%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : BOO025-1 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n008.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 06:14:48 AM UTC 2025
% Result : Unsatisfiable 0.98s 1.15s
% Output : CNFRefutation 0.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of clauses : 60 ( 60 unt; 0 nHn; 4 RR)
% Number of literals : 60 ( 59 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 115 ( 36 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(b,inverse(b)) != multiply(a,inverse(a)),
file('theBenchmark.p',prove_equal_identity) ).
cnf(c1,axiom,
pixley(X,X,Y) = Y,
file('theBenchmark.p',pixley1) ).
cnf(c2,axiom,
pixley(X,Y,Y) = X,
file('theBenchmark.p',pixley2) ).
cnf(c4,axiom,
add(X,inverse(X)) = n1,
file('theBenchmark.p',additive_inverse) ).
cnf(c5,axiom,
multiply(add(X,Y),Y) = Y,
file('theBenchmark.p',multiply_add) ).
cnf(c6,plain,
multiply(n1,inverse(X)) = inverse(X),
inference(equational,[status(thm)],[c4,c5]) ).
cnf(c7,axiom,
multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)),
file('theBenchmark.p',multiply_add_property) ).
cnf(c8,plain,
add(multiply(X,Y),multiply(Z,Y)) = multiply(Y,add(X,Z)),
inference(equational,[status(thm)],[c7]) ).
cnf(c9,plain,
multiply(X,add(add(Y,X),Z)) = add(X,multiply(Z,X)),
inference(equational,[status(thm)],[c5,c8]) ).
cnf(c10,plain,
add(multiply(X,Y),Y) = multiply(Y,add(X,add(Z,Y))),
inference(equational,[status(thm)],[c5,c8]) ).
cnf(c15,plain,
multiply(X,n1) = add(X,multiply(inverse(add(Y,X)),X)),
inference(equational,[status(thm)],[c4,c9]) ).
cnf(c16,plain,
multiply(multiply(X,add(Y,Z)),multiply(Z,X)) = multiply(Z,X),
inference(equational,[status(thm)],[c5,c8]) ).
cnf(c18,plain,
multiply(multiply(X,add(Y,add(Z,X))),X) = X,
inference(equational,[status(thm)],[c5,c16]) ).
cnf(c22,plain,
multiply(X,add(Y,inverse(Y))) = add(X,multiply(inverse(add(Z,X)),X)),
inference(equational,[status(thm)],[c4,c15]) ).
cnf(c23,plain,
multiply(X,add(Y,inverse(Y))) = multiply(X,n1),
inference(equational,[status(thm)],[c15,c22]) ).
cnf(c29,plain,
multiply(add(X,add(Y,inverse(Y))),n1) = add(Y,inverse(Y)),
inference(equational,[status(thm)],[c5,c23]) ).
cnf(c43,plain,
multiply(X,add(multiply(X,add(Y,add(Z,X))),W)) = add(X,multiply(W,X)),
inference(equational,[status(thm)],[c9,c10]) ).
cnf(c52,plain,
multiply(add(X,Y),multiply(Y,add(Z,add(X,Y)))) = multiply(Y,add(Z,add(X,Y))),
inference(equational,[status(thm)],[c5,c16]) ).
cnf(c53,plain,
multiply(add(X,Y),add(Y,Y)) = add(Y,Y),
inference(equational,[status(thm)],[c5,c43,c52]) ).
cnf(c63,axiom,
pixley(X,Y,Z) = add(multiply(X,inverse(Y)),add(multiply(X,Z),multiply(inverse(Y),Z))),
file('theBenchmark.p',pixley_defn) ).
cnf(c64,plain,
add(multiply(X,inverse(Y)),multiply(Z,add(X,inverse(Y)))) = pixley(X,Y,Z),
inference(equational,[status(thm)],[c8,c63]) ).
cnf(c65,plain,
add(multiply(X,inverse(X)),multiply(Y,n1)) = Y,
inference(equational,[status(thm)],[c1,c4,c64]) ).
cnf(c66,plain,
multiply(X,multiply(X,n1)) = multiply(X,n1),
inference(equational,[status(thm)],[c5,c65]) ).
cnf(c67,plain,
add(inverse(n1),multiply(X,n1)) = X,
inference(equational,[status(thm)],[c6,c65]) ).
cnf(c68,plain,
add(inverse(n1),n1) = add(X,n1),
inference(equational,[status(thm)],[c5,c67]) ).
cnf(c69,plain,
add(multiply(X,inverse(X)),n1) = add(Y,n1),
inference(equational,[status(thm)],[c5,c65]) ).
cnf(c70,plain,
add(X,add(Y,inverse(Y))) = add(multiply(Z,inverse(Z)),n1),
inference(equational,[status(thm)],[c4,c69]) ).
cnf(c71,plain,
add(X,add(Y,inverse(Y))) = add(Z,n1),
inference(equational,[status(thm)],[c69,c70]) ).
cnf(c72,plain,
add(X,n1) = add(Y,n1),
inference(equational,[status(thm)],[c4,c71]) ).
cnf(c74,plain,
add(inverse(n1),n1) = multiply(n1,add(X,add(Y,n1))),
inference(equational,[status(thm)],[c18,c67]) ).
cnf(c76,plain,
multiply(n1,add(X,add(Y,n1))) = add(Z,n1),
inference(equational,[status(thm)],[c68,c74]) ).
cnf(c82,plain,
multiply(X,multiply(n1,add(X,X))) = multiply(n1,add(X,X)),
inference(equational,[status(thm)],[c8,c53,c65]) ).
cnf(c83,plain,
multiply(add(X,n1),add(Y,n1)) = add(n1,n1),
inference(equational,[status(thm)],[c5,c9,c76,c82]) ).
cnf(c86,plain,
add(inverse(X),multiply(Y,add(n1,inverse(X)))) = pixley(n1,X,Y),
inference(equational,[status(thm)],[c6,c64]) ).
cnf(c90,plain,
multiply(n1,add(X,add(Y,n1))) = add(Z,add(W,inverse(W))),
inference(equational,[status(thm)],[c71,c74]) ).
cnf(c95,plain,
add(multiply(X,n1),multiply(Y,multiply(X,n1))) = multiply(multiply(X,n1),add(X,Y)),
inference(equational,[status(thm)],[c9,c65]) ).
cnf(c96,plain,
multiply(multiply(X,n1),add(X,X)) = multiply(n1,add(X,X)),
inference(equational,[status(thm)],[c8,c66,c95]) ).
cnf(c99,plain,
multiply(X,add(Y,add(Z,inverse(Z)))) = add(X,multiply(n1,X)),
inference(equational,[status(thm)],[c9,c71]) ).
cnf(c101,plain,
multiply(add(X,n1),add(Y,n1)) = add(Z,add(W,inverse(W))),
inference(equational,[status(thm)],[c71,c83]) ).
cnf(c119,plain,
multiply(add(X,X),add(Y,multiply(X,n1))) = multiply(add(X,X),add(Y,n1)),
inference(equational,[status(thm)],[c8,c96]) ).
cnf(c123,plain,
multiply(add(X,X),add(inverse(n1),n1)) = X,
inference(equational,[status(thm)],[c5,c67,c119]) ).
cnf(c124,plain,
add(n1,n1) = n1,
inference(equational,[status(thm)],[c83,c123]) ).
cnf(c125,plain,
add(X,n1) = n1,
inference(equational,[status(thm)],[c72,c124]) ).
cnf(c127,plain,
multiply(add(X,X),n1) = X,
inference(equational,[status(thm)],[c123,c125]) ).
cnf(c130,plain,
n1 = add(X,add(Y,inverse(Y))),
inference(equational,[status(thm)],[c5,c101,c124]) ).
cnf(c132,plain,
add(X,multiply(n1,X)) = multiply(X,n1),
inference(equational,[status(thm)],[c43,c125]) ).
cnf(c140,plain,
add(X,inverse(X)) = add(Y,add(Z,inverse(Z))),
inference(equational,[status(thm)],[c29,c90,c125,c130]) ).
cnf(c142,plain,
add(multiply(X,inverse(X)),Y) = add(Y,Y),
inference(equational,[status(thm)],[c65,c127]) ).
cnf(c143,plain,
multiply(n1,add(X,X)) = X,
inference(equational,[status(thm)],[c8,c65,c142]) ).
cnf(c144,plain,
multiply(X,X) = X,
inference(equational,[status(thm)],[c82,c143]) ).
cnf(c146,plain,
add(add(X,X),X) = X,
inference(equational,[status(thm)],[c127,c132,c143]) ).
cnf(c147,plain,
add(X,X) = X,
inference(equational,[status(thm)],[c9,c144,c146]) ).
cnf(c149,plain,
multiply(X,n1) = X,
inference(equational,[status(thm)],[c127,c147]) ).
cnf(c150,plain,
multiply(X,Y) = multiply(Y,X),
inference(equational,[status(thm)],[c8,c147]) ).
cnf(c152,plain,
multiply(X,add(Y,inverse(Y))) = X,
inference(equational,[status(thm)],[c99,c132,c140,c149]) ).
cnf(c153,plain,
add(inverse(n1),X) = X,
inference(equational,[status(thm)],[c1,c86,c152]) ).
cnf(c158,plain,
pixley(inverse(n1),X,Y) = multiply(inverse(X),Y),
inference(equational,[status(thm)],[c8,c64,c153]) ).
cnf(c159,plain,
multiply(X,inverse(X)) = inverse(n1),
inference(equational,[status(thm)],[c2,c150,c158]) ).
cnf(g1,plain,
multiply(b,inverse(b)) = multiply(a,inverse(a)),
inference(equational,[status(thm)],[c159]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO025-1 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n008.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 04:24:04 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.98/1.15 % SZS status Unsatisfiable
% 0.98/1.15 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------