%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : NUN089+2 : 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 : n011.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 0.23s 0.45s
% Output   : Proof 0.23s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.15  % Problem  : NUN089+2 : TPTP v8.1.2. Released v7.3.0.
% 0.14/0.16  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.38  % Computer : n011.cluster.edu
% 0.15/0.38  % Model    : x86_64 x86_64
% 0.15/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.38  % Memory   : 8042.1875MB
% 0.15/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38  % CPULimit : 300
% 0.15/0.38  % WCLimit  : 300
% 0.15/0.38  % DateTime : Sun Aug 27 09:13:25 EDT 2023
% 0.15/0.38  % CPUTime  : 
% 0.23/0.45  Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.23/0.45  
% 0.23/0.45  % SZS status Theorem
% 0.23/0.45  
% 0.23/0.45  % SZS output start Proof
% 0.23/0.45  Take the following subset of the input axioms:
% 0.23/0.45    fof(axiom_7a, axiom, ![X7, Y10]: (![Y20]: (~r1(Y20) | Y20!=Y10) | ~r2(X7, Y10))).
% 0.23/0.45    fof(zerouneqtwo, conjecture, ![Y1]: (![Y2]: (![Y3]: (~r1(Y3) | ~r2(Y3, Y2)) | ~r2(Y2, Y1)) | ![Y4]: (Y4!=Y1 | ~r1(Y4)))).
% 0.23/0.45  
% 0.23/0.45  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.23/0.45  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.23/0.45  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.23/0.45    fresh(y, y, x1...xn) = u
% 0.23/0.45    C => fresh(s, t, x1...xn) = v
% 0.23/0.45  where fresh is a fresh function symbol and x1..xn are the free
% 0.23/0.45  variables of u and v.
% 0.23/0.45  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.23/0.45  input problem has no model of domain size 1).
% 0.23/0.45  
% 0.23/0.45  The encoding turns the above axioms into the following unit equations and goals:
% 0.23/0.45  
% 0.23/0.45  Axiom 1 (zerouneqtwo): y4 = y1.
% 0.23/0.45  Axiom 2 (zerouneqtwo_2): r1(y4) = true2.
% 0.23/0.45  Axiom 3 (zerouneqtwo_3): r2(y2, y1) = true2.
% 0.23/0.45  
% 0.23/0.45  Goal 1 (axiom_7a): tuple(r1(X), r2(Y, X)) = tuple(true2, true2).
% 0.23/0.45  The goal is true when:
% 0.23/0.45    X = y1
% 0.23/0.45    Y = y2
% 0.23/0.45  
% 0.23/0.45  Proof:
% 0.23/0.45    tuple(r1(y1), r2(y2, y1))
% 0.23/0.45  = { by axiom 3 (zerouneqtwo_3) }
% 0.23/0.45    tuple(r1(y1), true2)
% 0.23/0.45  = { by axiom 1 (zerouneqtwo) R->L }
% 0.23/0.45    tuple(r1(y4), true2)
% 0.23/0.45  = { by axiom 2 (zerouneqtwo_2) }
% 0.23/0.45    tuple(true2, true2)
% 0.23/0.45  % SZS output end Proof
% 0.23/0.45  
% 0.23/0.45  RESULT: Theorem (the conjecture is true).
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