%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : LCL762-1 : 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 : n013.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 08:20:29 EDT 2023

% Result   : Unsatisfiable 9.00s 1.54s
% Output   : Proof 9.00s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : LCL762-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.10  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.31  % Computer : n013.cluster.edu
% 0.12/0.31  % Model    : x86_64 x86_64
% 0.12/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31  % Memory   : 8042.1875MB
% 0.12/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31  % CPULimit : 300
% 0.12/0.31  % WCLimit  : 300
% 0.12/0.31  % DateTime : Thu Aug 24 17:25:02 EDT 2023
% 0.12/0.31  % CPUTime  : 
% 9.00/1.54  Command-line arguments: --no-flatten-goal
% 9.00/1.54  
% 9.00/1.54  % SZS status Unsatisfiable
% 9.00/1.54  
% 9.00/1.54  % SZS output start Proof
% 9.00/1.54  Take the following subset of the input axioms:
% 9.00/1.54    fof(cls_conjecture_0, negated_conjecture, hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(v_n), c_List_Olist_ONil(tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB)))).
% 9.00/1.54    fof(cls_conjecture_1, negated_conjecture, ~hBOOL(hAPP(c_InductTermi_OIT, c_Lambda_OdB_OVar(v_n)))).
% 9.00/1.54    fof(cls_foldl__Nil_0, axiom, ![T_a, V_a, V_f, T_b]: c_List_Ofoldl(V_f, V_a, c_List_Olist_ONil(T_b), T_a, T_b)=V_a).
% 9.00/1.54  
% 9.00/1.54  Now clausify the problem and encode Horn clauses using encoding 3 of
% 9.00/1.54  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 9.00/1.54  We repeatedly replace C & s=t => u=v by the two clauses:
% 9.00/1.55    fresh(y, y, x1...xn) = u
% 9.00/1.55    C => fresh(s, t, x1...xn) = v
% 9.00/1.55  where fresh is a fresh function symbol and x1..xn are the free
% 9.00/1.55  variables of u and v.
% 9.00/1.55  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 9.00/1.55  input problem has no model of domain size 1).
% 9.00/1.55  
% 9.00/1.55  The encoding turns the above axioms into the following unit equations and goals:
% 9.00/1.55  
% 9.00/1.55  Axiom 1 (cls_foldl__Nil_0): c_List_Ofoldl(X, Y, c_List_Olist_ONil(Z), W, Z) = Y.
% 9.00/1.55  Axiom 2 (cls_conjecture_0): hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(v_n), c_List_Olist_ONil(tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB))) = true2.
% 9.00/1.55  
% 9.00/1.55  Goal 1 (cls_conjecture_1): hBOOL(hAPP(c_InductTermi_OIT, c_Lambda_OdB_OVar(v_n))) = true2.
% 9.00/1.55  Proof:
% 9.00/1.55    hBOOL(hAPP(c_InductTermi_OIT, c_Lambda_OdB_OVar(v_n)))
% 9.00/1.55  = { by axiom 1 (cls_foldl__Nil_0) R->L }
% 9.00/1.55    hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(v_n), c_List_Olist_ONil(tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB)))
% 9.00/1.55  = { by axiom 2 (cls_conjecture_0) }
% 9.00/1.55    true2
% 9.00/1.55  % SZS output end Proof
% 9.00/1.55  
% 9.00/1.55  RESULT: Unsatisfiable (the axioms are contradictory).
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