%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SWV415+1 : TPTP v8.1.2. Released v3.3.0.
% 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 23:04:09 EDT 2023

% Result   : Theorem 0.20s 0.48s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWV415+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : n011.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 : Tue Aug 29 09:08:26 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.48  Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.48  
% 0.20/0.48  % SZS status Theorem
% 0.20/0.48  
% 0.20/0.48  % SZS output start Proof
% 0.20/0.48  Take the following subset of the input axioms:
% 0.20/0.49    fof(ax42, axiom, ![U, V, W, X]: insert_cpq(triple(U, V, W), X)=triple(insert_pqp(U, X), insert_slb(V, pair(X, bottom)), W)).
% 0.20/0.49    fof(ax55, axiom, ![Y, U2, V2, W2, X2]: i(triple(U2, insert_slb(V2, pair(X2, Y)), W2))=insert_pq(i(triple(U2, V2, W2)), X2)).
% 0.20/0.49    fof(co2, conjecture, ![U2, V2, W2, X2]: i(insert_cpq(triple(U2, V2, W2), X2))=insert_pq(i(triple(U2, V2, W2)), X2)).
% 0.20/0.49    fof(main2_l12, lemma, ![U2, V2, W2, X2, Y2]: i(triple(U2, W2, X2))=i(triple(V2, W2, Y2))).
% 0.20/0.49  
% 0.20/0.49  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.49  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.49  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.49    fresh(y, y, x1...xn) = u
% 0.20/0.49    C => fresh(s, t, x1...xn) = v
% 0.20/0.49  where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.49  variables of u and v.
% 0.20/0.49  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.49  input problem has no model of domain size 1).
% 0.20/0.49  
% 0.20/0.49  The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.49  
% 0.20/0.49  Axiom 1 (main2_l12): i(triple(X, Y, Z)) = i(triple(W, Y, V)).
% 0.20/0.49  Axiom 2 (ax55): i(triple(X, insert_slb(Y, pair(Z, W)), V)) = insert_pq(i(triple(X, Y, V)), Z).
% 0.20/0.49  Axiom 3 (ax42): insert_cpq(triple(X, Y, Z), W) = triple(insert_pqp(X, W), insert_slb(Y, pair(W, bottom)), Z).
% 0.20/0.49  
% 0.20/0.49  Goal 1 (co2): i(insert_cpq(triple(u, v, w), x)) = insert_pq(i(triple(u, v, w)), x).
% 0.20/0.49  Proof:
% 0.20/0.49    i(insert_cpq(triple(u, v, w), x))
% 0.20/0.49  = { by axiom 3 (ax42) }
% 0.20/0.49    i(triple(insert_pqp(u, x), insert_slb(v, pair(x, bottom)), w))
% 0.20/0.49  = { by axiom 1 (main2_l12) }
% 0.20/0.49    i(triple(u, insert_slb(v, pair(x, bottom)), w))
% 0.20/0.49  = { by axiom 2 (ax55) }
% 0.20/0.49    insert_pq(i(triple(u, v, w)), x)
% 0.20/0.49  % SZS output end Proof
% 0.20/0.49  
% 0.20/0.49  RESULT: Theorem (the conjecture is true).
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