TSTP Solution File: SWV078+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV078+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 : n031.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 23:02:28 EDT 2023
% Result : Theorem 0.21s 0.59s
% 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
% 0.00/0.12 % Problem : SWV078+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n031.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 11:08:26 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.59 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.59
% 0.21/0.59 % SZS status Theorem
% 0.21/0.59
% 0.21/0.59 % SZS output start Proof
% 0.21/0.59 Take the following subset of the input axioms:
% 0.21/0.60 fof(cl5_nebula_array_0019, conjecture, (leq(n0, pv31) & leq(pv31, minus(n5, n1))) => ((n0!=pv70 => (leq(n0, pv31) & leq(pv31, minus(n5, n1)))) & (n0=pv70 => true))).
% 0.21/0.60 fof(ttrue, axiom, true).
% 0.21/0.60
% 0.21/0.60 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.60 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.60 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.60 fresh(y, y, x1...xn) = u
% 0.21/0.60 C => fresh(s, t, x1...xn) = v
% 0.21/0.60 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.60 variables of u and v.
% 0.21/0.60 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.60 input problem has no model of domain size 1).
% 0.21/0.60
% 0.21/0.60 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.60
% 0.21/0.60 Axiom 1 (ttrue): true = true3.
% 0.21/0.60 Axiom 2 (cl5_nebula_array_0019): leq(n0, pv31) = true3.
% 0.21/0.60 Axiom 3 (cl5_nebula_array_0019_1): leq(pv31, minus(n5, n1)) = true3.
% 0.21/0.60
% 0.21/0.60 Goal 1 (cl5_nebula_array_0019_4): tuple(leq(n0, pv31), leq(pv31, minus(n5, n1)), true) = tuple(true3, true3, true3).
% 0.21/0.60 Proof:
% 0.21/0.60 tuple(leq(n0, pv31), leq(pv31, minus(n5, n1)), true)
% 0.21/0.60 = { by axiom 2 (cl5_nebula_array_0019) }
% 0.21/0.60 tuple(true3, leq(pv31, minus(n5, n1)), true)
% 0.21/0.60 = { by axiom 3 (cl5_nebula_array_0019_1) }
% 0.21/0.60 tuple(true3, true3, true)
% 0.21/0.60 = { by axiom 1 (ttrue) }
% 0.21/0.60 tuple(true3, true3, true3)
% 0.21/0.60 % SZS output end Proof
% 0.21/0.60
% 0.21/0.60 RESULT: Theorem (the conjecture is true).
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