%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : RNG010-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 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 : n024.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 13:58:47 EDT 2023

% Result   : Unsatisfiable 0.20s 0.40s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : RNG010-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.07/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34  % Computer : n024.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Sun Aug 27 01:40:53 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.20/0.40  Command-line arguments: --no-flatten-goal
% 0.20/0.40  
% 0.20/0.40  % SZS status Unsatisfiable
% 0.20/0.40  
% 0.20/0.40  % SZS output start Proof
% 0.20/0.40  Take the following subset of the input axioms:
% 0.20/0.40    fof(associator_skew_symmetry1, axiom, ![X, Y, Z]: associator(Y, X, Z)!=additive_inverse(associator(X, Y, Z))).
% 0.20/0.40    fof(associator_skew_symmetry2, axiom, ![X2, Y2, Z2]: associator(Z2, Y2, X2)!=additive_inverse(associator(X2, Y2, Z2))).
% 0.20/0.40    fof(left_multiplicative_zero, axiom, ![X2]: multiply(additive_identity, X2)=additive_identity).
% 0.20/0.40    fof(middle_law, axiom, ![X2, Y2]: multiply(multiply(Y2, X2), Y2)!=multiply(Y2, multiply(X2, Y2))).
% 0.20/0.40    fof(right_multiplicative_zero, axiom, ![X2]: multiply(X2, additive_identity)=additive_identity).
% 0.20/0.40  
% 0.20/0.40  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.40  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.40  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.40    fresh(y, y, x1...xn) = u
% 0.20/0.40    C => fresh(s, t, x1...xn) = v
% 0.20/0.40  where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.40  variables of u and v.
% 0.20/0.40  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.40  input problem has no model of domain size 1).
% 0.20/0.40  
% 0.20/0.40  The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.40  
% 0.20/0.40  Axiom 1 (right_multiplicative_zero): multiply(X, additive_identity) = additive_identity.
% 0.20/0.40  Axiom 2 (left_multiplicative_zero): multiply(additive_identity, X) = additive_identity.
% 0.20/0.40  
% 0.20/0.40  Goal 1 (middle_law): multiply(multiply(X, Y), X) = multiply(X, multiply(Y, X)).
% 0.20/0.40  The goal is true when:
% 0.20/0.40    X = additive_identity
% 0.20/0.40    Y = X
% 0.20/0.40  
% 0.20/0.40  Proof:
% 0.20/0.40    multiply(multiply(additive_identity, X), additive_identity)
% 0.20/0.40  = { by axiom 1 (right_multiplicative_zero) }
% 0.20/0.40    additive_identity
% 0.20/0.40  = { by axiom 2 (left_multiplicative_zero) R->L }
% 0.20/0.40    multiply(additive_identity, multiply(X, additive_identity))
% 0.20/0.40  % SZS output end Proof
% 0.20/0.40  
% 0.20/0.40  RESULT: Unsatisfiable (the axioms are contradictory).
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