TSTP Solution File: SWV187+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV187+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 : n029.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 23:02:55 EDT 2023
% Result : Theorem 1.56s 0.58s
% Output : Proof 1.56s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV187+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.03/0.13 % 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 : n029.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 07:59:26 EDT 2023
% 0.13/0.35 % CPUTime :
% 1.56/0.58 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 1.56/0.58
% 1.56/0.58 % SZS status Theorem
% 1.56/0.58
% 1.56/0.58 % SZS output start Proof
% 1.56/0.58 Take the following subset of the input axioms:
% 1.56/0.58 fof(cl5_nebula_init_0111, conjecture, (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_select3(center_init, C, n0)=init) & ((gt(loopcounter, n1) => ![D]: ((leq(n0, D) & leq(D, n4)) => a_select2(muold_init, D)=init)) & ((gt(loopcounter, n1) => ![E]: ((leq(n0, E) & leq(E, n4)) => a_select2(rhoold_init, E)=init)) & (gt(loopcounter, n1) => ![F]: ((leq(n0, F) & leq(F, n4)) => a_select2(sigmaold_init, F)=init))))))) => ![G]: ((leq(n0, G) & leq(G, n4)) => a_select2(sigmaold_init, G)=init)).
% 1.56/0.58
% 1.56/0.58 Now clausify the problem and encode Horn clauses using encoding 3 of
% 1.56/0.58 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 1.56/0.58 We repeatedly replace C & s=t => u=v by the two clauses:
% 1.56/0.58 fresh(y, y, x1...xn) = u
% 1.56/0.58 C => fresh(s, t, x1...xn) = v
% 1.56/0.58 where fresh is a fresh function symbol and x1..xn are the free
% 1.56/0.58 variables of u and v.
% 1.56/0.58 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 1.56/0.58 input problem has no model of domain size 1).
% 1.56/0.58
% 1.56/0.58 The encoding turns the above axioms into the following unit equations and goals:
% 1.56/0.58
% 1.56/0.58 Axiom 1 (cl5_nebula_init_0111_1): leq(n0, g) = true3.
% 1.56/0.58 Axiom 2 (cl5_nebula_init_0111_2): leq(g, n4) = true3.
% 1.56/0.58 Axiom 3 (cl5_nebula_init_0111): gt(loopcounter, n1) = true3.
% 1.56/0.58 Axiom 4 (cl5_nebula_init_0111_6): fresh51(X, X, Y) = init.
% 1.56/0.58 Axiom 5 (cl5_nebula_init_0111_6): fresh43(X, X, Y) = a_select2(sigmaold_init, Y).
% 1.56/0.58 Axiom 6 (cl5_nebula_init_0111_6): fresh50(X, X, Y) = fresh51(gt(loopcounter, n1), true3, Y).
% 1.56/0.58 Axiom 7 (cl5_nebula_init_0111_6): fresh50(leq(n0, X), true3, X) = fresh43(leq(X, n4), true3, X).
% 1.56/0.58
% 1.56/0.58 Goal 1 (cl5_nebula_init_0111_3): a_select2(sigmaold_init, g) = init.
% 1.56/0.58 Proof:
% 1.56/0.58 a_select2(sigmaold_init, g)
% 1.56/0.58 = { by axiom 5 (cl5_nebula_init_0111_6) R->L }
% 1.56/0.58 fresh43(true3, true3, g)
% 1.56/0.58 = { by axiom 2 (cl5_nebula_init_0111_2) R->L }
% 1.56/0.58 fresh43(leq(g, n4), true3, g)
% 1.56/0.58 = { by axiom 7 (cl5_nebula_init_0111_6) R->L }
% 1.56/0.58 fresh50(leq(n0, g), true3, g)
% 1.56/0.58 = { by axiom 1 (cl5_nebula_init_0111_1) }
% 1.56/0.58 fresh50(true3, true3, g)
% 1.56/0.58 = { by axiom 6 (cl5_nebula_init_0111_6) }
% 1.56/0.58 fresh51(gt(loopcounter, n1), true3, g)
% 1.56/0.58 = { by axiom 3 (cl5_nebula_init_0111) }
% 1.56/0.58 fresh51(true3, true3, g)
% 1.56/0.58 = { by axiom 4 (cl5_nebula_init_0111_6) }
% 1.56/0.58 init
% 1.56/0.58 % SZS output end Proof
% 1.56/0.59
% 1.56/0.59 RESULT: Theorem (the conjecture is true).
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