%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : FLD039-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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 : n015.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 22:36:58 EDT 2023

% Result   : Unsatisfiable 0.18s 0.44s
% Output   : Proof 0.18s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : FLD039-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.14  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35  % Computer : n015.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Sun Aug 27 23:42:54 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.18/0.44  Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.18/0.44  
% 0.18/0.44  % SZS status Unsatisfiable
% 0.18/0.44  
% 0.18/0.44  % SZS output start Proof
% 0.18/0.44  Take the following subset of the input axioms:
% 0.18/0.44    fof(different_identities, axiom, ~equalish(additive_identity, multiplicative_identity)).
% 0.18/0.44    fof(multiplicative_identity_equals_additive_identity_3, negated_conjecture, equalish(multiplicative_identity, additive_identity)).
% 0.18/0.44    fof(symmetry_of_equality, axiom, ![X, Y]: (equalish(X, Y) | ~equalish(Y, X))).
% 0.18/0.44  
% 0.18/0.44  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.18/0.44  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.18/0.44  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.18/0.44    fresh(y, y, x1...xn) = u
% 0.18/0.44    C => fresh(s, t, x1...xn) = v
% 0.18/0.44  where fresh is a fresh function symbol and x1..xn are the free
% 0.18/0.44  variables of u and v.
% 0.18/0.44  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.18/0.44  input problem has no model of domain size 1).
% 0.18/0.44  
% 0.18/0.44  The encoding turns the above axioms into the following unit equations and goals:
% 0.18/0.44  
% 0.18/0.44  Axiom 1 (multiplicative_identity_equals_additive_identity_3): equalish(multiplicative_identity, additive_identity) = true.
% 0.18/0.44  Axiom 2 (symmetry_of_equality): fresh10(X, X, Y, Z) = true.
% 0.18/0.44  Axiom 3 (symmetry_of_equality): fresh10(equalish(X, Y), true, Y, X) = equalish(Y, X).
% 0.18/0.44  
% 0.18/0.44  Goal 1 (different_identities): equalish(additive_identity, multiplicative_identity) = true.
% 0.18/0.44  Proof:
% 0.18/0.44    equalish(additive_identity, multiplicative_identity)
% 0.18/0.44  = { by axiom 3 (symmetry_of_equality) R->L }
% 0.18/0.44    fresh10(equalish(multiplicative_identity, additive_identity), true, additive_identity, multiplicative_identity)
% 0.18/0.44  = { by axiom 1 (multiplicative_identity_equals_additive_identity_3) }
% 0.18/0.44    fresh10(true, true, additive_identity, multiplicative_identity)
% 0.18/0.44  = { by axiom 2 (symmetry_of_equality) }
% 0.18/0.44    true
% 0.18/0.44  % SZS output end Proof
% 0.18/0.44  
% 0.18/0.44  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------