TSTP Solution File: ANA023-10 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ANA023-10 : TPTP v8.1.2. Released v7.5.0.
% 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 : n007.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 17:21:06 EDT 2023
% Result : Unsatisfiable 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ANA023-10 : TPTP v8.1.2. Released v7.5.0.
% 0.13/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 18:23:26 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.40 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.40
% 0.20/0.40 % SZS status Unsatisfiable
% 0.20/0.40
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 Axiom 1 (tfree_tcs): class_Ring__and__Field_Oordered__idom(t_b) = true.
% 0.20/0.41 Axiom 2 (ifeq_axiom_001): ifeq(X, X, Y, Z) = Y.
% 0.20/0.41 Axiom 3 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.20/0.41 Axiom 4 (cls_conjecture_2): c_lessequals(v_k(v_x), v_f(v_x), t_b) = true.
% 0.20/0.41 Axiom 5 (clsrel_Ring__and__Field_Oordered__idom_54): ifeq(class_Ring__and__Field_Oordered__idom(X), true, class_OrderedGroup_Opordered__ab__group__add(X), true) = true.
% 0.20/0.41 Axiom 6 (clsrel_Ring__and__Field_Oordered__idom_23): ifeq(class_Ring__and__Field_Oordered__idom(X), true, class_OrderedGroup_Ocomm__monoid__add(X), true) = true.
% 0.20/0.41 Axiom 7 (clsrel_Ring__and__Field_Oordered__idom_33): ifeq(class_Ring__and__Field_Oordered__idom(X), true, class_Orderings_Olinorder(X), true) = true.
% 0.20/0.41 Axiom 8 (clsrel_Orderings_Olinorder_4): ifeq(class_Orderings_Olinorder(X), true, class_Orderings_Oorder(X), true) = true.
% 0.20/0.41 Axiom 9 (cls_conjecture_1): c_lessequals(c_0, c_minus(v_k(v_x), v_g(v_x), t_b), t_b) = true.
% 0.20/0.41 Axiom 10 (cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0): ifeq2(class_OrderedGroup_Ocomm__monoid__add(X), true, c_plus(c_0, Y, X), Y) = Y.
% 0.20/0.41 Axiom 11 (cls_OrderedGroup_Ocompare__rls__9_0): ifeq(class_OrderedGroup_Opordered__ab__group__add(X), true, ifeq(c_lessequals(Y, c_minus(Z, W, X), X), true, c_lessequals(c_plus(Y, W, X), Z, X), true), true) = true.
% 0.20/0.41 Axiom 12 (cls_OrderedGroup_Ocompare__rls__9_1): ifeq(class_OrderedGroup_Opordered__ab__group__add(X), true, ifeq(c_lessequals(c_plus(Y, Z, X), W, X), true, c_lessequals(Y, c_minus(W, Z, X), X), true), true) = true.
% 0.20/0.41 Axiom 13 (cls_Orderings_Oorder__class_Oorder__trans_0): ifeq(class_Orderings_Oorder(X), true, ifeq(c_lessequals(Y, Z, X), true, ifeq(c_lessequals(Z, W, X), true, c_lessequals(Y, W, X), true), true), true) = true.
% 0.20/0.41
% 0.20/0.41 Lemma 14: class_OrderedGroup_Opordered__ab__group__add(t_b) = true.
% 0.20/0.41 Proof:
% 0.20/0.41 class_OrderedGroup_Opordered__ab__group__add(t_b)
% 0.20/0.41 = { by axiom 2 (ifeq_axiom_001) R->L }
% 0.20/0.41 ifeq(true, true, class_OrderedGroup_Opordered__ab__group__add(t_b), true)
% 0.20/0.41 = { by axiom 1 (tfree_tcs) R->L }
% 0.20/0.41 ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Opordered__ab__group__add(t_b), true)
% 0.20/0.41 = { by axiom 5 (clsrel_Ring__and__Field_Oordered__idom_54) }
% 0.20/0.41 true
% 0.20/0.41
% 0.20/0.41 Lemma 15: c_plus(c_0, X, t_b) = X.
% 0.20/0.41 Proof:
% 0.20/0.41 c_plus(c_0, X, t_b)
% 0.20/0.41 = { by axiom 3 (ifeq_axiom) R->L }
% 0.20/0.41 ifeq2(true, true, c_plus(c_0, X, t_b), X)
% 0.20/0.41 = { by axiom 6 (clsrel_Ring__and__Field_Oordered__idom_23) R->L }
% 0.20/0.41 ifeq2(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Ocomm__monoid__add(t_b), true), true, c_plus(c_0, X, t_b), X)
% 0.20/0.41 = { by axiom 1 (tfree_tcs) }
% 0.20/0.41 ifeq2(ifeq(true, true, class_OrderedGroup_Ocomm__monoid__add(t_b), true), true, c_plus(c_0, X, t_b), X)
% 0.20/0.41 = { by axiom 2 (ifeq_axiom_001) }
% 0.20/0.41 ifeq2(class_OrderedGroup_Ocomm__monoid__add(t_b), true, c_plus(c_0, X, t_b), X)
% 0.20/0.41 = { by axiom 10 (cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) }
% 0.20/0.41 X
% 0.20/0.41
% 0.20/0.41 Goal 1 (cls_conjecture_3): c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b) = true.
% 0.20/0.41 Proof:
% 0.20/0.41 c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b)
% 0.20/0.41 = { by axiom 2 (ifeq_axiom_001) R->L }
% 0.20/0.41 ifeq(true, true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.20/0.41 = { by axiom 13 (cls_Orderings_Oorder__class_Oorder__trans_0) R->L }
% 0.20/0.41 ifeq(ifeq(class_Orderings_Oorder(t_b), true, ifeq(c_lessequals(v_g(v_x), v_k(v_x), t_b), true, ifeq(c_lessequals(v_k(v_x), v_f(v_x), t_b), true, c_lessequals(v_g(v_x), v_f(v_x), t_b), true), true), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.20/0.41 = { by lemma 15 R->L }
% 0.20/0.41 ifeq(ifeq(class_Orderings_Oorder(t_b), true, ifeq(c_lessequals(c_plus(c_0, v_g(v_x), t_b), v_k(v_x), t_b), true, ifeq(c_lessequals(v_k(v_x), v_f(v_x), t_b), true, c_lessequals(v_g(v_x), v_f(v_x), t_b), true), true), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.20/0.41 = { by axiom 2 (ifeq_axiom_001) R->L }
% 0.20/0.41 ifeq(ifeq(class_Orderings_Oorder(t_b), true, ifeq(ifeq(true, true, c_lessequals(c_plus(c_0, v_g(v_x), t_b), v_k(v_x), t_b), true), true, ifeq(c_lessequals(v_k(v_x), v_f(v_x), t_b), true, c_lessequals(v_g(v_x), v_f(v_x), t_b), true), true), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.20/0.41 = { by axiom 2 (ifeq_axiom_001) R->L }
% 0.20/0.41 ifeq(ifeq(class_Orderings_Oorder(t_b), true, ifeq(ifeq(true, true, ifeq(true, true, c_lessequals(c_plus(c_0, v_g(v_x), t_b), v_k(v_x), t_b), true), true), true, ifeq(c_lessequals(v_k(v_x), v_f(v_x), t_b), true, c_lessequals(v_g(v_x), v_f(v_x), t_b), true), true), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.20/0.41 = { by lemma 14 R->L }
% 0.20/0.41 ifeq(ifeq(class_Orderings_Oorder(t_b), true, ifeq(ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, ifeq(true, true, c_lessequals(c_plus(c_0, v_g(v_x), t_b), v_k(v_x), t_b), true), true), true, ifeq(c_lessequals(v_k(v_x), v_f(v_x), t_b), true, c_lessequals(v_g(v_x), v_f(v_x), t_b), true), true), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.20/0.41 = { by axiom 9 (cls_conjecture_1) R->L }
% 0.20/0.41 ifeq(ifeq(class_Orderings_Oorder(t_b), true, ifeq(ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, ifeq(c_lessequals(c_0, c_minus(v_k(v_x), v_g(v_x), t_b), t_b), true, c_lessequals(c_plus(c_0, v_g(v_x), t_b), v_k(v_x), t_b), true), true), true, ifeq(c_lessequals(v_k(v_x), v_f(v_x), t_b), true, c_lessequals(v_g(v_x), v_f(v_x), t_b), true), true), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.20/0.41 = { by axiom 11 (cls_OrderedGroup_Ocompare__rls__9_0) }
% 0.20/0.41 ifeq(ifeq(class_Orderings_Oorder(t_b), true, ifeq(true, true, ifeq(c_lessequals(v_k(v_x), v_f(v_x), t_b), true, c_lessequals(v_g(v_x), v_f(v_x), t_b), true), true), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.20/0.41 = { by axiom 2 (ifeq_axiom_001) R->L }
% 0.20/0.41 ifeq(ifeq(ifeq(true, true, class_Orderings_Oorder(t_b), true), true, ifeq(true, true, ifeq(c_lessequals(v_k(v_x), v_f(v_x), t_b), true, c_lessequals(v_g(v_x), v_f(v_x), t_b), true), true), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.20/0.41 = { by axiom 7 (clsrel_Ring__and__Field_Oordered__idom_33) R->L }
% 0.20/0.41 ifeq(ifeq(ifeq(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_Orderings_Olinorder(t_b), true), true, class_Orderings_Oorder(t_b), true), true, ifeq(true, true, ifeq(c_lessequals(v_k(v_x), v_f(v_x), t_b), true, c_lessequals(v_g(v_x), v_f(v_x), t_b), true), true), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.20/0.41 = { by axiom 1 (tfree_tcs) }
% 0.20/0.41 ifeq(ifeq(ifeq(ifeq(true, true, class_Orderings_Olinorder(t_b), true), true, class_Orderings_Oorder(t_b), true), true, ifeq(true, true, ifeq(c_lessequals(v_k(v_x), v_f(v_x), t_b), true, c_lessequals(v_g(v_x), v_f(v_x), t_b), true), true), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.20/0.41 = { by axiom 2 (ifeq_axiom_001) }
% 0.20/0.41 ifeq(ifeq(ifeq(class_Orderings_Olinorder(t_b), true, class_Orderings_Oorder(t_b), true), true, ifeq(true, true, ifeq(c_lessequals(v_k(v_x), v_f(v_x), t_b), true, c_lessequals(v_g(v_x), v_f(v_x), t_b), true), true), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.20/0.41 = { by axiom 8 (clsrel_Orderings_Olinorder_4) }
% 0.20/0.41 ifeq(ifeq(true, true, ifeq(true, true, ifeq(c_lessequals(v_k(v_x), v_f(v_x), t_b), true, c_lessequals(v_g(v_x), v_f(v_x), t_b), true), true), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.20/0.41 = { by axiom 2 (ifeq_axiom_001) }
% 0.20/0.42 ifeq(ifeq(true, true, ifeq(c_lessequals(v_k(v_x), v_f(v_x), t_b), true, c_lessequals(v_g(v_x), v_f(v_x), t_b), true), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.20/0.42 = { by axiom 2 (ifeq_axiom_001) }
% 0.20/0.42 ifeq(ifeq(c_lessequals(v_k(v_x), v_f(v_x), t_b), true, c_lessequals(v_g(v_x), v_f(v_x), t_b), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.20/0.42 = { by axiom 4 (cls_conjecture_2) }
% 0.20/0.42 ifeq(ifeq(true, true, c_lessequals(v_g(v_x), v_f(v_x), t_b), true), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.20/0.42 = { by axiom 2 (ifeq_axiom_001) }
% 0.20/0.42 ifeq(c_lessequals(v_g(v_x), v_f(v_x), t_b), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true)
% 0.20/0.42 = { by axiom 2 (ifeq_axiom_001) R->L }
% 0.20/0.42 ifeq(true, true, ifeq(c_lessequals(v_g(v_x), v_f(v_x), t_b), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true), true)
% 0.20/0.42 = { by lemma 14 R->L }
% 0.20/0.42 ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, ifeq(c_lessequals(v_g(v_x), v_f(v_x), t_b), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true), true)
% 0.20/0.42 = { by lemma 15 R->L }
% 0.20/0.42 ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b), true, ifeq(c_lessequals(c_plus(c_0, v_g(v_x), t_b), v_f(v_x), t_b), true, c_lessequals(c_0, c_minus(v_f(v_x), v_g(v_x), t_b), t_b), true), true)
% 0.20/0.42 = { by axiom 12 (cls_OrderedGroup_Ocompare__rls__9_1) }
% 0.20/0.42 true
% 0.20/0.42 % SZS output end Proof
% 0.20/0.42
% 0.20/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------