%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : ROB022-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n013.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 11.75s 11.92s
% Output : CNFRefutation 11.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of clauses : 34 ( 34 unt; 0 nHn; 12 RR)
% Number of literals : 34 ( 33 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 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,Y) = add(Y,X),
file('ROB001-0.ax',commutativity_of_add) ).
cnf(c2,axiom,
add(c,negate(c)) = c,
file('theBenchmark.p',condition) ).
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(Y,Z)) = add(Y,add(X,Z)),
inference(equational,[status(thm)],[c1,c3]) ).
cnf(c5,plain,
add(c,add(negate(c),X)) = add(c,X),
inference(equational,[status(thm)],[c2,c3]) ).
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(c),negate(add(c,c)))) = c,
inference(equational,[status(thm)],[c1,c2,c10]) ).
cnf(c13,plain,
negate(add(negate(add(X,Y)),negate(add(negate(Y),X)))) = X,
inference(equational,[status(thm)],[c1,c10]) ).
cnf(c14,plain,
negate(add(negate(add(X,Y)),negate(add(Y,negate(X))))) = Y,
inference(equational,[status(thm)],[c1,c10]) ).
cnf(c15,plain,
negate(add(c,negate(add(c,c)))) = negate(c),
inference(equational,[status(thm)],[c1,c2,c3,c11,c14]) ).
cnf(c18,plain,
negate(add(negate(add(negate(X),Y)),negate(add(Y,X)))) = Y,
inference(equational,[status(thm)],[c1,c13]) ).
cnf(c19,plain,
negate(add(negate(add(X,Y)),negate(add(negate(X),Y)))) = Y,
inference(equational,[status(thm)],[c1,c14]) ).
cnf(c20,plain,
negate(add(c,c)) = negate(c),
inference(equational,[status(thm)],[c1,c2,c11,c15,c19]) ).
cnf(c21,plain,
negate(add(negate(c),negate(c))) = c,
inference(equational,[status(thm)],[c11,c20]) ).
cnf(c23,plain,
negate(add(negate(add(X,negate(Y))),negate(add(Y,X)))) = X,
inference(equational,[status(thm)],[c1,c14]) ).
cnf(c24,plain,
negate(add(negate(c),negate(add(c,add(c,c))))) = c,
inference(equational,[status(thm)],[c3,c15,c23]) ).
cnf(c25,plain,
negate(add(c,negate(add(c,add(c,c))))) = negate(c),
inference(equational,[status(thm)],[c2,c3,c23,c24]) ).
cnf(c26,plain,
negate(add(c,add(c,c))) = negate(c),
inference(equational,[status(thm)],[c1,c2,c19,c24,c25]) ).
cnf(c27,plain,
add(c,c) = c,
inference(equational,[status(thm)],[c2,c3,c20,c21,c23,c26]) ).
cnf(c56,plain,
negate(add(X,negate(add(Y,add(X,negate(add(X,negate(Y)))))))) = negate(add(X,negate(Y))),
inference(equational,[status(thm)],[c1,c4,c13,c14]) ).
cnf(c85,plain,
negate(add(negate(add(X,add(Y,Z))),negate(add(negate(add(X,Z)),Y)))) = Y,
inference(equational,[status(thm)],[c4,c13]) ).
cnf(c86,plain,
negate(add(negate(add(X,add(Y,Z))),negate(add(Y,negate(add(X,Z)))))) = Y,
inference(equational,[status(thm)],[c4,c10]) ).
cnf(c91,plain,
negate(add(negate(add(c,X)),negate(add(negate(c),add(X,negate(c)))))) = X,
inference(equational,[status(thm)],[c1,c11,c27,c85]) ).
cnf(c103,plain,
add(negate(c),X) = X,
inference(equational,[status(thm)],[c3,c5,c14,c91]) ).
cnf(c108,plain,
negate(add(negate(X),negate(negate(X)))) = negate(c),
inference(equational,[status(thm)],[c10,c103]) ).
cnf(c109,plain,
negate(add(X,negate(X))) = negate(c),
inference(equational,[status(thm)],[c86,c108]) ).
cnf(c111,plain,
negate(negate(add(X,negate(negate(X))))) = negate(negate(X)),
inference(equational,[status(thm)],[c56,c103]) ).
cnf(c116,plain,
add(negate(add(X,negate(X))),Y) = Y,
inference(equational,[status(thm)],[c103,c109]) ).
cnf(c117,plain,
negate(negate(X)) = X,
inference(equational,[status(thm)],[c10,c111,c116]) ).
cnf(c249,plain,
add(negate(add(negate(X),Y)),negate(add(Y,X))) = negate(Y),
inference(equational,[status(thm)],[c18,c117]) ).
cnf(c282,plain,
add(negate(add(X,Y)),negate(add(negate(X),Y))) = negate(Y),
inference(equational,[status(thm)],[c1,c249]) ).
cnf(g1,plain,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) = b,
inference(equational,[status(thm)],[c117,c282]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ROB022-1 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 14 16:40:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 11.75/11.92 % SZS status Unsatisfiable
% 11.75/11.92 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------