TSTP Solution File: SEU230+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SEU230+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 : n011.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 17:51:42 EDT 2023
% Result : Theorem 0.22s 0.50s
% Output : Proof 0.22s
% 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 : SEU230+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
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % 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 : Wed Aug 23 12:26:22 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.50 Command-line arguments: --no-flatten-goal
% 0.22/0.50
% 0.22/0.50 % SZS status Theorem
% 0.22/0.50
% 0.22/0.51 % SZS output start Proof
% 0.22/0.51 Take the following subset of the input axioms:
% 0.22/0.51 fof(commutativity_k2_xboole_0, axiom, ![A, B]: set_union2(A, B)=set_union2(B, A)).
% 0.22/0.51 fof(d1_ordinal1, axiom, ![A3]: succ(A3)=set_union2(A3, singleton(A3))).
% 0.22/0.51 fof(d1_tarski, axiom, ![A2, B2]: (B2=singleton(A2) <=> ![C]: (in(C, B2) <=> C=A2))).
% 0.22/0.51 fof(d2_xboole_0, axiom, ![B2, C2, A2_2]: (C2=set_union2(A2_2, B2) <=> ![D]: (in(D, C2) <=> (in(D, A2_2) | in(D, B2))))).
% 0.22/0.51 fof(t10_ordinal1, conjecture, ![A3]: in(A3, succ(A3))).
% 0.22/0.51
% 0.22/0.51 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.51 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.51 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.51 fresh(y, y, x1...xn) = u
% 0.22/0.51 C => fresh(s, t, x1...xn) = v
% 0.22/0.51 where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.51 variables of u and v.
% 0.22/0.51 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.51 input problem has no model of domain size 1).
% 0.22/0.51
% 0.22/0.51 The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.51
% 0.22/0.51 Axiom 1 (commutativity_k2_xboole_0): set_union2(X, Y) = set_union2(Y, X).
% 0.22/0.51 Axiom 2 (d1_ordinal1): succ(X) = set_union2(X, singleton(X)).
% 0.22/0.51 Axiom 3 (d1_tarski_2): fresh20(X, X, Y, Z) = true2.
% 0.22/0.51 Axiom 4 (d2_xboole_0_2): fresh16(X, X, Y, Z) = true2.
% 0.22/0.51 Axiom 5 (d1_tarski_2): fresh20(X, singleton(Y), Y, X) = in(Y, X).
% 0.22/0.51 Axiom 6 (d2_xboole_0_3): fresh15(X, X, Y, Z, W) = true2.
% 0.22/0.51 Axiom 7 (d2_xboole_0_2): fresh17(X, X, Y, Z, W, V) = in(V, W).
% 0.22/0.51 Axiom 8 (d2_xboole_0_3): fresh15(in(X, Y), true2, Y, Z, X) = equiv(Y, Z, X).
% 0.22/0.51 Axiom 9 (d2_xboole_0_2): fresh17(equiv(X, Y, Z), true2, X, Y, W, Z) = fresh16(W, set_union2(X, Y), W, Z).
% 0.22/0.51
% 0.22/0.51 Goal 1 (t10_ordinal1): in(a, succ(a)) = true2.
% 0.22/0.51 Proof:
% 0.22/0.51 in(a, succ(a))
% 0.22/0.51 = { by axiom 2 (d1_ordinal1) }
% 0.22/0.51 in(a, set_union2(a, singleton(a)))
% 0.22/0.51 = { by axiom 1 (commutativity_k2_xboole_0) R->L }
% 0.22/0.51 in(a, set_union2(singleton(a), a))
% 0.22/0.51 = { by axiom 7 (d2_xboole_0_2) R->L }
% 0.22/0.51 fresh17(true2, true2, singleton(a), a, set_union2(singleton(a), a), a)
% 0.22/0.51 = { by axiom 6 (d2_xboole_0_3) R->L }
% 0.22/0.51 fresh17(fresh15(true2, true2, singleton(a), a, a), true2, singleton(a), a, set_union2(singleton(a), a), a)
% 0.22/0.51 = { by axiom 3 (d1_tarski_2) R->L }
% 0.22/0.51 fresh17(fresh15(fresh20(singleton(a), singleton(a), a, singleton(a)), true2, singleton(a), a, a), true2, singleton(a), a, set_union2(singleton(a), a), a)
% 0.22/0.51 = { by axiom 5 (d1_tarski_2) }
% 0.22/0.51 fresh17(fresh15(in(a, singleton(a)), true2, singleton(a), a, a), true2, singleton(a), a, set_union2(singleton(a), a), a)
% 0.22/0.51 = { by axiom 8 (d2_xboole_0_3) }
% 0.22/0.51 fresh17(equiv(singleton(a), a, a), true2, singleton(a), a, set_union2(singleton(a), a), a)
% 0.22/0.51 = { by axiom 9 (d2_xboole_0_2) }
% 0.22/0.51 fresh16(set_union2(singleton(a), a), set_union2(singleton(a), a), set_union2(singleton(a), a), a)
% 0.22/0.51 = { by axiom 4 (d2_xboole_0_2) }
% 0.22/0.51 true2
% 0.22/0.51 % SZS output end Proof
% 0.22/0.51
% 0.22/0.51 RESULT: Theorem (the conjecture is true).
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