TSTP Solution File: SEU200+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SEU200+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 : n008.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 17:51:31 EDT 2023
% Result : Theorem 0.21s 0.45s
% Output : Proof 0.21s
% 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 : SEU200+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 01:39:17 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.45 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.45
% 0.21/0.45 % SZS status Theorem
% 0.21/0.45
% 0.21/0.45 % SZS output start Proof
% 0.21/0.45 Take the following subset of the input axioms:
% 0.21/0.46 fof(dt_k8_relat_1, axiom, ![B, A2]: (relation(B) => relation(relation_rng_restriction(A2, B)))).
% 0.21/0.46 fof(t117_relat_1, axiom, ![B2, A2_2]: (relation(B2) => subset(relation_rng_restriction(A2_2, B2), B2))).
% 0.21/0.46 fof(t118_relat_1, conjecture, ![A, B2]: (relation(B2) => subset(relation_rng(relation_rng_restriction(A, B2)), relation_rng(B2)))).
% 0.21/0.46 fof(t25_relat_1, axiom, ![A2_2]: (relation(A2_2) => ![B2]: (relation(B2) => (subset(A2_2, B2) => (subset(relation_dom(A2_2), relation_dom(B2)) & subset(relation_rng(A2_2), relation_rng(B2))))))).
% 0.21/0.46
% 0.21/0.46 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.46 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.46 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.46 fresh(y, y, x1...xn) = u
% 0.21/0.46 C => fresh(s, t, x1...xn) = v
% 0.21/0.46 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.46 variables of u and v.
% 0.21/0.46 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.46 input problem has no model of domain size 1).
% 0.21/0.46
% 0.21/0.46 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.46
% 0.21/0.46 Axiom 1 (t118_relat_1): relation(b) = true2.
% 0.21/0.46 Axiom 2 (t25_relat_1_1): fresh26(X, X, Y, Z) = true2.
% 0.21/0.46 Axiom 3 (dt_k8_relat_1): fresh22(X, X, Y, Z) = true2.
% 0.21/0.46 Axiom 4 (t117_relat_1): fresh11(X, X, Y, Z) = true2.
% 0.21/0.46 Axiom 5 (t25_relat_1_1): fresh8(X, X, Y, Z) = subset(relation_rng(Y), relation_rng(Z)).
% 0.21/0.46 Axiom 6 (t25_relat_1_1): fresh25(X, X, Y, Z) = fresh26(relation(Y), true2, Y, Z).
% 0.21/0.46 Axiom 7 (dt_k8_relat_1): fresh22(relation(X), true2, Y, X) = relation(relation_rng_restriction(Y, X)).
% 0.21/0.46 Axiom 8 (t117_relat_1): fresh11(relation(X), true2, Y, X) = subset(relation_rng_restriction(Y, X), X).
% 0.21/0.46 Axiom 9 (t25_relat_1_1): fresh25(subset(X, Y), true2, X, Y) = fresh8(relation(Y), true2, X, Y).
% 0.21/0.46
% 0.21/0.46 Goal 1 (t118_relat_1_1): subset(relation_rng(relation_rng_restriction(a, b)), relation_rng(b)) = true2.
% 0.21/0.46 Proof:
% 0.21/0.46 subset(relation_rng(relation_rng_restriction(a, b)), relation_rng(b))
% 0.21/0.46 = { by axiom 5 (t25_relat_1_1) R->L }
% 0.21/0.46 fresh8(true2, true2, relation_rng_restriction(a, b), b)
% 0.21/0.46 = { by axiom 1 (t118_relat_1) R->L }
% 0.21/0.46 fresh8(relation(b), true2, relation_rng_restriction(a, b), b)
% 0.21/0.46 = { by axiom 9 (t25_relat_1_1) R->L }
% 0.21/0.46 fresh25(subset(relation_rng_restriction(a, b), b), true2, relation_rng_restriction(a, b), b)
% 0.21/0.46 = { by axiom 8 (t117_relat_1) R->L }
% 0.21/0.46 fresh25(fresh11(relation(b), true2, a, b), true2, relation_rng_restriction(a, b), b)
% 0.21/0.46 = { by axiom 1 (t118_relat_1) }
% 0.21/0.46 fresh25(fresh11(true2, true2, a, b), true2, relation_rng_restriction(a, b), b)
% 0.21/0.46 = { by axiom 4 (t117_relat_1) }
% 0.21/0.46 fresh25(true2, true2, relation_rng_restriction(a, b), b)
% 0.21/0.46 = { by axiom 6 (t25_relat_1_1) }
% 0.21/0.46 fresh26(relation(relation_rng_restriction(a, b)), true2, relation_rng_restriction(a, b), b)
% 0.21/0.46 = { by axiom 7 (dt_k8_relat_1) R->L }
% 0.21/0.46 fresh26(fresh22(relation(b), true2, a, b), true2, relation_rng_restriction(a, b), b)
% 0.21/0.46 = { by axiom 1 (t118_relat_1) }
% 0.21/0.46 fresh26(fresh22(true2, true2, a, b), true2, relation_rng_restriction(a, b), b)
% 0.21/0.46 = { by axiom 3 (dt_k8_relat_1) }
% 0.21/0.46 fresh26(true2, true2, relation_rng_restriction(a, b), b)
% 0.21/0.46 = { by axiom 2 (t25_relat_1_1) }
% 0.21/0.46 true2
% 0.21/0.46 % SZS output end Proof
% 0.21/0.46
% 0.21/0.46 RESULT: Theorem (the conjecture is true).
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