TSTP Solution File: SEU303+3 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SEU303+3 : 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 : n027.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 0.19s 0.57s
% Output : Proof 0.19s
% 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 : SEU303+3 : 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 : n027.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 15:27:31 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.57
% 0.19/0.57 % SZS status Theorem
% 0.19/0.57
% 0.19/0.57 % SZS output start Proof
% 0.19/0.57 Take the following subset of the input axioms:
% 0.19/0.57 fof(fc13_finset_1, axiom, ![B, A2]: ((relation(A2) & (function(A2) & finite(B))) => finite(relation_image(A2, B)))).
% 0.19/0.57 fof(t146_relat_1, axiom, ![A2_2]: (relation(A2_2) => relation_image(A2_2, relation_dom(A2_2))=relation_rng(A2_2))).
% 0.19/0.57 fof(t26_finset_1, conjecture, ![A]: ((relation(A) & function(A)) => (finite(relation_dom(A)) => finite(relation_rng(A))))).
% 0.19/0.58
% 0.19/0.58 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.58 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.58 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.58 fresh(y, y, x1...xn) = u
% 0.19/0.58 C => fresh(s, t, x1...xn) = v
% 0.19/0.58 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.58 variables of u and v.
% 0.19/0.58 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.58 input problem has no model of domain size 1).
% 0.19/0.58
% 0.19/0.58 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.58
% 0.19/0.58 Axiom 1 (t26_finset_1_1): function(a) = true2.
% 0.19/0.58 Axiom 2 (t26_finset_1_2): relation(a) = true2.
% 0.19/0.58 Axiom 3 (t26_finset_1): finite(relation_dom(a)) = true2.
% 0.19/0.58 Axiom 4 (t146_relat_1): fresh10(X, X, Y) = relation_rng(Y).
% 0.19/0.58 Axiom 5 (fc13_finset_1): fresh68(X, X, Y, Z) = true2.
% 0.19/0.58 Axiom 6 (fc13_finset_1): fresh25(X, X, Y, Z) = finite(relation_image(Y, Z)).
% 0.19/0.58 Axiom 7 (t146_relat_1): fresh10(relation(X), true2, X) = relation_image(X, relation_dom(X)).
% 0.19/0.58 Axiom 8 (fc13_finset_1): fresh67(X, X, Y, Z) = fresh68(finite(Z), true2, Y, Z).
% 0.19/0.58 Axiom 9 (fc13_finset_1): fresh67(relation(X), true2, X, Y) = fresh25(function(X), true2, X, Y).
% 0.19/0.58
% 0.19/0.58 Goal 1 (t26_finset_1_3): finite(relation_rng(a)) = true2.
% 0.19/0.58 Proof:
% 0.19/0.58 finite(relation_rng(a))
% 0.19/0.58 = { by axiom 4 (t146_relat_1) R->L }
% 0.19/0.58 finite(fresh10(true2, true2, a))
% 0.19/0.58 = { by axiom 2 (t26_finset_1_2) R->L }
% 0.19/0.58 finite(fresh10(relation(a), true2, a))
% 0.19/0.58 = { by axiom 7 (t146_relat_1) }
% 0.19/0.58 finite(relation_image(a, relation_dom(a)))
% 0.19/0.58 = { by axiom 6 (fc13_finset_1) R->L }
% 0.19/0.58 fresh25(true2, true2, a, relation_dom(a))
% 0.19/0.58 = { by axiom 1 (t26_finset_1_1) R->L }
% 0.19/0.58 fresh25(function(a), true2, a, relation_dom(a))
% 0.19/0.58 = { by axiom 9 (fc13_finset_1) R->L }
% 0.19/0.58 fresh67(relation(a), true2, a, relation_dom(a))
% 0.19/0.58 = { by axiom 2 (t26_finset_1_2) }
% 0.19/0.58 fresh67(true2, true2, a, relation_dom(a))
% 0.19/0.58 = { by axiom 8 (fc13_finset_1) }
% 0.19/0.58 fresh68(finite(relation_dom(a)), true2, a, relation_dom(a))
% 0.19/0.58 = { by axiom 3 (t26_finset_1) }
% 0.19/0.58 fresh68(true2, true2, a, relation_dom(a))
% 0.19/0.58 = { by axiom 5 (fc13_finset_1) }
% 0.19/0.58 true2
% 0.19/0.58 % SZS output end Proof
% 0.19/0.58
% 0.19/0.58 RESULT: Theorem (the conjecture is true).
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