%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SET824-2 : 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 : n017.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 15:33:21 EDT 2023

% Result   : Unsatisfiable 0.13s 0.37s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET824-2 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.13  % 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 : n017.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 : Sat Aug 26 09:00:40 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.37  Command-line arguments: --ground-connectedness --complete-subsets
% 0.13/0.37  
% 0.13/0.37  % SZS status Unsatisfiable
% 0.13/0.37  
% 0.13/0.37  % SZS output start Proof
% 0.13/0.37  Take the following subset of the input axioms:
% 0.13/0.37    fof(cls_Set_OComplD__dest_0, axiom, ![V_c, V_A, T_a]: (~c_in(V_c, V_A, T_a) | ~c_in(V_c, c_uminus(V_A, tc_set(T_a)), T_a))).
% 0.13/0.37    fof(cls_conjecture_0, negated_conjecture, ![V_U]: c_in(v_a, V_U, tc_IntDef_Oint)).
% 0.13/0.37  
% 0.13/0.37  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.13/0.37  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.13/0.37  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.13/0.37    fresh(y, y, x1...xn) = u
% 0.13/0.37    C => fresh(s, t, x1...xn) = v
% 0.13/0.37  where fresh is a fresh function symbol and x1..xn are the free
% 0.13/0.37  variables of u and v.
% 0.13/0.37  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.13/0.37  input problem has no model of domain size 1).
% 0.13/0.37  
% 0.13/0.37  The encoding turns the above axioms into the following unit equations and goals:
% 0.13/0.37  
% 0.13/0.38  Axiom 1 (cls_conjecture_0): c_in(v_a, X, tc_IntDef_Oint) = true2.
% 0.13/0.38  
% 0.13/0.38  Goal 1 (cls_Set_OComplD__dest_0): tuple(c_in(X, Y, Z), c_in(X, c_uminus(Y, tc_set(Z)), Z)) = tuple(true2, true2).
% 0.13/0.38  The goal is true when:
% 0.13/0.38    X = v_a
% 0.13/0.38    Y = X
% 0.13/0.38    Z = tc_IntDef_Oint
% 0.13/0.38  
% 0.13/0.38  Proof:
% 0.13/0.38    tuple(c_in(v_a, X, tc_IntDef_Oint), c_in(v_a, c_uminus(X, tc_set(tc_IntDef_Oint)), tc_IntDef_Oint))
% 0.13/0.38  = { by axiom 1 (cls_conjecture_0) }
% 0.13/0.38    tuple(true2, c_in(v_a, c_uminus(X, tc_set(tc_IntDef_Oint)), tc_IntDef_Oint))
% 0.13/0.38  = { by axiom 1 (cls_conjecture_0) }
% 0.13/0.38    tuple(true2, true2)
% 0.13/0.38  % SZS output end Proof
% 0.13/0.38  
% 0.13/0.38  RESULT: Unsatisfiable (the axioms are contradictory).
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