%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : BOO001-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n014.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 06:14:41 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.52s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of clauses : 10 ( 10 unt; 0 nHn; 3 RR)
% Number of literals : 10 ( 9 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-3 aty)
% Number of variables : 19 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
inverse(inverse(a)) != a,
file('theBenchmark.p',prove_inverse_is_self_cancelling) ).
cnf(c1,axiom,
multiply(X,Y,Y) = Y,
file('BOO001-0.ax',ternary_multiply_1) ).
cnf(c4,axiom,
multiply(X,Y,inverse(Y)) = X,
file('BOO001-0.ax',right_inverse) ).
cnf(c5,axiom,
multiply(multiply(X,Y,Z),W,multiply(X,Y,V)) = multiply(X,Y,multiply(Z,W,V)),
file('BOO001-0.ax',associativity) ).
cnf(c7,plain,
multiply(X,Y,multiply(Z,X,W)) = multiply(Z,X,multiply(X,Y,W)),
inference(equational,[status(thm)],[c1,c5]) ).
cnf(c8,plain,
multiply(X,Y,multiply(Z,X,Y)) = multiply(Z,X,Y),
inference(equational,[status(thm)],[c1,c7]) ).
cnf(c9,plain,
multiply(X,inverse(X),Y) = Y,
inference(equational,[status(thm)],[c4,c8]) ).
cnf(c10,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c4,c9]) ).
cnf(g1,plain,
inverse(inverse(a)) = a,
inference(equational,[status(thm)],[c10]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : BOO001-1 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.13 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Jul 14 04:21:49 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.18/0.52 % SZS status Unsatisfiable
% 0.18/0.52 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------