TSTP Solution File: SWV134+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV134+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 : n011.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 0.19s 0.70s
% 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
% 0.12/0.12 % Problem : SWV134+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
% 0.13/0.34 % Computer : n011.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 09:50:11 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.70 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.19/0.70
% 0.19/0.70 % SZS status Theorem
% 0.19/0.70
% 0.19/0.70 % SZS output start Proof
% 0.19/0.70 Take the following subset of the input axioms:
% 0.19/0.70 fof(gauss_array_0004, conjecture, (~leq(a_select2(s_values7, pv1325), a_select2(s_values7, s_worst7)) & (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(a_select2(s_values7, pv1325), a_select2(s_values7, s_best7)) & leq(a_select2(s_values7, pv1325), a_select2(s_values7, s_sworst7)))))))))))) => leq(n0, pv1325)).
% 0.19/0.70 fof(gt_2_0, axiom, gt(n2, n0)).
% 0.19/0.70 fof(leq_gt1, axiom, ![X, Y]: (gt(Y, X) => leq(X, Y))).
% 0.19/0.70 fof(transitivity_leq, axiom, ![Z, X2, Y2]: ((leq(X2, Y2) & leq(Y2, Z)) => leq(X2, Z))).
% 0.19/0.70
% 0.19/0.70 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.70 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.70 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.70 fresh(y, y, x1...xn) = u
% 0.19/0.70 C => fresh(s, t, x1...xn) = v
% 0.19/0.70 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.70 variables of u and v.
% 0.19/0.70 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.70 input problem has no model of domain size 1).
% 0.19/0.70
% 0.19/0.70 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.70
% 0.19/0.70 Axiom 1 (gauss_array_0004_5): leq(n2, pv1325) = true3.
% 0.19/0.70 Axiom 2 (gt_2_0): gt(n2, n0) = true3.
% 0.19/0.70 Axiom 3 (leq_gt1): fresh36(X, X, Y, Z) = true3.
% 0.19/0.70 Axiom 4 (transitivity_leq): fresh7(X, X, Y, Z) = true3.
% 0.19/0.70 Axiom 5 (transitivity_leq): fresh8(X, X, Y, Z, W) = leq(Y, W).
% 0.19/0.70 Axiom 6 (leq_gt1): fresh36(gt(X, Y), true3, Y, X) = leq(Y, X).
% 0.19/0.70 Axiom 7 (transitivity_leq): fresh8(leq(X, Y), true3, Z, X, Y) = fresh7(leq(Z, X), true3, Z, Y).
% 0.19/0.70
% 0.19/0.70 Goal 1 (gauss_array_0004_10): leq(n0, pv1325) = true3.
% 0.19/0.70 Proof:
% 0.19/0.70 leq(n0, pv1325)
% 0.19/0.70 = { by axiom 5 (transitivity_leq) R->L }
% 0.19/0.70 fresh8(true3, true3, n0, n2, pv1325)
% 0.19/0.70 = { by axiom 1 (gauss_array_0004_5) R->L }
% 0.19/0.70 fresh8(leq(n2, pv1325), true3, n0, n2, pv1325)
% 0.19/0.70 = { by axiom 7 (transitivity_leq) }
% 0.19/0.70 fresh7(leq(n0, n2), true3, n0, pv1325)
% 0.19/0.70 = { by axiom 6 (leq_gt1) R->L }
% 0.19/0.70 fresh7(fresh36(gt(n2, n0), true3, n0, n2), true3, n0, pv1325)
% 0.19/0.70 = { by axiom 2 (gt_2_0) }
% 0.19/0.70 fresh7(fresh36(true3, true3, n0, n2), true3, n0, pv1325)
% 0.19/0.70 = { by axiom 3 (leq_gt1) }
% 0.19/0.70 fresh7(true3, true3, n0, pv1325)
% 0.19/0.70 = { by axiom 4 (transitivity_leq) }
% 0.19/0.70 true3
% 0.19/0.70 % SZS output end Proof
% 0.19/0.70
% 0.19/0.70 RESULT: Theorem (the conjecture is true).
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