TSTP Solution File: ALG370-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : ALG370-1 : 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 : n032.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 16:43:05 EDT 2023
% Result : Unsatisfiable 60.49s 8.13s
% Output : Proof 60.49s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : ALG370-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.30 % Computer : n032.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Mon Aug 28 05:08:00 EDT 2023
% 0.12/0.30 % CPUTime :
% 60.49/8.13 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 60.49/8.13
% 60.49/8.13 % SZS status Unsatisfiable
% 60.49/8.13
% 60.49/8.13 % SZS output start Proof
% 60.49/8.13 Take the following subset of the input axioms:
% 60.49/8.13 fof(cls_CHAINED_0, axiom, c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_da____, v_m____, tc_RealDef_Oreal), v_e, tc_RealDef_Oreal)).
% 60.49/8.13 fof(cls_CHAINED_0_01, axiom, c_lessequals(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_w____, v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____, c_HOL_Ominus__class_Ominus(v_w____, v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(v_da____, v_m____, tc_RealDef_Oreal), tc_RealDef_Oreal)).
% 60.49/8.13 fof(cls_conjecture_0, negated_conjecture, ~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_w____, v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____, c_HOL_Ominus__class_Ominus(v_w____, v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), v_e, tc_RealDef_Oreal)).
% 60.49/8.13 fof(cls_xt1_I7_J_0, axiom, ![T_a, V_x, V_y, V_z]: (~class_Orderings_Oorder(T_a) | (c_HOL_Oord__class_Oless(V_z, V_x, T_a) | (~c_lessequals(V_z, V_y, T_a) | ~c_HOL_Oord__class_Oless(V_y, V_x, T_a))))).
% 60.49/8.13 fof(clsarity_RealDef__Oreal__Orderings_Oorder, axiom, class_Orderings_Oorder(tc_RealDef_Oreal)).
% 60.49/8.13
% 60.49/8.13 Now clausify the problem and encode Horn clauses using encoding 3 of
% 60.49/8.13 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 60.49/8.13 We repeatedly replace C & s=t => u=v by the two clauses:
% 60.49/8.13 fresh(y, y, x1...xn) = u
% 60.49/8.13 C => fresh(s, t, x1...xn) = v
% 60.49/8.13 where fresh is a fresh function symbol and x1..xn are the free
% 60.49/8.13 variables of u and v.
% 60.49/8.13 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 60.49/8.13 input problem has no model of domain size 1).
% 60.49/8.13
% 60.49/8.13 The encoding turns the above axioms into the following unit equations and goals:
% 60.49/8.13
% 60.49/8.13 Axiom 1 (clsarity_RealDef__Oreal__Orderings_Oorder): class_Orderings_Oorder(tc_RealDef_Oreal) = true2.
% 60.49/8.13 Axiom 2 (cls_CHAINED_0): c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_da____, v_m____, tc_RealDef_Oreal), v_e, tc_RealDef_Oreal) = true2.
% 60.49/8.13 Axiom 3 (cls_xt1_I7_J_0): fresh674(X, X, Y, Z, W) = true2.
% 60.49/8.13 Axiom 4 (cls_xt1_I7_J_0): fresh130(X, X, Y, Z, W, V) = c_HOL_Oord__class_Oless(Z, W, Y).
% 60.49/8.13 Axiom 5 (cls_xt1_I7_J_0): fresh673(X, X, Y, Z, W, V) = fresh674(c_HOL_Oord__class_Oless(V, W, Y), true2, Y, Z, W).
% 60.49/8.13 Axiom 6 (cls_xt1_I7_J_0): fresh673(class_Orderings_Oorder(X), true2, X, Y, Z, W) = fresh130(c_lessequals(Y, W, X), true2, X, Y, Z, W).
% 60.49/8.13 Axiom 7 (cls_CHAINED_0_01): c_lessequals(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_w____, v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____, c_HOL_Ominus__class_Ominus(v_w____, v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(v_da____, v_m____, tc_RealDef_Oreal), tc_RealDef_Oreal) = true2.
% 60.49/8.13
% 60.49/8.13 Goal 1 (cls_conjecture_0): c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_w____, v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____, c_HOL_Ominus__class_Ominus(v_w____, v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), v_e, tc_RealDef_Oreal) = true2.
% 60.49/8.13 Proof:
% 60.49/8.13 c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_w____, v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____, c_HOL_Ominus__class_Ominus(v_w____, v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), v_e, tc_RealDef_Oreal)
% 60.49/8.13 = { by axiom 4 (cls_xt1_I7_J_0) R->L }
% 60.49/8.13 fresh130(true2, true2, tc_RealDef_Oreal, c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_w____, v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____, c_HOL_Ominus__class_Ominus(v_w____, v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), v_e, c_HOL_Otimes__class_Otimes(v_da____, v_m____, tc_RealDef_Oreal))
% 60.49/8.13 = { by axiom 7 (cls_CHAINED_0_01) R->L }
% 60.49/8.13 fresh130(c_lessequals(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_w____, v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____, c_HOL_Ominus__class_Ominus(v_w____, v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(v_da____, v_m____, tc_RealDef_Oreal), tc_RealDef_Oreal), true2, tc_RealDef_Oreal, c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_w____, v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____, c_HOL_Ominus__class_Ominus(v_w____, v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), v_e, c_HOL_Otimes__class_Otimes(v_da____, v_m____, tc_RealDef_Oreal))
% 60.49/8.13 = { by axiom 6 (cls_xt1_I7_J_0) R->L }
% 60.49/8.13 fresh673(class_Orderings_Oorder(tc_RealDef_Oreal), true2, tc_RealDef_Oreal, c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_w____, v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____, c_HOL_Ominus__class_Ominus(v_w____, v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), v_e, c_HOL_Otimes__class_Otimes(v_da____, v_m____, tc_RealDef_Oreal))
% 60.49/8.13 = { by axiom 1 (clsarity_RealDef__Oreal__Orderings_Oorder) }
% 60.49/8.13 fresh673(true2, true2, tc_RealDef_Oreal, c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_w____, v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____, c_HOL_Ominus__class_Ominus(v_w____, v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), v_e, c_HOL_Otimes__class_Otimes(v_da____, v_m____, tc_RealDef_Oreal))
% 60.49/8.13 = { by axiom 5 (cls_xt1_I7_J_0) }
% 60.49/8.13 fresh674(c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_da____, v_m____, tc_RealDef_Oreal), v_e, tc_RealDef_Oreal), true2, tc_RealDef_Oreal, c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_w____, v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____, c_HOL_Ominus__class_Ominus(v_w____, v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), v_e)
% 60.49/8.13 = { by axiom 2 (cls_CHAINED_0) }
% 60.49/8.13 fresh674(true2, true2, tc_RealDef_Oreal, c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_w____, v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____, c_HOL_Ominus__class_Ominus(v_w____, v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), v_e)
% 60.49/8.13 = { by axiom 3 (cls_xt1_I7_J_0) }
% 60.49/8.13 true2
% 60.49/8.13 % SZS output end Proof
% 60.49/8.13
% 60.49/8.13 RESULT: Unsatisfiable (the axioms are contradictory).
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