%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : LCL789-1 : 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 : n009.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 08:20:39 EDT 2023

% Result   : Unsatisfiable 4.89s 0.97s
% Output   : Proof 4.89s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL789-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34  % Computer : n009.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Fri Aug 25 06:43:20 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 4.89/0.97  Command-line arguments: --no-flatten-goal
% 4.89/0.97  
% 4.89/0.97  % SZS status Unsatisfiable
% 4.89/0.97  
% 4.89/0.97  % SZS output start Proof
% 4.89/0.97  Take the following subset of the input axioms:
% 4.89/0.97    fof(cls_T_0, axiom, v_T____=hAPP(hAPP(c_Type_Otype_OFun, v_T_H_H____), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype))).
% 4.89/0.97    fof(cls_conjecture_0, negated_conjecture, ~c_Type_Otyping(v_e____, v_u____, hAPP(hAPP(c_Type_Otype_OFun, v_T_H_H____), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype)))).
% 4.89/0.97    fof(cls_uT_0, axiom, c_Type_Otyping(v_e____, v_u____, v_T____)).
% 4.89/0.97  
% 4.89/0.97  Now clausify the problem and encode Horn clauses using encoding 3 of
% 4.89/0.97  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 4.89/0.97  We repeatedly replace C & s=t => u=v by the two clauses:
% 4.89/0.97    fresh(y, y, x1...xn) = u
% 4.89/0.97    C => fresh(s, t, x1...xn) = v
% 4.89/0.97  where fresh is a fresh function symbol and x1..xn are the free
% 4.89/0.97  variables of u and v.
% 4.89/0.97  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 4.89/0.97  input problem has no model of domain size 1).
% 4.89/0.97  
% 4.89/0.97  The encoding turns the above axioms into the following unit equations and goals:
% 4.89/0.97  
% 4.89/0.97  Axiom 1 (cls_uT_0): c_Type_Otyping(v_e____, v_u____, v_T____) = true2.
% 4.89/0.97  Axiom 2 (cls_T_0): v_T____ = hAPP(hAPP(c_Type_Otype_OFun, v_T_H_H____), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype)).
% 4.89/0.97  
% 4.89/0.97  Goal 1 (cls_conjecture_0): c_Type_Otyping(v_e____, v_u____, hAPP(hAPP(c_Type_Otype_OFun, v_T_H_H____), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype))) = true2.
% 4.89/0.97  Proof:
% 4.89/0.97    c_Type_Otyping(v_e____, v_u____, hAPP(hAPP(c_Type_Otype_OFun, v_T_H_H____), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype)))
% 4.89/0.97  = { by axiom 2 (cls_T_0) R->L }
% 4.89/0.97    c_Type_Otyping(v_e____, v_u____, v_T____)
% 4.89/0.97  = { by axiom 1 (cls_uT_0) }
% 4.89/0.97    true2
% 4.89/0.97  % SZS output end Proof
% 4.89/0.97  
% 4.89/0.97  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------