TSTP Solution File: ALG417-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : ALG417-1 : TPTP v8.1.2. Released v4.1.0.
% 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 : n017.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 : Wed Aug 30 16:43:14 EDT 2023
% Result : Unsatisfiable 11.79s 1.93s
% Output : Proof 11.79s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : ALG417-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 03:03:57 EDT 2023
% 0.14/0.35 % CPUTime :
% 11.79/1.93 Command-line arguments: --ground-connectedness --complete-subsets
% 11.79/1.93
% 11.79/1.93 % SZS status Unsatisfiable
% 11.79/1.93
% 11.79/1.93 % SZS output start Proof
% 11.79/1.93 Take the following subset of the input axioms:
% 11.79/1.93 fof(cls_CHAINED_0_01, axiom, v_s____!=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))).
% 11.79/1.93 fof(cls_conjecture_0, negated_conjecture, v_k____=c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)).
% 11.79/1.93 fof(cls_kpn_0, axiom, v_s____=c_Polynomial_OpCons(v_k____, c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Complex_Ocomplex)).
% 11.79/1.93 fof(cls_pCons__0__0_0, axiom, ![T_a]: (~class_HOL_Ozero(T_a) | c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)), T_a)=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 11.79/1.93 fof(cls_sne_0, axiom, v_s____!=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))).
% 11.79/1.93 fof(clsarity_Complex__Ocomplex__HOL_Ozero, axiom, class_HOL_Ozero(tc_Complex_Ocomplex)).
% 11.79/1.93
% 11.79/1.93 Now clausify the problem and encode Horn clauses using encoding 3 of
% 11.79/1.93 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 11.79/1.93 We repeatedly replace C & s=t => u=v by the two clauses:
% 11.79/1.93 fresh(y, y, x1...xn) = u
% 11.79/1.93 C => fresh(s, t, x1...xn) = v
% 11.79/1.93 where fresh is a fresh function symbol and x1..xn are the free
% 11.79/1.93 variables of u and v.
% 11.79/1.93 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 11.79/1.93 input problem has no model of domain size 1).
% 11.79/1.93
% 11.79/1.93 The encoding turns the above axioms into the following unit equations and goals:
% 11.79/1.93
% 11.79/1.93 Axiom 1 (clsarity_Complex__Ocomplex__HOL_Ozero): class_HOL_Ozero(tc_Complex_Ocomplex) = true2.
% 11.79/1.93 Axiom 2 (cls_conjecture_0): v_k____ = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 11.79/1.93 Axiom 3 (cls_pCons__0__0_0): fresh171(X, X, Y) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(Y)).
% 11.79/1.93 Axiom 4 (cls_kpn_0): v_s____ = c_Polynomial_OpCons(v_k____, c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Complex_Ocomplex).
% 11.79/1.93 Axiom 5 (cls_pCons__0__0_0): fresh171(class_HOL_Ozero(X), true2, X) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X), c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X)), X).
% 11.79/1.93
% 11.79/1.93 Lemma 6: c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_s____.
% 11.79/1.93 Proof:
% 11.79/1.93 c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 11.79/1.93 = { by axiom 3 (cls_pCons__0__0_0) R->L }
% 11.79/1.93 fresh171(true2, true2, tc_Complex_Ocomplex)
% 11.79/1.93 = { by axiom 1 (clsarity_Complex__Ocomplex__HOL_Ozero) R->L }
% 11.79/1.93 fresh171(class_HOL_Ozero(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex)
% 11.79/1.93 = { by axiom 5 (cls_pCons__0__0_0) }
% 11.79/1.93 c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Complex_Ocomplex)
% 11.79/1.93 = { by axiom 2 (cls_conjecture_0) R->L }
% 11.79/1.93 c_Polynomial_OpCons(v_k____, c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Complex_Ocomplex)
% 11.79/1.93 = { by axiom 4 (cls_kpn_0) R->L }
% 11.79/1.93 v_s____
% 11.79/1.93
% 11.79/1.93 Goal 1 (cls_CHAINED_0_01): v_s____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)).
% 11.79/1.93 Proof:
% 11.79/1.93 v_s____
% 11.79/1.93 = { by lemma 6 R->L }
% 11.79/1.93 c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 11.79/1.93
% 11.79/1.93 Goal 2 (cls_sne_0): v_s____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)).
% 11.79/1.93 Proof:
% 11.79/1.93 v_s____
% 11.79/1.93 = { by lemma 6 R->L }
% 11.79/1.93 c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 11.79/1.93 % SZS output end Proof
% 11.79/1.93
% 11.79/1.93 RESULT: Unsatisfiable (the axioms are contradictory).
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