%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : HEN002-2 : 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 : n019.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 0.21s 0.41s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : HEN002-2 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.17/0.36  % Computer : n019.cluster.edu
% 0.17/0.36  % Model    : x86_64 x86_64
% 0.17/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.36  % Memory   : 8042.1875MB
% 0.17/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.36  % CPULimit : 300
% 0.17/0.36  % WCLimit  : 300
% 0.17/0.36  % DateTime : Thu Aug 24 13:26:28 EDT 2023
% 0.17/0.36  % CPUTime  : 
% 0.21/0.41  Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.41  
% 0.21/0.41  % SZS status Unsatisfiable
% 0.21/0.41  
% 0.21/0.41  % SZS output start Proof
% 0.21/0.41  Take the following subset of the input axioms:
% 0.21/0.41    fof(prove_zero_divide_anything_is_zero, negated_conjecture, ~quotient(zero, x, zero)).
% 0.21/0.41    fof(quotient_less_equal, axiom, ![X, Y]: (~less_equal(X, Y) | quotient(X, Y, zero))).
% 0.21/0.41    fof(zero_is_smallest, axiom, ![X2]: less_equal(zero, X2)).
% 0.21/0.41  
% 0.21/0.41  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.41  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.41  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.41    fresh(y, y, x1...xn) = u
% 0.21/0.41    C => fresh(s, t, x1...xn) = v
% 0.21/0.41  where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.41  variables of u and v.
% 0.21/0.41  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.41  input problem has no model of domain size 1).
% 0.21/0.41  
% 0.21/0.41  The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.41  
% 0.21/0.41  Axiom 1 (zero_is_smallest): less_equal(zero, X) = true.
% 0.21/0.41  Axiom 2 (quotient_less_equal): fresh5(X, X, Y, Z) = true.
% 0.21/0.41  Axiom 3 (quotient_less_equal): fresh5(less_equal(X, Y), true, X, Y) = quotient(X, Y, zero).
% 0.21/0.41  
% 0.21/0.41  Goal 1 (prove_zero_divide_anything_is_zero): quotient(zero, x, zero) = true.
% 0.21/0.41  Proof:
% 0.21/0.41    quotient(zero, x, zero)
% 0.21/0.41  = { by axiom 3 (quotient_less_equal) R->L }
% 0.21/0.41    fresh5(less_equal(zero, x), true, zero, x)
% 0.21/0.41  = { by axiom 1 (zero_is_smallest) }
% 0.21/0.41    fresh5(true, true, zero, x)
% 0.21/0.41  = { by axiom 2 (quotient_less_equal) }
% 0.21/0.41    true
% 0.21/0.41  % SZS output end Proof
% 0.21/0.41  
% 0.21/0.41  RESULT: Unsatisfiable (the axioms are contradictory).
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