TSTP Solution File: SWV069+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV069+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 : n026.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 0.21s 0.62s
% 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
% 0.00/0.13 % Problem : SWV069+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 08:55:20 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.62 Command-line arguments: --ground-connectedness --complete-subsets
% 0.21/0.62
% 0.21/0.62 % SZS status Theorem
% 0.21/0.62
% 0.21/0.63 % SZS output start Proof
% 0.21/0.63 Take the following subset of the input axioms:
% 0.21/0.63 fof(cl5_nebula_array_0010, conjecture, (leq(n0, pv10) & leq(pv10, minus(n135300, n1))) => (leq(n0, n0) & (leq(n0, pv10) & (leq(n0, minus(n5, n1)) & leq(pv10, minus(n135300, n1)))))).
% 0.21/0.63 fof(gt_5_0, axiom, gt(n5, n0)).
% 0.21/0.63 fof(leq_gt_pred, axiom, ![X, Y]: (leq(X, pred(Y)) <=> gt(Y, X))).
% 0.21/0.63 fof(pred_minus_1, axiom, ![X2]: minus(X2, n1)=pred(X2)).
% 0.21/0.63 fof(reflexivity_leq, axiom, ![X2]: leq(X2, X2)).
% 0.21/0.63 fof(sum_plus_base, axiom, ![Body]: sum(n0, tptp_minus_1, Body)=n0).
% 0.21/0.63 fof(sum_plus_base_float, axiom, ![Body2]: tptp_float_0_0=sum(n0, tptp_minus_1, Body2)).
% 0.21/0.63 fof(ttrue, axiom, true).
% 0.21/0.63
% 0.21/0.63 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.63 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.63 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.63 fresh(y, y, x1...xn) = u
% 0.21/0.63 C => fresh(s, t, x1...xn) = v
% 0.21/0.63 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.63 variables of u and v.
% 0.21/0.63 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.63 input problem has no model of domain size 1).
% 0.21/0.63
% 0.21/0.63 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.63
% 0.21/0.63 Axiom 1 (ttrue): true = true3.
% 0.21/0.63 Axiom 2 (pred_minus_1): minus(X, n1) = pred(X).
% 0.21/0.63 Axiom 3 (gt_5_0): gt(n5, n0) = true3.
% 0.21/0.63 Axiom 4 (reflexivity_leq): leq(X, X) = true3.
% 0.21/0.63 Axiom 5 (cl5_nebula_array_0010): leq(n0, pv10) = true3.
% 0.21/0.63 Axiom 6 (sum_plus_base_float): tptp_float_0_0 = sum(n0, tptp_minus_1, X).
% 0.21/0.63 Axiom 7 (sum_plus_base): sum(n0, tptp_minus_1, X) = n0.
% 0.21/0.63 Axiom 8 (leq_gt_pred): fresh35(X, X, Y, Z) = true3.
% 0.21/0.63 Axiom 9 (cl5_nebula_array_0010_1): leq(pv10, minus(n135300, n1)) = true3.
% 0.21/0.63 Axiom 10 (leq_gt_pred): fresh35(gt(X, Y), true3, Y, X) = leq(Y, pred(X)).
% 0.21/0.63
% 0.21/0.63 Lemma 11: n0 = tptp_float_0_0.
% 0.21/0.63 Proof:
% 0.21/0.63 n0
% 0.21/0.63 = { by axiom 7 (sum_plus_base) R->L }
% 0.21/0.63 sum(n0, tptp_minus_1, X)
% 0.21/0.63 = { by axiom 6 (sum_plus_base_float) R->L }
% 0.21/0.63 tptp_float_0_0
% 0.21/0.63
% 0.21/0.63 Goal 1 (cl5_nebula_array_0010_2): tuple(leq(n0, n0), leq(n0, minus(n5, n1)), leq(n0, pv10), leq(pv10, minus(n135300, n1))) = tuple(true3, true3, true3, true3).
% 0.21/0.63 Proof:
% 0.21/0.63 tuple(leq(n0, n0), leq(n0, minus(n5, n1)), leq(n0, pv10), leq(pv10, minus(n135300, n1)))
% 0.21/0.63 = { by axiom 4 (reflexivity_leq) }
% 0.21/0.63 tuple(true3, leq(n0, minus(n5, n1)), leq(n0, pv10), leq(pv10, minus(n135300, n1)))
% 0.21/0.63 = { by axiom 1 (ttrue) R->L }
% 0.21/0.63 tuple(true, leq(n0, minus(n5, n1)), leq(n0, pv10), leq(pv10, minus(n135300, n1)))
% 0.21/0.63 = { by axiom 5 (cl5_nebula_array_0010) }
% 0.21/0.63 tuple(true, leq(n0, minus(n5, n1)), true3, leq(pv10, minus(n135300, n1)))
% 0.21/0.63 = { by axiom 1 (ttrue) R->L }
% 0.21/0.63 tuple(true, leq(n0, minus(n5, n1)), true, leq(pv10, minus(n135300, n1)))
% 0.21/0.63 = { by lemma 11 }
% 0.21/0.63 tuple(true, leq(tptp_float_0_0, minus(n5, n1)), true, leq(pv10, minus(n135300, n1)))
% 0.21/0.63 = { by axiom 9 (cl5_nebula_array_0010_1) }
% 0.21/0.63 tuple(true, leq(tptp_float_0_0, minus(n5, n1)), true, true3)
% 0.21/0.63 = { by axiom 1 (ttrue) R->L }
% 0.21/0.63 tuple(true, leq(tptp_float_0_0, minus(n5, n1)), true, true)
% 0.21/0.63 = { by axiom 2 (pred_minus_1) }
% 0.21/0.63 tuple(true, leq(tptp_float_0_0, pred(n5)), true, true)
% 0.21/0.63 = { by lemma 11 R->L }
% 0.21/0.63 tuple(true, leq(n0, pred(n5)), true, true)
% 0.21/0.63 = { by axiom 10 (leq_gt_pred) R->L }
% 0.21/0.63 tuple(true, fresh35(gt(n5, n0), true3, n0, n5), true, true)
% 0.21/0.63 = { by axiom 1 (ttrue) R->L }
% 0.21/0.63 tuple(true, fresh35(gt(n5, n0), true, n0, n5), true, true)
% 0.21/0.63 = { by axiom 3 (gt_5_0) }
% 0.21/0.63 tuple(true, fresh35(true3, true, n0, n5), true, true)
% 0.21/0.63 = { by axiom 1 (ttrue) R->L }
% 0.21/0.63 tuple(true, fresh35(true, true, n0, n5), true, true)
% 0.21/0.63 = { by axiom 8 (leq_gt_pred) }
% 0.21/0.63 tuple(true, true3, true, true)
% 0.21/0.63 = { by axiom 1 (ttrue) R->L }
% 0.21/0.63 tuple(true, true, true, true)
% 0.21/0.63 = { by axiom 1 (ttrue) }
% 0.21/0.63 tuple(true3, true, true, true)
% 0.21/0.63 = { by axiom 1 (ttrue) }
% 0.21/0.63 tuple(true3, true3, true, true)
% 0.21/0.63 = { by axiom 1 (ttrue) }
% 0.21/0.63 tuple(true3, true3, true3, true)
% 0.21/0.63 = { by axiom 1 (ttrue) }
% 0.21/0.63 tuple(true3, true3, true3, true3)
% 0.21/0.63 % SZS output end Proof
% 0.21/0.63
% 0.21/0.63 RESULT: Theorem (the conjecture is true).
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