TSTP Solution File: SWV154+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SWV154+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 23:02:47 EDT 2023
% Result : Theorem 0.21s 0.61s
% 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
% 0.07/0.12 % Problem : SWV154+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.13 % 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 07:08:44 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.61 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.61
% 0.21/0.61 % SZS status Theorem
% 0.21/0.61
% 0.21/0.62 % SZS output start Proof
% 0.21/0.62 Take the following subset of the input axioms:
% 0.21/0.62 fof(cl5_nebula_norm_0004, conjecture, (pv70=sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10))))) & (leq(n0, pv10) & (leq(n0, pv12) & (leq(pv10, n135299) & (leq(pv12, n4) & (![A2]: ((leq(n0, A2) & leq(A2, pred(pv12))) => a_select3(q, pv10, A2)=divide(sqrt(times(minus(a_select3(center, A2, n0), a_select2(x, pv10)), minus(a_select3(center, A2, n0), a_select2(x, pv10)))), sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10))))))) & ![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, pv12)) => (pv12=C => divide(sqrt(times(minus(a_select3(center, pv12, n0), a_select2(x, pv10)), minus(a_select3(center, pv12, n0), a_select2(x, pv10)))), pv70)=divide(sqrt(times(minus(a_select3(center, C, n0), a_select2(x, pv10)), minus(a_select3(center, C, n0), a_select2(x, pv10)))), sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10))))))))).
% 0.21/0.62
% 0.21/0.62 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.62 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.62 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.62 fresh(y, y, x1...xn) = u
% 0.21/0.62 C => fresh(s, t, x1...xn) = v
% 0.21/0.62 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.62 variables of u and v.
% 0.21/0.62 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.62 input problem has no model of domain size 1).
% 0.21/0.62
% 0.21/0.62 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.62
% 0.21/0.62 Axiom 1 (cl5_nebula_norm_0004_1): pv12 = c.
% 0.21/0.62 Axiom 2 (cl5_nebula_norm_0004): pv70 = sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10))))).
% 0.21/0.62
% 0.21/0.62 Goal 1 (cl5_nebula_norm_0004_8): divide(sqrt(times(minus(a_select3(center, pv12, n0), a_select2(x, pv10)), minus(a_select3(center, pv12, n0), a_select2(x, pv10)))), pv70) = divide(sqrt(times(minus(a_select3(center, c, n0), a_select2(x, pv10)), minus(a_select3(center, c, n0), a_select2(x, pv10)))), sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)))))).
% 0.21/0.62 Proof:
% 0.21/0.62 divide(sqrt(times(minus(a_select3(center, pv12, n0), a_select2(x, pv10)), minus(a_select3(center, pv12, n0), a_select2(x, pv10)))), pv70)
% 0.21/0.62 = { by axiom 2 (cl5_nebula_norm_0004) }
% 0.21/0.62 divide(sqrt(times(minus(a_select3(center, pv12, n0), a_select2(x, pv10)), minus(a_select3(center, pv12, n0), a_select2(x, pv10)))), sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10))))))
% 0.21/0.62 = { by axiom 1 (cl5_nebula_norm_0004_1) }
% 0.21/0.62 divide(sqrt(times(minus(a_select3(center, c, n0), a_select2(x, pv10)), minus(a_select3(center, pv12, n0), a_select2(x, pv10)))), sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10))))))
% 0.21/0.62 = { by axiom 1 (cl5_nebula_norm_0004_1) }
% 0.21/0.62 divide(sqrt(times(minus(a_select3(center, c, n0), a_select2(x, pv10)), minus(a_select3(center, c, n0), a_select2(x, pv10)))), sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10))))))
% 0.21/0.62 % SZS output end Proof
% 0.21/0.62
% 0.21/0.62 RESULT: Theorem (the conjecture is true).
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