%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP470-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n003.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 06:44:07 AM UTC 2025
% Result : Unsatisfiable 1.53s 1.77s
% Output : CNFRefutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of clauses : 34 ( 34 unt; 0 nHn; 3 RR)
% Number of literals : 34 ( 33 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 : 116 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('theBenchmark.p',prove_these_axioms_2) ).
cnf(c1,axiom,
multiply(X,Y) = divide(X,inverse(Y)),
file('theBenchmark.p',multiply) ).
cnf(c2,axiom,
divide(inverse(divide(X,divide(Y,divide(Z,W)))),divide(divide(W,Z),X)) = Y,
file('theBenchmark.p',single_axiom) ).
cnf(c3,plain,
divide(inverse(divide(X,Y)),divide(divide(Z,divide(W,V)),X)) = inverse(divide(Z,divide(Y,divide(V,W)))),
inference(equational,[status(thm)],[c2]) ).
cnf(c4,plain,
inverse(divide(X,divide(divide(Y,divide(divide(Z,W),X)),divide(W,Z)))) = Y,
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c5,plain,
inverse(inverse(divide(X,divide(Y,divide(inverse(divide(divide(Z,W),Y)),divide(W,Z)))))) = X,
inference(equational,[status(thm)],[c3,c4]) ).
cnf(c6,plain,
divide(inverse(X),divide(divide(Y,Z),inverse(divide(divide(Z,Y),divide(X,divide(W,V)))))) = divide(V,W),
inference(equational,[status(thm)],[c2]) ).
cnf(c7,plain,
divide(divide(inverse(divide(X,Y)),divide(divide(Z,divide(W,V)),X)),divide(divide(W,V),Z)) = Y,
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c8,plain,
divide(divide(inverse(divide(X,Y)),divide(divide(Z,W),X)),divide(W,Z)) = Y,
inference(equational,[status(thm)],[c7]) ).
cnf(c12,plain,
divide(inverse(divide(divide(X,Y),Z)),W) = inverse(divide(inverse(divide(V,W)),divide(Z,divide(V,divide(Y,X))))),
inference(equational,[status(thm)],[c3,c8]) ).
cnf(c15,plain,
divide(inverse(X),divide(divide(Y,Z),inverse(divide(divide(Z,Y),divide(X,W))))) = divide(divide(divide(V,U),U2),inverse(divide(U2,divide(W,divide(U,V))))),
inference(equational,[status(thm)],[c2,c6]) ).
cnf(c16,plain,
divide(divide(divide(X,Y),Z),inverse(divide(Z,divide(divide(W,V),divide(Y,X))))) = divide(V,W),
inference(equational,[status(thm)],[c6,c15]) ).
cnf(c19,plain,
divide(divide(divide(X,Y),inverse(divide(divide(Y,X),divide(Z,W)))),inverse(Z)) = W,
inference(equational,[status(thm)],[c2,c15,c16]) ).
cnf(c20,plain,
divide(divide(divide(divide(divide(X,Y),Z),inverse(divide(Z,W))),inverse(W)),inverse(Y)) = X,
inference(equational,[status(thm)],[c8,c19]) ).
cnf(c21,plain,
divide(divide(X,inverse(Y)),inverse(inverse(divide(Z,W)))) = divide(divide(X,divide(inverse(W),Y)),Z),
inference(equational,[status(thm)],[c20]) ).
cnf(c22,plain,
divide(inverse(inverse(divide(X,Y))),divide(Z,inverse(W))) = divide(X,divide(Z,divide(inverse(Y),W))),
inference(equational,[status(thm)],[c16,c21]) ).
cnf(c24,plain,
divide(divide(divide(X,Y),Z),inverse(divide(Z,divide(W,divide(Y,X))))) = divide(divide(V,U),divide(inverse(divide(U2,W)),divide(divide(U,V),U2))),
inference(equational,[status(thm)],[c8,c16]) ).
cnf(c25,plain,
divide(divide(X,Y),divide(inverse(divide(Z,divide(W,V))),divide(divide(Y,X),Z))) = divide(V,W),
inference(equational,[status(thm)],[c16,c24]) ).
cnf(c26,plain,
divide(inverse(divide(X,Y)),divide(divide(Z,divide(W,V)),divide(V,W))) = inverse(divide(Z,divide(Y,X))),
inference(equational,[status(thm)],[c2,c25]) ).
cnf(c27,plain,
inverse(inverse(divide(X,divide(Y,Z)))) = divide(inverse(divide(divide(W,V),divide(X,divide(divide(V,W),Z)))),Y),
inference(equational,[status(thm)],[c12,c26]) ).
cnf(c28,plain,
divide(inverse(divide(X,Y)),Z) = inverse(inverse(divide(inverse(divide(W,divide(Y,X))),divide(Z,W)))),
inference(equational,[status(thm)],[c25,c27]) ).
cnf(c29,plain,
inverse(inverse(divide(X,divide(Y,inverse(inverse(Y)))))) = X,
inference(equational,[status(thm)],[c2,c5,c28]) ).
cnf(c30,plain,
inverse(divide(inverse(inverse(X)),divide(Y,Z))) = divide(inverse(divide(Z,Y)),X),
inference(equational,[status(thm)],[c28,c29]) ).
cnf(c31,plain,
inverse(divide(inverse(inverse(divide(X,Y))),divide(Z,divide(Y,X)))) = inverse(inverse(Z)),
inference(equational,[status(thm)],[c2,c28,c30]) ).
cnf(c32,plain,
inverse(divide(inverse(divide(inverse(inverse(X)),X)),Y)) = inverse(inverse(Y)),
inference(equational,[status(thm)],[c29,c30]) ).
cnf(c33,plain,
inverse(inverse(inverse(divide(X,inverse(inverse(X)))))) = inverse(divide(inverse(inverse(Y)),Y)),
inference(equational,[status(thm)],[c29,c32]) ).
cnf(c43,plain,
inverse(inverse(divide(divide(X,divide(Y,Z)),divide(Z,Y)))) = X,
inference(equational,[status(thm)],[c26,c29,c32]) ).
cnf(c44,plain,
divide(X,divide(inverse(inverse(Y)),Y)) = X,
inference(equational,[status(thm)],[c29,c43]) ).
cnf(c45,plain,
divide(X,divide(Y,Y)) = X,
inference(equational,[status(thm)],[c22,c44]) ).
cnf(c46,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c43,c45]) ).
cnf(c47,plain,
divide(X,X) = divide(Y,Y),
inference(equational,[status(thm)],[c33,c46]) ).
cnf(c49,plain,
inverse(divide(X,Y)) = divide(Y,X),
inference(equational,[status(thm)],[c31,c45,c46,c47]) ).
cnf(g1,plain,
multiply(multiply(inverse(b2),b2),a2) = a2,
inference(equational,[status(thm)],[c1,c45,c46,c49]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP470-1 : TPTP v9.0.0. Released v2.6.0.
% 0.11/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n003.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
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Jul 14 08:29:34 EDT 2025
% 0.11/0.32 % CPUTime :
% 1.53/1.77 % SZS status Unsatisfiable
% 1.53/1.77 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------