TSTP Solution File: ALG348-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ALG348-1 : 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 16:43:02 EDT 2023
% Result : Unsatisfiable 73.68s 9.84s
% Output : Proof 73.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : ALG348-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Mon Aug 28 04:47:15 EDT 2023
% 0.10/0.30 % CPUTime :
% 73.68/9.84 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 73.68/9.84
% 73.68/9.84 % SZS status Unsatisfiable
% 73.68/9.84
% 73.68/9.85 % SZS output start Proof
% 73.68/9.85 Take the following subset of the input axioms:
% 73.68/9.85 fof(cls_conjecture_0, negated_conjecture, c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_p, v_a, tc_Complex_Ocomplex), v_x, tc_Complex_Ocomplex)!=c_Polynomial_Opoly(v_p, c_HOL_Oplus__class_Oplus(v_a, v_x, tc_Complex_Ocomplex), tc_Complex_Ocomplex)).
% 73.68/9.85 fof(cls_poly__offset__poly_0, axiom, ![T_a, V_x, V_p, V_h]: (~class_Ring__and__Field_Ocomm__semiring__0(T_a) | c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p, V_h, T_a), V_x, T_a)=c_Polynomial_Opoly(V_p, c_HOL_Oplus__class_Oplus(V_h, V_x, T_a), T_a))).
% 73.68/9.85 fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0, axiom, class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)).
% 73.68/9.85
% 73.68/9.85 Now clausify the problem and encode Horn clauses using encoding 3 of
% 73.68/9.85 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 73.68/9.85 We repeatedly replace C & s=t => u=v by the two clauses:
% 73.68/9.85 fresh(y, y, x1...xn) = u
% 73.68/9.85 C => fresh(s, t, x1...xn) = v
% 73.68/9.85 where fresh is a fresh function symbol and x1..xn are the free
% 73.68/9.85 variables of u and v.
% 73.68/9.85 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 73.68/9.85 input problem has no model of domain size 1).
% 73.68/9.85
% 73.68/9.85 The encoding turns the above axioms into the following unit equations and goals:
% 73.68/9.85
% 73.68/9.85 Axiom 1 (clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0): class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) = true2.
% 73.68/9.85 Axiom 2 (cls_poly__offset__poly_0): fresh211(X, X, Y, Z, W, V) = c_Polynomial_Opoly(Z, c_HOL_Oplus__class_Oplus(W, V, Y), Y).
% 73.68/9.85 Axiom 3 (cls_poly__offset__poly_0): fresh211(class_Ring__and__Field_Ocomm__semiring__0(X), true2, X, Y, Z, W) = c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(Y, Z, X), W, X).
% 73.68/9.85
% 73.68/9.85 Goal 1 (cls_conjecture_0): c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_p, v_a, tc_Complex_Ocomplex), v_x, tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_p, c_HOL_Oplus__class_Oplus(v_a, v_x, tc_Complex_Ocomplex), tc_Complex_Ocomplex).
% 73.68/9.85 Proof:
% 73.68/9.85 c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_p, v_a, tc_Complex_Ocomplex), v_x, tc_Complex_Ocomplex)
% 73.68/9.85 = { by axiom 3 (cls_poly__offset__poly_0) R->L }
% 73.68/9.85 fresh211(class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, v_p, v_a, v_x)
% 73.68/9.85 = { by axiom 1 (clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) }
% 73.68/9.85 fresh211(true2, true2, tc_Complex_Ocomplex, v_p, v_a, v_x)
% 73.68/9.85 = { by axiom 2 (cls_poly__offset__poly_0) }
% 73.68/9.85 c_Polynomial_Opoly(v_p, c_HOL_Oplus__class_Oplus(v_a, v_x, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 73.68/9.85 % SZS output end Proof
% 73.68/9.85
% 73.68/9.85 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------