%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SWV388+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 23:04:03 EDT 2023

% Result   : Theorem 0.22s 0.47s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : SWV388+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.37  % Computer : n008.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Tue Aug 29 03:56:32 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 0.22/0.47  Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.22/0.47  
% 0.22/0.47  % SZS status Theorem
% 0.22/0.47  
% 0.22/0.47  % SZS output start Proof
% 0.22/0.47  Take the following subset of the input axioms:
% 0.22/0.47    fof(l24_co, conjecture, ![U, V, W]: (~check_cpq(triple(U, V, W)) => (~check_cpq(findmin_cpq_eff(triple(U, V, W))) | ~ok(findmin_cpq_eff(triple(U, V, W)))))).
% 0.22/0.47    fof(l24_l34, lemma, ![U2, V2, W2]: (~check_cpq(triple(U2, V2, W2)) => ~check_cpq(findmin_cpq_eff(triple(U2, V2, W2))))).
% 0.22/0.47  
% 0.22/0.47  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.47  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.47  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.47    fresh(y, y, x1...xn) = u
% 0.22/0.47    C => fresh(s, t, x1...xn) = v
% 0.22/0.47  where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.47  variables of u and v.
% 0.22/0.47  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.47  input problem has no model of domain size 1).
% 0.22/0.47  
% 0.22/0.47  The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.47  
% 0.22/0.47  Axiom 1 (l24_co): check_cpq(findmin_cpq_eff(triple(u, v, w))) = true2.
% 0.22/0.47  Axiom 2 (l24_l34): fresh4(X, X, Y, Z, W) = true2.
% 0.22/0.48  Axiom 3 (l24_l34): fresh4(check_cpq(findmin_cpq_eff(triple(X, Y, Z))), true2, X, Y, Z) = check_cpq(triple(X, Y, Z)).
% 0.22/0.48  
% 0.22/0.48  Goal 1 (l24_co_2): check_cpq(triple(u, v, w)) = true2.
% 0.22/0.48  Proof:
% 0.22/0.48    check_cpq(triple(u, v, w))
% 0.22/0.48  = { by axiom 3 (l24_l34) R->L }
% 0.22/0.48    fresh4(check_cpq(findmin_cpq_eff(triple(u, v, w))), true2, u, v, w)
% 0.22/0.48  = { by axiom 1 (l24_co) }
% 0.22/0.48    fresh4(true2, true2, u, v, w)
% 0.22/0.48  = { by axiom 2 (l24_l34) }
% 0.22/0.48    true2
% 0.22/0.48  % SZS output end Proof
% 0.22/0.48  
% 0.22/0.48  RESULT: Theorem (the conjecture is true).
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