TSTP Solution File: SWV176+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV176+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 : n023.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 23:02:52 EDT 2023
% Result : Theorem 1.48s 0.59s
% Output : Proof 1.48s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SWV176+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 07:50:10 EDT 2023
% 0.12/0.33 % CPUTime :
% 1.48/0.59 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 1.48/0.59
% 1.48/0.59 % SZS status Theorem
% 1.48/0.59
% 1.48/0.59 % SZS output start Proof
% 1.48/0.59 Take the following subset of the input axioms:
% 1.48/0.60 fof(cl5_nebula_init_0056, conjecture, (leq(n0, pv40) & (leq(n0, pv44) & (leq(pv40, n4) & (leq(pv44, n135299) & (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(muold_init, J)=init)).
% 1.48/0.60
% 1.48/0.60 Now clausify the problem and encode Horn clauses using encoding 3 of
% 1.48/0.60 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 1.48/0.60 We repeatedly replace C & s=t => u=v by the two clauses:
% 1.48/0.60 fresh(y, y, x1...xn) = u
% 1.48/0.60 C => fresh(s, t, x1...xn) = v
% 1.48/0.60 where fresh is a fresh function symbol and x1..xn are the free
% 1.48/0.60 variables of u and v.
% 1.48/0.60 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 1.48/0.60 input problem has no model of domain size 1).
% 1.48/0.60
% 1.48/0.60 The encoding turns the above axioms into the following unit equations and goals:
% 1.48/0.60
% 1.48/0.60 Axiom 1 (cl5_nebula_init_0056_3): leq(n0, j) = true3.
% 1.48/0.60 Axiom 2 (cl5_nebula_init_0056_6): leq(j, n4) = true3.
% 1.48/0.60 Axiom 3 (cl5_nebula_init_0056): gt(loopcounter, n1) = true3.
% 1.48/0.60 Axiom 4 (cl5_nebula_init_0056_8): fresh61(X, X, Y) = init.
% 1.48/0.60 Axiom 5 (cl5_nebula_init_0056_8): fresh42(X, X, Y) = a_select2(muold_init, Y).
% 1.48/0.60 Axiom 6 (cl5_nebula_init_0056_8): fresh60(X, X, Y) = fresh61(gt(loopcounter, n1), true3, Y).
% 1.48/0.60 Axiom 7 (cl5_nebula_init_0056_8): fresh60(leq(n0, X), true3, X) = fresh42(leq(X, n4), true3, X).
% 1.48/0.60
% 1.48/0.60 Goal 1 (cl5_nebula_init_0056_7): a_select2(muold_init, j) = init.
% 1.48/0.60 Proof:
% 1.48/0.60 a_select2(muold_init, j)
% 1.48/0.60 = { by axiom 5 (cl5_nebula_init_0056_8) R->L }
% 1.48/0.60 fresh42(true3, true3, j)
% 1.48/0.60 = { by axiom 2 (cl5_nebula_init_0056_6) R->L }
% 1.48/0.60 fresh42(leq(j, n4), true3, j)
% 1.48/0.60 = { by axiom 7 (cl5_nebula_init_0056_8) R->L }
% 1.48/0.60 fresh60(leq(n0, j), true3, j)
% 1.48/0.60 = { by axiom 1 (cl5_nebula_init_0056_3) }
% 1.48/0.60 fresh60(true3, true3, j)
% 1.48/0.60 = { by axiom 6 (cl5_nebula_init_0056_8) }
% 1.48/0.60 fresh61(gt(loopcounter, n1), true3, j)
% 1.48/0.60 = { by axiom 3 (cl5_nebula_init_0056) }
% 1.48/0.60 fresh61(true3, true3, j)
% 1.48/0.60 = { by axiom 4 (cl5_nebula_init_0056_8) }
% 1.48/0.60 init
% 1.48/0.60 % SZS output end Proof
% 1.48/0.60
% 1.48/0.60 RESULT: Theorem (the conjecture is true).
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