TSTP Solution File: SEU248+2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SEU248+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 : n026.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 17:51:48 EDT 2023
% Result : Theorem 28.90s 4.19s
% Output : Proof 28.90s
% 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 : SEU248+2 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13 % 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 : n026.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 18:23:31 EDT 2023
% 0.13/0.34 % CPUTime :
% 28.90/4.19 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 28.90/4.19
% 28.90/4.19 % SZS status Theorem
% 28.90/4.19
% 28.90/4.19 % SZS output start Proof
% 28.90/4.19 Take the following subset of the input axioms:
% 28.90/4.19 fof(dt_k8_relat_1, axiom, ![B, A2]: (relation(B) => relation(relation_rng_restriction(A2, B)))).
% 28.90/4.19 fof(l29_wellord1, conjecture, ![A, B2]: (relation(B2) => subset(relation_dom(relation_rng_restriction(A, B2)), relation_dom(B2)))).
% 28.90/4.19 fof(t117_relat_1, lemma, ![B2, A2_2]: (relation(B2) => subset(relation_rng_restriction(A2_2, B2), B2))).
% 28.90/4.19 fof(t25_relat_1, lemma, ![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))))))).
% 28.90/4.19
% 28.90/4.19 Now clausify the problem and encode Horn clauses using encoding 3 of
% 28.90/4.19 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 28.90/4.19 We repeatedly replace C & s=t => u=v by the two clauses:
% 28.90/4.19 fresh(y, y, x1...xn) = u
% 28.90/4.19 C => fresh(s, t, x1...xn) = v
% 28.90/4.19 where fresh is a fresh function symbol and x1..xn are the free
% 28.90/4.19 variables of u and v.
% 28.90/4.19 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 28.90/4.19 input problem has no model of domain size 1).
% 28.90/4.19
% 28.90/4.19 The encoding turns the above axioms into the following unit equations and goals:
% 28.90/4.19
% 28.90/4.19 Axiom 1 (l29_wellord1): relation(b11) = true2.
% 28.90/4.19 Axiom 2 (t25_relat_1): fresh641(X, X, Y, Z) = true2.
% 28.90/4.19 Axiom 3 (dt_k8_relat_1): fresh309(X, X, Y, Z) = true2.
% 28.90/4.19 Axiom 4 (t117_relat_1): fresh211(X, X, Y, Z) = true2.
% 28.90/4.19 Axiom 5 (t25_relat_1): fresh154(X, X, Y, Z) = subset(relation_dom(Y), relation_dom(Z)).
% 28.90/4.19 Axiom 6 (t25_relat_1): fresh640(X, X, Y, Z) = fresh641(relation(Y), true2, Y, Z).
% 28.90/4.19 Axiom 7 (dt_k8_relat_1): fresh309(relation(X), true2, Y, X) = relation(relation_rng_restriction(Y, X)).
% 28.90/4.19 Axiom 8 (t117_relat_1): fresh211(relation(X), true2, Y, X) = subset(relation_rng_restriction(Y, X), X).
% 28.90/4.19 Axiom 9 (t25_relat_1): fresh640(subset(X, Y), true2, X, Y) = fresh154(relation(Y), true2, X, Y).
% 28.90/4.19
% 28.90/4.19 Goal 1 (l29_wellord1_1): subset(relation_dom(relation_rng_restriction(a13, b11)), relation_dom(b11)) = true2.
% 28.90/4.19 Proof:
% 28.90/4.19 subset(relation_dom(relation_rng_restriction(a13, b11)), relation_dom(b11))
% 28.90/4.19 = { by axiom 5 (t25_relat_1) R->L }
% 28.90/4.19 fresh154(true2, true2, relation_rng_restriction(a13, b11), b11)
% 28.90/4.19 = { by axiom 1 (l29_wellord1) R->L }
% 28.90/4.19 fresh154(relation(b11), true2, relation_rng_restriction(a13, b11), b11)
% 28.90/4.19 = { by axiom 9 (t25_relat_1) R->L }
% 28.90/4.19 fresh640(subset(relation_rng_restriction(a13, b11), b11), true2, relation_rng_restriction(a13, b11), b11)
% 28.90/4.19 = { by axiom 8 (t117_relat_1) R->L }
% 28.90/4.19 fresh640(fresh211(relation(b11), true2, a13, b11), true2, relation_rng_restriction(a13, b11), b11)
% 28.90/4.19 = { by axiom 1 (l29_wellord1) }
% 28.90/4.19 fresh640(fresh211(true2, true2, a13, b11), true2, relation_rng_restriction(a13, b11), b11)
% 28.90/4.19 = { by axiom 4 (t117_relat_1) }
% 28.90/4.19 fresh640(true2, true2, relation_rng_restriction(a13, b11), b11)
% 28.90/4.19 = { by axiom 6 (t25_relat_1) }
% 28.90/4.19 fresh641(relation(relation_rng_restriction(a13, b11)), true2, relation_rng_restriction(a13, b11), b11)
% 28.90/4.19 = { by axiom 7 (dt_k8_relat_1) R->L }
% 28.90/4.19 fresh641(fresh309(relation(b11), true2, a13, b11), true2, relation_rng_restriction(a13, b11), b11)
% 28.90/4.19 = { by axiom 1 (l29_wellord1) }
% 28.90/4.19 fresh641(fresh309(true2, true2, a13, b11), true2, relation_rng_restriction(a13, b11), b11)
% 28.90/4.19 = { by axiom 3 (dt_k8_relat_1) }
% 28.90/4.19 fresh641(true2, true2, relation_rng_restriction(a13, b11), b11)
% 28.90/4.19 = { by axiom 2 (t25_relat_1) }
% 28.90/4.19 true2
% 28.90/4.19 % SZS output end Proof
% 28.90/4.19
% 28.90/4.19 RESULT: Theorem (the conjecture is true).
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