%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SWW469+5 : TPTP v8.1.2. Released v5.3.0.
% 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 : n015.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 00:55:01 EDT 2023

% Result   : Theorem 0.20s 0.55s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWW469+5 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35  % Computer : n015.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Sun Aug 27 19:21:54 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.55  Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.55  
% 0.20/0.55  % SZS status Theorem
% 0.20/0.55  
% 0.20/0.55  % SZS output start Proof
% 0.20/0.55  Take the following subset of the input axioms:
% 0.20/0.55    fof(conj_0, hypothesis, hBOOL(hoare_1883395792gleton)).
% 0.20/0.55    fof(conj_1, conjecture, ![T]: ~![S]: ti(state, S)=ti(state, T)).
% 0.20/0.55    fof(fact_0_state__not__singleton__def, axiom, hBOOL(hoare_1883395792gleton) <=> ?[S2, T2]: ti(state, S2)!=ti(state, T2)).
% 0.20/0.55  
% 0.20/0.55  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.55  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.55  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.55    fresh(y, y, x1...xn) = u
% 0.20/0.55    C => fresh(s, t, x1...xn) = v
% 0.20/0.55  where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.55  variables of u and v.
% 0.20/0.55  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.55  input problem has no model of domain size 1).
% 0.20/0.55  
% 0.20/0.55  The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.55  
% 0.20/0.55  Axiom 1 (conj_0): hBOOL(hoare_1883395792gleton) = true.
% 0.20/0.55  Axiom 2 (conj_1): ti(state, X) = ti(state, t).
% 0.20/0.55  
% 0.20/0.55  Goal 1 (fact_0_state__not__singleton__def_1): tuple(ti(state, s), hBOOL(hoare_1883395792gleton)) = tuple(ti(state, t2), true).
% 0.20/0.55  Proof:
% 0.20/0.55    tuple(ti(state, s), hBOOL(hoare_1883395792gleton))
% 0.20/0.55  = { by axiom 1 (conj_0) }
% 0.20/0.55    tuple(ti(state, s), true)
% 0.20/0.55  = { by axiom 2 (conj_1) }
% 0.20/0.55    tuple(ti(state, t), true)
% 0.20/0.55  = { by axiom 2 (conj_1) R->L }
% 0.20/0.55    tuple(ti(state, t2), true)
% 0.20/0.55  % SZS output end Proof
% 0.20/0.55  
% 0.20/0.55  RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------