TSTP Solution File: ALG379-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ALG379-1 : TPTP v8.1.2. Released v4.1.0.
% 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 : n026.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 16:43:07 EDT 2023
% Result : Unsatisfiable 77.40s 10.37s
% Output : Proof 77.40s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG379-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n026.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 : Mon Aug 28 04:13:49 EDT 2023
% 0.13/0.35 % CPUTime :
% 77.40/10.37 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 77.40/10.37
% 77.40/10.37 % SZS status Unsatisfiable
% 77.40/10.37
% 77.40/10.38 % SZS output start Proof
% 77.40/10.38 Take the following subset of the input axioms:
% 77.40/10.38 fof(cls_CHAINED_0, axiom, c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p, v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)=c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 77.40/10.38 fof(cls_abs__eq__0_0, axiom, ![T_a, V_a]: (~class_OrderedGroup_Opordered__ab__group__add__abs(T_a) | (c_HOL_Oabs__class_Oabs(V_a, T_a)!=c_HOL_Ozero__class_Ozero(T_a) | V_a=c_HOL_Ozero__class_Ozero(T_a)))).
% 77.40/10.38 fof(cls_add__0__left_0, axiom, ![T_a2, V_a2]: (~class_OrderedGroup_Omonoid__add(T_a2) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a2), V_a2, T_a2)=V_a2)).
% 77.40/10.38 fof(cls_conjecture_0, negated_conjecture, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p, v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)!=c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal)).
% 77.40/10.38 fof(cls_diff__add__cancel_0, axiom, ![V_b, T_a2, V_a2]: (~class_OrderedGroup_Ogroup__add(T_a2) | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a2, V_b, T_a2), V_b, T_a2)=V_a2)).
% 77.40/10.38 fof(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add, axiom, class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)).
% 77.40/10.38 fof(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add, axiom, class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal)).
% 77.40/10.38 fof(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs, axiom, class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)).
% 77.40/10.38
% 77.40/10.38 Now clausify the problem and encode Horn clauses using encoding 3 of
% 77.40/10.38 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 77.40/10.38 We repeatedly replace C & s=t => u=v by the two clauses:
% 77.40/10.38 fresh(y, y, x1...xn) = u
% 77.40/10.38 C => fresh(s, t, x1...xn) = v
% 77.40/10.38 where fresh is a fresh function symbol and x1..xn are the free
% 77.40/10.38 variables of u and v.
% 77.40/10.38 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 77.40/10.38 input problem has no model of domain size 1).
% 77.40/10.38
% 77.40/10.38 The encoding turns the above axioms into the following unit equations and goals:
% 77.40/10.38
% 77.40/10.38 Axiom 1 (clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs): class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) = true2.
% 77.40/10.38 Axiom 2 (clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add): class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) = true2.
% 77.40/10.38 Axiom 3 (clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add): class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal) = true2.
% 77.40/10.38 Axiom 4 (cls_abs__eq__0_0): fresh854(X, X, Y, Z) = c_HOL_Ozero__class_Ozero(Y).
% 77.40/10.38 Axiom 5 (cls_add__0__left_0): fresh33(X, X, Y, Z) = Z.
% 77.40/10.38 Axiom 6 (cls_abs__eq__0_0): fresh23(X, X, Y, Z) = Z.
% 77.40/10.38 Axiom 7 (cls_diff__add__cancel_0): fresh54(X, X, Y, Z, W) = Z.
% 77.40/10.38 Axiom 8 (cls_add__0__left_0): fresh33(class_OrderedGroup_Omonoid__add(X), true2, X, Y) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X), Y, X).
% 77.40/10.38 Axiom 9 (cls_diff__add__cancel_0): fresh54(class_OrderedGroup_Ogroup__add(X), true2, X, Y, Z) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(Y, Z, X), Z, X).
% 77.40/10.38 Axiom 10 (cls_abs__eq__0_0): fresh854(class_OrderedGroup_Opordered__ab__group__add__abs(X), true2, X, Y) = fresh23(c_HOL_Oabs__class_Oabs(Y, X), c_HOL_Ozero__class_Ozero(X), X, Y).
% 77.40/10.38 Axiom 11 (cls_CHAINED_0): c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p, v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).
% 77.40/10.38
% 77.40/10.38 Goal 1 (cls_conjecture_0): c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p, v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal).
% 77.40/10.38 Proof:
% 77.40/10.38 c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p, v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 77.40/10.38 = { by axiom 7 (cls_diff__add__cancel_0) R->L }
% 77.40/10.38 fresh54(true2, true2, tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p, v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal))
% 77.40/10.38 = { by axiom 2 (clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) R->L }
% 77.40/10.38 fresh54(class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), true2, tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p, v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal))
% 77.40/10.38 = { by axiom 9 (cls_diff__add__cancel_0) }
% 77.40/10.38 c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p, v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal), tc_RealDef_Oreal)
% 77.40/10.38 = { by axiom 6 (cls_abs__eq__0_0) R->L }
% 77.40/10.38 c_HOL_Oplus__class_Oplus(fresh23(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p, v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal), tc_RealDef_Oreal)), c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal), tc_RealDef_Oreal)
% 77.40/10.38 = { by axiom 11 (cls_CHAINED_0) R->L }
% 77.40/10.38 c_HOL_Oplus__class_Oplus(fresh23(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p, v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p, v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal), tc_RealDef_Oreal)), c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal), tc_RealDef_Oreal)
% 77.40/10.38 = { by axiom 10 (cls_abs__eq__0_0) R->L }
% 77.40/10.38 c_HOL_Oplus__class_Oplus(fresh854(class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal), true2, tc_RealDef_Oreal, c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p, v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal), tc_RealDef_Oreal)), c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal), tc_RealDef_Oreal)
% 77.40/10.38 = { by axiom 1 (clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) }
% 77.40/10.38 c_HOL_Oplus__class_Oplus(fresh854(true2, true2, tc_RealDef_Oreal, c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p, v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal), tc_RealDef_Oreal)), c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal), tc_RealDef_Oreal)
% 77.40/10.38 = { by axiom 4 (cls_abs__eq__0_0) }
% 77.40/10.38 c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal), tc_RealDef_Oreal)
% 77.40/10.38 = { by axiom 8 (cls_add__0__left_0) R->L }
% 77.40/10.38 fresh33(class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal), true2, tc_RealDef_Oreal, c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal))
% 77.40/10.38 = { by axiom 3 (clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) }
% 77.40/10.38 fresh33(true2, true2, tc_RealDef_Oreal, c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal))
% 77.40/10.38 = { by axiom 5 (cls_add__0__left_0) }
% 77.40/10.38 c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal)
% 77.40/10.38 % SZS output end Proof
% 77.40/10.38
% 77.40/10.38 RESULT: Unsatisfiable (the axioms are contradictory).
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