TSTP Solution File: SWW229+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SWW229+1 : TPTP v8.1.2. Released v5.2.0.
% 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 : n014.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 : Fri Sep 1 00:54:28 EDT 2023
% Result : Theorem 91.83s 12.20s
% Output : Proof 91.83s
% 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 : SWW229+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.16/0.34 % Computer : n014.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Sun Aug 27 21:23:46 EDT 2023
% 0.16/0.34 % CPUTime :
% 91.83/12.20 Command-line arguments: --no-flatten-goal
% 91.83/12.20
% 91.83/12.20 % SZS status Theorem
% 91.83/12.20
% 91.83/12.20 % SZS output start Proof
% 91.83/12.20 Take the following subset of the input axioms:
% 91.83/12.20 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector, axiom, class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)).
% 91.83/12.20 fof(conj_0, conjecture, c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), v_g____(hAPP(v_f____, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____))))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), v_z____)))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), v_g____(hAPP(v_f____, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____)))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), v_z____))))).
% 91.83/12.20 fof(fact_norm__triangle__ineq3, axiom, ![V_b, V_a, T_a]: (class_RealVector_Oreal__normed__vector(T_a) => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(T_a, V_a), c_RealVector_Onorm__class_Onorm(T_a, V_b))), c_RealVector_Onorm__class_Onorm(T_a, c_Groups_Ominus__class_Ominus(T_a, V_a, V_b))))).
% 91.83/12.20
% 91.83/12.20 Now clausify the problem and encode Horn clauses using encoding 3 of
% 91.83/12.20 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 91.83/12.20 We repeatedly replace C & s=t => u=v by the two clauses:
% 91.83/12.20 fresh(y, y, x1...xn) = u
% 91.83/12.20 C => fresh(s, t, x1...xn) = v
% 91.83/12.20 where fresh is a fresh function symbol and x1..xn are the free
% 91.83/12.20 variables of u and v.
% 91.83/12.20 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 91.83/12.20 input problem has no model of domain size 1).
% 91.83/12.20
% 91.83/12.20 The encoding turns the above axioms into the following unit equations and goals:
% 91.83/12.20
% 91.83/12.20 Axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__normed__vector): class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) = true2.
% 91.83/12.20 Axiom 2 (fact_norm__triangle__ineq3): fresh397(X, X, Y, Z, W) = true2.
% 91.83/12.20 Axiom 3 (fact_norm__triangle__ineq3): fresh397(class_RealVector_Oreal__normed__vector(X), true2, Y, Z, X) = c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(X, Z), c_RealVector_Onorm__class_Onorm(X, Y))), c_RealVector_Onorm__class_Onorm(X, c_Groups_Ominus__class_Ominus(X, Z, Y))).
% 91.83/12.20
% 91.83/12.20 Goal 1 (conj_0): c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), v_g____(hAPP(v_f____, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____))))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), v_z____)))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), v_g____(hAPP(v_f____, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____)))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), v_z____)))) = true2.
% 91.83/12.20 Proof:
% 91.83/12.20 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), v_g____(hAPP(v_f____, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____))))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), v_z____)))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), v_g____(hAPP(v_f____, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____)))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), v_z____))))
% 91.83/12.20 = { by axiom 3 (fact_norm__triangle__ineq3) R->L }
% 91.83/12.20 fresh397(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex), true2, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), v_z____), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), v_g____(hAPP(v_f____, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____)))), tc_Complex_Ocomplex)
% 91.83/12.20 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) }
% 91.83/12.20 fresh397(true2, true2, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), v_z____), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), v_g____(hAPP(v_f____, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____)))), tc_Complex_Ocomplex)
% 91.83/12.20 = { by axiom 2 (fact_norm__triangle__ineq3) }
% 91.83/12.20 true2
% 91.83/12.20 % SZS output end Proof
% 91.83/12.20
% 91.83/12.20 RESULT: Theorem (the conjecture is true).
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