%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : GRP041-2 : TPTP v8.1.2. Released v1.0.0.
% 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 01:16:45 EDT 2023

% Result   : Unsatisfiable 0.22s 0.42s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14  % Problem  : GRP041-2 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.15  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.16/0.36  % Computer : n013.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Tue Aug 29 02:17:32 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 0.22/0.42  Command-line arguments: --no-flatten-goal
% 0.22/0.42  
% 0.22/0.42  % SZS status Unsatisfiable
% 0.22/0.42  
% 0.22/0.42  % SZS output start Proof
% 0.22/0.42  Take the following subset of the input axioms:
% 0.22/0.42    fof(left_identity, axiom, ![X]: product(identity, X, X)).
% 0.22/0.42    fof(prove_reflexivity, negated_conjecture, ~equalish(a, a)).
% 0.22/0.42    fof(total_function2, axiom, ![Y, Z, W, X2]: (~product(X2, Y, Z) | (~product(X2, Y, W) | equalish(Z, W)))).
% 0.22/0.42  
% 0.22/0.42  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.42  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.42  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.42    fresh(y, y, x1...xn) = u
% 0.22/0.42    C => fresh(s, t, x1...xn) = v
% 0.22/0.42  where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.42  variables of u and v.
% 0.22/0.42  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.42  input problem has no model of domain size 1).
% 0.22/0.42  
% 0.22/0.42  The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.42  
% 0.22/0.42  Axiom 1 (left_identity): product(identity, X, X) = true.
% 0.22/0.42  Axiom 2 (total_function2): fresh(X, X, Y, Z) = true.
% 0.22/0.42  Axiom 3 (total_function2): fresh2(X, X, Y, Z, W, V) = equalish(W, V).
% 0.22/0.42  Axiom 4 (total_function2): fresh2(product(X, Y, Z), true, X, Y, W, Z) = fresh(product(X, Y, W), true, W, Z).
% 0.22/0.42  
% 0.22/0.42  Goal 1 (prove_reflexivity): equalish(a, a) = true.
% 0.22/0.42  Proof:
% 0.22/0.42    equalish(a, a)
% 0.22/0.42  = { by axiom 3 (total_function2) R->L }
% 0.22/0.42    fresh2(true, true, identity, a, a, a)
% 0.22/0.42  = { by axiom 1 (left_identity) R->L }
% 0.22/0.42    fresh2(product(identity, a, a), true, identity, a, a, a)
% 0.22/0.42  = { by axiom 4 (total_function2) }
% 0.22/0.42    fresh(product(identity, a, a), true, a, a)
% 0.22/0.42  = { by axiom 1 (left_identity) }
% 0.22/0.42    fresh(true, true, a, a)
% 0.22/0.42  = { by axiom 2 (total_function2) }
% 0.22/0.42    true
% 0.22/0.42  % SZS output end Proof
% 0.22/0.42  
% 0.22/0.42  RESULT: Unsatisfiable (the axioms are contradictory).
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