%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : ROB023-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% 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 : Tue Jul 15 07:43:29 AM UTC 2025
% Result : Unsatisfiable 5.18s 5.43s
% Output : CNFRefutation 5.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of clauses : 27 ( 27 unt; 0 nHn; 3 RR)
% Number of literals : 27 ( 26 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b,
file('theBenchmark.p',prove_huntingtons_axiom) ).
cnf(c1,axiom,
add(X,X) = X,
file('theBenchmark.p',x_plus_x_is_x) ).
cnf(c2,axiom,
add(X,Y) = add(Y,X),
file('ROB001-0.ax',commutativity_of_add) ).
cnf(c3,axiom,
add(add(X,Y),Z) = add(X,add(Y,Z)),
file('ROB001-0.ax',associativity_of_add) ).
cnf(c4,plain,
add(X,add(X,Y)) = add(X,Y),
inference(equational,[status(thm)],[c1,c3]) ).
cnf(c5,plain,
add(X,add(Y,Z)) = add(Y,add(X,Z)),
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c6,plain,
add(X,add(Y,X)) = add(Y,X),
inference(equational,[status(thm)],[c1,c5]) ).
cnf(c7,plain,
add(X,add(Y,add(X,Z))) = add(Y,add(X,Z)),
inference(equational,[status(thm)],[c4,c5]) ).
cnf(c9,plain,
add(X,add(Y,add(Z,X))) = add(Y,add(Z,X)),
inference(equational,[status(thm)],[c6,c7]) ).
cnf(c10,axiom,
negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X,
file('ROB001-0.ax',robbins_axiom) ).
cnf(c11,plain,
negate(add(negate(X),negate(add(X,negate(X))))) = X,
inference(equational,[status(thm)],[c1,c10]) ).
cnf(c12,plain,
negate(add(X,negate(add(X,negate(X))))) = negate(X),
inference(equational,[status(thm)],[c2,c6,c10,c11]) ).
cnf(c13,plain,
negate(add(negate(negate(X)),negate(add(X,negate(X))))) = negate(X),
inference(equational,[status(thm)],[c1,c2,c10]) ).
cnf(c14,plain,
negate(add(negate(add(X,Y)),negate(add(Y,negate(X))))) = Y,
inference(equational,[status(thm)],[c2,c10]) ).
cnf(c15,plain,
negate(add(negate(add(X,Y)),negate(add(negate(Y),X)))) = X,
inference(equational,[status(thm)],[c2,c10]) ).
cnf(c17,plain,
negate(add(negate(add(X,Y)),negate(add(negate(X),Y)))) = Y,
inference(equational,[status(thm)],[c2,c15]) ).
cnf(c26,plain,
negate(add(X,negate(add(X,add(negate(Y),negate(add(X,Y))))))) = negate(add(X,Y)),
inference(equational,[status(thm)],[c2,c5,c10]) ).
cnf(c38,plain,
negate(add(negate(X),negate(add(X,add(negate(X),negate(negate(X))))))) = negate(negate(X)),
inference(equational,[status(thm)],[c2,c5,c10,c13]) ).
cnf(c40,plain,
negate(add(X,negate(add(X,negate(add(Y,add(X,Z))))))) = negate(add(Y,add(X,Z))),
inference(equational,[status(thm)],[c1,c7,c26]) ).
cnf(c41,plain,
negate(add(X,add(negate(X),negate(negate(X))))) = negate(add(negate(X),negate(negate(X)))),
inference(equational,[status(thm)],[c38,c40]) ).
cnf(c42,plain,
negate(add(X,add(negate(X),negate(add(X,negate(X)))))) = negate(add(X,negate(X))),
inference(equational,[status(thm)],[c2,c3,c5,c9,c11,c41]) ).
cnf(c43,plain,
add(negate(X),negate(add(X,negate(X)))) = negate(X),
inference(equational,[status(thm)],[c2,c4,c11,c12,c17,c42]) ).
cnf(c44,plain,
negate(negate(X)) = X,
inference(equational,[status(thm)],[c11,c43]) ).
cnf(c93,plain,
add(negate(add(X,Y)),negate(add(Y,negate(X)))) = negate(Y),
inference(equational,[status(thm)],[c14,c44]) ).
cnf(c117,plain,
add(negate(add(X,Y)),negate(add(negate(X),Y))) = negate(Y),
inference(equational,[status(thm)],[c2,c93]) ).
cnf(g1,plain,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) = b,
inference(equational,[status(thm)],[c44,c117]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : ROB023-1 : TPTP v9.0.0. Released v1.0.0.
% 0.00/0.10 % Command : run_Leo-III %s %d THM
% 0.10/0.31 % Computer : n016.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon Jul 14 16:40:34 EDT 2025
% 0.10/0.31 % CPUTime :
% 5.18/5.43 % SZS status Unsatisfiable
% 5.18/5.43 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------