%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : BOO029-1 : TPTP v9.0.0. Released v2.2.0.
% 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 06:14:48 AM UTC 2025
% Result : Unsatisfiable 0.48s 0.67s
% Output : CNFRefutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 17 ( 17 unt; 0 nHn; 3 RR)
% Number of literals : 17 ( 16 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 33 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
add(b,inverse(b)) != add(a,inverse(a)),
file('theBenchmark.p',prove_equal_inverse) ).
cnf(c1,axiom,
add(X,Y) = add(Y,X),
file('theBenchmark.p',commutativity_of_add) ).
cnf(c2,axiom,
multiply(X,Y) = multiply(Y,X),
file('theBenchmark.p',commutativity_of_multiply) ).
cnf(c3,axiom,
add(add(X,Y),Z) = add(X,add(Y,Z)),
file('theBenchmark.p',associativity_of_add) ).
cnf(c7,axiom,
multiply(X,add(Y,add(X,Z))) = X,
file('theBenchmark.p',l2) ).
cnf(c8,axiom,
add(X,multiply(Y,multiply(X,Z))) = X,
file('theBenchmark.p',l1) ).
cnf(c16,plain,
multiply(X,add(Y,add(Z,X))) = X,
inference(equational,[status(thm)],[c1,c7]) ).
cnf(c21,axiom,
multiply(add(X,Y),add(X,inverse(Y))) = X,
file('theBenchmark.p',b1) ).
cnf(c22,axiom,
add(multiply(X,Y),multiply(X,inverse(Y))) = X,
file('theBenchmark.p',b2) ).
cnf(c25,plain,
add(X,add(Y,multiply(Z,X))) = add(X,Y),
inference(equational,[status(thm)],[c3,c8,c21]) ).
cnf(c26,plain,
add(inverse(X),multiply(Y,X)) = add(inverse(X),Y),
inference(equational,[status(thm)],[c22,c25]) ).
cnf(c27,plain,
add(X,add(inverse(X),Y)) = add(X,inverse(X)),
inference(equational,[status(thm)],[c25,c26]) ).
cnf(c28,plain,
multiply(X,add(Y,inverse(Y))) = X,
inference(equational,[status(thm)],[c16,c27]) ).
cnf(c49,plain,
multiply(add(X,inverse(X)),Y) = Y,
inference(equational,[status(thm)],[c2,c28]) ).
cnf(c50,plain,
add(X,inverse(X)) = add(Y,inverse(Y)),
inference(equational,[status(thm)],[c28,c49]) ).
cnf(g1,plain,
add(b,inverse(b)) = add(a,inverse(a)),
inference(equational,[status(thm)],[c50]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : BOO029-1 : TPTP v9.0.0. Released v2.2.0.
% 0.03/0.14 % Command : run_Leo-III %s %d THM
% 0.12/0.35 % Computer : n010.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Mon Jul 14 04:25:09 EDT 2025
% 0.18/0.36 % CPUTime :
% 0.48/0.67 % SZS status Unsatisfiable
% 0.48/0.67 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------