%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : BOO034-1 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n005.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 06:14:49 AM UTC 2025
% Result : Unsatisfiable 0.39s 0.56s
% Output : CNFRefutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of clauses : 18 ( 18 unt; 0 nHn; 3 RR)
% Number of literals : 18 ( 17 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-3 aty)
% Number of variables : 41 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c)) != b,
file('theBenchmark.p',prove_single_axiom) ).
cnf(c1,axiom,
multiply(X,Y,Y) = Y,
file('BOO001-0.ax',ternary_multiply_1) ).
cnf(c2,axiom,
multiply(X,X,Y) = X,
file('BOO001-0.ax',ternary_multiply_2) ).
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(c11,plain,
multiply(X,inverse(Y),Y) = X,
inference(equational,[status(thm)],[c4,c10]) ).
cnf(c13,plain,
multiply(multiply(X,Y,Z),W,Y) = multiply(X,Y,multiply(Z,W,Y)),
inference(equational,[status(thm)],[c1,c5]) ).
cnf(c21,plain,
multiply(X,Y,Z) = multiply(Z,X,multiply(X,Y,inverse(X))),
inference(equational,[status(thm)],[c4,c7]) ).
cnf(c23,plain,
multiply(X,Y,Z) = multiply(X,Z,multiply(inverse(Z),Y,Z)),
inference(equational,[status(thm)],[c4,c13]) ).
cnf(c24,plain,
multiply(inverse(X),Y,X) = Y,
inference(equational,[status(thm)],[c2,c8,c23]) ).
cnf(c25,plain,
multiply(X,Y,Z) = multiply(X,Z,Y),
inference(equational,[status(thm)],[c23,c24]) ).
cnf(c26,plain,
multiply(X,Y,Z) = multiply(Y,Z,X),
inference(equational,[status(thm)],[c9,c21,c25]) ).
cnf(g1,plain,
multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c)) = b,
inference(equational,[status(thm)],[c5,c9,c11,c25,c26]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO034-1 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n005.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
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Jul 14 04:24:19 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.39/0.56 % SZS status Unsatisfiable
% 0.39/0.56 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------