%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP478-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n004.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 06:44:08 AM UTC 2025
% Result : Unsatisfiable 3.72s 3.97s
% Output : CNFRefutation 3.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of clauses : 29 ( 29 unt; 0 nHn; 3 RR)
% Number of literals : 29 ( 28 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 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 : 113 ( 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,
multiply(X,Y) = divide(X,inverse(Y)),
file('theBenchmark.p',multiply) ).
cnf(c2,axiom,
divide(inverse(divide(divide(divide(X,X),Y),divide(Z,divide(Y,W)))),W) = Z,
file('theBenchmark.p',single_axiom) ).
cnf(c3,plain,
divide(inverse(divide(divide(divide(X,X),Y),Z)),W) = inverse(divide(divide(divide(V,V),U),divide(Z,divide(U,divide(Y,W))))),
inference(equational,[status(thm)],[c2]) ).
cnf(c4,plain,
divide(divide(inverse(divide(divide(divide(X,X),Y),Z)),W),divide(Y,W)) = Z,
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c5,plain,
inverse(divide(divide(divide(X,X),Y),Z)) = inverse(divide(divide(divide(W,W),Y),Z)),
inference(equational,[status(thm)],[c2,c3,c4]) ).
cnf(c7,plain,
inverse(divide(divide(divide(X,X),Y),divide(divide(Z,divide(W,V)),divide(Y,divide(W,V))))) = Z,
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c8,plain,
divide(divide(X,Y),divide(Z,Y)) = divide(divide(X,divide(W,V)),divide(Z,divide(W,V))),
inference(equational,[status(thm)],[c4,c7]) ).
cnf(c9,plain,
divide(divide(X,Y),divide(Z,Y)) = divide(divide(X,W),divide(Z,W)),
inference(equational,[status(thm)],[c4,c8]) ).
cnf(c11,plain,
inverse(divide(divide(divide(X,X),Y),divide(Z,Y))) = inverse(divide(divide(divide(W,W),V),divide(Z,V))),
inference(equational,[status(thm)],[c5,c9]) ).
cnf(c17,plain,
divide(divide(X,divide(Y,Z)),divide(divide(W,V),divide(Y,V))) = divide(divide(X,U),divide(divide(W,Z),U)),
inference(equational,[status(thm)],[c8,c9]) ).
cnf(c18,plain,
divide(divide(divide(X,Y),divide(Z,Y)),divide(W,divide(Z,V))) = divide(divide(divide(X,V),U),divide(W,U)),
inference(equational,[status(thm)],[c9]) ).
cnf(c19,plain,
divide(divide(divide(X,Y),Z),divide(divide(W,Y),Z)) = divide(divide(divide(X,V),U),divide(divide(W,V),U)),
inference(equational,[status(thm)],[c17,c18]) ).
cnf(c21,plain,
inverse(divide(divide(divide(X,Y),Z),divide(divide(W,Y),Z))) = inverse(divide(divide(divide(V,V),U),divide(divide(W,X),U))),
inference(equational,[status(thm)],[c11,c19]) ).
cnf(c22,plain,
divide(divide(divide(inverse(divide(divide(divide(X,X),Y),Z)),W),V),divide(U,V)) = divide(Z,divide(U,divide(Y,W))),
inference(equational,[status(thm)],[c3,c4]) ).
cnf(c23,plain,
divide(divide(inverse(divide(divide(divide(X,X),Y),divide(Z,Y))),W),divide(V,W)) = divide(Z,V),
inference(equational,[status(thm)],[c4,c9]) ).
cnf(c40,plain,
inverse(divide(divide(divide(X,Y),Z),divide(divide(W,Y),Z))) = inverse(divide(divide(divide(X,V),U),divide(divide(W,V),U))),
inference(equational,[status(thm)],[c19,c21]) ).
cnf(c42,plain,
inverse(divide(X,divide(Y,divide(Z,inverse(divide(divide(divide(W,W),Z),X)))))) = inverse(divide(divide(divide(V,V),U),divide(Y,U))),
inference(equational,[status(thm)],[c5,c22]) ).
cnf(c44,plain,
divide(X,divide(Y,inverse(divide(divide(divide(Z,Z),Y),divide(divide(W,W),V))))) = divide(X,V),
inference(equational,[status(thm)],[c4,c23,c42]) ).
cnf(c45,plain,
divide(X,inverse(divide(divide(divide(Y,Y),X),divide(divide(Z,Z),W)))) = W,
inference(equational,[status(thm)],[c4,c44]) ).
cnf(c47,plain,
divide(X,inverse(divide(divide(divide(Y,Y),Z),divide(divide(W,W),Z)))) = X,
inference(equational,[status(thm)],[c11,c45]) ).
cnf(c48,plain,
inverse(divide(divide(X,X),Y)) = inverse(divide(divide(Z,Z),Y)),
inference(equational,[status(thm)],[c5,c47]) ).
cnf(c49,plain,
inverse(divide(X,X)) = inverse(divide(Y,Y)),
inference(equational,[status(thm)],[c47,c48]) ).
cnf(c51,plain,
divide(divide(X,Y),divide(Z,Y)) = divide(X,Z),
inference(equational,[status(thm)],[c9,c47]) ).
cnf(c52,plain,
inverse(divide(divide(X,X),Y)) = Y,
inference(equational,[status(thm)],[c2,c3,c51]) ).
cnf(c53,plain,
divide(X,Y) = inverse(divide(Y,X)),
inference(equational,[status(thm)],[c40,c51,c52]) ).
cnf(c54,plain,
divide(X,X) = divide(Y,Y),
inference(equational,[status(thm)],[c49,c52,c53]) ).
cnf(g1,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(equational,[status(thm)],[c1,c54]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP478-1 : TPTP v9.0.0. Released v2.6.0.
% 0.06/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n004.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 08:29:34 EDT 2025
% 0.11/0.33 % CPUTime :
% 3.72/3.97 % SZS status Unsatisfiable
% 3.72/3.97 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------