%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : GRP019-1 : 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 : n029.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 01:16:36 EDT 2023

% Result   : Unsatisfiable 0.15s 0.36s
% Output   : Proof 0.15s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GRP019-1 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.12  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.32  % Computer : n029.cluster.edu
% 0.15/0.32  % Model    : x86_64 x86_64
% 0.15/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32  % Memory   : 8042.1875MB
% 0.15/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32  % CPULimit : 300
% 0.15/0.32  % WCLimit  : 300
% 0.15/0.32  % DateTime : Mon Aug 28 23:15:11 EDT 2023
% 0.15/0.32  % CPUTime  : 
% 0.15/0.36  Command-line arguments: --no-flatten-goal
% 0.15/0.36  
% 0.15/0.36  % SZS status Unsatisfiable
% 0.15/0.36  
% 0.15/0.36  % SZS output start Proof
% 0.15/0.36  Take the following subset of the input axioms:
% 0.15/0.36    fof(left_identity, axiom, ![X]: product(identity, X, X)).
% 0.15/0.36    fof(prove_id_times_X_is_X, negated_conjecture, multiply(identity, a)!=a).
% 0.15/0.36    fof(total_function1, axiom, ![Y, X2]: product(X2, Y, multiply(X2, Y))).
% 0.15/0.36    fof(total_function2, axiom, ![Z, W, X2, Y2]: (~product(X2, Y2, Z) | (~product(X2, Y2, W) | Z=W))).
% 0.15/0.36  
% 0.15/0.36  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.15/0.36  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.15/0.36  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.15/0.36    fresh(y, y, x1...xn) = u
% 0.15/0.36    C => fresh(s, t, x1...xn) = v
% 0.15/0.36  where fresh is a fresh function symbol and x1..xn are the free
% 0.15/0.36  variables of u and v.
% 0.15/0.36  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.15/0.36  input problem has no model of domain size 1).
% 0.15/0.36  
% 0.15/0.36  The encoding turns the above axioms into the following unit equations and goals:
% 0.15/0.36  
% 0.15/0.36  Axiom 1 (left_identity): product(identity, X, X) = true.
% 0.15/0.36  Axiom 2 (total_function2): fresh(X, X, Y, Z) = Z.
% 0.15/0.36  Axiom 3 (total_function1): product(X, Y, multiply(X, Y)) = true.
% 0.15/0.36  Axiom 4 (total_function2): fresh2(X, X, Y, Z, W, V) = W.
% 0.15/0.36  Axiom 5 (total_function2): fresh2(product(X, Y, Z), true, X, Y, W, Z) = fresh(product(X, Y, W), true, W, Z).
% 0.15/0.36  
% 0.15/0.36  Goal 1 (prove_id_times_X_is_X): multiply(identity, a) = a.
% 0.15/0.36  Proof:
% 0.15/0.36    multiply(identity, a)
% 0.15/0.36  = { by axiom 4 (total_function2) R->L }
% 0.15/0.36    fresh2(true, true, identity, a, multiply(identity, a), a)
% 0.15/0.36  = { by axiom 1 (left_identity) R->L }
% 0.15/0.36    fresh2(product(identity, a, a), true, identity, a, multiply(identity, a), a)
% 0.15/0.36  = { by axiom 5 (total_function2) }
% 0.15/0.36    fresh(product(identity, a, multiply(identity, a)), true, multiply(identity, a), a)
% 0.15/0.36  = { by axiom 3 (total_function1) }
% 0.15/0.36    fresh(true, true, multiply(identity, a), a)
% 0.15/0.36  = { by axiom 2 (total_function2) }
% 0.15/0.36    a
% 0.15/0.36  % SZS output end Proof
% 0.15/0.36  
% 0.15/0.36  RESULT: Unsatisfiable (the axioms are contradictory).
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