TSTP Solution File: SCT100-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SCT100-1 : 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 : n031.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 14:22:07 EDT 2023
% Result : Unsatisfiable 18.51s 2.72s
% Output : Proof 18.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SCT100-1 : 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 : n031.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 : Thu Aug 24 15:28:06 EDT 2023
% 0.12/0.34 % CPUTime :
% 18.51/2.72 Command-line arguments: --no-flatten-goal
% 18.51/2.72
% 18.51/2.72 % SZS status Unsatisfiable
% 18.51/2.72
% 18.51/2.72 % SZS output start Proof
% 18.51/2.72 Take the following subset of the input axioms:
% 18.51/2.73 fof(cls_CHAINED_0_01, axiom, c_in(c_Pair(v_c____, v_d____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), hAPP(v_F, c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat), v_h____, tc_nat, tc_fun(tc_nat, tc_bool), tc_Arrow__Order__Mirabelle_Oindi), v_n____, tc_Arrow__Order__Mirabelle_Oindi, tc_nat, tc_bool), tc_bool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop, v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), v_e____, tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), c_COMBC(c_COMBB(c_fequal(tc_nat), v_h____, tc_nat, tc_fun(tc_nat, tc_bool), tc_Arrow__Order__Mirabelle_Oindi), v_n____, tc_Arrow__Order__Mirabelle_Oindi, tc_nat, tc_bool), tc_bool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), c_COMBC(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove, v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), v_c____, tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), v_e____, tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot, v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), v_e____, tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))).
% 18.51/2.73 fof(cls_CHAINED_1, axiom, c_in(c_Pair(v_c____, v_d____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), hAPP(v_F, v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) | ~c_in(c_Pair(v_c____, v_d____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), hAPP(v_F, c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat), v_h____, tc_nat, tc_fun(tc_nat, tc_bool), tc_Arrow__Order__Mirabelle_Oindi), v_n____, tc_Arrow__Order__Mirabelle_Oindi, tc_nat, tc_bool), tc_bool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop, v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), v_e____, tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), c_COMBC(c_COMBB(c_fequal(tc_nat), v_h____, tc_nat, tc_fun(tc_nat, tc_bool), tc_Arrow__Order__Mirabelle_Oindi), v_n____, tc_Arrow__Order__Mirabelle_Oindi, tc_nat, tc_bool), tc_bool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), c_COMBC(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove, v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), v_c____, tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), v_e____, tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot, v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), v_e____, tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))).
% 18.51/2.73 fof(cls_conjecture_0, negated_conjecture, ~c_in(c_Pair(v_c____, v_d____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), hAPP(v_F, v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))).
% 18.51/2.73
% 18.51/2.73 Now clausify the problem and encode Horn clauses using encoding 3 of
% 18.51/2.73 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 18.51/2.73 We repeatedly replace C & s=t => u=v by the two clauses:
% 18.51/2.73 fresh(y, y, x1...xn) = u
% 18.51/2.73 C => fresh(s, t, x1...xn) = v
% 18.51/2.73 where fresh is a fresh function symbol and x1..xn are the free
% 18.51/2.73 variables of u and v.
% 18.51/2.73 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 18.51/2.73 input problem has no model of domain size 1).
% 18.51/2.73
% 18.51/2.73 The encoding turns the above axioms into the following unit equations and goals:
% 18.51/2.73
% 18.51/2.73 Axiom 1 (cls_CHAINED_1): fresh466(X, X) = true2.
% 18.51/2.73 Axiom 2 (cls_CHAINED_0_01): c_in(c_Pair(v_c____, v_d____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), hAPP(v_F, c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat), v_h____, tc_nat, tc_fun(tc_nat, tc_bool), tc_Arrow__Order__Mirabelle_Oindi), v_n____, tc_Arrow__Order__Mirabelle_Oindi, tc_nat, tc_bool), tc_bool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop, v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), v_e____, tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), c_COMBC(c_COMBB(c_fequal(tc_nat), v_h____, tc_nat, tc_fun(tc_nat, tc_bool), tc_Arrow__Order__Mirabelle_Oindi), v_n____, tc_Arrow__Order__Mirabelle_Oindi, tc_nat, tc_bool), tc_bool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), c_COMBC(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove, v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), v_c____, tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), v_e____, tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot, v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), v_e____, tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) = true2.
% 18.51/2.73 Axiom 3 (cls_CHAINED_1): fresh466(c_in(c_Pair(v_c____, v_d____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), hAPP(v_F, c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat), v_h____, tc_nat, tc_fun(tc_nat, tc_bool), tc_Arrow__Order__Mirabelle_Oindi), v_n____, tc_Arrow__Order__Mirabelle_Oindi, tc_nat, tc_bool), tc_bool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop, v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), v_e____, tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), c_COMBC(c_COMBB(c_fequal(tc_nat), v_h____, tc_nat, tc_fun(tc_nat, tc_bool), tc_Arrow__Order__Mirabelle_Oindi), v_n____, tc_Arrow__Order__Mirabelle_Oindi, tc_nat, tc_bool), tc_bool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), c_COMBC(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove, v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), v_c____, tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), v_e____, tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot, v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), v_e____, tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), true2) = c_in(c_Pair(v_c____, v_d____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), hAPP(v_F, v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)).
% 18.51/2.73
% 18.51/2.73 Goal 1 (cls_conjecture_0): c_in(c_Pair(v_c____, v_d____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), hAPP(v_F, v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)) = true2.
% 18.51/2.73 Proof:
% 18.51/2.73 c_in(c_Pair(v_c____, v_d____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), hAPP(v_F, v_P____), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt))
% 18.51/2.73 = { by axiom 3 (cls_CHAINED_1) R->L }
% 18.67/2.73 fresh466(c_in(c_Pair(v_c____, v_d____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), hAPP(v_F, c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat), v_h____, tc_nat, tc_fun(tc_nat, tc_bool), tc_Arrow__Order__Mirabelle_Oindi), v_n____, tc_Arrow__Order__Mirabelle_Oindi, tc_nat, tc_bool), tc_bool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop, v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), v_e____, tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), c_COMBC(c_COMBB(c_fequal(tc_nat), v_h____, tc_nat, tc_fun(tc_nat, tc_bool), tc_Arrow__Order__Mirabelle_Oindi), v_n____, tc_Arrow__Order__Mirabelle_Oindi, tc_nat, tc_bool), tc_bool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), c_COMBC(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove, v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_Arrow__Order__Mirabelle_Oindi), v_c____, tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), v_e____, tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot, v_P____, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), v_e____, tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_bool))), tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), true2)
% 18.67/2.73 = { by axiom 2 (cls_CHAINED_0_01) }
% 18.67/2.73 fresh466(true2, true2)
% 18.67/2.73 = { by axiom 1 (cls_CHAINED_1) }
% 18.67/2.73 true2
% 18.67/2.73 % SZS output end Proof
% 18.67/2.73
% 18.67/2.73 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------