TSTP Solution File: ALG373-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ALG373-1 : 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 : n025.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 16:43:06 EDT 2023
% Result : Unsatisfiable 43.18s 5.97s
% Output : Proof 43.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ALG373-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.35 % Computer : n025.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon Aug 28 06:07:54 EDT 2023
% 0.15/0.36 % CPUTime :
% 43.18/5.97 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 43.18/5.97
% 43.18/5.97 % SZS status Unsatisfiable
% 43.18/5.97
% 43.18/5.97 % SZS output start Proof
% 43.18/5.97 Take the following subset of the input axioms:
% 43.18/5.97 fof(cls_CHAINED_0, axiom, ![V_x, V_z]: (c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p, V_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex)!=c_HOL_Ouminus__class_Ouminus(V_x, tc_RealDef_Oreal) | (~c_lessequals(c_RealVector_Onorm__class_Onorm(V_z, tc_Complex_Ocomplex), v_r, tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(V_x, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)))).
% 43.18/5.97 fof(cls_abs__not__less__zero_0, axiom, ![T_a, V_a]: (~class_OrderedGroup_Opordered__ab__group__add__abs(T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a, T_a), c_HOL_Ozero__class_Ozero(T_a), T_a))).
% 43.18/5.97 fof(cls_conjecture_0, negated_conjecture, ![V_xb]: c_lessequals(c_RealVector_Onorm__class_Onorm(v_xa(V_xb), tc_Complex_Ocomplex), v_r, tc_RealDef_Oreal)).
% 43.18/5.97 fof(cls_conjecture_1, negated_conjecture, ![V_xb2]: c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p, v_xa(V_xb2), tc_Complex_Ocomplex), tc_Complex_Ocomplex)=c_HOL_Ouminus__class_Ouminus(v_x(V_xb2), tc_RealDef_Oreal)).
% 43.18/5.97 fof(cls_conjecture_2, negated_conjecture, ![V_xb2]: ~c_HOL_Oord__class_Oless(v_x(V_xb2), V_xb2, tc_RealDef_Oreal)).
% 43.18/5.97 fof(cls_le__number__of__eq__not__less_0, axiom, ![V_v, V_w, T_a2]: (~class_Orderings_Olinorder(T_a2) | (~class_Int_Onumber(T_a2) | (~c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w, T_a2), c_Int_Onumber__class_Onumber__of(V_v, T_a2), T_a2) | ~c_lessequals(c_Int_Onumber__class_Onumber__of(V_v, T_a2), c_Int_Onumber__class_Onumber__of(V_w, T_a2), T_a2))))).
% 43.18/5.97 fof(cls_less__le__not__le_1, axiom, ![V_y, T_a2, V_x2]: (~class_Orderings_Opreorder(T_a2) | (~c_lessequals(V_y, V_x2, T_a2) | ~c_HOL_Oord__class_Oless(V_x2, V_y, T_a2)))).
% 43.18/5.97 fof(cls_linorder__antisym__conv2_1, axiom, ![T_a2, V_x2]: (~class_Orderings_Olinorder(T_a2) | (~c_lessequals(V_x2, V_x2, T_a2) | ~c_HOL_Oord__class_Oless(V_x2, V_x2, T_a2)))).
% 43.18/5.97 fof(cls_linorder__neq__iff_1, axiom, ![T_a2, V_x2]: (~class_Orderings_Olinorder(T_a2) | ~c_HOL_Oord__class_Oless(V_x2, V_x2, T_a2))).
% 43.96/5.97 fof(cls_linorder__not__le_1, axiom, ![T_a2, V_x2, V_y2]: (~class_Orderings_Olinorder(T_a2) | (~c_lessequals(V_x2, V_y2, T_a2) | ~c_HOL_Oord__class_Oless(V_y2, V_x2, T_a2)))).
% 43.96/5.97 fof(cls_linorder__not__less_1, axiom, ![T_a2, V_x2, V_y2]: (~class_Orderings_Olinorder(T_a2) | (~c_HOL_Oord__class_Oless(V_x2, V_y2, T_a2) | ~c_lessequals(V_y2, V_x2, T_a2)))).
% 43.96/5.97 fof(cls_norm__not__less__zero_0, axiom, ![T_a2, V_x2]: (~class_RealVector_Oreal__normed__vector(T_a2) | ~c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_x2, T_a2), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal))).
% 43.96/5.97 fof(cls_not__less__iff__gr__or__eq_1, axiom, ![T_a2, V_x2, V_y2]: (~class_Orderings_Olinorder(T_a2) | (~c_HOL_Oord__class_Oless(V_x2, V_y2, T_a2) | ~c_HOL_Oord__class_Oless(V_y2, V_x2, T_a2)))).
% 43.96/5.97 fof(cls_not__square__less__zero_0, axiom, ![T_a2, V_a2]: (~class_Ring__and__Field_Oordered__ring__strict(T_a2) | ~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a2, V_a2, T_a2), c_HOL_Ozero__class_Ozero(T_a2), T_a2))).
% 43.96/5.97 fof(cls_order__less__asym_0, axiom, ![T_a2, V_x2, V_y2]: (~class_Orderings_Opreorder(T_a2) | (~c_HOL_Oord__class_Oless(V_y2, V_x2, T_a2) | ~c_HOL_Oord__class_Oless(V_x2, V_y2, T_a2)))).
% 43.96/5.97 fof(cls_order__less__asym_H_0, axiom, ![V_b, T_a2, V_a2]: (~class_Orderings_Opreorder(T_a2) | (~c_HOL_Oord__class_Oless(V_b, V_a2, T_a2) | ~c_HOL_Oord__class_Oless(V_a2, V_b, T_a2)))).
% 43.96/5.97 fof(cls_order__less__irrefl_0, axiom, ![T_a2, V_x2]: (~class_Orderings_Opreorder(T_a2) | ~c_HOL_Oord__class_Oless(V_x2, V_x2, T_a2))).
% 43.96/5.97 fof(cls_order__less__le_1, axiom, ![T_a2, V_x2]: (~class_Orderings_Oorder(T_a2) | ~c_HOL_Oord__class_Oless(V_x2, V_x2, T_a2))).
% 43.96/5.97 fof(cls_real__less__def_1, axiom, ![V_x2]: ~c_HOL_Oord__class_Oless(V_x2, V_x2, tc_RealDef_Oreal)).
% 43.96/5.97 fof(cls_xt1_I9_J_0, axiom, ![T_a2, V_a2, V_b2]: (~class_Orderings_Oorder(T_a2) | (~c_HOL_Oord__class_Oless(V_a2, V_b2, T_a2) | ~c_HOL_Oord__class_Oless(V_b2, V_a2, T_a2)))).
% 43.96/5.97 fof(cls_zero__less__abs__iff_0, axiom, ![T_a2]: (~class_OrderedGroup_Opordered__ab__group__add__abs(T_a2) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a2), c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a2), T_a2), T_a2))).
% 43.96/5.97 fof(cls_zero__less__norm__iff_0, axiom, ![T_a2]: (~class_RealVector_Oreal__normed__vector(T_a2) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(T_a2), T_a2), tc_RealDef_Oreal))).
% 43.96/5.97
% 43.96/5.97 Now clausify the problem and encode Horn clauses using encoding 3 of
% 43.96/5.97 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 43.96/5.97 We repeatedly replace C & s=t => u=v by the two clauses:
% 43.96/5.97 fresh(y, y, x1...xn) = u
% 43.96/5.97 C => fresh(s, t, x1...xn) = v
% 43.96/5.97 where fresh is a fresh function symbol and x1..xn are the free
% 43.96/5.97 variables of u and v.
% 43.96/5.97 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 43.96/5.97 input problem has no model of domain size 1).
% 43.96/5.97
% 43.96/5.97 The encoding turns the above axioms into the following unit equations and goals:
% 43.96/5.97
% 43.96/5.97 Axiom 1 (cls_CHAINED_0): fresh353(X, X, Y) = true2.
% 43.96/5.97 Axiom 2 (cls_CHAINED_0): fresh352(X, X, Y, Z) = c_HOL_Oord__class_Oless(Z, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal).
% 43.96/5.97 Axiom 3 (cls_conjecture_0): c_lessequals(c_RealVector_Onorm__class_Onorm(v_xa(X), tc_Complex_Ocomplex), v_r, tc_RealDef_Oreal) = true2.
% 43.96/5.97 Axiom 4 (cls_conjecture_1): c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p, v_xa(X), tc_Complex_Ocomplex), tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_x(X), tc_RealDef_Oreal).
% 43.96/5.97 Axiom 5 (cls_CHAINED_0): fresh352(c_lessequals(c_RealVector_Onorm__class_Onorm(X, tc_Complex_Ocomplex), v_r, tc_RealDef_Oreal), true2, X, Y) = fresh353(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p, X, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ouminus__class_Ouminus(Y, tc_RealDef_Oreal), Y).
% 43.96/5.97
% 43.96/5.97 Goal 1 (cls_conjecture_2): c_HOL_Oord__class_Oless(v_x(X), X, tc_RealDef_Oreal) = true2.
% 43.96/5.97 The goal is true when:
% 43.96/5.97 X = c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
% 43.96/5.97
% 43.96/5.97 Proof:
% 43.96/5.97 c_HOL_Oord__class_Oless(v_x(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)), c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)
% 43.96/5.97 = { by axiom 2 (cls_CHAINED_0) R->L }
% 43.96/5.97 fresh352(true2, true2, v_xa(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)), v_x(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)))
% 43.96/5.97 = { by axiom 3 (cls_conjecture_0) R->L }
% 43.96/5.97 fresh352(c_lessequals(c_RealVector_Onorm__class_Onorm(v_xa(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)), tc_Complex_Ocomplex), v_r, tc_RealDef_Oreal), true2, v_xa(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)), v_x(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)))
% 43.96/5.97 = { by axiom 5 (cls_CHAINED_0) }
% 43.96/5.97 fresh353(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p, v_xa(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ouminus__class_Ouminus(v_x(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)), tc_RealDef_Oreal), v_x(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)))
% 43.96/5.97 = { by axiom 4 (cls_conjecture_1) }
% 43.96/5.97 fresh353(c_HOL_Ouminus__class_Ouminus(v_x(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)), tc_RealDef_Oreal), c_HOL_Ouminus__class_Ouminus(v_x(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)), tc_RealDef_Oreal), v_x(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)))
% 43.96/5.97 = { by axiom 1 (cls_CHAINED_0) }
% 43.96/5.97 true2
% 43.96/5.97 % SZS output end Proof
% 43.96/5.97
% 43.96/5.97 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------