TSTP Solution File: SWV413+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SWV413+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 : n032.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 0.15s 0.36s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : SWV413+1 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue Aug 29 09:48:31 EDT 2023
% 0.10/0.30 % CPUTime :
% 0.15/0.36 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.15/0.36
% 0.15/0.36 % SZS status Theorem
% 0.15/0.36
% 0.15/0.36 % SZS output start Proof
% 0.15/0.36 Take the following subset of the input axioms:
% 0.15/0.36 fof(ax20, axiom, ![U]: ~contains_slb(create_slb, U)).
% 0.15/0.37 fof(ax22, axiom, ![V, U2]: ~pair_in_list(create_slb, U2, V)).
% 0.15/0.37 fof(l49_co, conjecture, ![W, X, U2, V2]: ((pair_in_list(U2, V2, W) & (strictly_less_than(V2, X) & less_than(X, W))) => ?[Y]: (pair_in_list(update_slb(U2, X), V2, Y) & less_than(X, Y)))).
% 0.15/0.37 fof(l49_li3637, lemma, ![U2, V2, W2, X2]: ((pair_in_list(U2, V2, W2) & less_than(X2, W2)) => pair_in_list(update_slb(U2, X2), V2, W2))).
% 0.15/0.37 fof(stricly_smaller_definition, axiom, ![U2, V2]: (strictly_less_than(U2, V2) <=> (less_than(U2, V2) & ~less_than(V2, U2)))).
% 0.15/0.37
% 0.15/0.37 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.15/0.37 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.15/0.37 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.15/0.37 fresh(y, y, x1...xn) = u
% 0.15/0.37 C => fresh(s, t, x1...xn) = v
% 0.15/0.37 where fresh is a fresh function symbol and x1..xn are the free
% 0.15/0.37 variables of u and v.
% 0.15/0.37 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.15/0.37 input problem has no model of domain size 1).
% 0.15/0.37
% 0.15/0.37 The encoding turns the above axioms into the following unit equations and goals:
% 0.15/0.37
% 0.15/0.37 Axiom 1 (l49_co): less_than(x, w) = true2.
% 0.15/0.37 Axiom 2 (l49_co_2): pair_in_list(u, v, w) = true2.
% 0.15/0.37 Axiom 3 (l49_li3637): fresh5(X, X, Y, Z, W, V) = pair_in_list(update_slb(Y, V), Z, W).
% 0.15/0.37 Axiom 4 (l49_li3637): fresh4(X, X, Y, Z, W, V) = true2.
% 0.15/0.37 Axiom 5 (l49_li3637): fresh5(pair_in_list(X, Y, Z), true2, X, Y, Z, W) = fresh4(less_than(W, Z), true2, X, Y, Z, W).
% 0.15/0.37
% 0.15/0.37 Goal 1 (l49_co_3): tuple(less_than(x, X), pair_in_list(update_slb(u, x), v, X)) = tuple(true2, true2).
% 0.15/0.37 The goal is true when:
% 0.15/0.37 X = w
% 0.15/0.37
% 0.15/0.37 Proof:
% 0.15/0.37 tuple(less_than(x, w), pair_in_list(update_slb(u, x), v, w))
% 0.15/0.37 = { by axiom 3 (l49_li3637) R->L }
% 0.15/0.37 tuple(less_than(x, w), fresh5(true2, true2, u, v, w, x))
% 0.15/0.37 = { by axiom 2 (l49_co_2) R->L }
% 0.15/0.37 tuple(less_than(x, w), fresh5(pair_in_list(u, v, w), true2, u, v, w, x))
% 0.15/0.37 = { by axiom 5 (l49_li3637) }
% 0.15/0.37 tuple(less_than(x, w), fresh4(less_than(x, w), true2, u, v, w, x))
% 0.15/0.37 = { by axiom 1 (l49_co) }
% 0.15/0.37 tuple(less_than(x, w), fresh4(true2, true2, u, v, w, x))
% 0.15/0.37 = { by axiom 4 (l49_li3637) }
% 0.15/0.37 tuple(less_than(x, w), true2)
% 0.15/0.37 = { by axiom 1 (l49_co) }
% 0.15/0.37 tuple(true2, true2)
% 0.15/0.37 % SZS output end Proof
% 0.15/0.37
% 0.15/0.37 RESULT: Theorem (the conjecture is true).
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