TSTP Solution File: SEU444+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SEU444+1 : TPTP v8.1.2. Released v3.4.0.
% 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 : n020.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 17:52:56 EDT 2023
% Result : Theorem 0.20s 0.44s
% 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
% 0.00/0.12 % Problem : SEU444+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n020.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 00:18:30 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.44 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.44
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44
% 0.20/0.44 % SZS output start Proof
% 0.20/0.44 Take the following subset of the input axioms:
% 0.20/0.44 fof(t51_relset_2, axiom, ![B, C, A2]: (m2_relset_1(C, B, A2) => (k1_funct_5(C)=k10_relset_1(A2, B, k6_relset_1(B, A2, C), A2) & k2_funct_5(C)=k10_relset_1(B, A2, C, B)))).
% 0.20/0.44 fof(t56_relset_2, conjecture, ![A, B2, C2]: (m2_relset_1(C2, B2, A) => (k1_funct_5(C2)=k10_relset_1(A, B2, k6_relset_1(B2, A, C2), A) & k10_relset_1(A, B2, k6_relset_1(B2, A, C2), k10_relset_1(B2, A, C2, B2))=k10_relset_1(A, B2, k6_relset_1(B2, A, C2), k2_funct_5(C2))))).
% 0.20/0.44
% 0.20/0.44 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.44 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.44 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.44 fresh(y, y, x1...xn) = u
% 0.20/0.44 C => fresh(s, t, x1...xn) = v
% 0.20/0.44 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.44 variables of u and v.
% 0.20/0.44 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.44 input problem has no model of domain size 1).
% 0.20/0.44
% 0.20/0.44 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.44
% 0.20/0.44 Axiom 1 (t56_relset_2): m2_relset_1(c3, b4, a4) = true2.
% 0.20/0.44 Axiom 2 (t51_relset_2): fresh7(X, X, Y, Z, W) = k1_funct_5(W).
% 0.20/0.44 Axiom 3 (t51_relset_2_1): fresh6(X, X, Y, Z, W) = k2_funct_5(W).
% 0.20/0.44 Axiom 4 (t51_relset_2): fresh7(m2_relset_1(X, Y, Z), true2, Z, Y, X) = k10_relset_1(Z, Y, k6_relset_1(Y, Z, X), Z).
% 0.20/0.44 Axiom 5 (t51_relset_2_1): fresh6(m2_relset_1(X, Y, Z), true2, Z, Y, X) = k10_relset_1(Y, Z, X, Y).
% 0.20/0.44
% 0.20/0.44 Goal 1 (t56_relset_2_1): tuple3(k1_funct_5(c3), k10_relset_1(a4, b4, k6_relset_1(b4, a4, c3), k10_relset_1(b4, a4, c3, b4))) = tuple3(k10_relset_1(a4, b4, k6_relset_1(b4, a4, c3), a4), k10_relset_1(a4, b4, k6_relset_1(b4, a4, c3), k2_funct_5(c3))).
% 0.20/0.44 Proof:
% 0.20/0.44 tuple3(k1_funct_5(c3), k10_relset_1(a4, b4, k6_relset_1(b4, a4, c3), k10_relset_1(b4, a4, c3, b4)))
% 0.20/0.44 = { by axiom 5 (t51_relset_2_1) R->L }
% 0.20/0.44 tuple3(k1_funct_5(c3), k10_relset_1(a4, b4, k6_relset_1(b4, a4, c3), fresh6(m2_relset_1(c3, b4, a4), true2, a4, b4, c3)))
% 0.20/0.44 = { by axiom 1 (t56_relset_2) }
% 0.20/0.44 tuple3(k1_funct_5(c3), k10_relset_1(a4, b4, k6_relset_1(b4, a4, c3), fresh6(true2, true2, a4, b4, c3)))
% 0.20/0.44 = { by axiom 3 (t51_relset_2_1) }
% 0.20/0.44 tuple3(k1_funct_5(c3), k10_relset_1(a4, b4, k6_relset_1(b4, a4, c3), k2_funct_5(c3)))
% 0.20/0.44 = { by axiom 2 (t51_relset_2) R->L }
% 0.20/0.44 tuple3(fresh7(true2, true2, a4, b4, c3), k10_relset_1(a4, b4, k6_relset_1(b4, a4, c3), k2_funct_5(c3)))
% 0.20/0.44 = { by axiom 1 (t56_relset_2) R->L }
% 0.20/0.44 tuple3(fresh7(m2_relset_1(c3, b4, a4), true2, a4, b4, c3), k10_relset_1(a4, b4, k6_relset_1(b4, a4, c3), k2_funct_5(c3)))
% 0.20/0.44 = { by axiom 4 (t51_relset_2) }
% 0.20/0.44 tuple3(k10_relset_1(a4, b4, k6_relset_1(b4, a4, c3), a4), k10_relset_1(a4, b4, k6_relset_1(b4, a4, c3), k2_funct_5(c3)))
% 0.20/0.44 % SZS output end Proof
% 0.20/0.44
% 0.20/0.44 RESULT: Theorem (the conjecture is true).
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