%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SWC035+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 : 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 20:53:32 EDT 2023

% Result   : Theorem 3.24s 0.81s
% Output   : Proof 3.24s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SWC035+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.12  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33  % Computer : n025.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Mon Aug 28 19:07:24 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 3.24/0.81  Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 3.24/0.81  
% 3.24/0.81  % SZS status Theorem
% 3.24/0.81  
% 3.24/0.81  % SZS output start Proof
% 3.24/0.81  Take the following subset of the input axioms:
% 3.24/0.82    fof(co1, conjecture, ![U]: (ssList(U) => ![V]: (ssList(V) => ![W]: (ssList(W) => ![X]: (ssList(X) => (nil!=V | (V!=X | (U!=W | (X!=W | nil=U))))))))).
% 3.24/0.82  
% 3.24/0.82  Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.24/0.82  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.24/0.82  We repeatedly replace C & s=t => u=v by the two clauses:
% 3.24/0.82    fresh(y, y, x1...xn) = u
% 3.24/0.82    C => fresh(s, t, x1...xn) = v
% 3.24/0.82  where fresh is a fresh function symbol and x1..xn are the free
% 3.24/0.82  variables of u and v.
% 3.24/0.82  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.24/0.82  input problem has no model of domain size 1).
% 3.24/0.82  
% 3.24/0.82  The encoding turns the above axioms into the following unit equations and goals:
% 3.24/0.82  
% 3.24/0.82  Axiom 1 (co1_1): u = w.
% 3.24/0.82  Axiom 2 (co1_2): v = x.
% 3.24/0.82  Axiom 3 (co1_3): x = w.
% 3.24/0.82  Axiom 4 (co1): nil = v.
% 3.24/0.82  
% 3.24/0.82  Goal 1 (co1_8): nil = u.
% 3.24/0.82  Proof:
% 3.24/0.82    nil
% 3.24/0.82  = { by axiom 4 (co1) }
% 3.24/0.82    v
% 3.24/0.82  = { by axiom 2 (co1_2) }
% 3.24/0.82    x
% 3.24/0.82  = { by axiom 3 (co1_3) }
% 3.24/0.82    w
% 3.24/0.82  = { by axiom 1 (co1_1) R->L }
% 3.24/0.82    u
% 3.24/0.82  % SZS output end Proof
% 3.24/0.82  
% 3.24/0.82  RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------