TSTP Solution File: SWV168+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV168+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 : n022.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 23:02:50 EDT 2023
% Result : Theorem 0.10s 0.61s
% Output : Proof 2.44s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.07 % Problem : SWV168+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.04/0.07 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.06/0.26 % Computer : n022.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 300
% 0.06/0.26 % DateTime : Tue Aug 29 03:13:38 EDT 2023
% 0.06/0.26 % CPUTime :
% 0.10/0.61 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.10/0.61
% 0.10/0.61 % SZS status Theorem
% 0.10/0.61
% 0.10/0.61 % SZS output start Proof
% 0.10/0.61 Take the following subset of the input axioms:
% 2.44/0.62 fof(cl5_nebula_init_0016, conjecture, (a_select2(mu_init, pv40)=init & (leq(n0, pv40) & (leq(n0, pv46) & (leq(pv40, n4) & (leq(pv46, n135299) & (![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)))))))))))))) => a_select3(q_init, pv46, pv40)=init).
% 2.44/0.62
% 2.44/0.62 Now clausify the problem and encode Horn clauses using encoding 3 of
% 2.44/0.62 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 2.44/0.62 We repeatedly replace C & s=t => u=v by the two clauses:
% 2.44/0.62 fresh(y, y, x1...xn) = u
% 2.44/0.62 C => fresh(s, t, x1...xn) = v
% 2.44/0.62 where fresh is a fresh function symbol and x1..xn are the free
% 2.44/0.62 variables of u and v.
% 2.44/0.62 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 2.44/0.62 input problem has no model of domain size 1).
% 2.44/0.62
% 2.44/0.62 The encoding turns the above axioms into the following unit equations and goals:
% 2.44/0.62
% 2.44/0.62 Axiom 1 (cl5_nebula_init_0016_1): leq(n0, pv40) = true3.
% 2.44/0.62 Axiom 2 (cl5_nebula_init_0016_2): leq(n0, pv46) = true3.
% 2.44/0.62 Axiom 3 (cl5_nebula_init_0016_3): leq(pv40, n4) = true3.
% 2.44/0.62 Axiom 4 (cl5_nebula_init_0016_4): leq(pv46, n135299) = true3.
% 2.44/0.62 Axiom 5 (cl5_nebula_init_0016_9): fresh55(X, X, Y, Z) = init.
% 2.44/0.62 Axiom 6 (cl5_nebula_init_0016_9): fresh53(X, X, Y, Z) = a_select3(q_init, Y, Z).
% 2.44/0.62 Axiom 7 (cl5_nebula_init_0016_9): fresh54(X, X, Y, Z) = fresh55(leq(Y, n135299), true3, Y, Z).
% 2.44/0.62 Axiom 8 (cl5_nebula_init_0016_9): fresh52(X, X, Y, Z) = fresh53(leq(Z, n4), true3, Y, Z).
% 2.44/0.62 Axiom 9 (cl5_nebula_init_0016_9): fresh52(leq(n0, X), true3, Y, X) = fresh54(leq(n0, Y), true3, Y, X).
% 2.44/0.62
% 2.44/0.62 Goal 1 (cl5_nebula_init_0016_5): a_select3(q_init, pv46, pv40) = init.
% 2.44/0.62 Proof:
% 2.44/0.62 a_select3(q_init, pv46, pv40)
% 2.44/0.62 = { by axiom 6 (cl5_nebula_init_0016_9) R->L }
% 2.44/0.62 fresh53(true3, true3, pv46, pv40)
% 2.44/0.62 = { by axiom 3 (cl5_nebula_init_0016_3) R->L }
% 2.44/0.62 fresh53(leq(pv40, n4), true3, pv46, pv40)
% 2.44/0.62 = { by axiom 8 (cl5_nebula_init_0016_9) R->L }
% 2.44/0.62 fresh52(true3, true3, pv46, pv40)
% 2.44/0.62 = { by axiom 1 (cl5_nebula_init_0016_1) R->L }
% 2.44/0.62 fresh52(leq(n0, pv40), true3, pv46, pv40)
% 2.44/0.62 = { by axiom 9 (cl5_nebula_init_0016_9) }
% 2.44/0.62 fresh54(leq(n0, pv46), true3, pv46, pv40)
% 2.44/0.62 = { by axiom 2 (cl5_nebula_init_0016_2) }
% 2.44/0.62 fresh54(true3, true3, pv46, pv40)
% 2.44/0.62 = { by axiom 7 (cl5_nebula_init_0016_9) }
% 2.44/0.62 fresh55(leq(pv46, n135299), true3, pv46, pv40)
% 2.44/0.62 = { by axiom 4 (cl5_nebula_init_0016_4) }
% 2.44/0.62 fresh55(true3, true3, pv46, pv40)
% 2.44/0.62 = { by axiom 5 (cl5_nebula_init_0016_9) }
% 2.44/0.62 init
% 2.44/0.62 % SZS output end Proof
% 2.44/0.62
% 2.44/0.62 RESULT: Theorem (the conjecture is true).
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