TSTP Solution File: ITP019+2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : ITP019+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 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 : n021.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 04:16:15 EDT 2023
% Result : Theorem 0.20s 0.43s
% 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 : ITP019+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 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 : n021.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 : Sun Aug 27 14:22:28 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.43 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.43
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 Take the following subset of the input axioms:
% 0.20/0.43 fof(conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0, axiom, ![V0z]: (mem(V0z, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)) => (ap(c_2Ecomplex_2Ecomplex__inv, V0z)=ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0) <=> V0z=ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)))).
% 0.20/0.43 fof(conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ, conjecture, ![V0z2]: (mem(V0z2, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)) => (V0z2!=ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0) => ap(c_2Ecomplex_2Ecomplex__inv, V0z2)!=ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)))).
% 0.20/0.43
% 0.20/0.43 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.43 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.43 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.43 fresh(y, y, x1...xn) = u
% 0.20/0.43 C => fresh(s, t, x1...xn) = v
% 0.20/0.43 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.43 variables of u and v.
% 0.20/0.43 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.43 input problem has no model of domain size 1).
% 0.20/0.43
% 0.20/0.43 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.43
% 0.20/0.43 Axiom 1 (conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ): ap(c_2Ecomplex_2Ecomplex__inv, v0z) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0).
% 0.20/0.43 Axiom 2 (conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0_1): fresh(X, X, Y) = Y.
% 0.20/0.43 Axiom 3 (conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0_1): fresh10(X, X, Y) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0).
% 0.20/0.43 Axiom 4 (conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ_1): mem(v0z, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)) = true2.
% 0.20/0.43 Axiom 5 (conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0_1): fresh10(mem(X, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)), true2, X) = fresh(ap(c_2Ecomplex_2Ecomplex__inv, X), ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0), X).
% 0.20/0.43
% 0.20/0.43 Goal 1 (conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ_2): v0z = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0).
% 0.20/0.43 Proof:
% 0.20/0.43 v0z
% 0.20/0.43 = { by axiom 2 (conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0_1) R->L }
% 0.20/0.43 fresh(ap(c_2Ecomplex_2Ecomplex__inv, v0z), ap(c_2Ecomplex_2Ecomplex__inv, v0z), v0z)
% 0.20/0.43 = { by axiom 1 (conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ) }
% 0.20/0.43 fresh(ap(c_2Ecomplex_2Ecomplex__inv, v0z), ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0), v0z)
% 0.20/0.43 = { by axiom 5 (conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0_1) R->L }
% 0.20/0.43 fresh10(mem(v0z, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)), true2, v0z)
% 0.20/0.43 = { by axiom 4 (conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ_1) }
% 0.20/0.43 fresh10(true2, true2, v0z)
% 0.20/0.43 = { by axiom 3 (conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0_1) }
% 0.20/0.43 ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)
% 0.20/0.43 % SZS output end Proof
% 0.20/0.43
% 0.20/0.43 RESULT: Theorem (the conjecture is true).
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