TSTP Solution File: SEU217+2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SEU217+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 : n011.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 17:51:36 EDT 2023
% Result : Theorem 19.64s 2.88s
% Output : Proof 19.64s
% 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 : SEU217+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 : n011.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 13:24:21 EDT 2023
% 0.13/0.35 % CPUTime :
% 19.64/2.88 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 19.64/2.88
% 19.64/2.88 % SZS status Theorem
% 19.64/2.88
% 19.64/2.88 % SZS output start Proof
% 19.64/2.88 Take the following subset of the input axioms:
% 19.64/2.88 fof(dt_k6_relat_1, axiom, ![A]: relation(identity_relation(A))).
% 19.64/2.88 fof(fc2_funct_1, axiom, ![A3]: (relation(identity_relation(A3)) & function(identity_relation(A3)))).
% 19.64/2.88 fof(t34_funct_1, lemma, ![B, A2]: ((relation(B) & function(B)) => (B=identity_relation(A2) <=> (relation_dom(B)=A2 & ![C]: (in(C, A2) => apply(B, C)=C))))).
% 19.64/2.88 fof(t35_funct_1, conjecture, ![A3, B2]: (in(B2, A3) => apply(identity_relation(A3), B2)=B2)).
% 19.64/2.88
% 19.64/2.88 Now clausify the problem and encode Horn clauses using encoding 3 of
% 19.64/2.88 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 19.64/2.88 We repeatedly replace C & s=t => u=v by the two clauses:
% 19.64/2.88 fresh(y, y, x1...xn) = u
% 19.64/2.88 C => fresh(s, t, x1...xn) = v
% 19.64/2.88 where fresh is a fresh function symbol and x1..xn are the free
% 19.64/2.88 variables of u and v.
% 19.64/2.88 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 19.64/2.88 input problem has no model of domain size 1).
% 19.64/2.88
% 19.64/2.88 The encoding turns the above axioms into the following unit equations and goals:
% 19.64/2.88
% 19.64/2.88 Axiom 1 (t35_funct_1): in(b2, a) = true2.
% 19.64/2.88 Axiom 2 (dt_k6_relat_1): relation(identity_relation(X)) = true2.
% 19.64/2.88 Axiom 3 (fc2_funct_1): function(identity_relation(X)) = true2.
% 19.64/2.88 Axiom 4 (t34_funct_1_2): fresh369(X, X, Y, Z) = Z.
% 19.64/2.88 Axiom 5 (t34_funct_1_2): fresh368(X, X, Y, Z, W) = fresh369(Z, identity_relation(Y), Z, W).
% 19.64/2.88 Axiom 6 (t34_funct_1_2): fresh108(X, X, Y, Z, W) = apply(Z, W).
% 19.64/2.88 Axiom 7 (t34_funct_1_2): fresh367(X, X, Y, Z, W) = fresh368(function(Z), true2, Y, Z, W).
% 19.64/2.88 Axiom 8 (t34_funct_1_2): fresh367(relation(X), true2, Y, X, Z) = fresh108(in(Z, Y), true2, Y, X, Z).
% 19.64/2.88
% 19.64/2.88 Goal 1 (t35_funct_1_1): apply(identity_relation(a), b2) = b2.
% 19.64/2.88 Proof:
% 19.64/2.88 apply(identity_relation(a), b2)
% 19.64/2.89 = { by axiom 6 (t34_funct_1_2) R->L }
% 19.64/2.89 fresh108(true2, true2, a, identity_relation(a), b2)
% 19.64/2.89 = { by axiom 1 (t35_funct_1) R->L }
% 19.64/2.89 fresh108(in(b2, a), true2, a, identity_relation(a), b2)
% 19.64/2.89 = { by axiom 8 (t34_funct_1_2) R->L }
% 19.64/2.89 fresh367(relation(identity_relation(a)), true2, a, identity_relation(a), b2)
% 19.64/2.89 = { by axiom 2 (dt_k6_relat_1) }
% 19.64/2.89 fresh367(true2, true2, a, identity_relation(a), b2)
% 19.64/2.89 = { by axiom 7 (t34_funct_1_2) }
% 19.64/2.89 fresh368(function(identity_relation(a)), true2, a, identity_relation(a), b2)
% 19.64/2.89 = { by axiom 3 (fc2_funct_1) }
% 19.64/2.89 fresh368(true2, true2, a, identity_relation(a), b2)
% 19.64/2.89 = { by axiom 5 (t34_funct_1_2) }
% 19.64/2.89 fresh369(identity_relation(a), identity_relation(a), identity_relation(a), b2)
% 19.64/2.89 = { by axiom 4 (t34_funct_1_2) }
% 19.64/2.89 b2
% 19.64/2.89 % SZS output end Proof
% 19.64/2.89
% 19.64/2.89 RESULT: Theorem (the conjecture is true).
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