TSTP Solution File: SWV087+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SWV087+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 : n024.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 23:02:32 EDT 2023
% Result : Theorem 0.19s 0.55s
% Output : Proof 0.19s
% 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 : SWV087+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
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 04:06:08 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.55 Command-line arguments: --no-flatten-goal
% 0.19/0.55
% 0.19/0.55 % SZS status Theorem
% 0.19/0.55
% 0.19/0.55 % SZS output start Proof
% 0.19/0.55 Take the following subset of the input axioms:
% 0.19/0.56 fof(cl5_nebula_array_0028, conjecture, geq(pv65, tptp_float_0_001) => ((~gt(plus(n1, loopcounter), n1) => true) & (gt(plus(n1, loopcounter), n1) => true))).
% 0.19/0.56 fof(ttrue, axiom, true).
% 0.19/0.56
% 0.19/0.56 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.56 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.56 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.56 fresh(y, y, x1...xn) = u
% 0.19/0.56 C => fresh(s, t, x1...xn) = v
% 0.19/0.56 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.56 variables of u and v.
% 0.19/0.56 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.56 input problem has no model of domain size 1).
% 0.19/0.56
% 0.19/0.56 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.56
% 0.19/0.56 Axiom 1 (ttrue): true = true3.
% 0.19/0.56 Axiom 2 (cl5_nebula_array_0028_3): fresh40(X, X) = true3.
% 0.19/0.56 Axiom 3 (cl5_nebula_array_0028_3): fresh40(true, true3) = gt(plus(n1, loopcounter), n1).
% 0.19/0.56
% 0.19/0.56 Goal 1 (cl5_nebula_array_0028_2): true = true3.
% 0.19/0.56 Proof:
% 0.19/0.56 true
% 0.19/0.56 = { by axiom 1 (ttrue) }
% 0.19/0.56 true3
% 0.19/0.56
% 0.19/0.56 Goal 2 (cl5_nebula_array_0028_1): tuple(gt(plus(n1, loopcounter), n1), true) = tuple(true3, true3).
% 0.19/0.56 Proof:
% 0.19/0.56 tuple(gt(plus(n1, loopcounter), n1), true)
% 0.19/0.56 = { by axiom 3 (cl5_nebula_array_0028_3) R->L }
% 0.19/0.56 tuple(fresh40(true, true3), true)
% 0.19/0.56 = { by axiom 1 (ttrue) R->L }
% 0.19/0.56 tuple(fresh40(true, true), true)
% 0.19/0.56 = { by axiom 2 (cl5_nebula_array_0028_3) }
% 0.19/0.56 tuple(true3, true)
% 0.19/0.56 = { by axiom 1 (ttrue) }
% 0.19/0.56 tuple(true3, true3)
% 0.19/0.56 % SZS output end Proof
% 0.19/0.56
% 0.19/0.56 RESULT: Theorem (the conjecture is true).
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