TSTP Solution File: SWV046+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV046+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 : n004.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 23:02:20 EDT 2023
% Result : Theorem 0.19s 0.62s
% 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
% 0.07/0.12 % Problem : SWV046+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.13 % 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 : n004.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 03:01:52 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.62 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.62
% 0.19/0.62 % SZS status Theorem
% 0.19/0.62
% 0.19/0.63 % SZS output start Proof
% 0.19/0.63 Take the following subset of the input axioms:
% 0.19/0.63 fof(cl5_nebula_norm_0010, conjecture, (pv78=sum(n0, minus(n135300, n1), a_select3(q, pv79, pv35)) & (pv80=sum(n0, minus(n135300, n1), times(a_select3(q, pv81, pv35), a_select2(x, pv81))) & (leq(n0, pv35) & leq(pv35, minus(n5, n1))))) => ((n0!=pv44 => (n0=sum(n0, minus(n0, n1), times(minus(a_select2(x, pv83), a_select2(tptp_update2(mu, pv35, divide(pv80, pv44)), pv35)), times(minus(a_select2(x, pv83), a_select2(tptp_update2(mu, pv35, divide(pv80, pv44)), pv35)), a_select3(q, pv83, pv35)))) & (pv78=sum(n0, minus(n135300, n1), a_select3(q, pv79, pv35)) & (leq(n0, pv35) & leq(pv35, minus(n5, n1)))))) & (n0=pv44 => true))).
% 0.19/0.63 fof(pred_minus_1, axiom, ![X]: minus(X, n1)=pred(X)).
% 0.19/0.63 fof(pred_succ, axiom, ![X2]: pred(succ(X2))=X2).
% 0.19/0.63 fof(succ_tptp_minus_1, axiom, succ(tptp_minus_1)=n0).
% 0.19/0.63 fof(sum_plus_base, axiom, ![Body]: sum(n0, tptp_minus_1, Body)=n0).
% 0.19/0.63 fof(ttrue, axiom, true).
% 0.19/0.63
% 0.19/0.63 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.63 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.63 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.63 fresh(y, y, x1...xn) = u
% 0.19/0.63 C => fresh(s, t, x1...xn) = v
% 0.19/0.63 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.63 variables of u and v.
% 0.19/0.63 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.63 input problem has no model of domain size 1).
% 0.19/0.63
% 0.19/0.63 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.63
% 0.19/0.63 Axiom 1 (ttrue): true = true3.
% 0.19/0.63 Axiom 2 (succ_tptp_minus_1): succ(tptp_minus_1) = n0.
% 0.19/0.63 Axiom 3 (cl5_nebula_norm_0010_2): leq(n0, pv35) = true3.
% 0.19/0.63 Axiom 4 (pred_minus_1): minus(X, n1) = pred(X).
% 0.19/0.63 Axiom 5 (pred_succ): pred(succ(X)) = X.
% 0.19/0.63 Axiom 6 (sum_plus_base): sum(n0, tptp_minus_1, X) = n0.
% 0.19/0.63 Axiom 7 (cl5_nebula_norm_0010_3): leq(pv35, minus(n5, n1)) = true3.
% 0.19/0.63 Axiom 8 (cl5_nebula_norm_0010): pv78 = sum(n0, minus(n135300, n1), a_select3(q, pv79, pv35)).
% 0.19/0.63
% 0.19/0.63 Goal 1 (cl5_nebula_norm_0010_5): tuple2(n0, pv78, leq(n0, pv35), leq(pv35, minus(n5, n1)), true) = tuple2(sum(n0, minus(n0, n1), times(minus(a_select2(x, pv83), a_select2(tptp_update2(mu, pv35, divide(pv80, pv44)), pv35)), times(minus(a_select2(x, pv83), a_select2(tptp_update2(mu, pv35, divide(pv80, pv44)), pv35)), a_select3(q, pv83, pv35)))), sum(n0, minus(n135300, n1), a_select3(q, pv79, pv35)), true3, true3, true3).
% 0.19/0.63 Proof:
% 0.19/0.63 tuple2(n0, pv78, leq(n0, pv35), leq(pv35, minus(n5, n1)), true)
% 0.19/0.63 = { by axiom 3 (cl5_nebula_norm_0010_2) }
% 0.19/0.63 tuple2(n0, pv78, true3, leq(pv35, minus(n5, n1)), true)
% 0.19/0.63 = { by axiom 7 (cl5_nebula_norm_0010_3) }
% 0.19/0.63 tuple2(n0, pv78, true3, true3, true)
% 0.19/0.63 = { by axiom 1 (ttrue) }
% 0.19/0.63 tuple2(n0, pv78, true3, true3, true3)
% 0.19/0.63 = { by axiom 6 (sum_plus_base) R->L }
% 0.19/0.63 tuple2(sum(n0, tptp_minus_1, times(minus(a_select2(x, pv83), a_select2(tptp_update2(mu, pv35, divide(pv80, pv44)), pv35)), times(minus(a_select2(x, pv83), a_select2(tptp_update2(mu, pv35, divide(pv80, pv44)), pv35)), a_select3(q, pv83, pv35)))), pv78, true3, true3, true3)
% 0.19/0.63 = { by axiom 5 (pred_succ) R->L }
% 0.19/0.63 tuple2(sum(n0, pred(succ(tptp_minus_1)), times(minus(a_select2(x, pv83), a_select2(tptp_update2(mu, pv35, divide(pv80, pv44)), pv35)), times(minus(a_select2(x, pv83), a_select2(tptp_update2(mu, pv35, divide(pv80, pv44)), pv35)), a_select3(q, pv83, pv35)))), pv78, true3, true3, true3)
% 0.19/0.63 = { by axiom 2 (succ_tptp_minus_1) }
% 0.19/0.63 tuple2(sum(n0, pred(n0), times(minus(a_select2(x, pv83), a_select2(tptp_update2(mu, pv35, divide(pv80, pv44)), pv35)), times(minus(a_select2(x, pv83), a_select2(tptp_update2(mu, pv35, divide(pv80, pv44)), pv35)), a_select3(q, pv83, pv35)))), pv78, true3, true3, true3)
% 0.19/0.63 = { by axiom 4 (pred_minus_1) R->L }
% 0.19/0.63 tuple2(sum(n0, minus(n0, n1), times(minus(a_select2(x, pv83), a_select2(tptp_update2(mu, pv35, divide(pv80, pv44)), pv35)), times(minus(a_select2(x, pv83), a_select2(tptp_update2(mu, pv35, divide(pv80, pv44)), pv35)), a_select3(q, pv83, pv35)))), pv78, true3, true3, true3)
% 0.19/0.63 = { by axiom 8 (cl5_nebula_norm_0010) }
% 0.19/0.64 tuple2(sum(n0, minus(n0, n1), times(minus(a_select2(x, pv83), a_select2(tptp_update2(mu, pv35, divide(pv80, pv44)), pv35)), times(minus(a_select2(x, pv83), a_select2(tptp_update2(mu, pv35, divide(pv80, pv44)), pv35)), a_select3(q, pv83, pv35)))), sum(n0, minus(n135300, n1), a_select3(q, pv79, pv35)), true3, true3, true3)
% 0.19/0.64 % SZS output end Proof
% 0.19/0.64
% 0.19/0.64 RESULT: Theorem (the conjecture is true).
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