TSTP Solution File: SET949+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SET949+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 : n023.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 15:33:49 EDT 2023
% Result : Theorem 0.10s 0.37s
% Output : Proof 0.10s
% 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 : SET949+1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.32 % Computer : n023.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Sat Aug 26 12:42:11 EDT 2023
% 0.10/0.32 % CPUTime :
% 0.10/0.37 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.10/0.37
% 0.10/0.37 % SZS status Theorem
% 0.10/0.37
% 0.10/0.37 % SZS output start Proof
% 0.10/0.37 Take the following subset of the input axioms:
% 0.10/0.37 fof(antisymmetry_r2_hidden, axiom, ![A, B]: (in(A, B) => ~in(B, A))).
% 0.10/0.37 fof(d2_zfmisc_1, axiom, ![C, A2, B2]: (C=cartesian_product2(A2, B2) <=> ![D]: (in(D, C) <=> ?[E, F]: (in(E, A2) & (in(F, B2) & D=ordered_pair(E, F)))))).
% 0.10/0.37 fof(fc1_zfmisc_1, axiom, ![A3, B2]: ~empty(ordered_pair(A3, B2))).
% 0.10/0.37 fof(t102_zfmisc_1, conjecture, ![A3, B2, C2]: ~(in(A3, cartesian_product2(B2, C2)) & ![D2, E2]: ordered_pair(D2, E2)!=A3)).
% 0.10/0.37
% 0.10/0.37 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.10/0.37 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.10/0.37 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.10/0.37 fresh(y, y, x1...xn) = u
% 0.10/0.37 C => fresh(s, t, x1...xn) = v
% 0.10/0.37 where fresh is a fresh function symbol and x1..xn are the free
% 0.10/0.37 variables of u and v.
% 0.10/0.37 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.10/0.37 input problem has no model of domain size 1).
% 0.10/0.37
% 0.10/0.37 The encoding turns the above axioms into the following unit equations and goals:
% 0.10/0.37
% 0.10/0.37 Axiom 1 (t102_zfmisc_1): in(a, cartesian_product2(b, c)) = true2.
% 0.10/0.37 Axiom 2 (d2_zfmisc_1_1): fresh10(X, X, Y, Z, W) = true2.
% 0.10/0.37 Axiom 3 (d2_zfmisc_1_5): fresh2(X, X, Y, Z, W) = W.
% 0.10/0.37 Axiom 4 (d2_zfmisc_1_1): fresh9(X, X, Y, Z, W, V) = equiv(Y, Z, V).
% 0.10/0.37 Axiom 5 (d2_zfmisc_1_1): fresh9(in(X, Y), true2, Z, W, Y, X) = fresh10(Y, cartesian_product2(Z, W), Z, W, X).
% 0.10/0.37 Axiom 6 (d2_zfmisc_1_5): fresh2(equiv(X, Y, Z), true2, X, Y, Z) = ordered_pair(e(X, Y, Z), f(X, Y, Z)).
% 0.10/0.38
% 0.10/0.38 Goal 1 (t102_zfmisc_1_1): ordered_pair(X, Y) = a.
% 0.10/0.38 The goal is true when:
% 0.10/0.38 X = e(b, c, a)
% 0.10/0.38 Y = f(b, c, a)
% 0.10/0.38
% 0.10/0.38 Proof:
% 0.10/0.38 ordered_pair(e(b, c, a), f(b, c, a))
% 0.10/0.38 = { by axiom 6 (d2_zfmisc_1_5) R->L }
% 0.10/0.38 fresh2(equiv(b, c, a), true2, b, c, a)
% 0.10/0.38 = { by axiom 4 (d2_zfmisc_1_1) R->L }
% 0.10/0.38 fresh2(fresh9(true2, true2, b, c, cartesian_product2(b, c), a), true2, b, c, a)
% 0.10/0.38 = { by axiom 1 (t102_zfmisc_1) R->L }
% 0.10/0.38 fresh2(fresh9(in(a, cartesian_product2(b, c)), true2, b, c, cartesian_product2(b, c), a), true2, b, c, a)
% 0.10/0.38 = { by axiom 5 (d2_zfmisc_1_1) }
% 0.10/0.38 fresh2(fresh10(cartesian_product2(b, c), cartesian_product2(b, c), b, c, a), true2, b, c, a)
% 0.10/0.38 = { by axiom 2 (d2_zfmisc_1_1) }
% 0.10/0.38 fresh2(true2, true2, b, c, a)
% 0.10/0.38 = { by axiom 3 (d2_zfmisc_1_5) }
% 0.10/0.38 a
% 0.10/0.38 % SZS output end Proof
% 0.10/0.38
% 0.10/0.38 RESULT: Theorem (the conjecture is true).
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