TSTP Solution File: SWV178+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV178+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 : n001.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 23:02:53 EDT 2023
% Result : Theorem 0.20s 0.62s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV178+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n001.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 08:04:52 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.62 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.62
% 0.20/0.62 % SZS status Theorem
% 0.20/0.62
% 0.20/0.62 % SZS output start Proof
% 0.20/0.62 Take the following subset of the input axioms:
% 0.20/0.63 fof(cl5_nebula_init_0066, conjecture, (leq(n0, pv40) & (leq(pv40, n4) & (gt(loopcounter, n1) & (![A2]: ((leq(n0, A2) & leq(A2, n135299)) => ![B]: ((leq(n0, B) & leq(B, n4)) => a_select3(q_init, A2, B)=init)) & (![C]: ((leq(n0, C) & leq(C, n4)) => a_select2(rho_init, C)=init) & (![D]: ((leq(n0, D) & leq(D, pred(pv40))) => a_select2(mu_init, D)=init) & (![E]: ((leq(n0, E) & leq(E, pred(pv40))) => a_select2(sigma_init, E)=init) & (![F]: ((leq(n0, F) & leq(F, n4)) => a_select3(center_init, F, n0)=init) & ((gt(loopcounter, n1) => ![G]: ((leq(n0, G) & leq(G, n4)) => a_select2(muold_init, G)=init)) & ((gt(loopcounter, n1) => ![H]: ((leq(n0, H) & leq(H, n4)) => a_select2(rhoold_init, H)=init)) & (gt(loopcounter, n1) => ![I]: ((leq(n0, I) & leq(I, n4)) => a_select2(sigmaold_init, I)=init)))))))))))) => ![J]: ((leq(n0, J) & leq(J, n4)) => a_select2(sigmaold_init, J)=init)).
% 0.20/0.63
% 0.20/0.63 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.63 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.63 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.63 fresh(y, y, x1...xn) = u
% 0.20/0.63 C => fresh(s, t, x1...xn) = v
% 0.20/0.63 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.63 variables of u and v.
% 0.20/0.63 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.63 input problem has no model of domain size 1).
% 0.20/0.63
% 0.20/0.63 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.63
% 0.20/0.63 Axiom 1 (cl5_nebula_init_0066_2): leq(n0, j) = true3.
% 0.20/0.63 Axiom 2 (cl5_nebula_init_0066_4): leq(j, n4) = true3.
% 0.20/0.63 Axiom 3 (cl5_nebula_init_0066): gt(loopcounter, n1) = true3.
% 0.20/0.63 Axiom 4 (cl5_nebula_init_0066_8): fresh57(X, X, Y) = init.
% 0.20/0.63 Axiom 5 (cl5_nebula_init_0066_8): fresh41(X, X, Y) = a_select2(sigmaold_init, Y).
% 0.20/0.63 Axiom 6 (cl5_nebula_init_0066_8): fresh56(X, X, Y) = fresh57(gt(loopcounter, n1), true3, Y).
% 0.20/0.63 Axiom 7 (cl5_nebula_init_0066_8): fresh56(leq(n0, X), true3, X) = fresh41(leq(X, n4), true3, X).
% 0.20/0.63
% 0.20/0.63 Goal 1 (cl5_nebula_init_0066_5): a_select2(sigmaold_init, j) = init.
% 0.20/0.63 Proof:
% 0.20/0.63 a_select2(sigmaold_init, j)
% 0.20/0.63 = { by axiom 5 (cl5_nebula_init_0066_8) R->L }
% 0.20/0.63 fresh41(true3, true3, j)
% 0.20/0.63 = { by axiom 2 (cl5_nebula_init_0066_4) R->L }
% 0.20/0.63 fresh41(leq(j, n4), true3, j)
% 0.20/0.63 = { by axiom 7 (cl5_nebula_init_0066_8) R->L }
% 0.20/0.63 fresh56(leq(n0, j), true3, j)
% 0.20/0.63 = { by axiom 1 (cl5_nebula_init_0066_2) }
% 0.20/0.63 fresh56(true3, true3, j)
% 0.20/0.63 = { by axiom 6 (cl5_nebula_init_0066_8) }
% 0.20/0.63 fresh57(gt(loopcounter, n1), true3, j)
% 0.20/0.63 = { by axiom 3 (cl5_nebula_init_0066) }
% 0.20/0.63 fresh57(true3, true3, j)
% 0.20/0.63 = { by axiom 4 (cl5_nebula_init_0066_8) }
% 0.20/0.63 init
% 0.20/0.63 % SZS output end Proof
% 0.20/0.63
% 0.20/0.63 RESULT: Theorem (the conjecture is true).
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