TSTP Solution File: SWV580-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV580-1 : 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 : n018.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 : Thu Aug 31 23:05:28 EDT 2023
% Result : Unsatisfiable 20.31s 3.00s
% Output : Proof 20.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV580-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.13 % 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 : n018.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 : Tue Aug 29 07:22:32 EDT 2023
% 0.12/0.34 % CPUTime :
% 20.31/3.00 Command-line arguments: --flatten
% 20.31/3.00
% 20.31/3.00 % SZS status Unsatisfiable
% 20.31/3.00
% 20.31/3.00 % SZS output start Proof
% 20.31/3.00 Take the following subset of the input axioms:
% 20.31/3.01 fof(cls_conjecture_0, negated_conjecture, c_Finite__Set_Osetsum(v_f, c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m, c_Orderings_Obot__class_Obot(tc_fun(tc_nat, tc_bool)), tc_nat), c_SetInterval_Oord__class_OgreaterThanLessThan(v_m, v_n, tc_nat), tc_fun(tc_nat, tc_bool)), tc_nat, t_a)!=c_Finite__Set_Osetsum(v_f, c_SetInterval_Oord__class_OatLeastLessThan(v_m, v_n, tc_nat), tc_nat, t_a)).
% 20.31/3.01 fof(cls_ivl__disj__un_I3_J_0, axiom, ![T_a, V_l, V_u]: (~class_Orderings_Olinorder(T_a) | (c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_l, c_Orderings_Obot__class_Obot(tc_fun(T_a, tc_bool)), T_a), c_SetInterval_Oord__class_OgreaterThanLessThan(V_l, V_u, T_a), tc_fun(T_a, tc_bool))=c_SetInterval_Oord__class_OatLeastLessThan(V_l, V_u, T_a) | ~c_HOL_Oord__class_Oless(V_l, V_u, T_a)))).
% 20.31/3.01 fof(cls_less_0, axiom, c_HOL_Oord__class_Oless(v_m, v_n, tc_nat)).
% 20.31/3.01 fof(clsarity_nat__OrderedGroup_Oab__semigroup__add, axiom, class_OrderedGroup_Oab__semigroup__add(tc_nat)).
% 20.31/3.01 fof(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add, axiom, class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat)).
% 20.31/3.01 fof(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add, axiom, class_OrderedGroup_Opordered__comm__monoid__add(tc_nat)).
% 20.31/3.01 fof(clsarity_nat__Orderings_Olinorder, axiom, class_Orderings_Olinorder(tc_nat)).
% 20.31/3.01 fof(clsarity_nat__Ring__and__Field_Oordered__semidom, axiom, class_Ring__and__Field_Oordered__semidom(tc_nat)).
% 20.31/3.01
% 20.31/3.01 Now clausify the problem and encode Horn clauses using encoding 3 of
% 20.31/3.01 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 20.31/3.01 We repeatedly replace C & s=t => u=v by the two clauses:
% 20.31/3.01 fresh(y, y, x1...xn) = u
% 20.31/3.01 C => fresh(s, t, x1...xn) = v
% 20.31/3.01 where fresh is a fresh function symbol and x1..xn are the free
% 20.31/3.01 variables of u and v.
% 20.31/3.01 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 20.31/3.01 input problem has no model of domain size 1).
% 20.31/3.01
% 20.31/3.01 The encoding turns the above axioms into the following unit equations and goals:
% 20.31/3.01
% 20.31/3.01 Axiom 1 (clsarity_nat__Ring__and__Field_Oordered__semidom): class_Ring__and__Field_Oordered__semidom(tc_nat) = true2.
% 20.31/3.01 Axiom 2 (clsarity_nat__OrderedGroup_Oab__semigroup__add): class_OrderedGroup_Oab__semigroup__add(tc_nat) = true2.
% 20.31/3.01 Axiom 3 (clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add): class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) = true2.
% 20.31/3.01 Axiom 4 (clsarity_nat__OrderedGroup_Opordered__comm__monoid__add): class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) = true2.
% 20.31/3.01 Axiom 5 (clsarity_nat__Orderings_Olinorder): class_Orderings_Olinorder(tc_nat) = true2.
% 20.31/3.01 Axiom 6 (cls_less_0): c_HOL_Oord__class_Oless(v_m, v_n, tc_nat) = true2.
% 20.31/3.01 Axiom 7 (cls_ivl__disj__un_I3_J_0): fresh441(X, X, Y, Z, W) = c_SetInterval_Oord__class_OatLeastLessThan(Z, W, Y).
% 20.31/3.01 Axiom 8 (cls_ivl__disj__un_I3_J_0): fresh440(X, X, Y, Z, W) = fresh441(c_HOL_Oord__class_Oless(Z, W, Y), true2, Y, Z, W).
% 20.31/3.01 Axiom 9 (cls_ivl__disj__un_I3_J_0): fresh440(class_Orderings_Olinorder(X), true2, X, Y, Z) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(Y, c_Orderings_Obot__class_Obot(tc_fun(X, tc_bool)), X), c_SetInterval_Oord__class_OgreaterThanLessThan(Y, Z, X), tc_fun(X, tc_bool)).
% 20.31/3.01
% 20.31/3.01 Lemma 10: class_OrderedGroup_Oab__semigroup__add(tc_nat) = class_Ring__and__Field_Oordered__semidom(tc_nat).
% 20.31/3.01 Proof:
% 20.31/3.01 class_OrderedGroup_Oab__semigroup__add(tc_nat)
% 20.31/3.01 = { by axiom 2 (clsarity_nat__OrderedGroup_Oab__semigroup__add) }
% 20.31/3.01 true2
% 20.31/3.01 = { by axiom 1 (clsarity_nat__Ring__and__Field_Oordered__semidom) R->L }
% 20.31/3.01 class_Ring__and__Field_Oordered__semidom(tc_nat)
% 20.31/3.01
% 20.31/3.01 Lemma 11: class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) = class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 20.31/3.01 Proof:
% 20.31/3.01 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat)
% 20.31/3.01 = { by axiom 3 (clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) }
% 20.31/3.01 true2
% 20.31/3.01 = { by axiom 1 (clsarity_nat__Ring__and__Field_Oordered__semidom) R->L }
% 20.31/3.01 class_Ring__and__Field_Oordered__semidom(tc_nat)
% 20.31/3.01 = { by lemma 10 R->L }
% 20.31/3.01 class_OrderedGroup_Oab__semigroup__add(tc_nat)
% 20.31/3.01
% 20.31/3.01 Lemma 12: class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) = class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat).
% 20.31/3.01 Proof:
% 20.31/3.01 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat)
% 20.31/3.01 = { by axiom 4 (clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) }
% 20.31/3.01 true2
% 20.31/3.01 = { by axiom 1 (clsarity_nat__Ring__and__Field_Oordered__semidom) R->L }
% 20.31/3.01 class_Ring__and__Field_Oordered__semidom(tc_nat)
% 20.31/3.01 = { by lemma 10 R->L }
% 20.31/3.01 class_OrderedGroup_Oab__semigroup__add(tc_nat)
% 20.31/3.01 = { by lemma 11 R->L }
% 20.79/3.01 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat)
% 20.79/3.01
% 20.79/3.01 Goal 1 (cls_conjecture_0): c_Finite__Set_Osetsum(v_f, c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m, c_Orderings_Obot__class_Obot(tc_fun(tc_nat, tc_bool)), tc_nat), c_SetInterval_Oord__class_OgreaterThanLessThan(v_m, v_n, tc_nat), tc_fun(tc_nat, tc_bool)), tc_nat, t_a) = c_Finite__Set_Osetsum(v_f, c_SetInterval_Oord__class_OatLeastLessThan(v_m, v_n, tc_nat), tc_nat, t_a).
% 20.79/3.01 Proof:
% 20.79/3.01 c_Finite__Set_Osetsum(v_f, c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m, c_Orderings_Obot__class_Obot(tc_fun(tc_nat, tc_bool)), tc_nat), c_SetInterval_Oord__class_OgreaterThanLessThan(v_m, v_n, tc_nat), tc_fun(tc_nat, tc_bool)), tc_nat, t_a)
% 20.79/3.01 = { by axiom 9 (cls_ivl__disj__un_I3_J_0) R->L }
% 20.79/3.01 c_Finite__Set_Osetsum(v_f, fresh440(class_Orderings_Olinorder(tc_nat), true2, tc_nat, v_m, v_n), tc_nat, t_a)
% 20.79/3.01 = { by axiom 1 (clsarity_nat__Ring__and__Field_Oordered__semidom) R->L }
% 20.79/3.01 c_Finite__Set_Osetsum(v_f, fresh440(class_Orderings_Olinorder(tc_nat), class_Ring__and__Field_Oordered__semidom(tc_nat), tc_nat, v_m, v_n), tc_nat, t_a)
% 20.79/3.01 = { by lemma 10 R->L }
% 20.79/3.01 c_Finite__Set_Osetsum(v_f, fresh440(class_Orderings_Olinorder(tc_nat), class_OrderedGroup_Oab__semigroup__add(tc_nat), tc_nat, v_m, v_n), tc_nat, t_a)
% 20.79/3.01 = { by lemma 11 R->L }
% 20.79/3.01 c_Finite__Set_Osetsum(v_f, fresh440(class_Orderings_Olinorder(tc_nat), class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat), tc_nat, v_m, v_n), tc_nat, t_a)
% 20.79/3.01 = { by lemma 12 R->L }
% 20.79/3.01 c_Finite__Set_Osetsum(v_f, fresh440(class_Orderings_Olinorder(tc_nat), class_OrderedGroup_Opordered__comm__monoid__add(tc_nat), tc_nat, v_m, v_n), tc_nat, t_a)
% 20.79/3.01 = { by axiom 5 (clsarity_nat__Orderings_Olinorder) }
% 20.79/3.01 c_Finite__Set_Osetsum(v_f, fresh440(true2, class_OrderedGroup_Opordered__comm__monoid__add(tc_nat), tc_nat, v_m, v_n), tc_nat, t_a)
% 20.79/3.01 = { by axiom 1 (clsarity_nat__Ring__and__Field_Oordered__semidom) R->L }
% 20.79/3.01 c_Finite__Set_Osetsum(v_f, fresh440(class_Ring__and__Field_Oordered__semidom(tc_nat), class_OrderedGroup_Opordered__comm__monoid__add(tc_nat), tc_nat, v_m, v_n), tc_nat, t_a)
% 20.79/3.01 = { by lemma 10 R->L }
% 20.79/3.01 c_Finite__Set_Osetsum(v_f, fresh440(class_OrderedGroup_Oab__semigroup__add(tc_nat), class_OrderedGroup_Opordered__comm__monoid__add(tc_nat), tc_nat, v_m, v_n), tc_nat, t_a)
% 20.79/3.01 = { by lemma 11 R->L }
% 20.79/3.01 c_Finite__Set_Osetsum(v_f, fresh440(class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat), class_OrderedGroup_Opordered__comm__monoid__add(tc_nat), tc_nat, v_m, v_n), tc_nat, t_a)
% 20.79/3.01 = { by lemma 12 R->L }
% 20.79/3.01 c_Finite__Set_Osetsum(v_f, fresh440(class_OrderedGroup_Opordered__comm__monoid__add(tc_nat), class_OrderedGroup_Opordered__comm__monoid__add(tc_nat), tc_nat, v_m, v_n), tc_nat, t_a)
% 20.79/3.01 = { by axiom 8 (cls_ivl__disj__un_I3_J_0) }
% 20.79/3.01 c_Finite__Set_Osetsum(v_f, fresh441(c_HOL_Oord__class_Oless(v_m, v_n, tc_nat), true2, tc_nat, v_m, v_n), tc_nat, t_a)
% 20.79/3.01 = { by axiom 1 (clsarity_nat__Ring__and__Field_Oordered__semidom) R->L }
% 20.79/3.01 c_Finite__Set_Osetsum(v_f, fresh441(c_HOL_Oord__class_Oless(v_m, v_n, tc_nat), class_Ring__and__Field_Oordered__semidom(tc_nat), tc_nat, v_m, v_n), tc_nat, t_a)
% 20.79/3.01 = { by lemma 10 R->L }
% 20.79/3.01 c_Finite__Set_Osetsum(v_f, fresh441(c_HOL_Oord__class_Oless(v_m, v_n, tc_nat), class_OrderedGroup_Oab__semigroup__add(tc_nat), tc_nat, v_m, v_n), tc_nat, t_a)
% 20.79/3.01 = { by lemma 11 R->L }
% 20.79/3.01 c_Finite__Set_Osetsum(v_f, fresh441(c_HOL_Oord__class_Oless(v_m, v_n, tc_nat), class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat), tc_nat, v_m, v_n), tc_nat, t_a)
% 20.79/3.01 = { by lemma 12 R->L }
% 20.79/3.01 c_Finite__Set_Osetsum(v_f, fresh441(c_HOL_Oord__class_Oless(v_m, v_n, tc_nat), class_OrderedGroup_Opordered__comm__monoid__add(tc_nat), tc_nat, v_m, v_n), tc_nat, t_a)
% 20.79/3.01 = { by axiom 6 (cls_less_0) }
% 20.79/3.01 c_Finite__Set_Osetsum(v_f, fresh441(true2, class_OrderedGroup_Opordered__comm__monoid__add(tc_nat), tc_nat, v_m, v_n), tc_nat, t_a)
% 20.79/3.01 = { by axiom 1 (clsarity_nat__Ring__and__Field_Oordered__semidom) R->L }
% 20.79/3.01 c_Finite__Set_Osetsum(v_f, fresh441(class_Ring__and__Field_Oordered__semidom(tc_nat), class_OrderedGroup_Opordered__comm__monoid__add(tc_nat), tc_nat, v_m, v_n), tc_nat, t_a)
% 20.79/3.01 = { by lemma 10 R->L }
% 20.79/3.01 c_Finite__Set_Osetsum(v_f, fresh441(class_OrderedGroup_Oab__semigroup__add(tc_nat), class_OrderedGroup_Opordered__comm__monoid__add(tc_nat), tc_nat, v_m, v_n), tc_nat, t_a)
% 20.79/3.01 = { by lemma 11 R->L }
% 20.79/3.01 c_Finite__Set_Osetsum(v_f, fresh441(class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat), class_OrderedGroup_Opordered__comm__monoid__add(tc_nat), tc_nat, v_m, v_n), tc_nat, t_a)
% 20.79/3.01 = { by lemma 12 R->L }
% 20.79/3.01 c_Finite__Set_Osetsum(v_f, fresh441(class_OrderedGroup_Opordered__comm__monoid__add(tc_nat), class_OrderedGroup_Opordered__comm__monoid__add(tc_nat), tc_nat, v_m, v_n), tc_nat, t_a)
% 20.79/3.01 = { by axiom 7 (cls_ivl__disj__un_I3_J_0) }
% 20.79/3.01 c_Finite__Set_Osetsum(v_f, c_SetInterval_Oord__class_OatLeastLessThan(v_m, v_n, tc_nat), tc_nat, t_a)
% 20.79/3.01 % SZS output end Proof
% 20.79/3.01
% 20.79/3.01 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------