%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : COL103-2 : TPTP v8.1.2. Released v3.2.0.
% 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 : n023.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 : Wed Aug 30 18:32:09 EDT 2023

% Result   : Unsatisfiable 0.19s 0.37s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : COL103-2 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.13  % 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 : n023.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 : Sun Aug 27 04:42:11 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.37  Command-line arguments: --no-flatten-goal
% 0.19/0.37  
% 0.19/0.37  % SZS status Unsatisfiable
% 0.19/0.37  
% 0.19/0.37  % SZS output start Proof
% 0.19/0.37  Take the following subset of the input axioms:
% 0.19/0.37    fof(cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0, axiom, ![V_a, T_a, V_r]: c_in(c_Pair(V_a, V_a, T_a, T_a), c_Transitive__Closure_Ortrancl(V_r, T_a), tc_prod(T_a, T_a))).
% 0.19/0.37    fof(cls_conjecture_0, negated_conjecture, ~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z, v_x), c_Comb_Ocomb_Oop_A_D_D(v_z, v_x), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Transitive__Closure_Ortrancl(c_Comb_Ocontract, tc_Comb_Ocomb), tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))).
% 0.19/0.37  
% 0.19/0.37  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.37  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.37  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.37    fresh(y, y, x1...xn) = u
% 0.19/0.37    C => fresh(s, t, x1...xn) = v
% 0.19/0.37  where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.37  variables of u and v.
% 0.19/0.37  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.37  input problem has no model of domain size 1).
% 0.19/0.37  
% 0.19/0.37  The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.37  
% 0.19/0.37  Axiom 1 (cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0): c_in(c_Pair(X, X, Y, Y), c_Transitive__Closure_Ortrancl(Z, Y), tc_prod(Y, Y)) = true.
% 0.19/0.37  
% 0.19/0.37  Goal 1 (cls_conjecture_0): c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z, v_x), c_Comb_Ocomb_Oop_A_D_D(v_z, v_x), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Transitive__Closure_Ortrancl(c_Comb_Ocontract, tc_Comb_Ocomb), tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) = true.
% 0.19/0.37  Proof:
% 0.19/0.37    c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z, v_x), c_Comb_Ocomb_Oop_A_D_D(v_z, v_x), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Transitive__Closure_Ortrancl(c_Comb_Ocontract, tc_Comb_Ocomb), tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))
% 0.19/0.37  = { by axiom 1 (cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) }
% 0.19/0.37    true
% 0.19/0.37  % SZS output end Proof
% 0.19/0.37  
% 0.19/0.37  RESULT: Unsatisfiable (the axioms are contradictory).
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