%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SWV405+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 : n008.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 23:04:07 EDT 2023

% Result   : Theorem 0.21s 0.42s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWV405+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.35  % Computer : n008.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Tue Aug 29 07:04:32 EDT 2023
% 0.21/0.35  % CPUTime  : 
% 0.21/0.42  Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.21/0.42  
% 0.21/0.42  % SZS status Theorem
% 0.21/0.42  
% 0.21/0.42  % SZS output start Proof
% 0.21/0.42  Take the following subset of the input axioms:
% 0.22/0.43    fof(ax20, axiom, ![U]: ~contains_slb(create_slb, U)).
% 0.22/0.43    fof(ax22, axiom, ![V, U2]: ~pair_in_list(create_slb, U2, V)).
% 0.22/0.43    fof(ax36, axiom, ![U2, V2]: check_cpq(triple(U2, create_slb, V2))).
% 0.22/0.43    fof(ax38, axiom, ![W, X, Y, U2, V2]: (strictly_less_than(X, Y) => (check_cpq(triple(U2, insert_slb(V2, pair(X, Y)), W)) <=> $false))).
% 0.22/0.43    fof(ax40, axiom, ![U2, V2]: (ok(triple(U2, V2, bad)) <=> $false)).
% 0.22/0.43    fof(l41_co, conjecture, ![U2, V2]: (check_cpq(triple(U2, create_slb, V2)) <=> ![W2, X2]: (pair_in_list(create_slb, W2, X2) => less_than(X2, W2)))).
% 0.22/0.43    fof(stricly_smaller_definition, axiom, ![U2, V2]: (strictly_less_than(U2, V2) <=> (less_than(U2, V2) & ~less_than(V2, U2)))).
% 0.22/0.43  
% 0.22/0.43  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.43  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.43  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.43    fresh(y, y, x1...xn) = u
% 0.22/0.43    C => fresh(s, t, x1...xn) = v
% 0.22/0.43  where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.43  variables of u and v.
% 0.22/0.43  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.43  input problem has no model of domain size 1).
% 0.22/0.43  
% 0.22/0.43  The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.43  
% 0.22/0.43  Axiom 1 (l41_co_2): fresh4(X, X) = true2.
% 0.22/0.43  Axiom 2 (ax36): check_cpq(triple(X, create_slb, Y)) = true2.
% 0.22/0.43  Axiom 3 (l41_co_2): fresh4(check_cpq(triple(u, create_slb, v)), true2) = pair_in_list(create_slb, w, x).
% 0.22/0.43  
% 0.22/0.43  Goal 1 (ax22): pair_in_list(create_slb, X, Y) = true2.
% 0.22/0.43  The goal is true when:
% 0.22/0.43    X = w
% 0.22/0.43    Y = x
% 0.22/0.43  
% 0.22/0.43  Proof:
% 0.22/0.43    pair_in_list(create_slb, w, x)
% 0.22/0.43  = { by axiom 3 (l41_co_2) R->L }
% 0.22/0.43    fresh4(check_cpq(triple(u, create_slb, v)), true2)
% 0.22/0.43  = { by axiom 2 (ax36) }
% 0.22/0.43    fresh4(true2, true2)
% 0.22/0.43  = { by axiom 1 (l41_co_2) }
% 0.22/0.43    true2
% 0.22/0.43  % SZS output end Proof
% 0.22/0.43  
% 0.22/0.43  RESULT: Theorem (the conjecture is true).
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