TSTP Solution File: LCL755-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL755-1 : 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 : n005.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 08:20:27 EDT 2023
% Result : Unsatisfiable 32.59s 4.60s
% Output : Proof 32.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LCL755-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.13 % 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 : n005.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 : Fri Aug 25 06:31:38 EDT 2023
% 0.12/0.34 % CPUTime :
% 32.59/4.60 Command-line arguments: --flatten
% 32.59/4.60
% 32.59/4.60 % SZS status Unsatisfiable
% 32.59/4.60
% 32.59/4.61 % SZS output start Proof
% 32.59/4.61 Take the following subset of the input axioms:
% 32.59/4.61 fof(cls_Lambda_0, axiom, ![V_r]: (c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r)) | ~c_InductTermi_OIT(V_r))).
% 32.59/4.61 fof(cls_conjecture_1, negated_conjecture, ![V_i, V_j]: c_InductTermi_OIT(c_Lambda_Osubst(v_ra, c_Lambda_OdB_OVar(V_i), V_j))).
% 32.59/4.61 fof(cls_conjecture_2, negated_conjecture, ~c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra, c_Lambda_OdB_OVar(c_Suc(v_ia)), c_Suc(v_ja))))).
% 32.59/4.61 fof(clsarity_nat__OrderedGroup_Ocomm__monoid__add, axiom, class_OrderedGroup_Ocomm__monoid__add(tc_nat)).
% 32.59/4.61 fof(clsarity_nat__OrderedGroup_Ocomm__monoid__mult, axiom, class_OrderedGroup_Ocomm__monoid__mult(tc_nat)).
% 32.59/4.61 fof(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le, axiom, class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat)).
% 32.59/4.61 fof(clsarity_nat__Orderings_Olinorder, axiom, class_Orderings_Olinorder(tc_nat)).
% 32.59/4.61 fof(clsarity_nat__Ring__and__Field_Ono__zero__divisors, axiom, class_Ring__and__Field_Ono__zero__divisors(tc_nat)).
% 32.59/4.61 fof(clsarity_nat__Ring__and__Field_Oordered__semiring, axiom, class_Ring__and__Field_Oordered__semiring(tc_nat)).
% 32.59/4.61
% 32.59/4.61 Now clausify the problem and encode Horn clauses using encoding 3 of
% 32.59/4.61 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 32.59/4.61 We repeatedly replace C & s=t => u=v by the two clauses:
% 32.59/4.61 fresh(y, y, x1...xn) = u
% 32.59/4.61 C => fresh(s, t, x1...xn) = v
% 32.59/4.61 where fresh is a fresh function symbol and x1..xn are the free
% 32.59/4.61 variables of u and v.
% 32.59/4.61 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 32.59/4.61 input problem has no model of domain size 1).
% 32.59/4.61
% 32.59/4.61 The encoding turns the above axioms into the following unit equations and goals:
% 32.59/4.61
% 32.59/4.61 Axiom 1 (clsarity_nat__Ring__and__Field_Ono__zero__divisors): class_Ring__and__Field_Ono__zero__divisors(tc_nat) = true2.
% 32.59/4.61 Axiom 2 (clsarity_nat__OrderedGroup_Ocomm__monoid__mult): class_OrderedGroup_Ocomm__monoid__mult(tc_nat) = true2.
% 32.59/4.61 Axiom 3 (clsarity_nat__Ring__and__Field_Oordered__semiring): class_Ring__and__Field_Oordered__semiring(tc_nat) = true2.
% 32.59/4.61 Axiom 4 (clsarity_nat__OrderedGroup_Ocomm__monoid__add): class_OrderedGroup_Ocomm__monoid__add(tc_nat) = true2.
% 32.59/4.61 Axiom 5 (clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le): class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) = true2.
% 32.59/4.61 Axiom 6 (clsarity_nat__Orderings_Olinorder): class_Orderings_Olinorder(tc_nat) = true2.
% 32.59/4.61 Axiom 7 (cls_Lambda_0): fresh576(X, X, Y) = true2.
% 32.59/4.61 Axiom 8 (cls_Lambda_0): fresh576(c_InductTermi_OIT(X), true2, X) = c_InductTermi_OIT(c_Lambda_OdB_OAbs(X)).
% 32.59/4.61 Axiom 9 (cls_conjecture_1): c_InductTermi_OIT(c_Lambda_Osubst(v_ra, c_Lambda_OdB_OVar(X), Y)) = true2.
% 32.59/4.61
% 32.59/4.61 Lemma 10: class_OrderedGroup_Ocomm__monoid__mult(tc_nat) = class_Ring__and__Field_Ono__zero__divisors(tc_nat).
% 32.59/4.61 Proof:
% 32.59/4.61 class_OrderedGroup_Ocomm__monoid__mult(tc_nat)
% 32.59/4.61 = { by axiom 2 (clsarity_nat__OrderedGroup_Ocomm__monoid__mult) }
% 32.59/4.61 true2
% 32.59/4.61 = { by axiom 1 (clsarity_nat__Ring__and__Field_Ono__zero__divisors) R->L }
% 32.59/4.61 class_Ring__and__Field_Ono__zero__divisors(tc_nat)
% 32.59/4.61
% 32.59/4.61 Lemma 11: class_Ring__and__Field_Oordered__semiring(tc_nat) = class_OrderedGroup_Ocomm__monoid__mult(tc_nat).
% 32.59/4.61 Proof:
% 32.59/4.61 class_Ring__and__Field_Oordered__semiring(tc_nat)
% 32.59/4.61 = { by axiom 3 (clsarity_nat__Ring__and__Field_Oordered__semiring) }
% 32.59/4.61 true2
% 32.59/4.61 = { by axiom 1 (clsarity_nat__Ring__and__Field_Ono__zero__divisors) R->L }
% 32.59/4.61 class_Ring__and__Field_Ono__zero__divisors(tc_nat)
% 32.59/4.61 = { by lemma 10 R->L }
% 32.59/4.61 class_OrderedGroup_Ocomm__monoid__mult(tc_nat)
% 32.59/4.61
% 32.59/4.61 Lemma 12: class_OrderedGroup_Ocomm__monoid__add(tc_nat) = class_Ring__and__Field_Oordered__semiring(tc_nat).
% 32.59/4.61 Proof:
% 32.59/4.61 class_OrderedGroup_Ocomm__monoid__add(tc_nat)
% 32.59/4.61 = { by axiom 4 (clsarity_nat__OrderedGroup_Ocomm__monoid__add) }
% 32.59/4.61 true2
% 32.59/4.61 = { by axiom 1 (clsarity_nat__Ring__and__Field_Ono__zero__divisors) R->L }
% 32.59/4.61 class_Ring__and__Field_Ono__zero__divisors(tc_nat)
% 32.59/4.61 = { by lemma 10 R->L }
% 32.59/4.61 class_OrderedGroup_Ocomm__monoid__mult(tc_nat)
% 32.59/4.61 = { by lemma 11 R->L }
% 32.59/4.61 class_Ring__and__Field_Oordered__semiring(tc_nat)
% 32.59/4.61
% 32.59/4.61 Lemma 13: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) = class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 32.59/4.61 Proof:
% 32.59/4.61 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat)
% 32.59/4.61 = { by axiom 5 (clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) }
% 32.59/4.61 true2
% 32.59/4.61 = { by axiom 1 (clsarity_nat__Ring__and__Field_Ono__zero__divisors) R->L }
% 32.59/4.61 class_Ring__and__Field_Ono__zero__divisors(tc_nat)
% 32.59/4.61 = { by lemma 10 R->L }
% 32.59/4.61 class_OrderedGroup_Ocomm__monoid__mult(tc_nat)
% 32.59/4.61 = { by lemma 11 R->L }
% 32.59/4.61 class_Ring__and__Field_Oordered__semiring(tc_nat)
% 32.59/4.61 = { by lemma 12 R->L }
% 32.59/4.61 class_OrderedGroup_Ocomm__monoid__add(tc_nat)
% 32.59/4.61
% 32.59/4.61 Lemma 14: class_Orderings_Olinorder(tc_nat) = class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).
% 32.59/4.61 Proof:
% 32.59/4.61 class_Orderings_Olinorder(tc_nat)
% 32.59/4.61 = { by axiom 6 (clsarity_nat__Orderings_Olinorder) }
% 32.59/4.61 true2
% 32.59/4.61 = { by axiom 1 (clsarity_nat__Ring__and__Field_Ono__zero__divisors) R->L }
% 32.59/4.61 class_Ring__and__Field_Ono__zero__divisors(tc_nat)
% 32.59/4.61 = { by lemma 10 R->L }
% 32.59/4.61 class_OrderedGroup_Ocomm__monoid__mult(tc_nat)
% 32.59/4.61 = { by lemma 11 R->L }
% 32.59/4.61 class_Ring__and__Field_Oordered__semiring(tc_nat)
% 32.59/4.61 = { by lemma 12 R->L }
% 32.59/4.61 class_OrderedGroup_Ocomm__monoid__add(tc_nat)
% 32.59/4.61 = { by lemma 13 R->L }
% 32.59/4.61 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat)
% 32.59/4.61
% 32.59/4.61 Goal 1 (cls_conjecture_2): c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra, c_Lambda_OdB_OVar(c_Suc(v_ia)), c_Suc(v_ja)))) = true2.
% 32.59/4.61 Proof:
% 32.59/4.61 c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra, c_Lambda_OdB_OVar(c_Suc(v_ia)), c_Suc(v_ja))))
% 32.59/4.61 = { by axiom 8 (cls_Lambda_0) R->L }
% 32.59/4.61 fresh576(c_InductTermi_OIT(c_Lambda_Osubst(v_ra, c_Lambda_OdB_OVar(c_Suc(v_ia)), c_Suc(v_ja))), true2, c_Lambda_Osubst(v_ra, c_Lambda_OdB_OVar(c_Suc(v_ia)), c_Suc(v_ja)))
% 32.59/4.61 = { by axiom 1 (clsarity_nat__Ring__and__Field_Ono__zero__divisors) R->L }
% 32.59/4.61 fresh576(c_InductTermi_OIT(c_Lambda_Osubst(v_ra, c_Lambda_OdB_OVar(c_Suc(v_ia)), c_Suc(v_ja))), class_Ring__and__Field_Ono__zero__divisors(tc_nat), c_Lambda_Osubst(v_ra, c_Lambda_OdB_OVar(c_Suc(v_ia)), c_Suc(v_ja)))
% 32.59/4.61 = { by lemma 10 R->L }
% 32.59/4.61 fresh576(c_InductTermi_OIT(c_Lambda_Osubst(v_ra, c_Lambda_OdB_OVar(c_Suc(v_ia)), c_Suc(v_ja))), class_OrderedGroup_Ocomm__monoid__mult(tc_nat), c_Lambda_Osubst(v_ra, c_Lambda_OdB_OVar(c_Suc(v_ia)), c_Suc(v_ja)))
% 32.59/4.61 = { by lemma 11 R->L }
% 32.59/4.61 fresh576(c_InductTermi_OIT(c_Lambda_Osubst(v_ra, c_Lambda_OdB_OVar(c_Suc(v_ia)), c_Suc(v_ja))), class_Ring__and__Field_Oordered__semiring(tc_nat), c_Lambda_Osubst(v_ra, c_Lambda_OdB_OVar(c_Suc(v_ia)), c_Suc(v_ja)))
% 32.59/4.61 = { by lemma 12 R->L }
% 32.59/4.61 fresh576(c_InductTermi_OIT(c_Lambda_Osubst(v_ra, c_Lambda_OdB_OVar(c_Suc(v_ia)), c_Suc(v_ja))), class_OrderedGroup_Ocomm__monoid__add(tc_nat), c_Lambda_Osubst(v_ra, c_Lambda_OdB_OVar(c_Suc(v_ia)), c_Suc(v_ja)))
% 32.59/4.61 = { by lemma 13 R->L }
% 32.59/4.61 fresh576(c_InductTermi_OIT(c_Lambda_Osubst(v_ra, c_Lambda_OdB_OVar(c_Suc(v_ia)), c_Suc(v_ja))), class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat), c_Lambda_Osubst(v_ra, c_Lambda_OdB_OVar(c_Suc(v_ia)), c_Suc(v_ja)))
% 32.59/4.61 = { by lemma 14 R->L }
% 32.59/4.61 fresh576(c_InductTermi_OIT(c_Lambda_Osubst(v_ra, c_Lambda_OdB_OVar(c_Suc(v_ia)), c_Suc(v_ja))), class_Orderings_Olinorder(tc_nat), c_Lambda_Osubst(v_ra, c_Lambda_OdB_OVar(c_Suc(v_ia)), c_Suc(v_ja)))
% 32.59/4.61 = { by axiom 9 (cls_conjecture_1) }
% 32.59/4.61 fresh576(true2, class_Orderings_Olinorder(tc_nat), c_Lambda_Osubst(v_ra, c_Lambda_OdB_OVar(c_Suc(v_ia)), c_Suc(v_ja)))
% 32.59/4.62 = { by axiom 1 (clsarity_nat__Ring__and__Field_Ono__zero__divisors) R->L }
% 32.59/4.62 fresh576(class_Ring__and__Field_Ono__zero__divisors(tc_nat), class_Orderings_Olinorder(tc_nat), c_Lambda_Osubst(v_ra, c_Lambda_OdB_OVar(c_Suc(v_ia)), c_Suc(v_ja)))
% 32.59/4.62 = { by lemma 10 R->L }
% 32.59/4.62 fresh576(class_OrderedGroup_Ocomm__monoid__mult(tc_nat), class_Orderings_Olinorder(tc_nat), c_Lambda_Osubst(v_ra, c_Lambda_OdB_OVar(c_Suc(v_ia)), c_Suc(v_ja)))
% 32.59/4.62 = { by lemma 11 R->L }
% 32.59/4.62 fresh576(class_Ring__and__Field_Oordered__semiring(tc_nat), class_Orderings_Olinorder(tc_nat), c_Lambda_Osubst(v_ra, c_Lambda_OdB_OVar(c_Suc(v_ia)), c_Suc(v_ja)))
% 32.59/4.62 = { by lemma 12 R->L }
% 32.59/4.62 fresh576(class_OrderedGroup_Ocomm__monoid__add(tc_nat), class_Orderings_Olinorder(tc_nat), c_Lambda_Osubst(v_ra, c_Lambda_OdB_OVar(c_Suc(v_ia)), c_Suc(v_ja)))
% 32.59/4.62 = { by lemma 13 R->L }
% 32.59/4.62 fresh576(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat), class_Orderings_Olinorder(tc_nat), c_Lambda_Osubst(v_ra, c_Lambda_OdB_OVar(c_Suc(v_ia)), c_Suc(v_ja)))
% 32.59/4.62 = { by lemma 14 R->L }
% 32.59/4.62 fresh576(class_Orderings_Olinorder(tc_nat), class_Orderings_Olinorder(tc_nat), c_Lambda_Osubst(v_ra, c_Lambda_OdB_OVar(c_Suc(v_ia)), c_Suc(v_ja)))
% 32.59/4.62 = { by axiom 7 (cls_Lambda_0) }
% 32.59/4.62 true2
% 32.59/4.62 % SZS output end Proof
% 32.59/4.62
% 32.59/4.62 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------