%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP011-4 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n009.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 06:43:16 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.47s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of clauses : 15 ( 15 unt; 0 nHn; 6 RR)
% Number of literals : 15 ( 14 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 13 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
b != d,
file('theBenchmark.p',prove_left_cancellation) ).
cnf(c1,axiom,
multiply(identity,X) = X,
file('theBenchmark.p',left_identity) ).
cnf(c2,axiom,
multiply(b,c) = multiply(d,c),
file('theBenchmark.p',product_equality) ).
cnf(c3,plain,
multiply(d,c) = multiply(b,c),
inference(equational,[status(thm)],[c2]) ).
cnf(c4,axiom,
multiply(inverse(X),X) = identity,
file('theBenchmark.p',left_inverse) ).
cnf(c5,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('theBenchmark.p',associativity) ).
cnf(c6,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference(equational,[status(thm)],[c1,c4,c5]) ).
cnf(c8,plain,
multiply(inverse(inverse(X)),identity) = X,
inference(equational,[status(thm)],[c4,c6]) ).
cnf(c9,plain,
multiply(inverse(inverse(X)),Y) = multiply(X,Y),
inference(equational,[status(thm)],[c6]) ).
cnf(c10,plain,
multiply(X,identity) = X,
inference(equational,[status(thm)],[c8,c9]) ).
cnf(c13,plain,
multiply(X,inverse(X)) = identity,
inference(equational,[status(thm)],[c4,c9]) ).
cnf(c14,plain,
multiply(d,multiply(c,X)) = multiply(b,multiply(c,X)),
inference(equational,[status(thm)],[c3,c5]) ).
cnf(c15,plain,
d = b,
inference(equational,[status(thm)],[c10,c13,c14]) ).
cnf(g1,plain,
b = d,
inference(equational,[status(thm)],[c15]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP011-4 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Jul 14 08:04:34 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.20/0.47 % SZS status Unsatisfiable
% 0.20/0.47 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------