%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SWV081+1 : TPTP v8.1.2. Bugfixed 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 : n013.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 23:02:29 EDT 2023

% Result   : Theorem 1.66s 0.59s
% Output   : Proof 1.66s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWV081+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.13  % 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 : n013.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 10:43:46 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 1.66/0.59  Command-line arguments: --no-flatten-goal
% 1.66/0.59  
% 1.66/0.59  % SZS status Theorem
% 1.66/0.59  
% 1.66/0.59  % SZS output start Proof
% 1.66/0.59  Take the following subset of the input axioms:
% 1.66/0.59    fof(cl5_nebula_array_0022, conjecture, (leq(n0, pv57) & leq(pv57, minus(n5, n1))) => (leq(n0, pv57) & leq(pv57, minus(n5, n1)))).
% 1.66/0.59    fof(pred_minus_1, axiom, ![X]: minus(X, n1)=pred(X)).
% 1.66/0.59    fof(ttrue, axiom, true).
% 1.66/0.59  
% 1.66/0.59  Now clausify the problem and encode Horn clauses using encoding 3 of
% 1.66/0.59  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 1.66/0.59  We repeatedly replace C & s=t => u=v by the two clauses:
% 1.66/0.59    fresh(y, y, x1...xn) = u
% 1.66/0.59    C => fresh(s, t, x1...xn) = v
% 1.66/0.59  where fresh is a fresh function symbol and x1..xn are the free
% 1.66/0.59  variables of u and v.
% 1.66/0.59  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 1.66/0.59  input problem has no model of domain size 1).
% 1.66/0.59  
% 1.66/0.59  The encoding turns the above axioms into the following unit equations and goals:
% 1.66/0.59  
% 1.66/0.59  Axiom 1 (ttrue): true = true3.
% 1.66/0.59  Axiom 2 (pred_minus_1): minus(X, n1) = pred(X).
% 1.66/0.59  Axiom 3 (cl5_nebula_array_0022): leq(n0, pv57) = true3.
% 1.66/0.59  Axiom 4 (cl5_nebula_array_0022_1): leq(pv57, minus(n5, n1)) = true3.
% 1.66/0.59  
% 1.66/0.59  Goal 1 (cl5_nebula_array_0022_2): tuple(leq(n0, pv57), leq(pv57, minus(n5, n1))) = tuple(true3, true3).
% 1.66/0.59  Proof:
% 1.66/0.59    tuple(leq(n0, pv57), leq(pv57, minus(n5, n1)))
% 1.66/0.59  = { by axiom 2 (pred_minus_1) }
% 1.66/0.59    tuple(leq(n0, pv57), leq(pv57, pred(n5)))
% 1.66/0.59  = { by axiom 3 (cl5_nebula_array_0022) }
% 1.66/0.59    tuple(true3, leq(pv57, pred(n5)))
% 1.66/0.59  = { by axiom 1 (ttrue) R->L }
% 1.66/0.59    tuple(true, leq(pv57, pred(n5)))
% 1.66/0.59  = { by axiom 2 (pred_minus_1) R->L }
% 1.66/0.59    tuple(true, leq(pv57, minus(n5, n1)))
% 1.66/0.59  = { by axiom 4 (cl5_nebula_array_0022_1) }
% 1.66/0.59    tuple(true, true3)
% 1.66/0.59  = { by axiom 1 (ttrue) R->L }
% 1.66/0.59    tuple(true, true)
% 1.66/0.59  = { by axiom 1 (ttrue) }
% 1.66/0.59    tuple(true3, true)
% 1.66/0.59  = { by axiom 1 (ttrue) }
% 1.66/0.59    tuple(true3, true3)
% 1.66/0.59  % SZS output end Proof
% 1.66/0.59  
% 1.66/0.59  RESULT: Theorem (the conjecture is true).
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