TSTP Solution File: SEU303+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SEU303+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 17:52:06 EDT 2023
% Result : Theorem 0.15s 0.40s
% 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
% 0.00/0.13 % Problem : SEU303+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
% 0.10/0.36 % Computer : n032.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8042.1875MB
% 0.10/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Aug 23 12:15:13 EDT 2023
% 0.10/0.36 % CPUTime :
% 0.15/0.40 Command-line arguments: --no-flatten-goal
% 0.15/0.40
% 0.15/0.40 % SZS status Theorem
% 0.15/0.40
% 0.15/0.40 % SZS output start Proof
% 0.15/0.40 Take the following subset of the input axioms:
% 0.15/0.40 fof(fc13_finset_1, axiom, ![B, A2]: ((relation(A2) & (function(A2) & finite(B))) => finite(relation_image(A2, B)))).
% 0.15/0.40 fof(t146_relat_1, axiom, ![A2_2]: (relation(A2_2) => relation_image(A2_2, relation_dom(A2_2))=relation_rng(A2_2))).
% 0.15/0.40 fof(t26_finset_1, conjecture, ![A]: ((relation(A) & function(A)) => (finite(relation_dom(A)) => finite(relation_rng(A))))).
% 0.15/0.40
% 0.15/0.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.15/0.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.15/0.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.15/0.40 fresh(y, y, x1...xn) = u
% 0.15/0.40 C => fresh(s, t, x1...xn) = v
% 0.15/0.40 where fresh is a fresh function symbol and x1..xn are the free
% 0.15/0.40 variables of u and v.
% 0.15/0.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.15/0.40 input problem has no model of domain size 1).
% 0.15/0.40
% 0.15/0.40 The encoding turns the above axioms into the following unit equations and goals:
% 0.15/0.40
% 0.15/0.40 Axiom 1 (t26_finset_1_1): function(a) = true.
% 0.15/0.40 Axiom 2 (t26_finset_1): relation(a) = true.
% 0.15/0.40 Axiom 3 (t26_finset_1_2): finite(relation_dom(a)) = true.
% 0.15/0.40 Axiom 4 (t146_relat_1): fresh2(X, X, Y) = relation_rng(Y).
% 0.15/0.40 Axiom 5 (fc13_finset_1): fresh7(X, X, Y, Z) = true.
% 0.15/0.40 Axiom 6 (fc13_finset_1): fresh3(X, X, Y, Z) = finite(relation_image(Y, Z)).
% 0.15/0.40 Axiom 7 (t146_relat_1): fresh2(relation(X), true, X) = relation_image(X, relation_dom(X)).
% 0.15/0.40 Axiom 8 (fc13_finset_1): fresh6(X, X, Y, Z) = fresh7(relation(Y), true, Y, Z).
% 0.15/0.40 Axiom 9 (fc13_finset_1): fresh6(finite(X), true, Y, X) = fresh3(function(Y), true, Y, X).
% 0.15/0.40
% 0.15/0.40 Goal 1 (t26_finset_1_3): finite(relation_rng(a)) = true.
% 0.15/0.40 Proof:
% 0.15/0.40 finite(relation_rng(a))
% 0.15/0.40 = { by axiom 4 (t146_relat_1) R->L }
% 0.15/0.40 finite(fresh2(true, true, a))
% 0.15/0.40 = { by axiom 2 (t26_finset_1) R->L }
% 0.15/0.40 finite(fresh2(relation(a), true, a))
% 0.15/0.40 = { by axiom 7 (t146_relat_1) }
% 0.15/0.40 finite(relation_image(a, relation_dom(a)))
% 0.15/0.40 = { by axiom 6 (fc13_finset_1) R->L }
% 0.15/0.40 fresh3(true, true, a, relation_dom(a))
% 0.15/0.40 = { by axiom 1 (t26_finset_1_1) R->L }
% 0.15/0.40 fresh3(function(a), true, a, relation_dom(a))
% 0.15/0.40 = { by axiom 9 (fc13_finset_1) R->L }
% 0.15/0.40 fresh6(finite(relation_dom(a)), true, a, relation_dom(a))
% 0.15/0.40 = { by axiom 3 (t26_finset_1_2) }
% 0.15/0.40 fresh6(true, true, a, relation_dom(a))
% 0.15/0.40 = { by axiom 8 (fc13_finset_1) }
% 0.15/0.40 fresh7(relation(a), true, a, relation_dom(a))
% 0.15/0.40 = { by axiom 2 (t26_finset_1) }
% 0.15/0.40 fresh7(true, true, a, relation_dom(a))
% 0.15/0.40 = { by axiom 5 (fc13_finset_1) }
% 0.15/0.40 true
% 0.15/0.40 % SZS output end Proof
% 0.15/0.40
% 0.15/0.40 RESULT: Theorem (the conjecture is true).
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