TSTP Solution File: SWV071+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SWV071+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 : n032.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 23:02:26 EDT 2023
% Result : Theorem 0.12s 0.46s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.08 % Problem : SWV071+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.04/0.09 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Tue Aug 29 03:51:16 EDT 2023
% 0.08/0.28 % CPUTime :
% 0.12/0.46 Command-line arguments: --no-flatten-goal
% 0.12/0.46
% 0.12/0.46 % SZS status Theorem
% 0.12/0.46
% 0.12/0.46 % SZS output start Proof
% 0.12/0.46 Take the following subset of the input axioms:
% 0.12/0.47 fof(cl5_nebula_array_0012, conjecture, (leq(n0, pv21) & (leq(n0, pv23) & (leq(pv21, minus(n5, n1)) & leq(pv23, minus(n135300, n1))))) => (leq(n0, pv21) & (leq(n0, pv23) & (leq(pv21, minus(n5, n1)) & leq(pv23, minus(n135300, n1)))))).
% 0.12/0.47 fof(pred_minus_1, axiom, ![X]: minus(X, n1)=pred(X)).
% 0.12/0.47 fof(ttrue, axiom, true).
% 0.12/0.47
% 0.12/0.47 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.12/0.47 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.12/0.47 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.12/0.47 fresh(y, y, x1...xn) = u
% 0.12/0.47 C => fresh(s, t, x1...xn) = v
% 0.12/0.47 where fresh is a fresh function symbol and x1..xn are the free
% 0.12/0.47 variables of u and v.
% 0.12/0.47 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.12/0.47 input problem has no model of domain size 1).
% 0.12/0.47
% 0.12/0.47 The encoding turns the above axioms into the following unit equations and goals:
% 0.12/0.47
% 0.12/0.47 Axiom 1 (ttrue): true = true3.
% 0.12/0.47 Axiom 2 (pred_minus_1): minus(X, n1) = pred(X).
% 0.12/0.47 Axiom 3 (cl5_nebula_array_0012): leq(n0, pv21) = true3.
% 0.12/0.47 Axiom 4 (cl5_nebula_array_0012_1): leq(n0, pv23) = true3.
% 0.12/0.47 Axiom 5 (cl5_nebula_array_0012_2): leq(pv21, minus(n5, n1)) = true3.
% 0.12/0.47 Axiom 6 (cl5_nebula_array_0012_3): leq(pv23, minus(n135300, n1)) = true3.
% 0.12/0.47
% 0.12/0.47 Goal 1 (cl5_nebula_array_0012_4): tuple(leq(n0, pv21), leq(n0, pv23), leq(pv21, minus(n5, n1)), leq(pv23, minus(n135300, n1))) = tuple(true3, true3, true3, true3).
% 0.12/0.47 Proof:
% 0.12/0.47 tuple(leq(n0, pv21), leq(n0, pv23), leq(pv21, minus(n5, n1)), leq(pv23, minus(n135300, n1)))
% 0.12/0.47 = { by axiom 2 (pred_minus_1) }
% 0.12/0.47 tuple(leq(n0, pv21), leq(n0, pv23), leq(pv21, pred(n5)), leq(pv23, minus(n135300, n1)))
% 0.12/0.47 = { by axiom 2 (pred_minus_1) }
% 0.12/0.47 tuple(leq(n0, pv21), leq(n0, pv23), leq(pv21, pred(n5)), leq(pv23, pred(n135300)))
% 0.12/0.47 = { by axiom 3 (cl5_nebula_array_0012) }
% 0.12/0.47 tuple(true3, leq(n0, pv23), leq(pv21, pred(n5)), leq(pv23, pred(n135300)))
% 0.12/0.47 = { by axiom 1 (ttrue) R->L }
% 0.12/0.47 tuple(true, leq(n0, pv23), leq(pv21, pred(n5)), leq(pv23, pred(n135300)))
% 0.12/0.47 = { by axiom 4 (cl5_nebula_array_0012_1) }
% 0.12/0.47 tuple(true, true3, leq(pv21, pred(n5)), leq(pv23, pred(n135300)))
% 0.12/0.47 = { by axiom 1 (ttrue) R->L }
% 0.12/0.47 tuple(true, true, leq(pv21, pred(n5)), leq(pv23, pred(n135300)))
% 0.12/0.47 = { by axiom 2 (pred_minus_1) R->L }
% 0.12/0.47 tuple(true, true, leq(pv21, minus(n5, n1)), leq(pv23, pred(n135300)))
% 0.12/0.47 = { by axiom 5 (cl5_nebula_array_0012_2) }
% 0.12/0.47 tuple(true, true, true3, leq(pv23, pred(n135300)))
% 0.12/0.47 = { by axiom 1 (ttrue) R->L }
% 0.12/0.47 tuple(true, true, true, leq(pv23, pred(n135300)))
% 0.12/0.47 = { by axiom 2 (pred_minus_1) R->L }
% 0.12/0.47 tuple(true, true, true, leq(pv23, minus(n135300, n1)))
% 0.12/0.47 = { by axiom 6 (cl5_nebula_array_0012_3) }
% 0.12/0.47 tuple(true, true, true, true3)
% 0.12/0.47 = { by axiom 1 (ttrue) R->L }
% 0.12/0.47 tuple(true, true, true, true)
% 0.12/0.47 = { by axiom 1 (ttrue) }
% 0.12/0.47 tuple(true3, true, true, true)
% 0.12/0.47 = { by axiom 1 (ttrue) }
% 0.12/0.47 tuple(true3, true3, true, true)
% 0.12/0.47 = { by axiom 1 (ttrue) }
% 0.12/0.47 tuple(true3, true3, true3, true)
% 0.12/0.47 = { by axiom 1 (ttrue) }
% 0.12/0.47 tuple(true3, true3, true3, true3)
% 0.12/0.47 % SZS output end Proof
% 0.12/0.47
% 0.12/0.47 RESULT: Theorem (the conjecture is true).
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