TSTP Solution File: ALG382-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : ALG382-1 : 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 : n007.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 16:43:08 EDT 2023
% Result : Unsatisfiable 61.83s 8.25s
% Output : Proof 61.83s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG382-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 05:25:12 EDT 2023
% 0.12/0.34 % CPUTime :
% 61.83/8.25 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 61.83/8.25
% 61.83/8.25 % SZS status Unsatisfiable
% 61.83/8.25
% 61.83/8.26 % SZS output start Proof
% 61.83/8.26 Take the following subset of the input axioms:
% 61.83/8.26 fof(cls_CHAINED_0, axiom, c_lessequals(c_HOL_Oplus__class_Oplus(v_da____, c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal)).
% 61.83/8.26 fof(cls_conjecture_0, negated_conjecture, ~c_lessequals(c_HOL_Oplus__class_Oplus(v_da____, c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), tc_RealDef_Oreal)).
% 61.83/8.26 fof(cls_real__mult__1_0, axiom, ![V_z]: c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), V_z, tc_RealDef_Oreal)=V_z).
% 61.83/8.26
% 61.83/8.26 Now clausify the problem and encode Horn clauses using encoding 3 of
% 61.83/8.26 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 61.83/8.26 We repeatedly replace C & s=t => u=v by the two clauses:
% 61.83/8.26 fresh(y, y, x1...xn) = u
% 61.83/8.26 C => fresh(s, t, x1...xn) = v
% 61.83/8.26 where fresh is a fresh function symbol and x1..xn are the free
% 61.83/8.26 variables of u and v.
% 61.83/8.26 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 61.83/8.26 input problem has no model of domain size 1).
% 61.83/8.26
% 61.83/8.26 The encoding turns the above axioms into the following unit equations and goals:
% 61.83/8.26
% 61.83/8.26 Axiom 1 (cls_real__mult__1_0): c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), X, tc_RealDef_Oreal) = X.
% 61.83/8.26 Axiom 2 (cls_CHAINED_0): c_lessequals(c_HOL_Oplus__class_Oplus(v_da____, c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal) = true2.
% 61.83/8.26
% 61.83/8.26 Goal 1 (cls_conjecture_0): c_lessequals(c_HOL_Oplus__class_Oplus(v_da____, c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), tc_RealDef_Oreal) = true2.
% 61.83/8.26 Proof:
% 61.83/8.26 c_lessequals(c_HOL_Oplus__class_Oplus(v_da____, c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 61.83/8.26 = { by axiom 1 (cls_real__mult__1_0) }
% 61.83/8.26 c_lessequals(c_HOL_Oplus__class_Oplus(v_da____, c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal)
% 61.83/8.26 = { by axiom 2 (cls_CHAINED_0) }
% 61.83/8.26 true2
% 61.83/8.26 % SZS output end Proof
% 61.83/8.26
% 61.83/8.26 RESULT: Unsatisfiable (the axioms are contradictory).
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