TSTP Solution File: ALG421-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ALG421-1 : 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 : n026.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 16:43:15 EDT 2023
% Result : Unsatisfiable 54.38s 7.53s
% Output : Proof 54.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG421-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 03:57:04 EDT 2023
% 0.14/0.35 % CPUTime :
% 54.38/7.53 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 54.38/7.53
% 54.38/7.53 % SZS status Unsatisfiable
% 54.38/7.53
% 54.38/7.54 % SZS output start Proof
% 54.38/7.54 Take the following subset of the input axioms:
% 54.38/7.54 fof(cls_conjecture_0, negated_conjecture, c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_s____, v_x, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_u____, v_x, tc_Complex_Ocomplex), tc_Complex_Ocomplex)!=c_Power_Opower__class_Opower(c_Polynomial_Opoly(v_r____, v_x, tc_Complex_Ocomplex), c_Polynomial_Odegree(v_s____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)).
% 54.38/7.54 fof(cls_poly__mult_0, axiom, ![T_a, V_x, V_p, V_q]: (~class_Ring__and__Field_Ocomm__semiring__0(T_a) | c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(V_p, V_q, tc_Polynomial_Opoly(T_a)), V_x, T_a)=c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(V_p, V_x, T_a), c_Polynomial_Opoly(V_q, V_x, T_a), T_a))).
% 54.38/7.54 fof(cls_poly__power_0, axiom, ![V_n, T_a2, V_x2, V_p2]: (~class_Ring__and__Field_Ocomm__semiring__1(T_a2) | c_Polynomial_Opoly(c_Power_Opower__class_Opower(V_p2, V_n, tc_Polynomial_Opoly(T_a2)), V_x2, T_a2)=c_Power_Opower__class_Opower(c_Polynomial_Opoly(V_p2, V_x2, T_a2), V_n, T_a2))).
% 54.38/7.54 fof(cls_u_0, axiom, c_Power_Opower__class_Opower(v_r____, c_Polynomial_Odegree(v_s____, tc_Complex_Ocomplex), tc_Polynomial_Opoly(tc_Complex_Ocomplex))=c_HOL_Otimes__class_Otimes(v_s____, v_u____, tc_Polynomial_Opoly(tc_Complex_Ocomplex))).
% 54.38/7.54 fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0, axiom, class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)).
% 54.38/7.54 fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1, axiom, class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)).
% 54.38/7.54
% 54.38/7.54 Now clausify the problem and encode Horn clauses using encoding 3 of
% 54.38/7.54 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 54.38/7.54 We repeatedly replace C & s=t => u=v by the two clauses:
% 54.38/7.54 fresh(y, y, x1...xn) = u
% 54.38/7.54 C => fresh(s, t, x1...xn) = v
% 54.38/7.54 where fresh is a fresh function symbol and x1..xn are the free
% 54.38/7.54 variables of u and v.
% 54.38/7.54 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 54.38/7.54 input problem has no model of domain size 1).
% 54.38/7.54
% 54.38/7.54 The encoding turns the above axioms into the following unit equations and goals:
% 54.38/7.54
% 54.38/7.54 Axiom 1 (clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1): class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) = true2.
% 54.38/7.54 Axiom 2 (clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0): class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) = true2.
% 54.38/7.54 Axiom 3 (cls_u_0): c_Power_Opower__class_Opower(v_r____, c_Polynomial_Odegree(v_s____, tc_Complex_Ocomplex), tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Otimes__class_Otimes(v_s____, v_u____, tc_Polynomial_Opoly(tc_Complex_Ocomplex)).
% 54.38/7.54 Axiom 4 (cls_poly__mult_0): fresh226(X, X, Y, Z, W, V) = c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(Z, W, tc_Polynomial_Opoly(Y)), V, Y).
% 54.38/7.54 Axiom 5 (cls_poly__power_0): fresh222(X, X, Y, Z, W, V) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(Z, V, Y), W, Y).
% 54.38/7.54 Axiom 6 (cls_poly__mult_0): fresh226(class_Ring__and__Field_Ocomm__semiring__0(X), true2, X, Y, Z, W) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(Y, W, X), c_Polynomial_Opoly(Z, W, X), X).
% 54.38/7.55 Axiom 7 (cls_poly__power_0): fresh222(class_Ring__and__Field_Ocomm__semiring__1(X), true2, X, Y, Z, W) = c_Polynomial_Opoly(c_Power_Opower__class_Opower(Y, Z, tc_Polynomial_Opoly(X)), W, X).
% 54.38/7.55
% 54.38/7.55 Goal 1 (cls_conjecture_0): c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_s____, v_x, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_u____, v_x, tc_Complex_Ocomplex), tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(v_r____, v_x, tc_Complex_Ocomplex), c_Polynomial_Odegree(v_s____, tc_Complex_Ocomplex), tc_Complex_Ocomplex).
% 54.38/7.55 Proof:
% 54.38/7.55 c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_s____, v_x, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_u____, v_x, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 54.38/7.55 = { by axiom 6 (cls_poly__mult_0) R->L }
% 54.38/7.55 fresh226(class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, v_s____, v_u____, v_x)
% 54.38/7.55 = { by axiom 2 (clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) }
% 54.38/7.55 fresh226(true2, true2, tc_Complex_Ocomplex, v_s____, v_u____, v_x)
% 54.38/7.55 = { by axiom 4 (cls_poly__mult_0) }
% 54.38/7.55 c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(v_s____, v_u____, tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_x, tc_Complex_Ocomplex)
% 54.38/7.55 = { by axiom 3 (cls_u_0) R->L }
% 54.38/7.55 c_Polynomial_Opoly(c_Power_Opower__class_Opower(v_r____, c_Polynomial_Odegree(v_s____, tc_Complex_Ocomplex), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_x, tc_Complex_Ocomplex)
% 54.38/7.55 = { by axiom 7 (cls_poly__power_0) R->L }
% 54.38/7.55 fresh222(class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, v_r____, c_Polynomial_Odegree(v_s____, tc_Complex_Ocomplex), v_x)
% 54.38/7.55 = { by axiom 1 (clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) }
% 54.38/7.55 fresh222(true2, true2, tc_Complex_Ocomplex, v_r____, c_Polynomial_Odegree(v_s____, tc_Complex_Ocomplex), v_x)
% 54.38/7.55 = { by axiom 5 (cls_poly__power_0) }
% 54.38/7.55 c_Power_Opower__class_Opower(c_Polynomial_Opoly(v_r____, v_x, tc_Complex_Ocomplex), c_Polynomial_Odegree(v_s____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 54.38/7.55 % SZS output end Proof
% 54.38/7.55
% 54.38/7.55 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------