%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SET118-7 : TPTP v8.1.2. Bugfixed v7.3.0.
% 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 : n026.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 15:31:22 EDT 2023

% Result   : Unsatisfiable 0.21s 0.58s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET118-7 : TPTP v8.1.2. Bugfixed v7.3.0.
% 0.00/0.14  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35  % Computer : n026.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 : Sat Aug 26 09:58:18 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.58  Command-line arguments: --no-flatten-goal
% 0.21/0.58  
% 0.21/0.58  % SZS status Unsatisfiable
% 0.21/0.58  
% 0.21/0.58  % SZS output start Proof
% 0.21/0.58  Take the following subset of the input axioms:
% 0.21/0.58    fof(cartesian_product4, axiom, ![X, Y, Z]: (~member(Z, cross_product(X, Y)) | ordered_pair(first(Z), second(Z))=Z)).
% 0.21/0.58    fof(ordered_pair_is_set, axiom, ![X2, Y2]: member(ordered_pair(X2, Y2), universal_class)).
% 0.21/0.58    fof(prove_corollary_2_to_ordered_pairs_are_sets_1, negated_conjecture, member(x, cross_product(universal_class, universal_class))).
% 0.21/0.58    fof(prove_corollary_2_to_ordered_pairs_are_sets_2, negated_conjecture, ~member(x, universal_class)).
% 0.21/0.58  
% 0.21/0.58  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.58  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.58  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.58    fresh(y, y, x1...xn) = u
% 0.21/0.58    C => fresh(s, t, x1...xn) = v
% 0.21/0.58  where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.58  variables of u and v.
% 0.21/0.58  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.58  input problem has no model of domain size 1).
% 0.21/0.58  
% 0.21/0.58  The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.58  
% 0.21/0.58  Axiom 1 (cartesian_product4): fresh21(X, X, Y) = Y.
% 0.21/0.58  Axiom 2 (prove_corollary_2_to_ordered_pairs_are_sets_1): member(x, cross_product(universal_class, universal_class)) = true2.
% 0.21/0.58  Axiom 3 (ordered_pair_is_set): member(ordered_pair(X, Y), universal_class) = true2.
% 0.21/0.58  Axiom 4 (cartesian_product4): fresh21(member(X, cross_product(Y, Z)), true2, X) = ordered_pair(first(X), second(X)).
% 0.21/0.58  
% 0.21/0.58  Goal 1 (prove_corollary_2_to_ordered_pairs_are_sets_2): member(x, universal_class) = true2.
% 0.21/0.58  Proof:
% 0.21/0.58    member(x, universal_class)
% 0.21/0.58  = { by axiom 1 (cartesian_product4) R->L }
% 0.21/0.58    member(fresh21(true2, true2, x), universal_class)
% 0.21/0.58  = { by axiom 2 (prove_corollary_2_to_ordered_pairs_are_sets_1) R->L }
% 0.21/0.58    member(fresh21(member(x, cross_product(universal_class, universal_class)), true2, x), universal_class)
% 0.21/0.58  = { by axiom 4 (cartesian_product4) }
% 0.21/0.58    member(ordered_pair(first(x), second(x)), universal_class)
% 0.21/0.58  = { by axiom 3 (ordered_pair_is_set) }
% 0.21/0.58    true2
% 0.21/0.58  % SZS output end Proof
% 0.21/0.58  
% 0.21/0.58  RESULT: Unsatisfiable (the axioms are contradictory).
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