TSTP Solution File: SEU047+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SEU047+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : n002.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 17:50:52 EDT 2023
% Result : Theorem 0.20s 0.47s
% Output : Proof 0.20s
% 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 : SEU047+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n002.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 24 00:52:01 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.20/0.47 Command-line arguments: --no-flatten-goal
% 0.20/0.47
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47
% 0.20/0.47 % SZS output start Proof
% 0.20/0.47 Take the following subset of the input axioms:
% 0.20/0.47 fof(t129_relat_1, axiom, ![B, C, A2]: (relation(C) => (subset(A2, B) => relation_rng_restriction(B, relation_rng_restriction(A2, C))=relation_rng_restriction(A2, C)))).
% 0.20/0.47 fof(t130_relat_1, axiom, ![B2, C2, A2_2]: (relation(C2) => (subset(A2_2, B2) => relation_rng_restriction(A2_2, relation_rng_restriction(B2, C2))=relation_rng_restriction(A2_2, C2)))).
% 0.20/0.47 fof(t97_funct_1, conjecture, ![A, B2, C2]: ((relation(C2) & function(C2)) => (subset(A, B2) => (relation_rng_restriction(B2, relation_rng_restriction(A, C2))=relation_rng_restriction(A, C2) & relation_rng_restriction(A, relation_rng_restriction(B2, C2))=relation_rng_restriction(A, C2))))).
% 0.20/0.47
% 0.20/0.47 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.47 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.47 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.47 fresh(y, y, x1...xn) = u
% 0.20/0.47 C => fresh(s, t, x1...xn) = v
% 0.20/0.47 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.47 variables of u and v.
% 0.20/0.47 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.47 input problem has no model of domain size 1).
% 0.20/0.47
% 0.20/0.47 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.47
% 0.20/0.47 Axiom 1 (t97_funct_1): relation(c) = true2.
% 0.20/0.47 Axiom 2 (t97_funct_1_2): subset(a, b) = true2.
% 0.20/0.47 Axiom 3 (t129_relat_1): fresh12(X, X, Y, Z, W) = relation_rng_restriction(Y, W).
% 0.20/0.47 Axiom 4 (t129_relat_1): fresh11(X, X, Y, Z, W) = relation_rng_restriction(Z, relation_rng_restriction(Y, W)).
% 0.20/0.47 Axiom 5 (t130_relat_1): fresh10(X, X, Y, Z, W) = relation_rng_restriction(Y, W).
% 0.20/0.47 Axiom 6 (t130_relat_1): fresh9(X, X, Y, Z, W) = relation_rng_restriction(Y, relation_rng_restriction(Z, W)).
% 0.20/0.47 Axiom 7 (t129_relat_1): fresh11(subset(X, Y), true2, X, Y, Z) = fresh12(relation(Z), true2, X, Y, Z).
% 0.20/0.47 Axiom 8 (t130_relat_1): fresh9(subset(X, Y), true2, X, Y, Z) = fresh10(relation(Z), true2, X, Y, Z).
% 0.20/0.47
% 0.20/0.47 Goal 1 (t97_funct_1_3): tuple3(relation_rng_restriction(a, relation_rng_restriction(b, c)), relation_rng_restriction(b, relation_rng_restriction(a, c))) = tuple3(relation_rng_restriction(a, c), relation_rng_restriction(a, c)).
% 0.20/0.47 Proof:
% 0.20/0.47 tuple3(relation_rng_restriction(a, relation_rng_restriction(b, c)), relation_rng_restriction(b, relation_rng_restriction(a, c)))
% 0.20/0.47 = { by axiom 4 (t129_relat_1) R->L }
% 0.20/0.47 tuple3(relation_rng_restriction(a, relation_rng_restriction(b, c)), fresh11(true2, true2, a, b, c))
% 0.20/0.47 = { by axiom 2 (t97_funct_1_2) R->L }
% 0.20/0.47 tuple3(relation_rng_restriction(a, relation_rng_restriction(b, c)), fresh11(subset(a, b), true2, a, b, c))
% 0.20/0.47 = { by axiom 7 (t129_relat_1) }
% 0.20/0.47 tuple3(relation_rng_restriction(a, relation_rng_restriction(b, c)), fresh12(relation(c), true2, a, b, c))
% 0.20/0.47 = { by axiom 1 (t97_funct_1) }
% 0.20/0.47 tuple3(relation_rng_restriction(a, relation_rng_restriction(b, c)), fresh12(true2, true2, a, b, c))
% 0.20/0.47 = { by axiom 3 (t129_relat_1) }
% 0.20/0.47 tuple3(relation_rng_restriction(a, relation_rng_restriction(b, c)), relation_rng_restriction(a, c))
% 0.20/0.47 = { by axiom 6 (t130_relat_1) R->L }
% 0.20/0.47 tuple3(fresh9(true2, true2, a, b, c), relation_rng_restriction(a, c))
% 0.20/0.47 = { by axiom 2 (t97_funct_1_2) R->L }
% 0.20/0.47 tuple3(fresh9(subset(a, b), true2, a, b, c), relation_rng_restriction(a, c))
% 0.20/0.47 = { by axiom 8 (t130_relat_1) }
% 0.20/0.47 tuple3(fresh10(relation(c), true2, a, b, c), relation_rng_restriction(a, c))
% 0.20/0.47 = { by axiom 1 (t97_funct_1) }
% 0.20/0.47 tuple3(fresh10(true2, true2, a, b, c), relation_rng_restriction(a, c))
% 0.20/0.47 = { by axiom 5 (t130_relat_1) }
% 0.20/0.47 tuple3(relation_rng_restriction(a, c), relation_rng_restriction(a, c))
% 0.20/0.47 % SZS output end Proof
% 0.20/0.47
% 0.20/0.47 RESULT: Theorem (the conjecture is true).
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