TSTP Solution File: SWV412+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SWV412+1 : TPTP v8.1.2. Released 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 : n027.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 23:04:09 EDT 2023
% Result : Theorem 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWV412+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n027.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Aug 29 09:20:53 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.43 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.43
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43
% 0.21/0.43 % SZS output start Proof
% 0.21/0.43 Take the following subset of the input axioms:
% 0.21/0.43 fof(l48_co, conjecture, ![U, V, W, X]: ((pair_in_list(U, V, W) & (strictly_less_than(V, X) & strictly_less_than(W, X))) => pair_in_list(update_slb(U, X), V, X))).
% 0.21/0.43 fof(l48_li3839, lemma, ![U2, V2, W2, X2]: ((pair_in_list(U2, V2, W2) & strictly_less_than(W2, X2)) => pair_in_list(update_slb(U2, X2), V2, X2))).
% 0.21/0.43
% 0.21/0.43 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.43 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.43 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.43 fresh(y, y, x1...xn) = u
% 0.21/0.43 C => fresh(s, t, x1...xn) = v
% 0.21/0.43 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.43 variables of u and v.
% 0.21/0.43 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.43 input problem has no model of domain size 1).
% 0.21/0.43
% 0.21/0.43 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.43
% 0.21/0.43 Axiom 1 (l48_co_1): strictly_less_than(w, x) = true2.
% 0.21/0.43 Axiom 2 (l48_co_2): pair_in_list(u, v, w) = true2.
% 0.21/0.43 Axiom 3 (l48_li3839): fresh4(X, X, Y, Z, W) = true2.
% 0.21/0.43 Axiom 4 (l48_li3839): fresh5(X, X, Y, Z, W, V) = pair_in_list(update_slb(Y, V), Z, V).
% 0.21/0.43 Axiom 5 (l48_li3839): fresh5(pair_in_list(X, Y, Z), true2, X, Y, Z, W) = fresh4(strictly_less_than(Z, W), true2, X, Y, W).
% 0.21/0.43
% 0.21/0.43 Goal 1 (l48_co_3): pair_in_list(update_slb(u, x), v, x) = true2.
% 0.21/0.43 Proof:
% 0.21/0.43 pair_in_list(update_slb(u, x), v, x)
% 0.21/0.43 = { by axiom 4 (l48_li3839) R->L }
% 0.21/0.43 fresh5(true2, true2, u, v, w, x)
% 0.21/0.43 = { by axiom 2 (l48_co_2) R->L }
% 0.21/0.43 fresh5(pair_in_list(u, v, w), true2, u, v, w, x)
% 0.21/0.43 = { by axiom 5 (l48_li3839) }
% 0.21/0.43 fresh4(strictly_less_than(w, x), true2, u, v, x)
% 0.21/0.43 = { by axiom 1 (l48_co_1) }
% 0.21/0.43 fresh4(true2, true2, u, v, x)
% 0.21/0.43 = { by axiom 3 (l48_li3839) }
% 0.21/0.43 true2
% 0.21/0.43 % SZS output end Proof
% 0.21/0.43
% 0.21/0.43 RESULT: Theorem (the conjecture is true).
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