%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : NUM854+2 : TPTP v8.1.2. Released v4.1.0.
% 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 : n016.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 11:58:40 EDT 2023

% Result   : Theorem 0.16s 0.39s
% Output   : Proof 0.16s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM854+2 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.32  % Computer : n016.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 : Fri Aug 25 14:37:55 EDT 2023
% 0.11/0.33  % CPUTime  : 
% 0.16/0.39  Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.16/0.39  
% 0.16/0.39  % SZS status Theorem
% 0.16/0.39  
% 0.16/0.39  % SZS output start Proof
% 0.16/0.39  Take the following subset of the input axioms:
% 0.16/0.39    fof('ass(cond(299, 0), 2)', axiom, ![Vd456, Vd457, Vd458]: (greater(Vd457, Vd458) => greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))).
% 0.16/0.39    fof('holds(conjunct1(314), 510, 0)', axiom, greater(vd508, vd509)).
% 0.16/0.39    fof('holds(conjunct1(315), 514, 0)', conjecture, greater(vmul(vd508, vd511), vmul(vd509, vd511))).
% 0.16/0.39  
% 0.16/0.39  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.16/0.39  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.16/0.39  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.16/0.39    fresh(y, y, x1...xn) = u
% 0.16/0.39    C => fresh(s, t, x1...xn) = v
% 0.16/0.39  where fresh is a fresh function symbol and x1..xn are the free
% 0.16/0.39  variables of u and v.
% 0.16/0.39  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.16/0.39  input problem has no model of domain size 1).
% 0.16/0.39  
% 0.16/0.39  The encoding turns the above axioms into the following unit equations and goals:
% 0.16/0.39  
% 0.16/0.39  Axiom 1 (holds(conjunct1(314), 510, 0)): greater(vd508, vd509) = true2.
% 0.16/0.39  Axiom 2 (ass(cond(299, 0), 2)): fresh8(X, X, Y, Z, W) = true2.
% 0.16/0.39  Axiom 3 (ass(cond(299, 0), 2)): fresh8(greater(X, Y), true2, Z, X, Y) = greater(vmul(X, Z), vmul(Y, Z)).
% 0.16/0.39  
% 0.16/0.39  Goal 1 (holds(conjunct1(315), 514, 0)): greater(vmul(vd508, vd511), vmul(vd509, vd511)) = true2.
% 0.16/0.39  Proof:
% 0.16/0.39    greater(vmul(vd508, vd511), vmul(vd509, vd511))
% 0.16/0.39  = { by axiom 3 (ass(cond(299, 0), 2)) R->L }
% 0.16/0.39    fresh8(greater(vd508, vd509), true2, vd511, vd508, vd509)
% 0.16/0.39  = { by axiom 1 (holds(conjunct1(314), 510, 0)) }
% 0.16/0.39    fresh8(true2, true2, vd511, vd508, vd509)
% 0.16/0.39  = { by axiom 2 (ass(cond(299, 0), 2)) }
% 0.16/0.39    true2
% 0.16/0.39  % SZS output end Proof
% 0.16/0.39  
% 0.16/0.39  RESULT: Theorem (the conjecture is true).
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