%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : ROB004-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n012.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 1.15s 1.37s
% Output : CNFRefutation 1.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 7
% Syntax : Number of clauses : 59 ( 59 unt; 0 nHn; 11 RR)
% Number of literals : 59 ( 58 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 77 ( 9 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,
negate(d) = c,
file('theBenchmark.p',negate_d_is_c) ).
cnf(c2,axiom,
add(c,d) = d,
file('theBenchmark.p',c_plus_d_is_d) ).
cnf(c3,axiom,
add(c,c) = c,
file('theBenchmark.p',c_plus_c_is_c) ).
cnf(c4,axiom,
add(X,Y) = add(Y,X),
file('ROB001-0.ax',commutativity_of_add) ).
cnf(c5,axiom,
add(add(X,Y),Z) = add(X,add(Y,Z)),
file('ROB001-0.ax',associativity_of_add) ).
cnf(c6,plain,
add(c,add(c,X)) = add(c,X),
inference(equational,[status(thm)],[c3,c5]) ).
cnf(c7,plain,
add(c,add(d,X)) = add(d,X),
inference(equational,[status(thm)],[c2,c5]) ).
cnf(c8,plain,
add(X,add(Y,Z)) = add(Y,add(X,Z)),
inference(equational,[status(thm)],[c4,c5]) ).
cnf(c9,plain,
add(c,add(X,d)) = add(X,d),
inference(equational,[status(thm)],[c2,c8]) ).
cnf(c10,plain,
add(c,add(X,c)) = add(X,c),
inference(equational,[status(thm)],[c3,c8]) ).
cnf(c11,plain,
add(c,add(X,add(d,Y))) = add(d,add(X,Y)),
inference(equational,[status(thm)],[c7,c8]) ).
cnf(c12,plain,
add(c,add(X,add(c,Y))) = add(c,add(X,Y)),
inference(equational,[status(thm)],[c6,c8]) ).
cnf(c14,plain,
add(c,add(X,add(Y,d))) = add(d,add(X,Y)),
inference(equational,[status(thm)],[c4,c11]) ).
cnf(c15,plain,
add(d,add(X,c)) = add(X,d),
inference(equational,[status(thm)],[c2,c5,c9,c10,c14]) ).
cnf(c22,axiom,
negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X,
file('ROB001-0.ax',robbins_axiom) ).
cnf(c23,plain,
negate(add(c,negate(c))) = c,
inference(equational,[status(thm)],[c1,c2,c3,c22]) ).
cnf(c24,plain,
negate(add(c,negate(add(c,negate(negate(c)))))) = c,
inference(equational,[status(thm)],[c22,c23]) ).
cnf(c25,plain,
negate(add(negate(add(X,c)),negate(add(X,d)))) = X,
inference(equational,[status(thm)],[c1,c4,c22]) ).
cnf(c26,plain,
negate(add(negate(add(X,c)),negate(add(d,X)))) = X,
inference(equational,[status(thm)],[c4,c25]) ).
cnf(c27,plain,
add(X,c) = X,
inference(equational,[status(thm)],[c3,c5,c15,c25,c26]) ).
cnf(c28,plain,
add(c,X) = X,
inference(equational,[status(thm)],[c10,c27]) ).
cnf(c29,plain,
negate(negate(c)) = c,
inference(equational,[status(thm)],[c1,c3,c26,c27]) ).
cnf(c30,plain,
negate(add(negate(X),negate(negate(X)))) = c,
inference(equational,[status(thm)],[c22,c28]) ).
cnf(c31,plain,
negate(add(X,negate(X))) = c,
inference(equational,[status(thm)],[c22,c30]) ).
cnf(c33,plain,
negate(add(negate(X),negate(add(X,d)))) = X,
inference(equational,[status(thm)],[c4,c25,c28]) ).
cnf(c34,plain,
negate(negate(add(negate(c),d))) = negate(c),
inference(equational,[status(thm)],[c3,c24,c28,c29,c33]) ).
cnf(c36,plain,
negate(add(negate(add(X,Y)),negate(add(Y,negate(X))))) = Y,
inference(equational,[status(thm)],[c4,c22]) ).
cnf(c37,plain,
d = negate(c),
inference(equational,[status(thm)],[c1,c2,c4,c28,c34,c36]) ).
cnf(c38,plain,
negate(add(negate(X),negate(add(negate(c),X)))) = X,
inference(equational,[status(thm)],[c1,c4,c27,c36,c37]) ).
cnf(c39,plain,
negate(add(negate(X),negate(add(X,negate(c))))) = X,
inference(equational,[status(thm)],[c6,c28,c36]) ).
cnf(c42,plain,
negate(add(negate(add(X,Y)),negate(add(negate(Y),X)))) = X,
inference(equational,[status(thm)],[c4,c22]) ).
cnf(c45,plain,
negate(add(negate(add(negate(X),Y)),negate(add(Y,X)))) = Y,
inference(equational,[status(thm)],[c4,c42]) ).
cnf(c46,plain,
negate(add(negate(add(X,negate(Y))),negate(add(Y,X)))) = X,
inference(equational,[status(thm)],[c4,c36]) ).
cnf(c47,plain,
negate(add(negate(add(X,Y)),negate(add(negate(X),Y)))) = Y,
inference(equational,[status(thm)],[c4,c42]) ).
cnf(c48,plain,
add(negate(add(X,negate(X))),Y) = Y,
inference(equational,[status(thm)],[c28,c31]) ).
cnf(c51,plain,
negate(negate(add(X,negate(negate(X))))) = negate(negate(X)),
inference(equational,[status(thm)],[c27,c30,c47]) ).
cnf(c52,plain,
negate(negate(X)) = X,
inference(equational,[status(thm)],[c22,c28,c31,c51]) ).
cnf(c53,plain,
add(X,X) = X,
inference(equational,[status(thm)],[c51,c52]) ).
cnf(c54,plain,
negate(c) = add(X,negate(X)),
inference(equational,[status(thm)],[c31,c52]) ).
cnf(c57,plain,
add(X,add(X,Y)) = add(X,Y),
inference(equational,[status(thm)],[c5,c53]) ).
cnf(c58,plain,
add(X,negate(c)) = add(X,negate(X)),
inference(equational,[status(thm)],[c54,c57]) ).
cnf(c59,plain,
add(X,negate(c)) = negate(c),
inference(equational,[status(thm)],[c54,c58]) ).
cnf(c61,plain,
add(negate(c),X) = negate(c),
inference(equational,[status(thm)],[c11,c27,c28,c29,c37,c53,c58,c59]) ).
cnf(c62,plain,
negate(add(X,add(Y,negate(add(X,Y))))) = c,
inference(equational,[status(thm)],[c5,c12,c27,c28,c45,c52]) ).
cnf(c63,plain,
negate(c) = add(X,add(Y,negate(add(X,Y)))),
inference(equational,[status(thm)],[c3,c5,c29,c39,c59,c62]) ).
cnf(c64,plain,
negate(c) = add(X,add(Y,negate(Y))),
inference(equational,[status(thm)],[c12,c28,c59,c63]) ).
cnf(c65,plain,
negate(c) = add(X,add(Y,negate(X))),
inference(equational,[status(thm)],[c8,c64]) ).
cnf(c68,plain,
add(X,add(negate(X),Y)) = add(X,negate(X)),
inference(equational,[status(thm)],[c5,c28,c29,c45,c52,c64]) ).
cnf(c69,plain,
add(negate(X),add(Y,X)) = negate(c),
inference(equational,[status(thm)],[c27,c29,c38,c61,c65]) ).
cnf(c71,plain,
add(X,negate(add(negate(X),Y))) = X,
inference(equational,[status(thm)],[c22,c48,c52,c68]) ).
cnf(c74,plain,
add(X,negate(add(Y,negate(add(X,Y))))) = X,
inference(equational,[status(thm)],[c4,c27,c45,c52,c62]) ).
cnf(c79,plain,
add(negate(X),negate(add(X,Y))) = negate(X),
inference(equational,[status(thm)],[c27,c29,c39,c59,c71]) ).
cnf(c80,plain,
add(negate(X),negate(add(Y,X))) = negate(X),
inference(equational,[status(thm)],[c5,c27,c29,c69,c74]) ).
cnf(c84,plain,
add(X,negate(add(Y,X))) = add(X,negate(Y)),
inference(equational,[status(thm)],[c4,c5,c27,c46,c52,c62,c79]) ).
cnf(c118,plain,
add(negate(add(X,Y)),negate(add(Y,negate(X)))) = negate(Y),
inference(equational,[status(thm)],[c4,c80,c84]) ).
cnf(c119,plain,
add(negate(add(X,Y)),negate(add(negate(X),Y))) = negate(Y),
inference(equational,[status(thm)],[c4,c118]) ).
cnf(g1,plain,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) = b,
inference(equational,[status(thm)],[c52,c119]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : ROB004-1 : TPTP v9.0.0. Released v1.0.0.
% 0.12/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n012.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 16:38:34 EDT 2025
% 0.12/0.33 % CPUTime :
% 1.15/1.37 % SZS status Unsatisfiable
% 1.15/1.37 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------