TSTP Solution File: SEU177+2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SEU177+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 : n028.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 17:51:24 EDT 2023
% Result : Theorem 3.65s 0.86s
% Output : Proof 3.65s
% 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 : SEU177+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
% 0.13/0.34 % Computer : n028.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 : Thu Aug 24 02:03:49 EDT 2023
% 0.13/0.34 % CPUTime :
% 3.65/0.86 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 3.65/0.86
% 3.65/0.86 % SZS status Theorem
% 3.65/0.86
% 3.65/0.86 % SZS output start Proof
% 3.65/0.86 Take the following subset of the input axioms:
% 3.65/0.86 fof(d4_relat_1, axiom, ![A2]: (relation(A2) => ![B]: (B=relation_dom(A2) <=> ![C]: (in(C, B) <=> ?[D]: in(ordered_pair(C, D), A2))))).
% 3.65/0.86 fof(d5_relat_1, axiom, ![A2_2]: (relation(A2_2) => ![B2]: (B2=relation_rng(A2_2) <=> ![C2]: (in(C2, B2) <=> ?[D2]: in(ordered_pair(D2, C2), A2_2))))).
% 3.65/0.86 fof(t20_relat_1, conjecture, ![A, B2, C2]: (relation(C2) => (in(ordered_pair(A, B2), C2) => (in(A, relation_dom(C2)) & in(B2, relation_rng(C2)))))).
% 3.65/0.86
% 3.65/0.86 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.65/0.86 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.65/0.86 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.65/0.86 fresh(y, y, x1...xn) = u
% 3.65/0.86 C => fresh(s, t, x1...xn) = v
% 3.65/0.86 where fresh is a fresh function symbol and x1..xn are the free
% 3.65/0.86 variables of u and v.
% 3.65/0.86 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.65/0.86 input problem has no model of domain size 1).
% 3.65/0.86
% 3.65/0.86 The encoding turns the above axioms into the following unit equations and goals:
% 3.65/0.86
% 3.65/0.86 Axiom 1 (t20_relat_1_1): relation(c4) = true2.
% 3.65/0.86 Axiom 2 (d4_relat_1_1): fresh210(X, X, Y, Z) = true2.
% 3.65/0.86 Axiom 3 (d5_relat_1_1): fresh204(X, X, Y, Z) = true2.
% 3.65/0.86 Axiom 4 (t20_relat_1): in(ordered_pair(a, b2), c4) = true2.
% 3.65/0.86 Axiom 5 (d4_relat_1_1): fresh134(X, X, Y, Z, W) = in(W, Z).
% 3.65/0.86 Axiom 6 (d5_relat_1_1): fresh117(X, X, Y, Z, W) = in(W, Z).
% 3.65/0.86 Axiom 7 (d4_relat_1_1): fresh209(X, X, Y, Z, W, V) = fresh210(Z, relation_dom(Y), Z, W).
% 3.65/0.86 Axiom 8 (d5_relat_1_1): fresh203(X, X, Y, Z, W, V) = fresh204(Z, relation_rng(Y), Z, W).
% 3.65/0.86 Axiom 9 (d4_relat_1_1): fresh209(relation(X), true2, X, Y, Z, W) = fresh134(in(ordered_pair(Z, W), X), true2, X, Y, Z).
% 3.65/0.86 Axiom 10 (d5_relat_1_1): fresh203(relation(X), true2, X, Y, Z, W) = fresh117(in(ordered_pair(W, Z), X), true2, X, Y, Z).
% 3.65/0.86
% 3.65/0.86 Goal 1 (t20_relat_1_2): tuple2(in(a, relation_dom(c4)), in(b2, relation_rng(c4))) = tuple2(true2, true2).
% 3.65/0.86 Proof:
% 3.65/0.86 tuple2(in(a, relation_dom(c4)), in(b2, relation_rng(c4)))
% 3.65/0.86 = { by axiom 5 (d4_relat_1_1) R->L }
% 3.65/0.86 tuple2(fresh134(true2, true2, c4, relation_dom(c4), a), in(b2, relation_rng(c4)))
% 3.65/0.86 = { by axiom 4 (t20_relat_1) R->L }
% 3.65/0.86 tuple2(fresh134(in(ordered_pair(a, b2), c4), true2, c4, relation_dom(c4), a), in(b2, relation_rng(c4)))
% 3.65/0.86 = { by axiom 9 (d4_relat_1_1) R->L }
% 3.65/0.86 tuple2(fresh209(relation(c4), true2, c4, relation_dom(c4), a, b2), in(b2, relation_rng(c4)))
% 3.65/0.86 = { by axiom 1 (t20_relat_1_1) }
% 3.65/0.86 tuple2(fresh209(true2, true2, c4, relation_dom(c4), a, b2), in(b2, relation_rng(c4)))
% 3.65/0.86 = { by axiom 7 (d4_relat_1_1) }
% 3.65/0.86 tuple2(fresh210(relation_dom(c4), relation_dom(c4), relation_dom(c4), a), in(b2, relation_rng(c4)))
% 3.65/0.86 = { by axiom 2 (d4_relat_1_1) }
% 3.65/0.86 tuple2(true2, in(b2, relation_rng(c4)))
% 3.65/0.86 = { by axiom 6 (d5_relat_1_1) R->L }
% 3.65/0.86 tuple2(true2, fresh117(true2, true2, c4, relation_rng(c4), b2))
% 3.65/0.86 = { by axiom 4 (t20_relat_1) R->L }
% 3.65/0.86 tuple2(true2, fresh117(in(ordered_pair(a, b2), c4), true2, c4, relation_rng(c4), b2))
% 3.65/0.86 = { by axiom 10 (d5_relat_1_1) R->L }
% 3.65/0.86 tuple2(true2, fresh203(relation(c4), true2, c4, relation_rng(c4), b2, a))
% 3.65/0.86 = { by axiom 1 (t20_relat_1_1) }
% 3.65/0.86 tuple2(true2, fresh203(true2, true2, c4, relation_rng(c4), b2, a))
% 3.65/0.86 = { by axiom 8 (d5_relat_1_1) }
% 3.65/0.86 tuple2(true2, fresh204(relation_rng(c4), relation_rng(c4), relation_rng(c4), b2))
% 3.65/0.86 = { by axiom 3 (d5_relat_1_1) }
% 3.65/0.86 tuple2(true2, true2)
% 3.65/0.86 % SZS output end Proof
% 3.65/0.86
% 3.65/0.86 RESULT: Theorem (the conjecture is true).
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