%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : NUN089+1 : TPTP v8.1.2. Released v7.3.0.
% 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 : n009.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 12:51:57 EDT 2023

% Result   : Theorem 0.14s 0.44s
% Output   : Proof 0.14s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem  : NUN089+1 : TPTP v8.1.2. Released v7.3.0.
% 0.05/0.10  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.30  % Computer : n009.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 300
% 0.10/0.30  % DateTime : Sun Aug 27 08:57:20 EDT 2023
% 0.10/0.30  % CPUTime  : 
% 0.14/0.44  Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.14/0.44  
% 0.14/0.44  % SZS status Theorem
% 0.14/0.44  
% 0.14/0.44  % SZS output start Proof
% 0.14/0.44  Take the following subset of the input axioms:
% 0.14/0.44    fof(axiom_7a, axiom, ![X7, Y10]: (![Y20]: (~id(Y20, Y10) | ~r1(Y20)) | ~r2(X7, Y10))).
% 0.14/0.44    fof(zerounidtwo, conjecture, ![Y1]: (![Y2]: (![Y3]: (~r1(Y3) | ~r2(Y3, Y2)) | ~r2(Y2, Y1)) | ![Y4]: (~id(Y4, Y1) | ~r1(Y4)))).
% 0.14/0.44  
% 0.14/0.44  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.14/0.44  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.14/0.44  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.14/0.44    fresh(y, y, x1...xn) = u
% 0.14/0.44    C => fresh(s, t, x1...xn) = v
% 0.14/0.44  where fresh is a fresh function symbol and x1..xn are the free
% 0.14/0.44  variables of u and v.
% 0.14/0.44  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.14/0.44  input problem has no model of domain size 1).
% 0.14/0.44  
% 0.14/0.44  The encoding turns the above axioms into the following unit equations and goals:
% 0.14/0.44  
% 0.14/0.44  Axiom 1 (zerounidtwo_2): r1(y4) = true2.
% 0.14/0.44  Axiom 2 (zerounidtwo): id(y4, y1) = true2.
% 0.14/0.44  Axiom 3 (zerounidtwo_3): r2(y2, y1) = true2.
% 0.14/0.44  
% 0.14/0.44  Goal 1 (axiom_7a): tuple(id(X, Y), r1(X), r2(Z, Y)) = tuple(true2, true2, true2).
% 0.14/0.44  The goal is true when:
% 0.14/0.44    X = y4
% 0.14/0.44    Y = y1
% 0.14/0.44    Z = y2
% 0.14/0.44  
% 0.14/0.44  Proof:
% 0.14/0.44    tuple(id(y4, y1), r1(y4), r2(y2, y1))
% 0.14/0.44  = { by axiom 2 (zerounidtwo) }
% 0.14/0.44    tuple(true2, r1(y4), r2(y2, y1))
% 0.14/0.44  = { by axiom 1 (zerounidtwo_2) }
% 0.14/0.44    tuple(true2, true2, r2(y2, y1))
% 0.14/0.44  = { by axiom 3 (zerounidtwo_3) }
% 0.14/0.44    tuple(true2, true2, true2)
% 0.14/0.44  % SZS output end Proof
% 0.14/0.44  
% 0.14/0.44  RESULT: Theorem (the conjecture is true).
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