordered__idom_50): ifeq(class_Ring__and__Field_Oordered__idom(X), true, class_OrderedGroup_Olordered__ab__group__abs(X), true) = true.
% 4.17/0.91 Axiom 6 (clsrel_Ring__and__Field_Oordered__idom_42): ifeq(class_Ring__and__Field_Oordered__idom(X), true, class_Ring__and__Field_Opordered__semiring(X), true) = true.
% 4.17/0.91 Axiom 7 (clsrel_Ring__and__Field_Oordered__idom_40): ifeq(class_Ring__and__Field_Oordered__idom(X), true, class_Ring__and__Field_Opordered__cancel__semiring(X), true) = true.
% 4.17/0.91 Axiom 8 (clsrel_OrderedGroup_Olordered__ab__group__abs_17): ifeq(class_OrderedGroup_Olordered__ab__group__abs(X), true, class_Orderings_Oorder(X), true) = true.
% 4.17/0.91 Axiom 9 (cls_OrderedGroup_Oabs__ge__zero_0): ifeq(class_OrderedGroup_Olordered__ab__group__abs(X), true, c_lessequals(c_0, c_HOL_Oabs(Y, X), X), true) = true.
% 4.17/0.91 Axiom 10 (cls_conjecture_2): c_lessequals(c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), t_b) = true.
% 4.17/0.91 Axiom 11 (cls_conjecture_3): c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b) = true.
% 4.17/0.91 Axiom 12 (cls_conjecture_4): c_times(c_times(v_c, v_ca, t_b), c_HOL_Oabs(c_times(v_f(v_x), v_g(v_x), t_b), t_b), t_b) = c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b).
% 4.17/0.91 Axiom 13 (cls_Orderings_Oorder__less__imp__le_0): ifeq(c_less(X, Y, Z), true, ifeq(class_Orderings_Oorder(Z), true, c_lessequals(X, Y, Z), true), true) = true.
% 4.17/0.91 Axiom 14 (cls_Ring__and__Field_Oabs__mult_0): ifeq2(class_Ring__and__Field_Oordered__idom(X), true, c_times(c_HOL_Oabs(Y, X), c_HOL_Oabs(Z, X), X), c_HOL_Oabs(c_times(Y, Z, X), X)) = c_HOL_Oabs(c_times(Y, Z, X), X).
% 4.17/0.91 Axiom 15 (cls_Ring__and__Field_Omult__nonneg__nonneg_0): ifeq(class_Ring__and__Field_Opordered__cancel__semiring(X), true, ifeq(c_lessequals(c_0, Y, X), true, ifeq(c_lessequals(c_0, Z, X), true, c_lessequals(c_0, c_times(Y, Z, X), X), true), true), true) = true.
% 4.17/0.91 Axiom 16 (cls_Ring__and__Field_Omult__mono_0): ifeq(c_lessequals(c_0, X, Y), true, ifeq(c_lessequals(c_0, Z, Y), true, ifeq(c_lessequals(W, X, Y), true, ifeq(c_lessequals(Z, V, Y), true, ifeq(class_Ring__and__Field_Opordered__semiring(Y), true, c_lessequals(c_times(W, Z, Y), c_times(X, V, Y), Y), true), true), true), true), true) = true.
% 4.17/0.91
% 4.17/0.91 Lemma 17: class_OrderedGroup_Olordered__ab__group__abs(t_b) = true.
% 4.17/0.91 Proof:
% 4.17/0.91 class_OrderedGroup_Olordered__ab__group__abs(t_b)
% 4.17/0.91 = { by axiom 3 (ifeq_axiom_001) R->L }
% 4.17/0.91 ifeq(true, true, class_OrderedGroup_Olordered__ab__group__abs(t_b), true)
% 4.17/0.91 = { by axiom 1 (tfree_tcs) R->L }
% 4.17/0.91 ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Olordered__ab__group__abs(t_b), true)
% 4.17/0.91 = { by axiom 5 (clsrel_Ring__and__Field_Oordered__idom_50) }
% 4.17/0.91 true
% 4.17/0.91
% 4.17/0.91 Lemma 18: c_lessequals(c_0, c_HOL_Oabs(X, t_b), t_b) = true.
% 4.17/0.91 Proof:
% 4.17/0.91 c_lessequals(c_0, c_HOL_Oabs(X, t_b), t_b)
% 4.17/0.91 = { by axiom 3 (ifeq_axiom_001) R->L }
% 4.17/0.91 ifeq(true, true, c_lessequals(c_0, c_HOL_Oabs(X, t_b), t_b), true)
% 4.17/0.91 = { by lemma 17 R->L }
% 4.17/0.91 ifeq(class_OrderedGroup_Olordered__ab__group__abs(t_b), true, c_lessequals(c_0, c_HOL_Oabs(X, t_b), t_b), true)
% 4.17/0.91 = { by axiom 9 (cls_OrderedGroup_Oabs__ge__zero_0) }
% 4.17/0.91 true
% 4.17/0.91
% 4.17/0.91 Goal 1 (cls_conjecture_5): c_lessequals(c_HOL_Oabs(c_times(v_a(v_x), v_b(v_x), t_b), t_b), c_times(c_times(v_c, v_ca, t_b), c_HOL_Oabs(c_times(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b) = true.
% 4.17/0.91 Proof:
% 4.17/0.91 c_lessequals(c_HOL_Oabs(c_times(v_a(v_x), v_b(v_x), t_b), t_b), c_times(c_times(v_c, v_ca, t_b), c_HOL_Oabs(c_times(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b)
% 4.17/0.91 = { by axiom 12 (cls_conjecture_4) }
% 4.17/0.91 c_lessequals(c_HOL_Oabs(c_times(v_a(v_x), v_b(v_x), t_b), t_b), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b)
% 4.17/0.91 = { by axiom 14 (cls_Ring__and__Field_Oabs__mult_0) R->L }
% 4.17/0.91 c_lessequals(ifeq2(class_Ring__and__Field_Oordered__idom(t_b), true, c_times(c_HOL_Oabs(v_a(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_HOL_Oabs(c_times(v_a(v_x), v_b(v_x), t_b), t_b)), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b)
% 4.17/0.91 = { by axiom 1 (tfree_tcs) }
% 4.17/0.91 c_lessequals(ifeq2(true, true, c_times(c_HOL_Oabs(v_a(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_HOL_Oabs(c_times(v_a(v_x), v_b(v_x), t_b), t_b)), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b)
% 4.17/0.91 = { by axiom 4 (ifeq_axiom) }
% 4.17/0.91 c_lessequals(c_times(c_HOL_Oabs(v_a(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b)
% 4.17/0.91 = { by axiom 3 (ifeq_axiom_001) R->L }
% 4.17/0.91 ifeq(true, true, c_lessequals(c_times(c_HOL_Oabs(v_a(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true)
% 4.17/0.91 = { by axiom 3 (ifeq_axiom_001) R->L }
% 4.17/0.91 ifeq(true, true, ifeq(true, true, c_lessequals(c_times(c_HOL_Oabs(v_a(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true)
% 4.17/0.91 = { by lemma 18 R->L }
% 4.17/0.91 ifeq(c_lessequals(c_0, c_HOL_Oabs(v_b(v_x), t_b), t_b), true, ifeq(true, true, c_lessequals(c_times(c_HOL_Oabs(v_a(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true)
% 4.17/0.91 = { by axiom 11 (cls_conjecture_3) R->L }
% 4.17/0.91 ifeq(c_lessequals(c_0, c_HOL_Oabs(v_b(v_x), t_b), t_b), true, ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, c_lessequals(c_times(c_HOL_Oabs(v_a(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true)
% 4.17/0.91 = { by axiom 3 (ifeq_axiom_001) R->L }
% 4.17/0.91 ifeq(c_lessequals(c_0, c_HOL_Oabs(v_b(v_x), t_b), t_b), true, ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, ifeq(true, true, c_lessequals(c_times(c_HOL_Oabs(v_a(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true), true)
% 4.17/0.91 = { by axiom 6 (clsrel_Ring__and__Field_Oordered__idom_42) R->L }
% 4.17/0.91 ifeq(c_lessequals(c_0, c_HOL_Oabs(v_b(v_x), t_b), t_b), true, ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, ifeq(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_Ring__and__Field_Opordered__semiring(t_b), true), true, c_lessequals(c_times(c_HOL_Oabs(v_a(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true), true)
% 4.17/0.91 = { by axiom 1 (tfree_tcs) }
% 4.17/0.91 ifeq(c_lessequals(c_0, c_HOL_Oabs(v_b(v_x), t_b), t_b), true, ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, ifeq(ifeq(true, true, class_Ring__and__Field_Opordered__semiring(t_b), true), true, c_lessequals(c_times(c_HOL_Oabs(v_a(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true), true)
% 4.17/0.91 = { by axiom 3 (ifeq_axiom_001) }
% 4.17/0.91 ifeq(c_lessequals(c_0, c_HOL_Oabs(v_b(v_x), t_b), t_b), true, ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, ifeq(class_Ring__and__Field_Opordered__semiring(t_b), true, c_lessequals(c_times(c_HOL_Oabs(v_a(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true), true)
% 4.17/0.91 = { by axiom 3 (ifeq_axiom_001) R->L }
% 4.17/0.91 ifeq(c_lessequals(c_0, c_HOL_Oabs(v_b(v_x), t_b), t_b), true, ifeq(true, true, ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, ifeq(class_Ring__and__Field_Opordered__semiring(t_b), true, c_lessequals(c_times(c_HOL_Oabs(v_a(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true), true), true)
% 4.17/0.91 = { by axiom 3 (ifeq_axiom_001) R->L }
% 4.17/0.91 ifeq(true, true, ifeq(c_lessequals(c_0, c_HOL_Oabs(v_b(v_x), t_b), t_b), true, ifeq(true, true, ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, ifeq(class_Ring__and__Field_Opordered__semiring(t_b), true, c_lessequals(c_times(c_HOL_Oabs(v_a(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true), true), true), true)
% 4.17/0.91 = { by axiom 15 (cls_Ring__and__Field_Omult__nonneg__nonneg_0) R->L }
% 4.17/0.91 ifeq(ifeq(class_Ring__and__Field_Opordered__cancel__semiring(t_b), true, ifeq(c_lessequals(c_0, v_c, t_b), true, ifeq(c_lessequals(c_0, c_HOL_Oabs(v_f(v_x), t_b), t_b), true, c_lessequals(c_0, c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), t_b), true), true), true), true, ifeq(c_lessequals(c_0, c_HOL_Oabs(v_b(v_x), t_b), t_b), true, ifeq(true, true, ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, ifeq(class_Ring__and__Field_Opordered__semiring(t_b), true, c_lessequals(c_times(c_HOL_Oabs(v_a(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true), true), true), true)
% 4.17/0.91 = { by lemma 18 }
% 4.17/0.91 ifeq(ifeq(class_Ring__and__Field_Opordered__cancel__semiring(t_b), true, ifeq(c_lessequals(c_0, v_c, t_b), true, ifeq(true, true, c_lessequals(c_0, c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), t_b), true), true), true), true, ifeq(c_lessequals(c_0, c_HOL_Oabs(v_b(v_x), t_b), t_b), true, ifeq(true, true, ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, ifeq(class_Ring__and__Field_Opordered__semiring(t_b), true, c_lessequals(c_times(c_HOL_Oabs(v_a(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true), true), true), true)
% 4.17/0.91 = { by axiom 3 (ifeq_axiom_001) R->L }
% 4.17/0.91 ifeq(ifeq(ifeq(true, true, class_Ring__and__Field_Opordered__cancel__semiring(t_b), true), true, ifeq(c_lessequals(c_0, v_c, t_b), true, ifeq(true, true, c_lessequals(c_0, c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), t_b), true), true), true), true, ifeq(c_lessequals(c_0, c_HOL_Oabs(v_b(v_x), t_b), t_b), true, ifeq(true, true, ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, ifeq(class_Ring__and__Field_Opordered__semiring(t_b), true, c_lessequals(c_times(c_HOL_Oabs(v_a(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true), true), true), true)
% 4.17/0.91 = { by axiom 1 (tfree_tcs) R->L }
% 4.17/0.91 ifeq(ifeq(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_Ring__and__Field_Opordered__cancel__semiring(t_b), true), true, ifeq(c_lessequals(c_0, v_c, t_b), true, ifeq(true, true, c_lessequals(c_0, c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), t_b), true), true), true), true, ifeq(c_lessequals(c_0, c_HOL_Oabs(v_b(v_x), t_b), t_b), true, ifeq(true, true, ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, ifeq(class_Ring__and__Field_Opordered__semiring(t_b), true, c_lessequals(c_times(c_HOL_Oabs(v_a(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true), true), true), true)
% 4.17/0.91 = { by axiom 7 (clsrel_Ring__and__Field_Oordered__idom_40) }
% 4.17/0.91 ifeq(ifeq(true, true, ifeq(c_lessequals(c_0, v_c, t_b), true, ifeq(true, true, c_lessequals(c_0, c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), t_b), true), true), true), true, ifeq(c_lessequals(c_0, c_HOL_Oabs(v_b(v_x), t_b), t_b), true, ifeq(true, true, ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, ifeq(class_Ring__and__Field_Opordered__semiring(t_b), true, c_lessequals(c_times(c_HOL_Oabs(v_a(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true), true), true), true)
% 4.17/0.91 = { by axiom 3 (ifeq_axiom_001) }
% 4.17/0.91 ifeq(ifeq(c_lessequals(c_0, v_c, t_b), true, ifeq(true, true, c_lessequals(c_0, c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), t_b), true), true), true, ifeq(c_lessequals(c_0, c_HOL_Oabs(v_b(v_x), t_b), t_b), true, ifeq(true, true, ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, ifeq(class_Ring__and__Field_Opordered__semiring(t_b), true, c_lessequals(c_times(c_HOL_Oabs(v_a(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true), true), true), true)
% 4.17/0.91 = { by axiom 3 (ifeq_axiom_001) }
% 4.17/0.91 ifeq(ifeq(c_lessequals(c_0, v_c, t_b), true, c_lessequals(c_0, c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), t_b), true), true, ifeq(c_lessequals(c_0, c_HOL_Oabs(v_b(v_x), t_b), t_b), true, ifeq(true, true, ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, ifeq(class_Ring__and__Field_Opordered__semiring(t_b), true, c_lessequals(c_times(c_HOL_Oabs(v_a(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true), true), true), true)
% 4.17/0.91 = { by axiom 3 (ifeq_axiom_001) R->L }
% 4.17/0.91 ifeq(ifeq(ifeq(true, true, c_lessequals(c_0, v_c, t_b), true), true, c_lessequals(c_0, c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), t_b), true), true, ifeq(c_lessequals(c_0, c_HOL_Oabs(v_b(v_x), t_b), t_b), true, ifeq(true, true, ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, ifeq(class_Ring__and__Field_Opordered__semiring(t_b), true, c_lessequals(c_times(c_HOL_Oabs(v_a(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true), true), true), true)
% 4.17/0.91 = { by axiom 8 (clsrel_OrderedGroup_Olordered__ab__group__abs_17) R->L }
% 4.17/0.91 ifeq(ifeq(ifeq(ifeq(class_OrderedGroup_Olordered__ab__group__abs(t_b), true, class_Orderings_Oorder(t_b), true), true, c_lessequals(c_0, v_c, t_b), true), true, c_lessequals(c_0, c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), t_b), true), true, ifeq(c_lessequals(c_0, c_HOL_Oabs(v_b(v_x), t_b), t_b), true, ifeq(true, true, ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, ifeq(class_Ring__and__Field_Opordered__semiring(t_b), true, c_lessequals(c_times(c_HOL_Oabs(v_a(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true), true), true), true)
% 4.17/0.91 = { by lemma 17 }
% 4.17/0.91 ifeq(ifeq(ifeq(ifeq(true, true, class_Orderings_Oorder(t_b), true), true, c_lessequals(c_0, v_c, t_b), true), true, c_lessequals(c_0, c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), t_b), true), true, ifeq(c_lessequals(c_0, c_HOL_Oabs(v_b(v_x), t_b), t_b), true, ifeq(true, true, ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, ifeq(class_Ring__and__Field_Opordered__semiring(t_b), true, c_lessequals(c_times(c_HOL_Oabs(v_a(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true), true), true), true)
% 4.17/0.91 = { by axiom 3 (ifeq_axiom_001) }
% 4.17/0.91 ifeq(ifeq(ifeq(class_Orderings_Oorder(t_b), true, c_lessequals(c_0, v_c, t_b), true), true, c_lessequals(c_0, c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), t_b), true), true, ifeq(c_lessequals(c_0, c_HOL_Oabs(v_b(v_x), t_b), t_b), true, ifeq(true, true, ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, ifeq(class_Ring__and__Field_Opordered__semiring(t_b), true, c_lessequals(c_times(c_HOL_Oabs(v_a(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true), true), true), true)
% 4.17/0.91 = { by axiom 3 (ifeq_axiom_001) R->L }
% 4.17/0.91 ifeq(ifeq(ifeq(true, true, ifeq(class_Orderings_Oorder(t_b), true, c_lessequals(c_0, v_c, t_b), true), true), true, c_lessequals(c_0, c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), t_b), true), true, ifeq(c_lessequals(c_0, c_HOL_Oabs(v_b(v_x), t_b), t_b), true, ifeq(true, true, ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, ifeq(class_Ring__and__Field_Opordered__semiring(t_b), true, c_lessequals(c_times(c_HOL_Oabs(v_a(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true), true), true), true)
% 4.17/0.91 = { by axiom 2 (cls_conjecture_0) R->L }
% 4.17/0.91 ifeq(ifeq(ifeq(c_less(c_0, v_c, t_b), true, ifeq(class_Orderings_Oorder(t_b), true, c_lessequals(c_0, v_c, t_b), true), true), true, c_lessequals(c_0, c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), t_b), true), true, ifeq(c_lessequals(c_0, c_HOL_Oabs(v_b(v_x), t_b), t_b), true, ifeq(true, true, ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, ifeq(class_Ring__and__Field_Opordered__semiring(t_b), true, c_lessequals(c_times(c_HOL_Oabs(v_a(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true), true), true), true)
% 4.17/0.91 = { by axiom 13 (cls_Orderings_Oorder__less__imp__le_0) }
% 4.17/0.91 ifeq(ifeq(true, true, c_lessequals(c_0, c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), t_b), true), true, ifeq(c_lessequals(c_0, c_HOL_Oabs(v_b(v_x), t_b), t_b), true, ifeq(true, true, ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, ifeq(class_Ring__and__Field_Opordered__semiring(t_b), true, c_lessequals(c_times(c_HOL_Oabs(v_a(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true), true), true), true)
% 4.17/0.91 = { by axiom 3 (ifeq_axiom_001) }
% 4.17/0.91 ifeq(c_lessequals(c_0, c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), t_b), true, ifeq(c_lessequals(c_0, c_HOL_Oabs(v_b(v_x), t_b), t_b), true, ifeq(true, true, ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, ifeq(class_Ring__and__Field_Opordered__semiring(t_b), true, c_lessequals(c_times(c_HOL_Oabs(v_a(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true), true), true), true)
% 4.17/0.92 = { by axiom 10 (cls_conjecture_2) R->L }
% 4.17/0.92 ifeq(c_lessequals(c_0, c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), t_b), true, ifeq(c_lessequals(c_0, c_HOL_Oabs(v_b(v_x), t_b), t_b), true, ifeq(c_lessequals(c_HOL_Oabs(v_a(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), t_b), true, ifeq(c_lessequals(c_HOL_Oabs(v_b(v_x), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), true, ifeq(class_Ring__and__Field_Opordered__semiring(t_b), true, c_lessequals(c_times(c_HOL_Oabs(v_a(v_x), t_b), c_HOL_Oabs(v_b(v_x), t_b), t_b), c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b), true), true), true), true), true)
% 4.17/0.92 = { by axiom 16 (cls_Ring__and__Field_Omult__mono_0) }
% 4.17/0.92 true
% 4.17/0.92 % SZS output end Proof
% 4.17/0.92
% 4.17/0.92 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------