%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : NUM318+1 : TPTP v8.1.2. Released v3.1.0.
% 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 : n008.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 11:55:53 EDT 2023

% Result   : Theorem 7.90s 1.44s
% Output   : Proof 7.90s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : NUM318+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.15  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.36  % Computer : n008.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Fri Aug 25 15:14:47 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 7.90/1.44  Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 7.90/1.44  
% 7.90/1.44  % SZS status Theorem
% 7.90/1.44  
% 7.90/1.44  % SZS output start Proof
% 7.90/1.44  Take the following subset of the input axioms:
% 7.90/1.44    fof(rdn5, axiom, rdn_translate(n5, rdn_pos(rdnn(n5)))).
% 7.90/1.44    fof(rdnn5, axiom, rdn_translate(nn5, rdn_neg(rdnn(n5)))).
% 7.90/1.44    fof(sum_entry_point_posx_negx, axiom, ![RDN_X, POS_X, NEG_X]: ((rdn_translate(POS_X, rdn_pos(RDN_X)) & rdn_translate(NEG_X, rdn_neg(RDN_X))) => sum(POS_X, NEG_X, n0))).
% 7.90/1.44    fof(sum_n5_nn5_n0, conjecture, sum(n5, nn5, n0)).
% 7.90/1.44  
% 7.90/1.44  Now clausify the problem and encode Horn clauses using encoding 3 of
% 7.90/1.44  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 7.90/1.44  We repeatedly replace C & s=t => u=v by the two clauses:
% 7.90/1.44    fresh(y, y, x1...xn) = u
% 7.90/1.44    C => fresh(s, t, x1...xn) = v
% 7.90/1.44  where fresh is a fresh function symbol and x1..xn are the free
% 7.90/1.44  variables of u and v.
% 7.90/1.44  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 7.90/1.44  input problem has no model of domain size 1).
% 7.90/1.44  
% 7.90/1.44  The encoding turns the above axioms into the following unit equations and goals:
% 7.90/1.44  
% 7.90/1.44  Axiom 1 (rdn5): rdn_translate(n5, rdn_pos(rdnn(n5))) = true2.
% 7.90/1.44  Axiom 2 (rdnn5): rdn_translate(nn5, rdn_neg(rdnn(n5))) = true2.
% 7.90/1.44  Axiom 3 (sum_entry_point_posx_negx): fresh7(X, X, Y, Z) = true2.
% 7.90/1.44  Axiom 4 (sum_entry_point_posx_negx): fresh8(X, X, Y, Z, W) = sum(Y, Z, n0).
% 7.90/1.44  Axiom 5 (sum_entry_point_posx_negx): fresh8(rdn_translate(X, rdn_neg(Y)), true2, Z, X, Y) = fresh7(rdn_translate(Z, rdn_pos(Y)), true2, Z, X).
% 7.90/1.44  
% 7.90/1.44  Goal 1 (sum_n5_nn5_n0): sum(n5, nn5, n0) = true2.
% 7.90/1.44  Proof:
% 7.90/1.44    sum(n5, nn5, n0)
% 7.90/1.44  = { by axiom 4 (sum_entry_point_posx_negx) R->L }
% 7.90/1.44    fresh8(true2, true2, n5, nn5, rdnn(n5))
% 7.90/1.44  = { by axiom 2 (rdnn5) R->L }
% 7.90/1.44    fresh8(rdn_translate(nn5, rdn_neg(rdnn(n5))), true2, n5, nn5, rdnn(n5))
% 7.90/1.44  = { by axiom 5 (sum_entry_point_posx_negx) }
% 7.90/1.44    fresh7(rdn_translate(n5, rdn_pos(rdnn(n5))), true2, n5, nn5)
% 7.90/1.44  = { by axiom 1 (rdn5) }
% 7.90/1.44    fresh7(true2, true2, n5, nn5)
% 7.90/1.44  = { by axiom 3 (sum_entry_point_posx_negx) }
% 7.90/1.44    true2
% 7.90/1.44  % SZS output end Proof
% 7.90/1.44  
% 7.90/1.44  RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------