%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SWC359+1 : TPTP v8.1.2. Released v2.4.0.
% 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 : n022.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 20:55:09 EDT 2023

% Result   : Theorem 3.54s 0.87s
% Output   : Proof 3.54s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.15  % Problem  : SWC359+1 : TPTP v8.1.2. Released v2.4.0.
% 0.10/0.16  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.17/0.37  % Computer : n022.cluster.edu
% 0.17/0.37  % Model    : x86_64 x86_64
% 0.17/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37  % Memory   : 8042.1875MB
% 0.17/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37  % CPULimit : 300
% 0.17/0.37  % WCLimit  : 300
% 0.17/0.37  % DateTime : Mon Aug 28 18:36:09 EDT 2023
% 0.24/0.38  % CPUTime  : 
% 3.54/0.87  Command-line arguments: --no-flatten-goal
% 3.54/0.87  
% 3.54/0.87  % SZS status Theorem
% 3.54/0.87  
% 3.54/0.87  % SZS output start Proof
% 3.54/0.87  Take the following subset of the input axioms:
% 3.54/0.87    fof(co1, conjecture, ![U]: (ssList(U) => ![V]: (ssList(V) => ![W]: (ssList(W) => ![X]: (ssList(X) => (V!=X | (U!=W | (~neq(V, nil) | (~segmentP(X, W) | (~equalelemsP(W) | (?[Y]: (ssList(Y) & (neq(W, Y) & (segmentP(X, Y) & (segmentP(Y, W) & equalelemsP(Y))))) | segmentP(V, U)))))))))))).
% 3.54/0.87  
% 3.54/0.87  Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.54/0.87  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.54/0.87  We repeatedly replace C & s=t => u=v by the two clauses:
% 3.54/0.87    fresh(y, y, x1...xn) = u
% 3.54/0.87    C => fresh(s, t, x1...xn) = v
% 3.54/0.87  where fresh is a fresh function symbol and x1..xn are the free
% 3.54/0.87  variables of u and v.
% 3.54/0.87  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.54/0.87  input problem has no model of domain size 1).
% 3.54/0.87  
% 3.54/0.87  The encoding turns the above axioms into the following unit equations and goals:
% 3.54/0.87  
% 3.54/0.87  Axiom 1 (co1_1): v = x.
% 3.54/0.87  Axiom 2 (co1): u = w.
% 3.54/0.87  Axiom 3 (co1_7): segmentP(x, w) = true2.
% 3.54/0.87  
% 3.54/0.87  Goal 1 (co1_10): segmentP(v, u) = true2.
% 3.54/0.87  Proof:
% 3.54/0.87    segmentP(v, u)
% 3.54/0.87  = { by axiom 2 (co1) }
% 3.54/0.87    segmentP(v, w)
% 3.54/0.87  = { by axiom 1 (co1_1) }
% 3.54/0.87    segmentP(x, w)
% 3.54/0.87  = { by axiom 3 (co1_7) }
% 3.54/0.87    true2
% 3.54/0.87  % SZS output end Proof
% 3.54/0.87  
% 3.54/0.87  RESULT: Theorem (the conjecture is true).
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