TSTP Solution File: SWW229+1 by Twee---2.5.0
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% File : Twee---2.5.0
% Problem : SWW229+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% Computer : n020.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 : Mon Jun 24 18:26:36 EDT 2024
% Result : Theorem 53.38s 7.07s
% Output : Proof 53.38s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWW229+1 : TPTP v8.2.0. Released v5.2.0.
% 0.07/0.13 % Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jun 19 08:11:09 EDT 2024
% 0.13/0.34 % CPUTime :
% 53.38/7.07 Command-line arguments: --random-mode --random-mode-goal-directed --no-flatten-goal --no-connectedness --no-ground-joining
% 53.38/7.07
% 53.38/7.07 % SZS status Theorem
% 53.38/7.07
% 53.38/7.07 % SZS output start Proof
% 53.38/7.07 Take the following subset of the input axioms:
% 53.38/7.07 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector, axiom, class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)).
% 53.38/7.07 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____))))).
% 53.38/7.07 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))))).
% 53.38/7.07
% 53.38/7.07 Now clausify the problem and encode Horn clauses using encoding 3 of
% 53.38/7.07 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 53.38/7.07 We repeatedly replace C & s=t => u=v by the two clauses:
% 53.38/7.07 fresh(y, y, x1...xn) = u
% 53.38/7.07 C => fresh(s, t, x1...xn) = v
% 53.38/7.07 where fresh is a fresh function symbol and x1..xn are the free
% 53.38/7.07 variables of u and v.
% 53.38/7.07 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 53.38/7.07 input problem has no model of domain size 1).
% 53.38/7.07
% 53.38/7.07 The encoding turns the above axioms into the following unit equations and goals:
% 53.38/7.07
% 53.38/7.07 Axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__normed__vector): class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) = true2.
% 53.38/7.07 Axiom 2 (fact_norm__triangle__ineq3): fresh397(X, X, Y, Z, W) = true2.
% 53.38/7.07 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))).
% 53.38/7.07
% 53.38/7.07 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.
% 53.38/7.07 Proof:
% 53.38/7.07 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____))))
% 53.38/7.07 = { by axiom 3 (fact_norm__triangle__ineq3) R->L }
% 53.38/7.07 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)
% 53.38/7.07 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) }
% 53.38/7.07 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)
% 53.38/7.07 = { by axiom 2 (fact_norm__triangle__ineq3) }
% 53.38/7.07 true2
% 53.38/7.07 % SZS output end Proof
% 53.38/7.07
% 53.38/7.07 RESULT: Theorem (the conjecture is true).
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