TSTP Solution File: SEU217+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SEU217+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 : n029.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 0.19s 0.43s
% Output : Proof 0.19s
% 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+1 : 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 : n029.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 02:01:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.43 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.43
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43
% 0.19/0.44 % SZS output start Proof
% 0.19/0.44 Take the following subset of the input axioms:
% 0.19/0.44 fof(dt_k6_relat_1, axiom, ![A]: relation(identity_relation(A))).
% 0.19/0.44 fof(fc2_funct_1, axiom, ![A3]: (relation(identity_relation(A3)) & function(identity_relation(A3)))).
% 0.19/0.44 fof(t34_funct_1, axiom, ![B, A2]: ((relation(B) & function(B)) => (B=identity_relation(A2) <=> (relation_dom(B)=A2 & ![C]: (in(C, A2) => apply(B, C)=C))))).
% 0.19/0.44 fof(t35_funct_1, conjecture, ![A3, B2]: (in(B2, A3) => apply(identity_relation(A3), B2)=B2)).
% 0.19/0.44
% 0.19/0.44 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.44 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.44 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.44 fresh(y, y, x1...xn) = u
% 0.19/0.44 C => fresh(s, t, x1...xn) = v
% 0.19/0.44 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.44 variables of u and v.
% 0.19/0.44 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.44 input problem has no model of domain size 1).
% 0.19/0.44
% 0.19/0.44 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.44
% 0.19/0.44 Axiom 1 (fc2_funct_1_1): function(identity_relation(X)) = true2.
% 0.19/0.44 Axiom 2 (t35_funct_1): in(b, a) = true2.
% 0.19/0.44 Axiom 3 (dt_k6_relat_1): relation(identity_relation(X)) = true2.
% 0.19/0.44 Axiom 4 (t34_funct_1_3): fresh21(X, X, Y, Z) = Z.
% 0.19/0.44 Axiom 5 (t34_funct_1_3): fresh20(X, X, Y, Z, W) = fresh21(Z, identity_relation(Y), Z, W).
% 0.19/0.44 Axiom 6 (t34_funct_1_3): fresh19(X, X, Y, Z, W) = apply(Z, W).
% 0.19/0.44 Axiom 7 (t34_funct_1_3): fresh18(X, X, Y, Z, W) = fresh19(relation(Z), true2, Y, Z, W).
% 0.19/0.44 Axiom 8 (t34_funct_1_3): fresh18(in(X, Y), true2, Y, Z, X) = fresh20(function(Z), true2, Y, Z, X).
% 0.19/0.44
% 0.19/0.44 Goal 1 (t35_funct_1_1): apply(identity_relation(a), b) = b.
% 0.19/0.44 Proof:
% 0.19/0.44 apply(identity_relation(a), b)
% 0.19/0.44 = { by axiom 6 (t34_funct_1_3) R->L }
% 0.19/0.44 fresh19(true2, true2, a, identity_relation(a), b)
% 0.19/0.44 = { by axiom 3 (dt_k6_relat_1) R->L }
% 0.19/0.44 fresh19(relation(identity_relation(a)), true2, a, identity_relation(a), b)
% 0.19/0.44 = { by axiom 7 (t34_funct_1_3) R->L }
% 0.19/0.44 fresh18(true2, true2, a, identity_relation(a), b)
% 0.19/0.44 = { by axiom 2 (t35_funct_1) R->L }
% 0.19/0.44 fresh18(in(b, a), true2, a, identity_relation(a), b)
% 0.19/0.44 = { by axiom 8 (t34_funct_1_3) }
% 0.19/0.44 fresh20(function(identity_relation(a)), true2, a, identity_relation(a), b)
% 0.19/0.44 = { by axiom 1 (fc2_funct_1_1) }
% 0.19/0.44 fresh20(true2, true2, a, identity_relation(a), b)
% 0.19/0.44 = { by axiom 5 (t34_funct_1_3) }
% 0.19/0.44 fresh21(identity_relation(a), identity_relation(a), identity_relation(a), b)
% 0.19/0.44 = { by axiom 4 (t34_funct_1_3) }
% 0.19/0.44 b
% 0.19/0.44 % SZS output end Proof
% 0.19/0.44
% 0.19/0.44 RESULT: Theorem (the conjecture is true).
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