TSTP Solution File: SWV056+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SWV056+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 : n024.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 23:02:22 EDT 2023
% Result : Theorem 0.19s 0.53s
% 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 : SWV056+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 : n024.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 03:45:08 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.53 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.19/0.53
% 0.19/0.53 % SZS status Theorem
% 0.19/0.53
% 0.19/0.53 % SZS output start Proof
% 0.19/0.53 Take the following subset of the input axioms:
% 0.19/0.53 fof(cl5_nebula_norm_0040, conjecture, (leq(n0, pv25) & leq(pv25, minus(n5, n1))) => (n0=sum(n0, minus(n0, n1), a_select3(q, pv77, pv25)) & (leq(n0, pv25) & leq(pv25, minus(n5, n1))))).
% 0.19/0.53 fof(pred_minus_1, axiom, ![X]: minus(X, n1)=pred(X)).
% 0.19/0.53 fof(pred_succ, axiom, ![X2]: pred(succ(X2))=X2).
% 0.19/0.53 fof(succ_tptp_minus_1, axiom, succ(tptp_minus_1)=n0).
% 0.19/0.53 fof(sum_plus_base, axiom, ![Body]: sum(n0, tptp_minus_1, Body)=n0).
% 0.19/0.53
% 0.19/0.53 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.53 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.53 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.53 fresh(y, y, x1...xn) = u
% 0.19/0.53 C => fresh(s, t, x1...xn) = v
% 0.19/0.53 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.53 variables of u and v.
% 0.19/0.53 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.53 input problem has no model of domain size 1).
% 0.19/0.53
% 0.19/0.53 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.53
% 0.19/0.53 Axiom 1 (cl5_nebula_norm_0040): leq(n0, pv25) = true3.
% 0.19/0.53 Axiom 2 (succ_tptp_minus_1): succ(tptp_minus_1) = n0.
% 0.19/0.53 Axiom 3 (pred_minus_1): minus(X, n1) = pred(X).
% 0.19/0.53 Axiom 4 (cl5_nebula_norm_0040_1): leq(pv25, minus(n5, n1)) = true3.
% 0.19/0.53 Axiom 5 (pred_succ): pred(succ(X)) = X.
% 0.19/0.53 Axiom 6 (sum_plus_base): sum(n0, tptp_minus_1, X) = n0.
% 0.19/0.53
% 0.19/0.53 Goal 1 (cl5_nebula_norm_0040_2): tuple(n0, leq(n0, pv25), leq(pv25, minus(n5, n1))) = tuple(sum(n0, minus(n0, n1), a_select3(q, pv77, pv25)), true3, true3).
% 0.19/0.53 Proof:
% 0.19/0.53 tuple(n0, leq(n0, pv25), leq(pv25, minus(n5, n1)))
% 0.19/0.53 = { by axiom 1 (cl5_nebula_norm_0040) }
% 0.19/0.53 tuple(n0, true3, leq(pv25, minus(n5, n1)))
% 0.19/0.53 = { by axiom 4 (cl5_nebula_norm_0040_1) }
% 0.19/0.53 tuple(n0, true3, true3)
% 0.19/0.53 = { by axiom 6 (sum_plus_base) R->L }
% 0.19/0.53 tuple(sum(n0, tptp_minus_1, a_select3(q, pv77, pv25)), true3, true3)
% 0.19/0.53 = { by axiom 5 (pred_succ) R->L }
% 0.19/0.53 tuple(sum(n0, pred(succ(tptp_minus_1)), a_select3(q, pv77, pv25)), true3, true3)
% 0.19/0.53 = { by axiom 3 (pred_minus_1) R->L }
% 0.19/0.53 tuple(sum(n0, minus(succ(tptp_minus_1), n1), a_select3(q, pv77, pv25)), true3, true3)
% 0.19/0.53 = { by axiom 2 (succ_tptp_minus_1) }
% 0.19/0.53 tuple(sum(n0, minus(n0, n1), a_select3(q, pv77, pv25)), true3, true3)
% 0.19/0.53 % SZS output end Proof
% 0.19/0.53
% 0.19/0.53 RESULT: Theorem (the conjecture is true).
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