%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : GRP023-1 : 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 : n010.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 01:16:37 EDT 2023

% Result   : Unsatisfiable 0.14s 0.40s
% Output   : Proof 0.14s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : GRP023-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35  % Computer : n010.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Tue Aug 29 01:17:49 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.14/0.40  Command-line arguments: --flatten
% 0.14/0.40  
% 0.14/0.40  % SZS status Unsatisfiable
% 0.14/0.40  
% 0.14/0.41  % SZS output start Proof
% 0.14/0.41  Take the following subset of the input axioms:
% 0.14/0.41    fof(left_inverse, axiom, ![X]: product(inverse(X), X, identity)).
% 0.14/0.41    fof(prove_inverse_of_id_is_id, negated_conjecture, inverse(identity)!=identity).
% 0.14/0.41    fof(right_identity, axiom, ![X2]: product(X2, identity, X2)).
% 0.14/0.41    fof(total_function2, axiom, ![Y, Z, W, X2]: (~product(X2, Y, Z) | (~product(X2, Y, W) | Z=W))).
% 0.14/0.41  
% 0.14/0.41  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.14/0.41  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.14/0.41  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.14/0.41    fresh(y, y, x1...xn) = u
% 0.14/0.41    C => fresh(s, t, x1...xn) = v
% 0.14/0.41  where fresh is a fresh function symbol and x1..xn are the free
% 0.14/0.41  variables of u and v.
% 0.14/0.41  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.14/0.41  input problem has no model of domain size 1).
% 0.14/0.41  
% 0.14/0.41  The encoding turns the above axioms into the following unit equations and goals:
% 0.14/0.41  
% 0.14/0.41  Axiom 1 (right_identity): product(X, identity, X) = true.
% 0.14/0.41  Axiom 2 (total_function2): fresh(X, X, Y, Z) = Z.
% 0.14/0.41  Axiom 3 (left_inverse): product(inverse(X), X, identity) = true.
% 0.14/0.41  Axiom 4 (total_function2): fresh2(X, X, Y, Z, W, V) = W.
% 0.14/0.41  Axiom 5 (total_function2): fresh2(product(X, Y, Z), true, X, Y, W, Z) = fresh(product(X, Y, W), true, W, Z).
% 0.14/0.41  
% 0.14/0.41  Goal 1 (prove_inverse_of_id_is_id): inverse(identity) = identity.
% 0.14/0.41  Proof:
% 0.14/0.41    inverse(identity)
% 0.14/0.41  = { by axiom 2 (total_function2) R->L }
% 0.14/0.41    fresh(true, true, identity, inverse(identity))
% 0.14/0.41  = { by axiom 3 (left_inverse) R->L }
% 0.14/0.41    fresh(product(inverse(identity), identity, identity), true, identity, inverse(identity))
% 0.14/0.41  = { by axiom 5 (total_function2) R->L }
% 0.14/0.41    fresh2(product(inverse(identity), identity, inverse(identity)), true, inverse(identity), identity, identity, inverse(identity))
% 0.14/0.41  = { by axiom 1 (right_identity) }
% 0.14/0.41    fresh2(true, true, inverse(identity), identity, identity, inverse(identity))
% 0.14/0.41  = { by axiom 4 (total_function2) }
% 0.14/0.41    identity
% 0.14/0.41  % SZS output end Proof
% 0.14/0.41  
% 0.14/0.41  RESULT: Unsatisfiable (the axioms are contradictory).
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