TSTP Solution File: SEU089+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SEU089+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : n013.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 17:50:58 EDT 2023
% Result : Theorem 3.51s 0.88s
% Output : Proof 3.51s
% 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 : SEU089+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n013.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 : Wed Aug 23 14:20:47 EDT 2023
% 0.13/0.34 % CPUTime :
% 3.51/0.88 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 3.51/0.88
% 3.51/0.88 % SZS status Theorem
% 3.51/0.88
% 3.51/0.88 % SZS output start Proof
% 3.51/0.88 Take the following subset of the input axioms:
% 3.51/0.88 fof(d3_zfmisc_1, axiom, ![A, B, C]: cartesian_product3(A, B, C)=cartesian_product2(cartesian_product2(A, B), C)).
% 3.51/0.88 fof(fc14_finset_1, axiom, ![A2, B2]: ((finite(A2) & finite(B2)) => finite(cartesian_product2(A2, B2)))).
% 3.51/0.88 fof(t20_finset_1, conjecture, ![A3, B2, C2]: ((finite(A3) & (finite(B2) & finite(C2))) => finite(cartesian_product3(A3, B2, C2)))).
% 3.51/0.88
% 3.51/0.88 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.51/0.88 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.51/0.88 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.51/0.88 fresh(y, y, x1...xn) = u
% 3.51/0.88 C => fresh(s, t, x1...xn) = v
% 3.51/0.88 where fresh is a fresh function symbol and x1..xn are the free
% 3.51/0.88 variables of u and v.
% 3.51/0.88 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.51/0.88 input problem has no model of domain size 1).
% 3.51/0.88
% 3.51/0.88 The encoding turns the above axioms into the following unit equations and goals:
% 3.51/0.88
% 3.51/0.88 Axiom 1 (t20_finset_1): finite(b) = true2.
% 3.51/0.88 Axiom 2 (t20_finset_1_1): finite(c) = true2.
% 3.51/0.88 Axiom 3 (t20_finset_1_2): finite(a) = true2.
% 3.51/0.88 Axiom 4 (d3_zfmisc_1): cartesian_product3(X, Y, Z) = cartesian_product2(cartesian_product2(X, Y), Z).
% 3.51/0.88 Axiom 5 (fc14_finset_1): fresh14(X, X, Y, Z) = finite(cartesian_product2(Y, Z)).
% 3.51/0.88 Axiom 6 (fc14_finset_1): fresh13(X, X, Y, Z) = true2.
% 3.51/0.88 Axiom 7 (fc14_finset_1): fresh14(finite(X), true2, Y, X) = fresh13(finite(Y), true2, Y, X).
% 3.51/0.88
% 3.51/0.88 Goal 1 (t20_finset_1_3): finite(cartesian_product3(a, b, c)) = true2.
% 3.51/0.88 Proof:
% 3.51/0.88 finite(cartesian_product3(a, b, c))
% 3.51/0.88 = { by axiom 4 (d3_zfmisc_1) }
% 3.51/0.89 finite(cartesian_product2(cartesian_product2(a, b), c))
% 3.51/0.89 = { by axiom 5 (fc14_finset_1) R->L }
% 3.51/0.89 fresh14(true2, true2, cartesian_product2(a, b), c)
% 3.51/0.89 = { by axiom 2 (t20_finset_1_1) R->L }
% 3.51/0.89 fresh14(finite(c), true2, cartesian_product2(a, b), c)
% 3.51/0.89 = { by axiom 7 (fc14_finset_1) }
% 3.51/0.89 fresh13(finite(cartesian_product2(a, b)), true2, cartesian_product2(a, b), c)
% 3.51/0.89 = { by axiom 5 (fc14_finset_1) R->L }
% 3.51/0.89 fresh13(fresh14(true2, true2, a, b), true2, cartesian_product2(a, b), c)
% 3.51/0.89 = { by axiom 1 (t20_finset_1) R->L }
% 3.51/0.89 fresh13(fresh14(finite(b), true2, a, b), true2, cartesian_product2(a, b), c)
% 3.51/0.89 = { by axiom 7 (fc14_finset_1) }
% 3.51/0.89 fresh13(fresh13(finite(a), true2, a, b), true2, cartesian_product2(a, b), c)
% 3.51/0.89 = { by axiom 3 (t20_finset_1_2) }
% 3.51/0.89 fresh13(fresh13(true2, true2, a, b), true2, cartesian_product2(a, b), c)
% 3.51/0.89 = { by axiom 6 (fc14_finset_1) }
% 3.51/0.89 fresh13(true2, true2, cartesian_product2(a, b), c)
% 3.51/0.89 = { by axiom 6 (fc14_finset_1) }
% 3.51/0.89 true2
% 3.51/0.89 % SZS output end Proof
% 3.51/0.89
% 3.51/0.89 RESULT: Theorem (the conjecture is true).
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