%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : ROB003-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n010.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 07:43:26 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.49s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of clauses : 18 ( 18 unt; 0 nHn; 4 RR)
% Number of literals : 18 ( 17 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 23 ( 2 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,c) = c,
file('theBenchmark.p',there_exists_a_constant) ).
cnf(c2,axiom,
add(X,Y) = add(Y,X),
file('ROB001-0.ax',commutativity_of_add) ).
cnf(c3,plain,
add(c,X) = c,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,axiom,
add(add(X,Y),Z) = add(X,add(Y,Z)),
file('ROB001-0.ax',associativity_of_add) ).
cnf(c6,axiom,
negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X,
file('ROB001-0.ax',robbins_axiom) ).
cnf(c7,plain,
negate(add(negate(c),negate(c))) = c,
inference(equational,[status(thm)],[c3,c6]) ).
cnf(c8,plain,
negate(add(negate(c),negate(add(X,negate(c))))) = X,
inference(equational,[status(thm)],[c1,c6]) ).
cnf(c9,plain,
negate(add(negate(c),negate(add(negate(c),X)))) = X,
inference(equational,[status(thm)],[c2,c8]) ).
cnf(c10,plain,
negate(add(negate(add(X,Y)),negate(add(Y,negate(X))))) = Y,
inference(equational,[status(thm)],[c2,c6]) ).
cnf(c11,plain,
negate(add(negate(add(X,Y)),negate(add(negate(Y),X)))) = X,
inference(equational,[status(thm)],[c2,c6]) ).
cnf(c13,plain,
negate(add(negate(add(X,Y)),negate(add(negate(X),Y)))) = Y,
inference(equational,[status(thm)],[c2,c11]) ).
cnf(c14,plain,
negate(add(negate(add(X,negate(Y))),negate(add(Y,X)))) = X,
inference(equational,[status(thm)],[c2,c10]) ).
cnf(c15,plain,
add(negate(c),X) = X,
inference(equational,[status(thm)],[c1,c4,c7,c9,c14]) ).
cnf(c16,plain,
negate(negate(X)) = X,
inference(equational,[status(thm)],[c9,c15]) ).
cnf(c36,plain,
add(negate(add(X,Y)),negate(add(negate(X),Y))) = negate(Y),
inference(equational,[status(thm)],[c13,c16]) ).
cnf(g1,plain,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) = b,
inference(equational,[status(thm)],[c16,c36]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ROB003-1 : TPTP v9.0.0. Released v1.0.0.
% 0.06/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n010.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 16:38:49 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.49 % SZS status Unsatisfiable
% 0.20/0.49 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------