TSTP Solution File: SWV158+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV158+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 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 : n021.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 : Thu Aug 31 23:02:48 EDT 2023
% Result : Theorem 0.21s 0.64s
% Output : Proof 0.21s
% 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 : SWV158+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 05:13:29 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.64 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.21/0.64
% 0.21/0.64 % SZS status Theorem
% 0.21/0.64
% 0.21/0.64 % SZS output start Proof
% 0.21/0.64 Take the following subset of the input axioms:
% 0.21/0.65 fof(cl5_nebula_norm_0008, conjecture, (pv84=sum(n0, n4, divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index)), minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index))), tptp_minus_2), times(a_select2(sigma, tptp_sum_index), a_select2(sigma, tptp_sum_index)))), a_select2(rho, tptp_sum_index)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, tptp_sum_index)))) & (leq(n0, pv10) & (leq(n0, pv47) & (leq(pv10, n135299) & (leq(pv47, n4) & (![A2]: ((leq(n0, A2) & leq(A2, pred(pv47))) => a_select3(q, pv10, A2)=divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, A2)), minus(a_select2(x, pv10), a_select2(mu, A2))), tptp_minus_2), times(a_select2(sigma, A2), a_select2(sigma, A2)))), a_select2(rho, A2)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, A2))), sum(n0, n4, divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index)), minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index))), tptp_minus_2), times(a_select2(sigma, tptp_sum_index), a_select2(sigma, tptp_sum_index)))), a_select2(rho, tptp_sum_index)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, tptp_sum_index)))))) & ![B]: ((leq(n0, B) & leq(B, pred(pv10))) => sum(n0, n4, a_select3(q, B, tptp_sum_index))=n1))))))) => ![C]: ((leq(n0, C) & leq(C, pv47)) => (pv47=C => divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, pv47)), minus(a_select2(x, pv10), a_select2(mu, pv47))), tptp_minus_2), times(a_select2(sigma, pv47), a_select2(sigma, pv47)))), a_select2(rho, pv47)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, pv47))), pv84)=divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, C)), minus(a_select2(x, pv10), a_select2(mu, C))), tptp_minus_2), times(a_select2(sigma, C), a_select2(sigma, C)))), a_select2(rho, C)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, C))), sum(n0, n4, divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index)), minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index))), tptp_minus_2), times(a_select2(sigma, tptp_sum_index), a_select2(sigma, tptp_sum_index)))), a_select2(rho, tptp_sum_index)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, tptp_sum_index)))))))).
% 0.21/0.65
% 0.21/0.65 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.65 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.65 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.65 fresh(y, y, x1...xn) = u
% 0.21/0.65 C => fresh(s, t, x1...xn) = v
% 0.21/0.65 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.65 variables of u and v.
% 0.21/0.65 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.65 input problem has no model of domain size 1).
% 0.21/0.65
% 0.21/0.65 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.65
% 0.21/0.65 Axiom 1 (cl5_nebula_norm_0008_1): pv47 = c.
% 0.21/0.65 Axiom 2 (cl5_nebula_norm_0008): pv84 = sum(n0, n4, divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index)), minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index))), tptp_minus_2), times(a_select2(sigma, tptp_sum_index), a_select2(sigma, tptp_sum_index)))), a_select2(rho, tptp_sum_index)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, tptp_sum_index)))).
% 0.21/0.65
% 0.21/0.65 Goal 1 (cl5_nebula_norm_0008_8): divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, pv47)), minus(a_select2(x, pv10), a_select2(mu, pv47))), tptp_minus_2), times(a_select2(sigma, pv47), a_select2(sigma, pv47)))), a_select2(rho, pv47)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, pv47))), pv84) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, c)), minus(a_select2(x, pv10), a_select2(mu, c))), tptp_minus_2), times(a_select2(sigma, c), a_select2(sigma, c)))), a_select2(rho, c)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, c))), sum(n0, n4, divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index)), minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index))), tptp_minus_2), times(a_select2(sigma, tptp_sum_index), a_select2(sigma, tptp_sum_index)))), a_select2(rho, tptp_sum_index)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, tptp_sum_index))))).
% 0.21/0.65 Proof:
% 0.21/0.65 divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, pv47)), minus(a_select2(x, pv10), a_select2(mu, pv47))), tptp_minus_2), times(a_select2(sigma, pv47), a_select2(sigma, pv47)))), a_select2(rho, pv47)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, pv47))), pv84)
% 0.21/0.65 = { by axiom 2 (cl5_nebula_norm_0008) }
% 0.21/0.65 divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, pv47)), minus(a_select2(x, pv10), a_select2(mu, pv47))), tptp_minus_2), times(a_select2(sigma, pv47), a_select2(sigma, pv47)))), a_select2(rho, pv47)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, pv47))), sum(n0, n4, divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index)), minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index))), tptp_minus_2), times(a_select2(sigma, tptp_sum_index), a_select2(sigma, tptp_sum_index)))), a_select2(rho, tptp_sum_index)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, tptp_sum_index)))))
% 0.21/0.65 = { by axiom 1 (cl5_nebula_norm_0008_1) }
% 0.21/0.65 divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, c)), minus(a_select2(x, pv10), a_select2(mu, pv47))), tptp_minus_2), times(a_select2(sigma, pv47), a_select2(sigma, pv47)))), a_select2(rho, pv47)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, pv47))), sum(n0, n4, divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index)), minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index))), tptp_minus_2), times(a_select2(sigma, tptp_sum_index), a_select2(sigma, tptp_sum_index)))), a_select2(rho, tptp_sum_index)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, tptp_sum_index)))))
% 0.21/0.65 = { by axiom 1 (cl5_nebula_norm_0008_1) }
% 0.21/0.65 divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, c)), minus(a_select2(x, pv10), a_select2(mu, c))), tptp_minus_2), times(a_select2(sigma, pv47), a_select2(sigma, pv47)))), a_select2(rho, pv47)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, pv47))), sum(n0, n4, divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index)), minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index))), tptp_minus_2), times(a_select2(sigma, tptp_sum_index), a_select2(sigma, tptp_sum_index)))), a_select2(rho, tptp_sum_index)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, tptp_sum_index)))))
% 0.21/0.65 = { by axiom 1 (cl5_nebula_norm_0008_1) }
% 0.21/0.65 divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, c)), minus(a_select2(x, pv10), a_select2(mu, c))), tptp_minus_2), times(a_select2(sigma, c), a_select2(sigma, pv47)))), a_select2(rho, pv47)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, pv47))), sum(n0, n4, divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index)), minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index))), tptp_minus_2), times(a_select2(sigma, tptp_sum_index), a_select2(sigma, tptp_sum_index)))), a_select2(rho, tptp_sum_index)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, tptp_sum_index)))))
% 0.21/0.65 = { by axiom 1 (cl5_nebula_norm_0008_1) }
% 0.21/0.65 divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, c)), minus(a_select2(x, pv10), a_select2(mu, c))), tptp_minus_2), times(a_select2(sigma, c), a_select2(sigma, c)))), a_select2(rho, pv47)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, pv47))), sum(n0, n4, divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index)), minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index))), tptp_minus_2), times(a_select2(sigma, tptp_sum_index), a_select2(sigma, tptp_sum_index)))), a_select2(rho, tptp_sum_index)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, tptp_sum_index)))))
% 0.21/0.65 = { by axiom 1 (cl5_nebula_norm_0008_1) }
% 0.21/0.65 divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, c)), minus(a_select2(x, pv10), a_select2(mu, c))), tptp_minus_2), times(a_select2(sigma, c), a_select2(sigma, c)))), a_select2(rho, c)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, pv47))), sum(n0, n4, divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index)), minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index))), tptp_minus_2), times(a_select2(sigma, tptp_sum_index), a_select2(sigma, tptp_sum_index)))), a_select2(rho, tptp_sum_index)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, tptp_sum_index)))))
% 0.21/0.65 = { by axiom 1 (cl5_nebula_norm_0008_1) }
% 0.21/0.66 divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, c)), minus(a_select2(x, pv10), a_select2(mu, c))), tptp_minus_2), times(a_select2(sigma, c), a_select2(sigma, c)))), a_select2(rho, c)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, c))), sum(n0, n4, divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index)), minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index))), tptp_minus_2), times(a_select2(sigma, tptp_sum_index), a_select2(sigma, tptp_sum_index)))), a_select2(rho, tptp_sum_index)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, tptp_sum_index)))))
% 0.21/0.66 % SZS output end Proof
% 0.21/0.66
% 0.21/0.66 RESULT: Theorem (the conjecture is true).
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