TSTP Solution File: SEU225+2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SEU225+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 : n023.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 17:51:40 EDT 2023
% Result : Theorem 265.11s 34.08s
% Output : Proof 265.11s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU225+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n023.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 23 17:38:28 EDT 2023
% 0.14/0.34 % CPUTime :
% 265.11/34.08 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 265.11/34.08
% 265.11/34.08 % SZS status Theorem
% 265.11/34.08
% 265.11/34.08 % SZS output start Proof
% 265.11/34.08 Take the following subset of the input axioms:
% 265.11/34.08 fof(dt_k6_relat_1, axiom, ![A]: relation(identity_relation(A))).
% 265.11/34.08 fof(fc2_funct_1, axiom, ![A3]: (relation(identity_relation(A3)) & function(identity_relation(A3)))).
% 265.11/34.08 fof(t23_funct_1, lemma, ![B, A2]: ((relation(B) & function(B)) => ![C]: ((relation(C) & function(C)) => (in(A2, relation_dom(B)) => apply(relation_composition(B, C), A2)=apply(C, apply(B, A2)))))).
% 265.11/34.08 fof(t35_funct_1, lemma, ![B2, A2_2]: (in(B2, A2_2) => apply(identity_relation(A2_2), B2)=B2)).
% 265.11/34.08 fof(t71_relat_1, lemma, ![A3]: (relation_dom(identity_relation(A3))=A3 & relation_rng(identity_relation(A3))=A3)).
% 265.11/34.08 fof(t72_funct_1, conjecture, ![B2, A3, C2]: ((relation(C2) & function(C2)) => (in(B2, A3) => apply(relation_dom_restriction(C2, A3), B2)=apply(C2, B2)))).
% 265.11/34.08 fof(t94_relat_1, lemma, ![B2, A2_2]: (relation(B2) => relation_dom_restriction(B2, A2_2)=relation_composition(identity_relation(A2_2), B2))).
% 265.11/34.08
% 265.11/34.08 Now clausify the problem and encode Horn clauses using encoding 3 of
% 265.11/34.08 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 265.11/34.08 We repeatedly replace C & s=t => u=v by the two clauses:
% 265.11/34.08 fresh(y, y, x1...xn) = u
% 265.11/34.08 C => fresh(s, t, x1...xn) = v
% 265.11/34.08 where fresh is a fresh function symbol and x1..xn are the free
% 265.11/34.08 variables of u and v.
% 265.11/34.08 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 265.11/34.08 input problem has no model of domain size 1).
% 265.11/34.08
% 265.11/34.08 The encoding turns the above axioms into the following unit equations and goals:
% 265.11/34.08
% 265.11/34.08 Axiom 1 (t72_funct_1_2): relation(c) = true2.
% 265.11/34.08 Axiom 2 (t72_funct_1_1): function(c) = true2.
% 265.11/34.08 Axiom 3 (t72_funct_1): in(b2, a) = true2.
% 265.11/34.08 Axiom 4 (dt_k6_relat_1): relation(identity_relation(X)) = true2.
% 265.11/34.08 Axiom 5 (t71_relat_1): relation_dom(identity_relation(X)) = X.
% 265.11/34.08 Axiom 6 (fc2_funct_1): function(identity_relation(X)) = true2.
% 265.11/34.08 Axiom 7 (t94_relat_1): fresh60(X, X, Y, Z) = relation_dom_restriction(Z, Y).
% 265.11/34.08 Axiom 8 (t35_funct_1): fresh18(X, X, Y, Z) = Z.
% 265.11/34.08 Axiom 9 (t23_funct_1): fresh479(X, X, Y, Z, W) = apply(relation_composition(Z, W), Y).
% 265.11/34.08 Axiom 10 (t23_funct_1): fresh130(X, X, Y, Z, W) = apply(W, apply(Z, Y)).
% 265.11/34.08 Axiom 11 (t94_relat_1): fresh60(relation(X), true2, Y, X) = relation_composition(identity_relation(Y), X).
% 265.11/34.08 Axiom 12 (t23_funct_1): fresh478(X, X, Y, Z, W) = fresh479(function(Z), true2, Y, Z, W).
% 265.11/34.08 Axiom 13 (t23_funct_1): fresh477(X, X, Y, Z, W) = fresh478(function(W), true2, Y, Z, W).
% 265.11/34.08 Axiom 14 (t23_funct_1): fresh476(X, X, Y, Z, W) = fresh477(relation(Z), true2, Y, Z, W).
% 265.11/34.08 Axiom 15 (t35_funct_1): fresh18(in(X, Y), true2, Y, X) = apply(identity_relation(Y), X).
% 265.11/34.08 Axiom 16 (t23_funct_1): fresh476(relation(X), true2, Y, Z, X) = fresh130(in(Y, relation_dom(Z)), true2, Y, Z, X).
% 265.11/34.08
% 265.11/34.08 Goal 1 (t72_funct_1_3): apply(relation_dom_restriction(c, a), b2) = apply(c, b2).
% 265.11/34.08 Proof:
% 265.11/34.08 apply(relation_dom_restriction(c, a), b2)
% 265.11/34.08 = { by axiom 7 (t94_relat_1) R->L }
% 265.11/34.08 apply(fresh60(true2, true2, a, c), b2)
% 265.11/34.08 = { by axiom 1 (t72_funct_1_2) R->L }
% 265.11/34.08 apply(fresh60(relation(c), true2, a, c), b2)
% 265.11/34.08 = { by axiom 11 (t94_relat_1) }
% 265.11/34.08 apply(relation_composition(identity_relation(a), c), b2)
% 265.11/34.08 = { by axiom 9 (t23_funct_1) R->L }
% 265.11/34.08 fresh479(true2, true2, b2, identity_relation(a), c)
% 265.11/34.08 = { by axiom 6 (fc2_funct_1) R->L }
% 265.11/34.08 fresh479(function(identity_relation(a)), true2, b2, identity_relation(a), c)
% 265.11/34.08 = { by axiom 12 (t23_funct_1) R->L }
% 265.11/34.08 fresh478(true2, true2, b2, identity_relation(a), c)
% 265.11/34.08 = { by axiom 2 (t72_funct_1_1) R->L }
% 265.11/34.08 fresh478(function(c), true2, b2, identity_relation(a), c)
% 265.11/34.08 = { by axiom 13 (t23_funct_1) R->L }
% 265.11/34.08 fresh477(true2, true2, b2, identity_relation(a), c)
% 265.11/34.08 = { by axiom 4 (dt_k6_relat_1) R->L }
% 265.11/34.08 fresh477(relation(identity_relation(a)), true2, b2, identity_relation(a), c)
% 265.11/34.08 = { by axiom 14 (t23_funct_1) R->L }
% 265.11/34.08 fresh476(true2, true2, b2, identity_relation(a), c)
% 265.11/34.08 = { by axiom 1 (t72_funct_1_2) R->L }
% 265.11/34.08 fresh476(relation(c), true2, b2, identity_relation(a), c)
% 265.11/34.08 = { by axiom 16 (t23_funct_1) }
% 265.11/34.08 fresh130(in(b2, relation_dom(identity_relation(a))), true2, b2, identity_relation(a), c)
% 265.11/34.08 = { by axiom 5 (t71_relat_1) }
% 265.11/34.08 fresh130(in(b2, a), true2, b2, identity_relation(a), c)
% 265.11/34.08 = { by axiom 3 (t72_funct_1) }
% 265.11/34.08 fresh130(true2, true2, b2, identity_relation(a), c)
% 265.11/34.08 = { by axiom 10 (t23_funct_1) }
% 265.11/34.08 apply(c, apply(identity_relation(a), b2))
% 265.11/34.08 = { by axiom 15 (t35_funct_1) R->L }
% 265.11/34.08 apply(c, fresh18(in(b2, a), true2, a, b2))
% 265.11/34.08 = { by axiom 3 (t72_funct_1) }
% 265.11/34.08 apply(c, fresh18(true2, true2, a, b2))
% 265.11/34.08 = { by axiom 8 (t35_funct_1) }
% 265.11/34.08 apply(c, b2)
% 265.11/34.08 % SZS output end Proof
% 265.11/34.08
% 265.11/34.08 RESULT: Theorem (the conjecture is true).
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