TSTP Solution File: SEU223+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SEU223+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 : n019.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 17:51:39 EDT 2023
% Result : Theorem 0.22s 0.64s
% 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
% 0.00/0.14 % Problem : SEU223+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.36 % Computer : n019.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Aug 23 15:51:44 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.64 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.22/0.64
% 0.22/0.64 % SZS status Theorem
% 0.22/0.64
% 0.22/0.64 % SZS output start Proof
% 0.22/0.64 Take the following subset of the input axioms:
% 0.22/0.65 fof(dt_k7_relat_1, axiom, ![B, A2]: (relation(A2) => relation(relation_dom_restriction(A2, B)))).
% 0.22/0.65 fof(fc4_funct_1, axiom, ![B2, A2_2]: ((relation(A2_2) & function(A2_2)) => (relation(relation_dom_restriction(A2_2, B2)) & function(relation_dom_restriction(A2_2, B2))))).
% 0.22/0.65 fof(t68_funct_1, axiom, ![B2, A2_2]: ((relation(B2) & function(B2)) => ![C]: ((relation(C) & function(C)) => (B2=relation_dom_restriction(C, A2_2) <=> (relation_dom(B2)=set_intersection2(relation_dom(C), A2_2) & ![D]: (in(D, relation_dom(B2)) => apply(B2, D)=apply(C, D))))))).
% 0.22/0.65 fof(t70_funct_1, conjecture, ![A, B2, C2]: ((relation(C2) & function(C2)) => (in(B2, relation_dom(relation_dom_restriction(C2, A))) => apply(relation_dom_restriction(C2, A), B2)=apply(C2, B2)))).
% 0.22/0.65
% 0.22/0.65 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.65 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.65 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.65 fresh(y, y, x1...xn) = u
% 0.22/0.65 C => fresh(s, t, x1...xn) = v
% 0.22/0.65 where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.65 variables of u and v.
% 0.22/0.65 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.65 input problem has no model of domain size 1).
% 0.22/0.65
% 0.22/0.65 The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.65
% 0.22/0.65 Axiom 1 (t70_funct_1): relation(c) = true2.
% 0.22/0.65 Axiom 2 (t70_funct_1_1): function(c) = true2.
% 0.22/0.65 Axiom 3 (dt_k7_relat_1): fresh21(X, X, Y, Z) = true2.
% 0.22/0.65 Axiom 4 (fc4_funct_1_1): fresh12(X, X, Y, Z) = function(relation_dom_restriction(Y, Z)).
% 0.22/0.65 Axiom 5 (fc4_funct_1_1): fresh11(X, X, Y, Z) = true2.
% 0.22/0.65 Axiom 6 (t70_funct_1_2): in(b, relation_dom(relation_dom_restriction(c, a))) = true2.
% 0.22/0.65 Axiom 7 (t68_funct_1_1): fresh34(X, X, Y, Z, W) = apply(Z, W).
% 0.22/0.65 Axiom 8 (dt_k7_relat_1): fresh21(relation(X), true2, X, Y) = relation(relation_dom_restriction(X, Y)).
% 0.22/0.65 Axiom 9 (fc4_funct_1_1): fresh12(function(X), true2, X, Y) = fresh11(relation(X), true2, X, Y).
% 0.22/0.65 Axiom 10 (t68_funct_1_1): fresh32(X, X, Y, Z, W, V) = apply(Z, V).
% 0.22/0.65 Axiom 11 (t68_funct_1_1): fresh33(X, X, Y, Z, W, V) = fresh34(Z, relation_dom_restriction(W, Y), Z, W, V).
% 0.22/0.65 Axiom 12 (t68_funct_1_1): fresh30(X, X, Y, Z, W, V) = fresh33(relation(W), true2, Y, Z, W, V).
% 0.22/0.65 Axiom 13 (t68_funct_1_1): fresh31(X, X, Y, Z, W, V) = fresh32(relation(Z), true2, Y, Z, W, V).
% 0.22/0.65 Axiom 14 (t68_funct_1_1): fresh29(X, X, Y, Z, W, V) = fresh31(function(Z), true2, Y, Z, W, V).
% 0.22/0.65 Axiom 15 (t68_funct_1_1): fresh29(in(X, relation_dom(Y)), true2, Z, Y, W, X) = fresh30(function(W), true2, Z, Y, W, X).
% 0.22/0.65
% 0.22/0.65 Goal 1 (t70_funct_1_3): apply(relation_dom_restriction(c, a), b) = apply(c, b).
% 0.22/0.65 Proof:
% 0.22/0.65 apply(relation_dom_restriction(c, a), b)
% 0.22/0.65 = { by axiom 10 (t68_funct_1_1) R->L }
% 0.22/0.65 fresh32(true2, true2, a, relation_dom_restriction(c, a), c, b)
% 0.22/0.65 = { by axiom 3 (dt_k7_relat_1) R->L }
% 0.22/0.65 fresh32(fresh21(true2, true2, c, a), true2, a, relation_dom_restriction(c, a), c, b)
% 0.22/0.65 = { by axiom 1 (t70_funct_1) R->L }
% 0.22/0.65 fresh32(fresh21(relation(c), true2, c, a), true2, a, relation_dom_restriction(c, a), c, b)
% 0.22/0.65 = { by axiom 8 (dt_k7_relat_1) }
% 0.22/0.65 fresh32(relation(relation_dom_restriction(c, a)), true2, a, relation_dom_restriction(c, a), c, b)
% 0.22/0.65 = { by axiom 13 (t68_funct_1_1) R->L }
% 0.22/0.65 fresh31(true2, true2, a, relation_dom_restriction(c, a), c, b)
% 0.22/0.65 = { by axiom 5 (fc4_funct_1_1) R->L }
% 0.22/0.65 fresh31(fresh11(true2, true2, c, a), true2, a, relation_dom_restriction(c, a), c, b)
% 0.22/0.65 = { by axiom 1 (t70_funct_1) R->L }
% 0.22/0.65 fresh31(fresh11(relation(c), true2, c, a), true2, a, relation_dom_restriction(c, a), c, b)
% 0.22/0.65 = { by axiom 9 (fc4_funct_1_1) R->L }
% 0.22/0.65 fresh31(fresh12(function(c), true2, c, a), true2, a, relation_dom_restriction(c, a), c, b)
% 0.22/0.65 = { by axiom 2 (t70_funct_1_1) }
% 0.22/0.65 fresh31(fresh12(true2, true2, c, a), true2, a, relation_dom_restriction(c, a), c, b)
% 0.22/0.65 = { by axiom 4 (fc4_funct_1_1) }
% 0.22/0.65 fresh31(function(relation_dom_restriction(c, a)), true2, a, relation_dom_restriction(c, a), c, b)
% 0.22/0.65 = { by axiom 14 (t68_funct_1_1) R->L }
% 0.22/0.65 fresh29(true2, true2, a, relation_dom_restriction(c, a), c, b)
% 0.22/0.65 = { by axiom 6 (t70_funct_1_2) R->L }
% 0.22/0.65 fresh29(in(b, relation_dom(relation_dom_restriction(c, a))), true2, a, relation_dom_restriction(c, a), c, b)
% 0.22/0.65 = { by axiom 15 (t68_funct_1_1) }
% 0.22/0.65 fresh30(function(c), true2, a, relation_dom_restriction(c, a), c, b)
% 0.22/0.65 = { by axiom 2 (t70_funct_1_1) }
% 0.22/0.65 fresh30(true2, true2, a, relation_dom_restriction(c, a), c, b)
% 0.22/0.65 = { by axiom 12 (t68_funct_1_1) }
% 0.22/0.65 fresh33(relation(c), true2, a, relation_dom_restriction(c, a), c, b)
% 0.22/0.65 = { by axiom 1 (t70_funct_1) }
% 0.22/0.65 fresh33(true2, true2, a, relation_dom_restriction(c, a), c, b)
% 0.22/0.65 = { by axiom 11 (t68_funct_1_1) }
% 0.22/0.65 fresh34(relation_dom_restriction(c, a), relation_dom_restriction(c, a), relation_dom_restriction(c, a), c, b)
% 0.22/0.65 = { by axiom 7 (t68_funct_1_1) }
% 0.22/0.65 apply(c, b)
% 0.22/0.65 % SZS output end Proof
% 0.22/0.65
% 0.22/0.65 RESULT: Theorem (the conjecture is true).
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