%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SYN120-1 : TPTP v8.1.2. Released v1.1.0.
% 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 : n007.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 : Fri Sep  1 03:33:14 EDT 2023

% Result   : Unsatisfiable 11.58s 1.94s
% Output   : Proof 11.58s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SYN120-1 : TPTP v8.1.2. Released v1.1.0.
% 0.07/0.14  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35  % Computer : n007.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Sat Aug 26 17:15:57 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 11.58/1.94  Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 11.58/1.94  
% 11.58/1.94  % SZS status Unsatisfiable
% 11.58/1.94  
% 11.58/1.94  % SZS output start Proof
% 11.58/1.94  Take the following subset of the input axioms:
% 11.58/1.94    fof(axiom_3, axiom, n0(d, e)).
% 11.58/1.94    fof(prove_this, negated_conjecture, ~l1(e, e)).
% 11.58/1.94    fof(rule_002, axiom, ![G, H]: (l1(G, G) | ~n0(H, G))).
% 11.58/1.94  
% 11.58/1.94  Now clausify the problem and encode Horn clauses using encoding 3 of
% 11.58/1.94  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 11.58/1.94  We repeatedly replace C & s=t => u=v by the two clauses:
% 11.58/1.94    fresh(y, y, x1...xn) = u
% 11.58/1.94    C => fresh(s, t, x1...xn) = v
% 11.58/1.94  where fresh is a fresh function symbol and x1..xn are the free
% 11.58/1.94  variables of u and v.
% 11.58/1.94  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 11.58/1.94  input problem has no model of domain size 1).
% 11.58/1.94  
% 11.58/1.94  The encoding turns the above axioms into the following unit equations and goals:
% 11.58/1.94  
% 11.58/1.94  Axiom 1 (axiom_3): n0(d, e) = true.
% 11.58/1.94  Axiom 2 (rule_002): fresh441(X, X, Y) = true.
% 11.58/1.94  Axiom 3 (rule_002): fresh441(n0(X, Y), true, Y) = l1(Y, Y).
% 11.58/1.94  
% 11.58/1.94  Goal 1 (prove_this): l1(e, e) = true.
% 11.58/1.94  Proof:
% 11.58/1.94    l1(e, e)
% 11.58/1.94  = { by axiom 3 (rule_002) R->L }
% 11.58/1.94    fresh441(n0(d, e), true, e)
% 11.58/1.94  = { by axiom 1 (axiom_3) }
% 11.58/1.94    fresh441(true, true, e)
% 11.58/1.94  = { by axiom 2 (rule_002) }
% 11.58/1.94    true
% 11.58/1.94  % SZS output end Proof
% 11.58/1.94  
% 11.58/1.94  RESULT: Unsatisfiable (the axioms are contradictory).
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