%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SYO611-1 : TPTP v8.1.2. Released v7.1.0.
% 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 : n019.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 04:58:41 EDT 2023

% Result   : Unsatisfiable 0.20s 0.39s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SYO611-1 : TPTP v8.1.2. Released v7.1.0.
% 0.00/0.13  % 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 : n019.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 : Sat Aug 26 05:51:13 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.39  Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.39  
% 0.20/0.39  % SZS status Unsatisfiable
% 0.20/0.39  
% 0.20/0.39  % SZS output start Proof
% 0.20/0.39  Take the following subset of the input axioms:
% 0.20/0.39    fof(sos_01, axiom, ![A]: le(A, A)).
% 0.20/0.39    fof(sos_04, axiom, ![A2]: eq(f(A2), a0)).
% 0.20/0.39    fof(sos_05, axiom, ![A0, A1]: (~eq(f(A0), a0) | (~eq(f(A1), a0) | ~le(s(A0), A1)))).
% 0.20/0.39  
% 0.20/0.39  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.39  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.39  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.39    fresh(y, y, x1...xn) = u
% 0.20/0.39    C => fresh(s, t, x1...xn) = v
% 0.20/0.39  where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.39  variables of u and v.
% 0.20/0.39  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.39  input problem has no model of domain size 1).
% 0.20/0.39  
% 0.20/0.39  The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.39  
% 0.20/0.39  Axiom 1 (sos_01): le(X, X) = true2.
% 0.20/0.39  Axiom 2 (sos_04): eq(f(X), a0) = true2.
% 0.20/0.39  
% 0.20/0.39  Goal 1 (sos_05): tuple(le(s(X), Y), eq(f(X), a0), eq(f(Y), a0)) = tuple(true2, true2, true2).
% 0.20/0.39  The goal is true when:
% 0.20/0.39    X = X
% 0.20/0.39    Y = s(X)
% 0.20/0.39  
% 0.20/0.39  Proof:
% 0.20/0.39    tuple(le(s(X), s(X)), eq(f(X), a0), eq(f(s(X)), a0))
% 0.20/0.39  = { by axiom 2 (sos_04) }
% 0.20/0.39    tuple(le(s(X), s(X)), true2, eq(f(s(X)), a0))
% 0.20/0.39  = { by axiom 2 (sos_04) }
% 0.20/0.39    tuple(le(s(X), s(X)), true2, true2)
% 0.20/0.39  = { by axiom 1 (sos_01) }
% 0.20/0.39    tuple(true2, true2, true2)
% 0.20/0.39  % SZS output end Proof
% 0.20/0.39  
% 0.20/0.39  RESULT: Unsatisfiable (the axioms are contradictory).
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