%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP445-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n016.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 06:44:04 AM UTC 2025
% Result : Unsatisfiable 60.28s 60.52s
% Output : CNFRefutation 60.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of clauses : 32 ( 32 unt; 0 nHn; 3 RR)
% Number of literals : 32 ( 31 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('theBenchmark.p',prove_these_axioms_1) ).
cnf(c1,axiom,
inverse(X) = divide(divide(Y,Y),X),
file('theBenchmark.p',inverse) ).
cnf(c2,plain,
divide(divide(X,X),Y) = inverse(Y),
inference(equational,[status(thm)],[c1]) ).
cnf(c3,plain,
divide(inverse(divide(X,X)),Y) = inverse(Y),
inference(equational,[status(thm)],[c2]) ).
cnf(c4,axiom,
multiply(X,Y) = divide(X,divide(divide(Z,Z),Y)),
file('theBenchmark.p',multiply) ).
cnf(c5,plain,
divide(X,inverse(Y)) = multiply(X,Y),
inference(equational,[status(thm)],[c2,c4]) ).
cnf(c6,plain,
multiply(divide(X,X),Y) = inverse(inverse(Y)),
inference(equational,[status(thm)],[c2,c5]) ).
cnf(c7,plain,
divide(multiply(inverse(X),X),Y) = inverse(Y),
inference(equational,[status(thm)],[c2,c5]) ).
cnf(c9,plain,
multiply(inverse(divide(X,X)),Y) = inverse(inverse(Y)),
inference(equational,[status(thm)],[c2,c6]) ).
cnf(c12,plain,
multiply(inverse(inverse(divide(X,X))),Y) = inverse(inverse(Y)),
inference(equational,[status(thm)],[c3,c6]) ).
cnf(c15,plain,
divide(inverse(inverse(multiply(inverse(X),X))),Y) = inverse(Y),
inference(equational,[status(thm)],[c3,c7]) ).
cnf(c19,plain,
divide(inverse(inverse(inverse(multiply(inverse(X),X)))),Y) = inverse(Y),
inference(equational,[status(thm)],[c2,c15]) ).
cnf(c38,axiom,
divide(X,divide(divide(divide(divide(X,X),Y),Z),divide(divide(divide(X,X),X),Z))) = Y,
file('theBenchmark.p',single_axiom) ).
cnf(c39,plain,
divide(X,divide(divide(inverse(Y),Z),divide(inverse(X),Z))) = Y,
inference(equational,[status(thm)],[c2,c38]) ).
cnf(c40,plain,
multiply(X,multiply(inverse(X),Y)) = Y,
inference(equational,[status(thm)],[c2,c5,c39]) ).
cnf(c41,plain,
inverse(inverse(inverse(inverse(X)))) = X,
inference(equational,[status(thm)],[c6,c9,c40]) ).
cnf(c42,plain,
multiply(inverse(inverse(X)),Y) = multiply(X,Y),
inference(equational,[status(thm)],[c40]) ).
cnf(c43,plain,
inverse(multiply(divide(inverse(X),Y),Y)) = X,
inference(equational,[status(thm)],[c2,c3,c5,c39]) ).
cnf(c44,plain,
inverse(multiply(inverse(X),X)) = divide(Y,Y),
inference(equational,[status(thm)],[c3,c43]) ).
cnf(c45,plain,
divide(X,X) = divide(Y,Y),
inference(equational,[status(thm)],[c12,c41,c44]) ).
cnf(c47,plain,
divide(X,X) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c19,c41,c45]) ).
cnf(c55,plain,
multiply(X,divide(Y,Y)) = X,
inference(equational,[status(thm)],[c5,c39,c44,c47]) ).
cnf(c56,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c42,c55]) ).
cnf(c57,plain,
multiply(X,inverse(Y)) = divide(X,Y),
inference(equational,[status(thm)],[c5,c56]) ).
cnf(c59,plain,
multiply(X,multiply(inverse(Y),Y)) = X,
inference(equational,[status(thm)],[c19,c41,c55]) ).
cnf(c60,plain,
inverse(multiply(divide(X,Y),Y)) = multiply(divide(inverse(X),Z),Z),
inference(equational,[status(thm)],[c43]) ).
cnf(c61,plain,
multiply(divide(X,Y),Y) = X,
inference(equational,[status(thm)],[c43,c56,c60]) ).
cnf(c62,plain,
divide(multiply(X,Y),Y) = X,
inference(equational,[status(thm)],[c5,c57,c61]) ).
cnf(c65,plain,
divide(X,multiply(inverse(Y),Y)) = X,
inference(equational,[status(thm)],[c59,c62]) ).
cnf(c66,plain,
multiply(inverse(X),X) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c47,c65]) ).
cnf(g1,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(equational,[status(thm)],[c66]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP445-1 : TPTP v9.0.0. Released v2.6.0.
% 0.06/0.11 % Command : run_Leo-III %s %d THM
% 0.12/0.32 % Computer : n016.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Jul 14 08:28:19 EDT 2025
% 0.12/0.32 % CPUTime :
% 60.28/60.52 % SZS status Unsatisfiable
% 60.28/60.52 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------