%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SWV402+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : n025.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 23:04:06 EDT 2023

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

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWV402+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34  % Computer : n025.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Tue Aug 29 09:56:40 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.40  Command-line arguments: --no-flatten-goal
% 0.20/0.40  
% 0.20/0.40  % SZS status Theorem
% 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(ax20, axiom, ![U]: ~contains_slb(create_slb, U)).
% 0.20/0.40    fof(ax22, axiom, ![V, U2]: ~pair_in_list(create_slb, U2, V)).
% 0.20/0.40    fof(l38_co, conjecture, ![W, X, U2, V2]: ((pair_in_list(create_slb, V2, W) & strictly_less_than(W, X)) => pair_in_list(update_slb(create_slb, X), V2, X))).
% 0.20/0.40    fof(stricly_smaller_definition, axiom, ![U2, V2]: (strictly_less_than(U2, V2) <=> (less_than(U2, V2) & ~less_than(V2, U2)))).
% 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 (l38_co_1): pair_in_list(create_slb, v, w) = true2.
% 0.20/0.40  
% 0.20/0.40  Goal 1 (ax22): pair_in_list(create_slb, X, Y) = true2.
% 0.20/0.40  The goal is true when:
% 0.20/0.40    X = v
% 0.20/0.40    Y = w
% 0.20/0.40  
% 0.20/0.40  Proof:
% 0.20/0.40    pair_in_list(create_slb, v, w)
% 0.20/0.40  = { by axiom 1 (l38_co_1) }
% 0.20/0.40    true2
% 0.20/0.40  % SZS output end Proof
% 0.20/0.40  
% 0.20/0.40  RESULT: Theorem (the conjecture is true).
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