TSTP Solution File: ALG414-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : ALG414-1 : 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 : n032.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 31.38s 4.41s
% Output : Proof 31.38s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : ALG414-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Mon Aug 28 04:43:30 EDT 2023
% 0.09/0.29 % CPUTime :
% 31.38/4.41 Command-line arguments: --no-flatten-goal
% 31.38/4.41
% 31.38/4.41 % SZS status Unsatisfiable
% 31.38/4.41
% 31.38/4.42 % SZS output start Proof
% 31.38/4.42 Take the following subset of the input axioms:
% 31.38/4.42 fof(cls_CHAINED_0, axiom, c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)!=c_RealVector_Onorm__class_Onorm(v_d____, tc_Complex_Ocomplex)).
% 31.38/4.42 fof(cls_CHAINED_0_01, axiom, c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)=c_RealVector_Onorm__class_Onorm(v_d____, tc_Complex_Ocomplex)).
% 31.38/4.42
% 31.38/4.42 Now clausify the problem and encode Horn clauses using encoding 3 of
% 31.38/4.42 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 31.38/4.42 We repeatedly replace C & s=t => u=v by the two clauses:
% 31.38/4.42 fresh(y, y, x1...xn) = u
% 31.38/4.42 C => fresh(s, t, x1...xn) = v
% 31.38/4.42 where fresh is a fresh function symbol and x1..xn are the free
% 31.38/4.42 variables of u and v.
% 31.38/4.42 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 31.38/4.42 input problem has no model of domain size 1).
% 31.38/4.42
% 31.38/4.42 The encoding turns the above axioms into the following unit equations and goals:
% 31.38/4.42
% 31.38/4.42 Axiom 1 (cls_CHAINED_0_01): c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(v_d____, tc_Complex_Ocomplex).
% 31.38/4.42
% 31.38/4.42 Goal 1 (cls_CHAINED_0): c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(v_d____, tc_Complex_Ocomplex).
% 31.38/4.42 Proof:
% 31.38/4.42 c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 31.38/4.42 = { by axiom 1 (cls_CHAINED_0_01) }
% 31.38/4.42 c_RealVector_Onorm__class_Onorm(v_d____, tc_Complex_Ocomplex)
% 31.38/4.42 % SZS output end Proof
% 31.38/4.42
% 31.38/4.42 RESULT: Unsatisfiable (the axioms are contradictory).
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