TSTP Solution File: SWV065+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SWV065+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 : n016.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 23:02:25 EDT 2023
% Result : Theorem 1.42s 0.58s
% Output : Proof 1.42s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV065+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.06/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33 % Computer : n016.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 07:06:45 EDT 2023
% 0.13/0.34 % CPUTime :
% 1.42/0.58 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 1.42/0.58
% 1.42/0.58 % SZS status Theorem
% 1.42/0.58
% 1.42/0.59 % SZS output start Proof
% 1.42/0.59 Take the following subset of the input axioms:
% 1.42/0.59 fof(cl5_nebula_array_0006, conjecture, (leq(n0, pv10) & (leq(n0, pv53) & (leq(pv10, minus(n135300, n1)) & leq(pv53, minus(n5, n1))))) => (leq(n0, n0) & (leq(n0, pv10) & (leq(n0, pv53) & (leq(pv10, minus(n135300, n1)) & leq(pv53, minus(n5, n1))))))).
% 1.42/0.59 fof(reflexivity_leq, axiom, ![X]: leq(X, X)).
% 1.42/0.59
% 1.42/0.59 Now clausify the problem and encode Horn clauses using encoding 3 of
% 1.42/0.59 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 1.42/0.59 We repeatedly replace C & s=t => u=v by the two clauses:
% 1.42/0.59 fresh(y, y, x1...xn) = u
% 1.42/0.59 C => fresh(s, t, x1...xn) = v
% 1.42/0.59 where fresh is a fresh function symbol and x1..xn are the free
% 1.42/0.59 variables of u and v.
% 1.42/0.59 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 1.42/0.59 input problem has no model of domain size 1).
% 1.42/0.59
% 1.42/0.59 The encoding turns the above axioms into the following unit equations and goals:
% 1.42/0.59
% 1.42/0.59 Axiom 1 (reflexivity_leq): leq(X, X) = true3.
% 1.42/0.59 Axiom 2 (cl5_nebula_array_0006): leq(n0, pv10) = true3.
% 1.42/0.59 Axiom 3 (cl5_nebula_array_0006_1): leq(n0, pv53) = true3.
% 1.42/0.59 Axiom 4 (cl5_nebula_array_0006_2): leq(pv10, minus(n135300, n1)) = true3.
% 1.42/0.59 Axiom 5 (cl5_nebula_array_0006_3): leq(pv53, minus(n5, n1)) = true3.
% 1.42/0.59
% 1.42/0.59 Goal 1 (cl5_nebula_array_0006_4): tuple(leq(n0, n0), leq(n0, pv10), leq(n0, pv53), leq(pv10, minus(n135300, n1)), leq(pv53, minus(n5, n1))) = tuple(true3, true3, true3, true3, true3).
% 1.42/0.59 Proof:
% 1.42/0.59 tuple(leq(n0, n0), leq(n0, pv10), leq(n0, pv53), leq(pv10, minus(n135300, n1)), leq(pv53, minus(n5, n1)))
% 1.42/0.59 = { by axiom 1 (reflexivity_leq) }
% 1.42/0.59 tuple(true3, leq(n0, pv10), leq(n0, pv53), leq(pv10, minus(n135300, n1)), leq(pv53, minus(n5, n1)))
% 1.42/0.59 = { by axiom 2 (cl5_nebula_array_0006) }
% 1.42/0.59 tuple(true3, true3, leq(n0, pv53), leq(pv10, minus(n135300, n1)), leq(pv53, minus(n5, n1)))
% 1.42/0.59 = { by axiom 3 (cl5_nebula_array_0006_1) }
% 1.42/0.59 tuple(true3, true3, true3, leq(pv10, minus(n135300, n1)), leq(pv53, minus(n5, n1)))
% 1.42/0.59 = { by axiom 4 (cl5_nebula_array_0006_2) }
% 1.42/0.59 tuple(true3, true3, true3, true3, leq(pv53, minus(n5, n1)))
% 1.42/0.59 = { by axiom 5 (cl5_nebula_array_0006_3) }
% 1.42/0.59 tuple(true3, true3, true3, true3, true3)
% 1.42/0.59 % SZS output end Proof
% 1.42/0.59
% 1.42/0.59 RESULT: Theorem (the conjecture is true).
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