%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : FLD071-1 : 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 : n007.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 22:37:13 EDT 2023

% Result   : Unsatisfiable 0.20s 0.45s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : FLD071-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.08/0.13  % 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 : n007.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 23:18:57 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.45  Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.45  
% 0.20/0.45  % SZS status Unsatisfiable
% 0.20/0.45  
% 0.20/0.45  % SZS output start Proof
% 0.20/0.45  Take the following subset of the input axioms:
% 0.20/0.45    fof(compatibility_of_order_relation_and_multiplication, axiom, ![Y, Z]: (less_or_equal(additive_identity, multiply(Y, Z)) | (~less_or_equal(additive_identity, Y) | ~less_or_equal(additive_identity, Z)))).
% 0.20/0.45    fof(less_or_equal_3, negated_conjecture, less_or_equal(additive_identity, a)).
% 0.20/0.45    fof(less_or_equal_4, negated_conjecture, less_or_equal(additive_identity, b)).
% 0.20/0.45    fof(not_less_or_equal_5, negated_conjecture, ~less_or_equal(additive_identity, multiply(a, b))).
% 0.20/0.45  
% 0.20/0.45  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.45  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.45  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.45    fresh(y, y, x1...xn) = u
% 0.20/0.45    C => fresh(s, t, x1...xn) = v
% 0.20/0.45  where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.45  variables of u and v.
% 0.20/0.45  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.45  input problem has no model of domain size 1).
% 0.20/0.45  
% 0.20/0.45  The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.45  
% 0.20/0.46  Axiom 1 (less_or_equal_3): less_or_equal(additive_identity, a) = true.
% 0.20/0.46  Axiom 2 (less_or_equal_4): less_or_equal(additive_identity, b) = true.
% 0.20/0.46  Axiom 3 (compatibility_of_order_relation_and_multiplication): fresh15(X, X, Y, Z) = true.
% 0.20/0.46  Axiom 4 (compatibility_of_order_relation_and_multiplication): fresh16(X, X, Y, Z) = less_or_equal(additive_identity, multiply(Y, Z)).
% 0.20/0.46  Axiom 5 (compatibility_of_order_relation_and_multiplication): fresh16(less_or_equal(additive_identity, X), true, Y, X) = fresh15(less_or_equal(additive_identity, Y), true, Y, X).
% 0.20/0.46  
% 0.20/0.46  Goal 1 (not_less_or_equal_5): less_or_equal(additive_identity, multiply(a, b)) = true.
% 0.20/0.46  Proof:
% 0.20/0.46    less_or_equal(additive_identity, multiply(a, b))
% 0.20/0.46  = { by axiom 4 (compatibility_of_order_relation_and_multiplication) R->L }
% 0.20/0.46    fresh16(true, true, a, b)
% 0.20/0.46  = { by axiom 2 (less_or_equal_4) R->L }
% 0.20/0.46    fresh16(less_or_equal(additive_identity, b), true, a, b)
% 0.20/0.46  = { by axiom 5 (compatibility_of_order_relation_and_multiplication) }
% 0.20/0.46    fresh15(less_or_equal(additive_identity, a), true, a, b)
% 0.20/0.46  = { by axiom 1 (less_or_equal_3) }
% 0.20/0.46    fresh15(true, true, a, b)
% 0.20/0.46  = { by axiom 3 (compatibility_of_order_relation_and_multiplication) }
% 0.20/0.46    true
% 0.20/0.46  % SZS output end Proof
% 0.20/0.46  
% 0.20/0.46  RESULT: Unsatisfiable (the axioms are contradictory).
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