%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : HEN001-3 : 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 : n005.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 01:56:50 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
% 0.11/0.12  % Problem  : HEN001-3 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33  % Computer : n005.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu Aug 24 13:26:38 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.37  Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 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(identity_is_largest, axiom, ![X]: less_equal(X, identity)).
% 0.19/0.37    fof(prove_a_divide_id_is_zero, negated_conjecture, divide(a, identity)!=zero).
% 0.19/0.37    fof(quotient_less_equal1, axiom, ![Y, X2]: (~less_equal(X2, Y) | divide(X2, Y)=zero)).
% 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 (identity_is_largest): less_equal(X, identity) = true.
% 0.19/0.37  Axiom 2 (quotient_less_equal1): fresh3(X, X, Y, Z) = zero.
% 0.19/0.37  Axiom 3 (quotient_less_equal1): fresh3(less_equal(X, Y), true, X, Y) = divide(X, Y).
% 0.19/0.37  
% 0.19/0.37  Goal 1 (prove_a_divide_id_is_zero): divide(a, identity) = zero.
% 0.19/0.37  Proof:
% 0.19/0.37    divide(a, identity)
% 0.19/0.37  = { by axiom 3 (quotient_less_equal1) R->L }
% 0.19/0.37    fresh3(less_equal(a, identity), true, a, identity)
% 0.19/0.37  = { by axiom 1 (identity_is_largest) }
% 0.19/0.37    fresh3(true, true, a, identity)
% 0.19/0.37  = { by axiom 2 (quotient_less_equal1) }
% 0.19/0.37    zero
% 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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