%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP476-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n001.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 2.57s 2.79s
% Output : CNFRefutation 2.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of clauses : 39 ( 39 unt; 0 nHn; 3 RR)
% Number of literals : 39 ( 38 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 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 : 154 ( 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(divide(divide(X,Y),Z),divide(W,Z))),divide(Y,X)) = W,
file('theBenchmark.p',single_axiom) ).
cnf(c3,plain,
divide(inverse(divide(divide(divide(X,Y),divide(Z,W)),V)),divide(Y,X)) = inverse(divide(divide(divide(W,Z),U),divide(V,U))),
inference(equational,[status(thm)],[c2]) ).
cnf(c4,plain,
inverse(divide(divide(divide(X,Y),Z),divide(divide(W,divide(Y,X)),Z))) = W,
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c5,plain,
inverse(divide(divide(divide(X,Y),Z),divide(W,Z))) = inverse(divide(divide(divide(X,Y),V),divide(W,V))),
inference(equational,[status(thm)],[c2,c4]) ).
cnf(c6,plain,
inverse(divide(divide(X,Y),divide(Z,Y))) = inverse(divide(divide(X,W),divide(Z,W))),
inference(equational,[status(thm)],[c2,c5]) ).
cnf(c7,plain,
divide(divide(inverse(divide(divide(divide(X,Y),divide(Z,W)),V)),divide(Y,X)),divide(Z,W)) = V,
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c8,plain,
divide(divide(inverse(divide(divide(divide(X,Y),Z),W)),divide(Y,X)),Z) = W,
inference(equational,[status(thm)],[c7]) ).
cnf(c10,plain,
inverse(divide(X,divide(divide(Y,divide(divide(Z,W),inverse(divide(divide(divide(W,Z),V),X)))),V))) = Y,
inference(equational,[status(thm)],[c4,c8]) ).
cnf(c11,plain,
divide(divide(inverse(divide(X,Y)),divide(divide(Z,W),inverse(divide(divide(divide(W,Z),V),X)))),V) = Y,
inference(equational,[status(thm)],[c8]) ).
cnf(c12,plain,
divide(inverse(divide(X,divide(Y,Z))),divide(divide(W,V),inverse(divide(divide(divide(V,W),Z),X)))) = Y,
inference(equational,[status(thm)],[c2,c8]) ).
cnf(c13,plain,
divide(X,divide(divide(Y,Z),inverse(divide(divide(divide(Z,Y),W),V)))) = divide(X,divide(divide(U,U2),inverse(divide(divide(divide(U2,U),W),V)))),
inference(equational,[status(thm)],[c10,c12]) ).
cnf(c14,plain,
divide(divide(X,Y),inverse(divide(divide(divide(Y,X),Z),W))) = divide(divide(V,U),inverse(divide(divide(divide(U,V),Z),W))),
inference(equational,[status(thm)],[c11,c13]) ).
cnf(c15,plain,
divide(divide(X,Y),inverse(divide(divide(divide(Y,X),Z),divide(W,Z)))) = divide(divide(V,U),inverse(divide(divide(divide(U,V),U2),divide(W,U2)))),
inference(equational,[status(thm)],[c6,c14]) ).
cnf(c18,plain,
divide(X,divide(divide(Y,Z),inverse(divide(divide(divide(Z,Y),W),divide(divide(V,U),W))))) = divide(X,divide(U,V)),
inference(equational,[status(thm)],[c4,c12]) ).
cnf(c19,plain,
divide(divide(X,Y),inverse(divide(divide(divide(Y,X),Z),divide(divide(W,V),Z)))) = divide(V,W),
inference(equational,[status(thm)],[c7,c18]) ).
cnf(c20,plain,
divide(divide(inverse(divide(X,Y)),divide(Z,W)),V) = inverse(divide(divide(divide(V,divide(W,Z)),U),divide(divide(Y,X),U))),
inference(equational,[status(thm)],[c8,c19]) ).
cnf(c21,plain,
divide(divide(divide(X,Y),Z),divide(divide(inverse(divide(W,V)),divide(Y,X)),Z)) = divide(W,V),
inference(equational,[status(thm)],[c15,c19,c20]) ).
cnf(c22,plain,
divide(divide(X,Y),divide(Z,Y)) = divide(divide(X,W),divide(Z,W)),
inference(equational,[status(thm)],[c6,c21]) ).
cnf(c31,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)],[c22]) ).
cnf(c32,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)],[c22]) ).
cnf(c33,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)],[c31,c32]) ).
cnf(c34,plain,
divide(divide(divide(inverse(divide(X,Y)),divide(Z,W)),V),divide(divide(W,Z),V)) = divide(Y,X),
inference(equational,[status(thm)],[c12,c19,c20]) ).
cnf(c35,plain,
divide(divide(divide(X,Y),inverse(divide(Z,W))),inverse(divide(W,Z))) = divide(X,Y),
inference(equational,[status(thm)],[c19,c34]) ).
cnf(c36,plain,
divide(divide(X,Y),inverse(divide(Y,X))) = divide(divide(Z,W),inverse(divide(W,Z))),
inference(equational,[status(thm)],[c14,c35]) ).
cnf(c38,plain,
divide(divide(X,inverse(divide(Y,Z))),inverse(divide(Z,Y))) = X,
inference(equational,[status(thm)],[c11,c35]) ).
cnf(c40,plain,
divide(divide(divide(X,Y),Z),divide(divide(W,Y),Z)) = divide(X,W),
inference(equational,[status(thm)],[c33,c38]) ).
cnf(c41,plain,
divide(divide(X,Y),inverse(divide(Y,Z))) = divide(X,Z),
inference(equational,[status(thm)],[c19,c40]) ).
cnf(c42,plain,
divide(X,X) = divide(Y,Y),
inference(equational,[status(thm)],[c36,c41]) ).
cnf(c46,plain,
divide(divide(X,Y),divide(Z,Y)) = divide(X,Z),
inference(equational,[status(thm)],[c33,c40,c41]) ).
cnf(c47,plain,
inverse(divide(X,Y)) = divide(Y,X),
inference(equational,[status(thm)],[c4,c40,c46]) ).
cnf(c48,plain,
inverse(inverse(divide(X,Y))) = divide(X,Y),
inference(equational,[status(thm)],[c47]) ).
cnf(c49,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c11,c48]) ).
cnf(c50,plain,
divide(inverse(divide(X,Y)),divide(Z,X)) = divide(Y,Z),
inference(equational,[status(thm)],[c2,c40]) ).
cnf(c52,plain,
divide(divide(X,X),divide(Y,Z)) = divide(Z,Y),
inference(equational,[status(thm)],[c42,c46]) ).
cnf(c53,plain,
divide(X,divide(Y,Y)) = X,
inference(equational,[status(thm)],[c2,c46,c50,c52]) ).
cnf(g1,plain,
multiply(multiply(inverse(b2),b2),a2) = a2,
inference(equational,[status(thm)],[c1,c47,c49,c53]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP476-1 : TPTP v9.0.0. Released v2.6.0.
% 0.12/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 14 08:29:49 EDT 2025
% 0.12/0.33 % CPUTime :
% 2.57/2.79 % SZS status Unsatisfiable
% 2.57/2.79 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------