TSTP Solution File: SWV159+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV159+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 : n001.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 0.20s 0.67s
% Output : Proof 0.20s
% 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 : SWV159+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n001.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 : Tue Aug 29 10:53:07 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.67 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.20/0.67
% 0.20/0.67 % SZS status Theorem
% 0.20/0.67
% 0.20/0.67 % SZS output start Proof
% 0.20/0.67 Take the following subset of the input axioms:
% 0.20/0.68 fof(cl5_nebula_norm_0009, 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, pred(pv10))) => (pv10!=C => sum(n0, n4, a_select3(q, C, tptp_sum_index))=n1))).
% 0.20/0.68
% 0.20/0.68 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.68 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.68 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.68 fresh(y, y, x1...xn) = u
% 0.20/0.68 C => fresh(s, t, x1...xn) = v
% 0.20/0.68 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.68 variables of u and v.
% 0.20/0.68 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.68 input problem has no model of domain size 1).
% 0.20/0.68
% 0.20/0.68 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.68
% 0.20/0.68 Axiom 1 (cl5_nebula_norm_0009_3): leq(n0, c) = true3.
% 0.20/0.68 Axiom 2 (cl5_nebula_norm_0009_6): leq(c, pred(pv10)) = true3.
% 0.20/0.68 Axiom 3 (cl5_nebula_norm_0009_10): fresh42(X, X, Y) = n1.
% 0.20/0.68 Axiom 4 (cl5_nebula_norm_0009_10): fresh41(X, X, Y) = sum(n0, n4, a_select3(q, Y, tptp_sum_index)).
% 0.20/0.68 Axiom 5 (cl5_nebula_norm_0009_10): fresh41(leq(n0, X), true3, X) = fresh42(leq(X, pred(pv10)), true3, X).
% 0.20/0.68
% 0.20/0.68 Goal 1 (cl5_nebula_norm_0009_7): sum(n0, n4, a_select3(q, c, tptp_sum_index)) = n1.
% 0.20/0.68 Proof:
% 0.20/0.68 sum(n0, n4, a_select3(q, c, tptp_sum_index))
% 0.20/0.68 = { by axiom 4 (cl5_nebula_norm_0009_10) R->L }
% 0.20/0.68 fresh41(true3, true3, c)
% 0.20/0.68 = { by axiom 1 (cl5_nebula_norm_0009_3) R->L }
% 0.20/0.68 fresh41(leq(n0, c), true3, c)
% 0.20/0.68 = { by axiom 5 (cl5_nebula_norm_0009_10) }
% 0.20/0.68 fresh42(leq(c, pred(pv10)), true3, c)
% 0.20/0.68 = { by axiom 2 (cl5_nebula_norm_0009_6) }
% 0.20/0.68 fresh42(true3, true3, c)
% 0.20/0.68 = { by axiom 3 (cl5_nebula_norm_0009_10) }
% 0.20/0.68 n1
% 0.20/0.68 % SZS output end Proof
% 0.20/0.68
% 0.20/0.68 RESULT: Theorem (the conjecture is true).
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