%------------------------------------------------------------------------------
% File     : Twee---2.5.0
% Problem  : SWW469_1 : TPTP v8.2.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : parallel-twee /export/starexec/sandbox2/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding

% Computer : n028.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 : Mon Jun 24 18:27:02 EDT 2024

% Result   : Theorem 0.17s 0.36s
% Output   : Proof 0.17s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SWW469_1 : TPTP v8.2.0. Released v5.3.0.
% 0.00/0.11  % Command  : parallel-twee /export/starexec/sandbox2/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.11/0.32  % Computer : n028.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Wed Jun 19 08:09:24 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.17/0.36  Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.17/0.36  
% 0.17/0.36  % SZS status Theorem
% 0.17/0.36  
% 0.17/0.36  % SZS output start Proof
% 0.17/0.36  Take the following subset of the input axioms:
% 0.17/0.36    tff(type, type, state: $tType).
% 0.17/0.36    tff(type, type, hoare_1310879719gleton: $i).
% 0.17/0.36    tff(conj_1, conjecture, ![T: state]: ~![S: $i]: S=T).
% 0.17/0.36    tff(fact_0_state__not__singleton__def, axiom, hoare_1310879719gleton <=> ?[S2: state, T2: state]: S2!=T2).
% 0.17/0.36  
% 0.17/0.36  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.17/0.36  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.17/0.36  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.17/0.36    fresh(y, y, x1...xn) = u
% 0.17/0.36    C => fresh(s, t, x1...xn) = v
% 0.17/0.36  where fresh is a fresh function symbol and x1..xn are the free
% 0.17/0.36  variables of u and v.
% 0.17/0.36  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.17/0.36  input problem has no model of domain size 1).
% 0.17/0.36  
% 0.17/0.36  The encoding turns the above axioms into the following unit equations and goals:
% 0.17/0.36  
% 0.17/0.36  Axiom 1 (conj_1): X = t.
% 0.17/0.36  
% 0.17/0.36  Lemma 4: tuple(X, Y) = true.
% 0.17/0.36  Proof:
% 0.17/0.36    tuple(X, Y)
% 0.17/0.36  = { by axiom 1 (conj_1) }
% 0.17/0.36    t
% 0.17/0.36  = { by axiom 1 (conj_1) R->L }
% 0.17/0.36    true
% 0.17/0.36  
% 0.17/0.36  Goal 1 (fact_0_state__not__singleton__def_1): tuple(s, hoare_1310879719gleton) = tuple(t2, true).
% 0.17/0.36  Proof:
% 0.17/0.36    tuple(s, hoare_1310879719gleton)
% 0.17/0.36  = { by lemma 4 }
% 0.17/0.36    true
% 0.17/0.36  = { by lemma 4 R->L }
% 0.17/0.36    tuple(t2, true)
% 0.17/0.36  % SZS output end Proof
% 0.17/0.36  
% 0.17/0.36  RESULT: Theorem (the conjecture is true).
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