TSTP Solution File: SEU219+2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SEU219+2 : 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 : n018.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 17:51:37 EDT 2023
% Result : Theorem 11.38s 1.83s
% Output : Proof 11.38s
% 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 : SEU219+2 : 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
% 0.14/0.33 % Computer : n018.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Wed Aug 23 18:35:26 EDT 2023
% 0.14/0.33 % CPUTime :
% 11.38/1.83 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 11.38/1.83
% 11.38/1.83 % SZS status Theorem
% 11.38/1.83
% 11.38/1.83 % SZS output start Proof
% 11.38/1.83 Take the following subset of the input axioms:
% 11.38/1.83 fof(d9_funct_1, axiom, ![A2]: ((relation(A2) & function(A2)) => (one_to_one(A2) => function_inverse(A2)=relation_inverse(A2)))).
% 11.38/1.83 fof(t37_relat_1, lemma, ![A2_2]: (relation(A2_2) => (relation_rng(A2_2)=relation_dom(relation_inverse(A2_2)) & relation_dom(A2_2)=relation_rng(relation_inverse(A2_2))))).
% 11.38/1.83 fof(t55_funct_1, conjecture, ![A]: ((relation(A) & function(A)) => (one_to_one(A) => (relation_rng(A)=relation_dom(function_inverse(A)) & relation_dom(A)=relation_rng(function_inverse(A)))))).
% 11.38/1.83
% 11.38/1.83 Now clausify the problem and encode Horn clauses using encoding 3 of
% 11.38/1.83 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 11.38/1.83 We repeatedly replace C & s=t => u=v by the two clauses:
% 11.38/1.83 fresh(y, y, x1...xn) = u
% 11.38/1.83 C => fresh(s, t, x1...xn) = v
% 11.38/1.83 where fresh is a fresh function symbol and x1..xn are the free
% 11.38/1.83 variables of u and v.
% 11.38/1.83 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 11.38/1.83 input problem has no model of domain size 1).
% 11.38/1.83
% 11.38/1.83 The encoding turns the above axioms into the following unit equations and goals:
% 11.38/1.83
% 11.38/1.83 Axiom 1 (t55_funct_1_1): relation(a) = true2.
% 11.38/1.83 Axiom 2 (t55_funct_1): function(a) = true2.
% 11.38/1.83 Axiom 3 (t55_funct_1_2): one_to_one(a) = true2.
% 11.38/1.83 Axiom 4 (d9_funct_1): fresh473(X, X, Y) = relation_inverse(Y).
% 11.38/1.83 Axiom 5 (d9_funct_1): fresh238(X, X, Y) = function_inverse(Y).
% 11.38/1.83 Axiom 6 (t37_relat_1): fresh109(X, X, Y) = relation_dom(Y).
% 11.38/1.83 Axiom 7 (t37_relat_1_1): fresh108(X, X, Y) = relation_rng(Y).
% 11.38/1.83 Axiom 8 (d9_funct_1): fresh472(X, X, Y) = fresh473(function(Y), true2, Y).
% 11.38/1.83 Axiom 9 (d9_funct_1): fresh472(one_to_one(X), true2, X) = fresh238(relation(X), true2, X).
% 11.38/1.83 Axiom 10 (t37_relat_1): fresh109(relation(X), true2, X) = relation_rng(relation_inverse(X)).
% 11.38/1.83 Axiom 11 (t37_relat_1_1): fresh108(relation(X), true2, X) = relation_dom(relation_inverse(X)).
% 11.38/1.83
% 11.38/1.83 Lemma 12: relation_inverse(a) = function_inverse(a).
% 11.38/1.83 Proof:
% 11.38/1.83 relation_inverse(a)
% 11.38/1.83 = { by axiom 4 (d9_funct_1) R->L }
% 11.38/1.83 fresh473(true2, true2, a)
% 11.38/1.83 = { by axiom 2 (t55_funct_1) R->L }
% 11.38/1.83 fresh473(function(a), true2, a)
% 11.38/1.83 = { by axiom 8 (d9_funct_1) R->L }
% 11.38/1.83 fresh472(true2, true2, a)
% 11.38/1.83 = { by axiom 3 (t55_funct_1_2) R->L }
% 11.38/1.83 fresh472(one_to_one(a), true2, a)
% 11.38/1.83 = { by axiom 9 (d9_funct_1) }
% 11.38/1.83 fresh238(relation(a), true2, a)
% 11.38/1.83 = { by axiom 1 (t55_funct_1_1) }
% 11.38/1.83 fresh238(true2, true2, a)
% 11.38/1.83 = { by axiom 5 (d9_funct_1) }
% 11.38/1.83 function_inverse(a)
% 11.38/1.83
% 11.38/1.83 Goal 1 (t55_funct_1_3): tuple5(relation_rng(a), relation_dom(a)) = tuple5(relation_dom(function_inverse(a)), relation_rng(function_inverse(a))).
% 11.38/1.83 Proof:
% 11.38/1.83 tuple5(relation_rng(a), relation_dom(a))
% 11.38/1.83 = { by axiom 7 (t37_relat_1_1) R->L }
% 11.38/1.83 tuple5(fresh108(true2, true2, a), relation_dom(a))
% 11.38/1.83 = { by axiom 1 (t55_funct_1_1) R->L }
% 11.38/1.83 tuple5(fresh108(relation(a), true2, a), relation_dom(a))
% 11.38/1.83 = { by axiom 11 (t37_relat_1_1) }
% 11.38/1.83 tuple5(relation_dom(relation_inverse(a)), relation_dom(a))
% 11.38/1.83 = { by lemma 12 }
% 11.38/1.83 tuple5(relation_dom(function_inverse(a)), relation_dom(a))
% 11.38/1.83 = { by axiom 6 (t37_relat_1) R->L }
% 11.38/1.83 tuple5(relation_dom(function_inverse(a)), fresh109(true2, true2, a))
% 11.38/1.83 = { by axiom 1 (t55_funct_1_1) R->L }
% 11.38/1.83 tuple5(relation_dom(function_inverse(a)), fresh109(relation(a), true2, a))
% 11.38/1.83 = { by axiom 10 (t37_relat_1) }
% 11.38/1.83 tuple5(relation_dom(function_inverse(a)), relation_rng(relation_inverse(a)))
% 11.38/1.83 = { by lemma 12 }
% 11.38/1.83 tuple5(relation_dom(function_inverse(a)), relation_rng(function_inverse(a)))
% 11.38/1.83 % SZS output end Proof
% 11.38/1.83
% 11.38/1.83 RESULT: Theorem (the conjecture is true).
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