%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : ROB005-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n011.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 07:43:27 AM UTC 2025
% Result : Unsatisfiable 11.89s 12.03s
% Output : CNFRefutation 11.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of clauses : 54 ( 54 unt; 0 nHn; 17 RR)
% Number of literals : 54 ( 53 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 : 67 ( 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(c,c) = c,
file('theBenchmark.p',idempotence) ).
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(c,add(c,X)) = add(c,X),
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(c,add(X,c)) = add(X,c),
inference(equational,[status(thm)],[c1,c5]) ).
cnf(c7,plain,
add(c,add(X,add(c,Y))) = add(X,add(c,Y)),
inference(equational,[status(thm)],[c4,c5]) ).
cnf(c8,plain,
add(c,add(X,add(Y,c))) = add(X,add(c,Y)),
inference(equational,[status(thm)],[c2,c7]) ).
cnf(c9,plain,
add(c,add(X,add(Y,c))) = add(X,add(Y,c)),
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(c),negate(add(c,negate(c))))) = c,
inference(equational,[status(thm)],[c1,c10]) ).
cnf(c12,plain,
negate(add(negate(add(X,Y)),negate(add(Y,negate(X))))) = Y,
inference(equational,[status(thm)],[c2,c10]) ).
cnf(c13,plain,
negate(add(negate(add(X,Y)),negate(add(negate(Y),X)))) = X,
inference(equational,[status(thm)],[c2,c10]) ).
cnf(c14,plain,
negate(add(negate(add(X,Y)),negate(add(negate(X),Y)))) = Y,
inference(equational,[status(thm)],[c2,c13]) ).
cnf(c15,plain,
negate(add(negate(add(negate(X),Y)),negate(add(Y,X)))) = Y,
inference(equational,[status(thm)],[c2,c13]) ).
cnf(c18,plain,
add(c,add(X,add(Y,add(c,Z)))) = add(X,add(Y,add(c,Z))),
inference(equational,[status(thm)],[c3,c7]) ).
cnf(c21,plain,
negate(add(c,negate(add(c,add(negate(c),negate(c)))))) = negate(c),
inference(equational,[status(thm)],[c2,c5,c10,c11]) ).
cnf(c24,plain,
negate(add(negate(c),negate(add(c,add(negate(c),negate(c)))))) = c,
inference(equational,[status(thm)],[c2,c3,c5,c9,c12,c21]) ).
cnf(c25,plain,
negate(add(c,add(negate(c),negate(c)))) = negate(add(c,negate(c))),
inference(equational,[status(thm)],[c2,c14,c21,c24]) ).
cnf(c26,plain,
negate(add(c,negate(add(c,negate(c))))) = negate(c),
inference(equational,[status(thm)],[c21,c25]) ).
cnf(c30,plain,
negate(add(negate(add(c,X)),negate(add(c,add(X,negate(c)))))) = add(c,X),
inference(equational,[status(thm)],[c3,c4,c12]) ).
cnf(c32,plain,
negate(add(X,negate(add(X,add(Y,negate(add(X,negate(Y)))))))) = negate(add(X,negate(Y))),
inference(equational,[status(thm)],[c2,c5,c10,c13]) ).
cnf(c33,plain,
negate(add(X,negate(add(Y,add(X,negate(add(X,negate(Y)))))))) = negate(add(X,negate(Y))),
inference(equational,[status(thm)],[c2,c5,c12,c13]) ).
cnf(c46,plain,
negate(add(negate(add(c,X)),negate(add(c,add(negate(c),X))))) = add(c,X),
inference(equational,[status(thm)],[c2,c30]) ).
cnf(c47,plain,
negate(add(negate(add(X,c)),negate(add(c,add(X,negate(c)))))) = add(c,X),
inference(equational,[status(thm)],[c2,c30]) ).
cnf(c53,plain,
negate(add(negate(add(X,add(Y,Z))),negate(add(Y,negate(add(X,Z)))))) = Y,
inference(equational,[status(thm)],[c5,c10]) ).
cnf(c55,plain,
negate(add(negate(add(X,c)),negate(add(c,add(negate(c),X))))) = add(c,X),
inference(equational,[status(thm)],[c2,c47]) ).
cnf(c57,plain,
negate(add(negate(add(c,X)),negate(add(negate(c),add(X,c))))) = add(c,X),
inference(equational,[status(thm)],[c4,c8,c9,c46]) ).
cnf(c60,plain,
negate(add(negate(add(X,add(Y,Z))),negate(add(negate(Z),add(X,Y))))) = add(X,Y),
inference(equational,[status(thm)],[c3,c13]) ).
cnf(c74,plain,
negate(add(negate(add(X,negate(add(Y,Z)))),negate(add(Y,add(X,Z))))) = X,
inference(equational,[status(thm)],[c2,c53]) ).
cnf(c75,plain,
negate(add(c,negate(add(c,add(negate(c),add(negate(c),negate(c))))))) = negate(c),
inference(equational,[status(thm)],[c3,c5,c18,c21,c25,c26,c33]) ).
cnf(c76,plain,
negate(add(negate(add(c,add(negate(c),X))),negate(add(X,c)))) = add(c,X),
inference(equational,[status(thm)],[c2,c55]) ).
cnf(c85,plain,
negate(add(negate(add(X,add(Y,Z))),negate(add(negate(Y),add(Z,X))))) = add(Z,X),
inference(equational,[status(thm)],[c2,c3,c60]) ).
cnf(c110,plain,
negate(add(negate(add(negate(X),add(Y,Z))),negate(add(Z,add(X,Y))))) = add(Y,Z),
inference(equational,[status(thm)],[c2,c85]) ).
cnf(c121,plain,
negate(add(negate(c),negate(add(c,add(negate(c),add(negate(c),negate(c))))))) = c,
inference(equational,[status(thm)],[c2,c3,c5,c9,c11,c24,c25,c32]) ).
cnf(c122,plain,
negate(add(c,add(negate(c),add(negate(c),negate(c))))) = negate(add(c,negate(c))),
inference(equational,[status(thm)],[c2,c14,c75,c121]) ).
cnf(c123,plain,
add(c,add(negate(c),negate(c))) = add(c,negate(c)),
inference(equational,[status(thm)],[c3,c57,c76,c122]) ).
cnf(c125,plain,
add(c,add(negate(c),add(negate(c),X))) = add(c,add(negate(c),X)),
inference(equational,[status(thm)],[c3,c123]) ).
cnf(c145,plain,
negate(add(negate(add(negate(c),add(negate(add(c,negate(c))),X))),negate(add(X,c)))) = X,
inference(equational,[status(thm)],[c3,c11,c12]) ).
cnf(c146,plain,
negate(add(negate(c),negate(add(c,add(negate(c),negate(add(c,negate(c)))))))) = c,
inference(equational,[status(thm)],[c1,c2,c5,c145]) ).
cnf(c147,plain,
negate(add(c,negate(add(c,add(negate(c),negate(add(c,negate(c)))))))) = negate(c),
inference(equational,[status(thm)],[c74,c125,c146]) ).
cnf(c148,plain,
negate(add(c,add(negate(c),negate(add(c,negate(c)))))) = negate(add(c,negate(c))),
inference(equational,[status(thm)],[c2,c14,c146,c147]) ).
cnf(c149,plain,
add(c,negate(add(c,negate(c)))) = c,
inference(equational,[status(thm)],[c11,c26,c46,c148]) ).
cnf(c150,plain,
add(negate(add(c,negate(c))),X) = X,
inference(equational,[status(thm)],[c110,c145,c149]) ).
cnf(c156,plain,
negate(negate(add(X,negate(negate(X))))) = negate(negate(X)),
inference(equational,[status(thm)],[c33,c150]) ).
cnf(c158,plain,
negate(add(negate(X),negate(negate(X)))) = negate(add(c,negate(c))),
inference(equational,[status(thm)],[c10,c150]) ).
cnf(c159,plain,
negate(negate(negate(X))) = negate(X),
inference(equational,[status(thm)],[c10,c150,c156,c158]) ).
cnf(c160,plain,
negate(negate(X)) = X,
inference(equational,[status(thm)],[c15,c145,c150,c159]) ).
cnf(c249,plain,
add(negate(add(X,Y)),negate(add(X,negate(Y)))) = negate(X),
inference(equational,[status(thm)],[c10,c160]) ).
cnf(c265,plain,
add(negate(add(X,Y)),negate(add(negate(Y),X))) = negate(X),
inference(equational,[status(thm)],[c2,c249]) ).
cnf(c277,plain,
add(negate(add(X,Y)),negate(add(negate(X),Y))) = negate(Y),
inference(equational,[status(thm)],[c2,c265]) ).
cnf(g1,plain,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) = b,
inference(equational,[status(thm)],[c160,c277]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ROB005-1 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n011.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 : Mon Jul 14 16:38:49 EDT 2025
% 0.11/0.32 % CPUTime :
% 11.89/12.03 % SZS status Unsatisfiable
% 11.89/12.03 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------