TSTP Solution File: ALG432-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ALG432-1 : 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 : n004.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 16:43:17 EDT 2023
% Result : Unsatisfiable 73.02s 9.69s
% Output : Proof 73.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG432-1 : 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 : n004.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 03:00:37 EDT 2023
% 0.14/0.34 % CPUTime :
% 73.02/9.69 Command-line arguments: --no-flatten-goal
% 73.02/9.69
% 73.02/9.69 % SZS status Unsatisfiable
% 73.02/9.69
% 73.02/9.69 % SZS output start Proof
% 73.02/9.69 Take the following subset of the input axioms:
% 73.02/9.69 fof(cls_class__semiring_Omul__0_0, axiom, ![T_a, V_x]: (~class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a), V_x, T_a)=c_HOL_Ozero__class_Ozero(T_a))).
% 73.02/9.69 fof(cls_class__semiring_Omul__c_0, axiom, ![V_y, T_a2, V_x2]: (~class_Ring__and__Field_Ocomm__semiring__1(T_a2) | c_HOL_Otimes__class_Otimes(V_x2, V_y, T_a2)=c_HOL_Otimes__class_Otimes(V_y, V_x2, T_a2))).
% 73.02/9.69 fof(cls_conjecture_0, negated_conjecture, c_Polynomial_Opoly(v_p, v_x, tc_Complex_Ocomplex)=c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)).
% 73.02/9.69 fof(cls_conjecture_1, negated_conjecture, c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), v_p, tc_Complex_Ocomplex), v_x, tc_Complex_Ocomplex)!=c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)).
% 73.02/9.69 fof(cls_monoid__add__class_Oadd__0__right_0, axiom, ![V_a, T_a2]: (~class_OrderedGroup_Omonoid__add(T_a2) | c_HOL_Oplus__class_Oplus(V_a, c_HOL_Ozero__class_Ozero(T_a2), T_a2)=V_a)).
% 73.02/9.69 fof(cls_poly__pCons_0, axiom, ![V_p, T_a2, V_a2, V_x2]: (~class_Ring__and__Field_Ocomm__semiring__0(T_a2) | c_Polynomial_Opoly(c_Polynomial_OpCons(V_a2, V_p, T_a2), V_x2, T_a2)=c_HOL_Oplus__class_Oplus(V_a2, c_HOL_Otimes__class_Otimes(V_x2, c_Polynomial_Opoly(V_p, V_x2, T_a2), T_a2), T_a2))).
% 73.02/9.69 fof(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add, axiom, class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex)).
% 73.02/9.69 fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0, axiom, class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)).
% 73.02/9.69 fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1, axiom, class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)).
% 73.02/9.69
% 73.02/9.69 Now clausify the problem and encode Horn clauses using encoding 3 of
% 73.02/9.69 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 73.02/9.69 We repeatedly replace C & s=t => u=v by the two clauses:
% 73.02/9.69 fresh(y, y, x1...xn) = u
% 73.02/9.69 C => fresh(s, t, x1...xn) = v
% 73.02/9.69 where fresh is a fresh function symbol and x1..xn are the free
% 73.02/9.69 variables of u and v.
% 73.02/9.69 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 73.02/9.69 input problem has no model of domain size 1).
% 73.02/9.69
% 73.02/9.69 The encoding turns the above axioms into the following unit equations and goals:
% 73.02/9.69
% 73.02/9.69 Axiom 1 (clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add): class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) = true2.
% 73.02/9.69 Axiom 2 (clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0): class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) = true2.
% 73.02/9.69 Axiom 3 (clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1): class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) = true2.
% 73.02/9.69 Axiom 4 (cls_conjecture_0): c_Polynomial_Opoly(v_p, v_x, tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 73.02/9.70 Axiom 5 (cls_class__semiring_Omul__0_0): fresh653(X, X, Y, Z) = c_HOL_Ozero__class_Ozero(Y).
% 73.02/9.70 Axiom 6 (cls_monoid__add__class_Oadd__0__right_0): fresh19(X, X, Y, Z) = Z.
% 73.02/9.70 Axiom 7 (cls_class__semiring_Omul__0_0): fresh653(class_Ring__and__Field_Ocomm__semiring__1(X), true2, X, Y) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X), Y, X).
% 73.02/9.70 Axiom 8 (cls_class__semiring_Omul__c_0): fresh651(X, X, Y, Z, W) = c_HOL_Otimes__class_Otimes(W, Z, Y).
% 73.02/9.70 Axiom 9 (cls_monoid__add__class_Oadd__0__right_0): fresh19(class_OrderedGroup_Omonoid__add(X), true2, X, Y) = c_HOL_Oplus__class_Oplus(Y, c_HOL_Ozero__class_Ozero(X), X).
% 73.02/9.70 Axiom 10 (cls_class__semiring_Omul__c_0): fresh651(class_Ring__and__Field_Ocomm__semiring__1(X), true2, X, Y, Z) = c_HOL_Otimes__class_Otimes(Y, Z, X).
% 73.02/9.70 Axiom 11 (cls_poly__pCons_0): fresh276(X, X, Y, Z, W, V) = c_Polynomial_Opoly(c_Polynomial_OpCons(Z, W, Y), V, Y).
% 73.02/9.70 Axiom 12 (cls_poly__pCons_0): fresh276(class_Ring__and__Field_Ocomm__semiring__0(X), true2, X, Y, Z, W) = c_HOL_Oplus__class_Oplus(Y, c_HOL_Otimes__class_Otimes(W, c_Polynomial_Opoly(Z, W, X), X), X).
% 73.02/9.70
% 73.02/9.70 Goal 1 (cls_conjecture_1): c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), v_p, tc_Complex_Ocomplex), v_x, tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 73.02/9.70 Proof:
% 73.02/9.70 c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), v_p, tc_Complex_Ocomplex), v_x, tc_Complex_Ocomplex)
% 73.02/9.70 = { by axiom 11 (cls_poly__pCons_0) R->L }
% 73.02/9.70 fresh276(true2, true2, tc_Complex_Ocomplex, c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), v_p, v_x)
% 73.02/9.70 = { by axiom 2 (clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) R->L }
% 73.02/9.70 fresh276(class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), v_p, v_x)
% 73.02/9.70 = { by axiom 12 (cls_poly__pCons_0) }
% 73.02/9.70 c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), c_HOL_Otimes__class_Otimes(v_x, c_Polynomial_Opoly(v_p, v_x, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 73.02/9.70 = { by axiom 4 (cls_conjecture_0) }
% 73.02/9.70 c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), c_HOL_Otimes__class_Otimes(v_x, c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 73.02/9.70 = { by axiom 8 (cls_class__semiring_Omul__c_0) R->L }
% 73.02/9.70 c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), fresh651(true2, true2, tc_Complex_Ocomplex, c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), v_x), tc_Complex_Ocomplex)
% 73.02/9.70 = { by axiom 3 (clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) R->L }
% 73.02/9.70 c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), fresh651(class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), v_x), tc_Complex_Ocomplex)
% 73.02/9.70 = { by axiom 10 (cls_class__semiring_Omul__c_0) }
% 73.02/9.70 c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), v_x, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 73.02/9.70 = { by axiom 7 (cls_class__semiring_Omul__0_0) R->L }
% 73.02/9.70 c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), fresh653(class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, v_x), tc_Complex_Ocomplex)
% 73.02/9.70 = { by axiom 3 (clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) }
% 73.02/9.70 c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), fresh653(true2, true2, tc_Complex_Ocomplex, v_x), tc_Complex_Ocomplex)
% 73.02/9.70 = { by axiom 5 (cls_class__semiring_Omul__0_0) }
% 73.02/9.70 c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 73.02/9.70 = { by axiom 9 (cls_monoid__add__class_Oadd__0__right_0) R->L }
% 73.02/9.70 fresh19(class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
% 73.02/9.70 = { by axiom 1 (clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) }
% 73.02/9.70 fresh19(true2, true2, tc_Complex_Ocomplex, c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
% 73.02/9.70 = { by axiom 6 (cls_monoid__add__class_Oadd__0__right_0) }
% 73.02/9.70 c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
% 73.02/9.70 % SZS output end Proof
% 73.02/9.70
% 73.02/9.70 RESULT: Unsatisfiable (the axioms are contradictory).
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