%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : LCL792-1 : 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 08:20:40 EDT 2023

% Result   : Unsatisfiable 92.21s 12.15s
% Output   : Proof 92.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : LCL792-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34  % Computer : n018.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Fri Aug 25 03:03:58 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 92.21/12.15  Command-line arguments: --no-flatten-goal
% 92.21/12.15  
% 92.21/12.15  % SZS status Unsatisfiable
% 92.21/12.15  
% 92.21/12.16  % SZS output start Proof
% 92.21/12.16  Take the following subset of the input axioms:
% 92.21/12.16    fof(cls_char__size_0, axiom, ![V_c]: c_String_Ochar_Ochar__size(V_c)=c_HOL_Ozero__class_Ozero(tc_nat)).
% 92.21/12.16    fof(cls_conjecture_0, negated_conjecture, ~c_InductTermi_OIT(c_Lambda_Olift(v_u____, c_HOL_Ozero__class_Ozero(tc_nat)))).
% 92.21/12.16    fof(cls_lift__IT_0, axiom, ![V_i, V_t]: (c_InductTermi_OIT(c_Lambda_Olift(V_t, V_i)) | ~c_InductTermi_OIT(V_t))).
% 92.21/12.16    fof(cls_uIT_0, axiom, c_InductTermi_OIT(v_u____)).
% 92.21/12.16  
% 92.21/12.16  Now clausify the problem and encode Horn clauses using encoding 3 of
% 92.21/12.16  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 92.21/12.16  We repeatedly replace C & s=t => u=v by the two clauses:
% 92.21/12.16    fresh(y, y, x1...xn) = u
% 92.21/12.16    C => fresh(s, t, x1...xn) = v
% 92.21/12.16  where fresh is a fresh function symbol and x1..xn are the free
% 92.21/12.16  variables of u and v.
% 92.21/12.16  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 92.21/12.16  input problem has no model of domain size 1).
% 92.21/12.16  
% 92.21/12.16  The encoding turns the above axioms into the following unit equations and goals:
% 92.21/12.16  
% 92.21/12.16  Axiom 1 (cls_uIT_0): c_InductTermi_OIT(v_u____) = true2.
% 92.21/12.16  Axiom 2 (cls_char__size_0): c_String_Ochar_Ochar__size(X) = c_HOL_Ozero__class_Ozero(tc_nat).
% 92.21/12.16  Axiom 3 (cls_lift__IT_0): fresh564(X, X, Y, Z) = true2.
% 92.21/12.16  Axiom 4 (cls_lift__IT_0): fresh564(c_InductTermi_OIT(X), true2, X, Y) = c_InductTermi_OIT(c_Lambda_Olift(X, Y)).
% 92.21/12.16  
% 92.21/12.16  Goal 1 (cls_conjecture_0): c_InductTermi_OIT(c_Lambda_Olift(v_u____, c_HOL_Ozero__class_Ozero(tc_nat))) = true2.
% 92.21/12.16  Proof:
% 92.21/12.16    c_InductTermi_OIT(c_Lambda_Olift(v_u____, c_HOL_Ozero__class_Ozero(tc_nat)))
% 92.21/12.16  = { by axiom 2 (cls_char__size_0) R->L }
% 92.21/12.16    c_InductTermi_OIT(c_Lambda_Olift(v_u____, c_String_Ochar_Ochar__size(X)))
% 92.21/12.16  = { by axiom 4 (cls_lift__IT_0) R->L }
% 92.21/12.16    fresh564(c_InductTermi_OIT(v_u____), true2, v_u____, c_String_Ochar_Ochar__size(X))
% 92.21/12.16  = { by axiom 1 (cls_uIT_0) }
% 92.21/12.16    fresh564(true2, true2, v_u____, c_String_Ochar_Ochar__size(X))
% 92.21/12.16  = { by axiom 3 (cls_lift__IT_0) }
% 92.21/12.16    true2
% 92.21/12.16  % SZS output end Proof
% 92.21/12.16  
% 92.21/12.16  RESULT: Unsatisfiable (the axioms are contradictory).
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