TSTP Solution File: SEU267+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SEU267+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 : n031.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 17:51:55 EDT 2023
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU267+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n031.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % 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 : Wed Aug 23 16:21:20 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.41 Command-line arguments: --no-flatten-goal
% 0.20/0.41
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 Take the following subset of the input axioms:
% 0.20/0.41 fof(d1_mcart_1, axiom, ![A2]: (?[B2, C2]: A2=ordered_pair(B2, C2) => ![B]: (B=pair_first(A2) <=> ![C, D]: (A2=ordered_pair(C, D) => B=C)))).
% 0.20/0.41 fof(d2_mcart_1, axiom, ![A2_2]: (?[C3, B2_2]: A2_2=ordered_pair(B2_2, C3) => ![B3]: (B3=pair_second(A2_2) <=> ![D2, C2_2]: (A2_2=ordered_pair(C2_2, D2) => B3=D2)))).
% 0.20/0.42 fof(t7_mcart_1, conjecture, ![A, B3]: (pair_first(ordered_pair(A, B3))=A & pair_second(ordered_pair(A, B3))=B3)).
% 0.20/0.42
% 0.20/0.42 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.42 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.42 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.42 fresh(y, y, x1...xn) = u
% 0.20/0.42 C => fresh(s, t, x1...xn) = v
% 0.20/0.42 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.42 variables of u and v.
% 0.20/0.42 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.42 input problem has no model of domain size 1).
% 0.20/0.42
% 0.20/0.42 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.42
% 0.20/0.42 Axiom 1 (d1_mcart_1_1): fresh14(X, X, Y, Z) = Z.
% 0.20/0.42 Axiom 2 (d2_mcart_1_1): fresh12(X, X, Y, Z) = Z.
% 0.20/0.42 Axiom 3 (d2_mcart_1_1): fresh(X, X, Y, Z, W, V, U) = V.
% 0.20/0.42 Axiom 4 (d1_mcart_1_1): fresh3(X, X, Y, Z, W, V, U) = V.
% 0.20/0.42 Axiom 5 (d1_mcart_1_1): fresh13(X, X, Y, Z, W, V, U, T) = fresh14(Y, ordered_pair(Z, W), V, U).
% 0.20/0.42 Axiom 6 (d2_mcart_1_1): fresh11(X, X, Y, Z, W, V, U, T) = fresh12(Y, ordered_pair(Z, W), V, T).
% 0.20/0.42 Axiom 7 (d2_mcart_1_1): fresh11(X, pair_second(Y), Y, Z, W, X, V, U) = fresh(Y, ordered_pair(V, U), Y, Z, W, X, U).
% 0.20/0.42 Axiom 8 (d1_mcart_1_1): fresh13(X, pair_first(Y), Y, Z, W, X, V, U) = fresh3(Y, ordered_pair(V, U), Y, Z, W, X, V).
% 0.20/0.42
% 0.20/0.42 Goal 1 (t7_mcart_1): tuple2(pair_first(ordered_pair(a2, b2)), pair_second(ordered_pair(a, b))) = tuple2(a2, b).
% 0.20/0.42 Proof:
% 0.20/0.42 tuple2(pair_first(ordered_pair(a2, b2)), pair_second(ordered_pair(a, b)))
% 0.20/0.42 = { by axiom 3 (d2_mcart_1_1) R->L }
% 0.20/0.42 tuple2(pair_first(ordered_pair(a2, b2)), fresh(ordered_pair(a, b), ordered_pair(a, b), ordered_pair(a, b), a, b, pair_second(ordered_pair(a, b)), b))
% 0.20/0.42 = { by axiom 7 (d2_mcart_1_1) R->L }
% 0.20/0.42 tuple2(pair_first(ordered_pair(a2, b2)), fresh11(pair_second(ordered_pair(a, b)), pair_second(ordered_pair(a, b)), ordered_pair(a, b), a, b, pair_second(ordered_pair(a, b)), a, b))
% 0.20/0.42 = { by axiom 6 (d2_mcart_1_1) }
% 0.20/0.42 tuple2(pair_first(ordered_pair(a2, b2)), fresh12(ordered_pair(a, b), ordered_pair(a, b), pair_second(ordered_pair(a, b)), b))
% 0.20/0.42 = { by axiom 2 (d2_mcart_1_1) }
% 0.20/0.42 tuple2(pair_first(ordered_pair(a2, b2)), b)
% 0.20/0.42 = { by axiom 4 (d1_mcart_1_1) R->L }
% 0.20/0.42 tuple2(fresh3(ordered_pair(a2, b2), ordered_pair(a2, b2), ordered_pair(a2, b2), a2, b2, pair_first(ordered_pair(a2, b2)), a2), b)
% 0.20/0.42 = { by axiom 8 (d1_mcart_1_1) R->L }
% 0.20/0.42 tuple2(fresh13(pair_first(ordered_pair(a2, b2)), pair_first(ordered_pair(a2, b2)), ordered_pair(a2, b2), a2, b2, pair_first(ordered_pair(a2, b2)), a2, b2), b)
% 0.20/0.42 = { by axiom 5 (d1_mcart_1_1) }
% 0.20/0.42 tuple2(fresh14(ordered_pair(a2, b2), ordered_pair(a2, b2), pair_first(ordered_pair(a2, b2)), a2), b)
% 0.20/0.42 = { by axiom 1 (d1_mcart_1_1) }
% 0.20/0.42 tuple2(a2, b)
% 0.20/0.42 % SZS output end Proof
% 0.20/0.42
% 0.20/0.42 RESULT: Theorem (the conjecture is true).
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