TSTP Solution File: SWV135+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV135+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 : n006.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 23:02:42 EDT 2023
% Result : Theorem 3.82s 0.88s
% Output : Proof 3.82s
% 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 : SWV135+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
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 03:18:51 EDT 2023
% 0.13/0.34 % CPUTime :
% 3.82/0.88 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 3.82/0.88
% 3.82/0.88 % SZS status Theorem
% 3.82/0.88
% 3.82/0.89 % SZS output start Proof
% 3.82/0.89 Take the following subset of the input axioms:
% 3.82/0.89 fof(gauss_array_0005, conjecture, (leq(n0, s_best7) & (leq(n0, s_sworst7) & (leq(n0, s_worst7) & (leq(n2, pv1325) & (leq(s_best7, n3) & (leq(s_sworst7, n3) & (leq(s_worst7, n3) & leq(pv1325, n3)))))))) => leq(n0, pv1325)).
% 3.82/0.89 fof(gt_1_0, axiom, gt(n1, n0)).
% 3.82/0.89 fof(leq_gt1, axiom, ![X, Y]: (gt(Y, X) => leq(X, Y))).
% 3.82/0.89 fof(leq_succ_gt, axiom, ![X2, Y2]: (leq(succ(X2), Y2) => gt(Y2, X2))).
% 3.82/0.89 fof(successor_1, axiom, succ(n0)=n1).
% 3.82/0.89 fof(successor_2, axiom, succ(succ(n0))=n2).
% 3.82/0.89 fof(transitivity_gt, axiom, ![Z, X2, Y2]: ((gt(X2, Y2) & gt(Y2, Z)) => gt(X2, Z))).
% 3.82/0.89
% 3.82/0.89 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.82/0.89 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.82/0.89 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.82/0.89 fresh(y, y, x1...xn) = u
% 3.82/0.89 C => fresh(s, t, x1...xn) = v
% 3.82/0.89 where fresh is a fresh function symbol and x1..xn are the free
% 3.82/0.89 variables of u and v.
% 3.82/0.89 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.82/0.89 input problem has no model of domain size 1).
% 3.82/0.89
% 3.82/0.89 The encoding turns the above axioms into the following unit equations and goals:
% 3.82/0.89
% 3.82/0.89 Axiom 1 (successor_1): succ(n0) = n1.
% 3.82/0.89 Axiom 2 (gauss_array_0005_3): leq(n2, pv1325) = true3.
% 3.82/0.89 Axiom 3 (successor_2): succ(succ(n0)) = n2.
% 3.82/0.89 Axiom 4 (gt_1_0): gt(n1, n0) = true3.
% 3.82/0.89 Axiom 5 (leq_gt1): fresh36(X, X, Y, Z) = true3.
% 3.82/0.89 Axiom 6 (leq_succ_gt): fresh31(X, X, Y, Z) = true3.
% 3.82/0.89 Axiom 7 (transitivity_gt): fresh9(X, X, Y, Z) = true3.
% 3.82/0.89 Axiom 8 (transitivity_gt): fresh10(X, X, Y, Z, W) = gt(Y, W).
% 3.82/0.89 Axiom 9 (leq_gt1): fresh36(gt(X, Y), true3, Y, X) = leq(Y, X).
% 3.82/0.89 Axiom 10 (leq_succ_gt): fresh31(leq(succ(X), Y), true3, X, Y) = gt(Y, X).
% 3.82/0.89 Axiom 11 (transitivity_gt): fresh10(gt(X, Y), true3, Z, X, Y) = fresh9(gt(Z, X), true3, Z, Y).
% 3.82/0.89
% 3.82/0.89 Goal 1 (gauss_array_0005_8): leq(n0, pv1325) = true3.
% 3.82/0.89 Proof:
% 3.82/0.89 leq(n0, pv1325)
% 3.82/0.89 = { by axiom 9 (leq_gt1) R->L }
% 3.82/0.89 fresh36(gt(pv1325, n0), true3, n0, pv1325)
% 3.82/0.89 = { by axiom 8 (transitivity_gt) R->L }
% 3.82/0.89 fresh36(fresh10(true3, true3, pv1325, n1, n0), true3, n0, pv1325)
% 3.82/0.89 = { by axiom 4 (gt_1_0) R->L }
% 3.82/0.89 fresh36(fresh10(gt(n1, n0), true3, pv1325, n1, n0), true3, n0, pv1325)
% 3.82/0.89 = { by axiom 11 (transitivity_gt) }
% 3.82/0.89 fresh36(fresh9(gt(pv1325, n1), true3, pv1325, n0), true3, n0, pv1325)
% 3.82/0.89 = { by axiom 10 (leq_succ_gt) R->L }
% 3.82/0.89 fresh36(fresh9(fresh31(leq(succ(n1), pv1325), true3, n1, pv1325), true3, pv1325, n0), true3, n0, pv1325)
% 3.82/0.89 = { by axiom 1 (successor_1) R->L }
% 3.82/0.89 fresh36(fresh9(fresh31(leq(succ(succ(n0)), pv1325), true3, n1, pv1325), true3, pv1325, n0), true3, n0, pv1325)
% 3.82/0.89 = { by axiom 3 (successor_2) }
% 3.82/0.89 fresh36(fresh9(fresh31(leq(n2, pv1325), true3, n1, pv1325), true3, pv1325, n0), true3, n0, pv1325)
% 3.82/0.89 = { by axiom 2 (gauss_array_0005_3) }
% 3.82/0.89 fresh36(fresh9(fresh31(true3, true3, n1, pv1325), true3, pv1325, n0), true3, n0, pv1325)
% 3.82/0.89 = { by axiom 6 (leq_succ_gt) }
% 3.82/0.89 fresh36(fresh9(true3, true3, pv1325, n0), true3, n0, pv1325)
% 3.82/0.89 = { by axiom 7 (transitivity_gt) }
% 3.82/0.89 fresh36(true3, true3, n0, pv1325)
% 3.82/0.89 = { by axiom 5 (leq_gt1) }
% 3.82/0.89 true3
% 3.82/0.89 % SZS output end Proof
% 3.82/0.89
% 3.82/0.89 RESULT: Theorem (the conjecture is true).
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