%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : BOO002-2 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n013.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 06:14:41 AM UTC 2025
% Result : Unsatisfiable 0.78s 1.00s
% Output : CNFRefutation 0.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of clauses : 26 ( 26 unt; 0 nHn; 3 RR)
% Number of literals : 26 ( 25 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-3 aty)
% Number of variables : 76 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(a,inverse(a),b) != b,
file('theBenchmark.p',prove_equation) ).
cnf(c1,axiom,
multiply(X,Y,Y) = Y,
file('theBenchmark.p',ternary_multiply_1) ).
cnf(c2,axiom,
multiply(X,X,Y) = X,
file('theBenchmark.p',ternary_multiply_2) ).
cnf(c3,axiom,
multiply(X,Y,X) = X,
file('theBenchmark.p',extra_lemma) ).
cnf(c4,axiom,
multiply(inverse(X),X,Y) = Y,
file('theBenchmark.p',left_inverse) ).
cnf(c5,axiom,
multiply(multiply(X,Y,Z),W,multiply(X,Y,V)) = multiply(X,Y,multiply(Z,W,V)),
file('theBenchmark.p',associativity) ).
cnf(c6,plain,
multiply(X,Y,multiply(X,Z,W)) = multiply(X,Z,multiply(X,Y,W)),
inference(equational,[status(thm)],[c3,c5]) ).
cnf(c7,plain,
multiply(X,Y,multiply(X,Z,Y)) = multiply(X,Z,Y),
inference(equational,[status(thm)],[c1,c6]) ).
cnf(c8,plain,
multiply(X,Y,multiply(Z,X,W)) = multiply(Z,X,multiply(X,Y,W)),
inference(equational,[status(thm)],[c1,c5]) ).
cnf(c9,plain,
multiply(X,Y,multiply(Z,X,Y)) = multiply(Z,X,Y),
inference(equational,[status(thm)],[c1,c8]) ).
cnf(c11,plain,
multiply(multiply(X,Y,Z),W,X) = multiply(X,Y,multiply(Z,W,X)),
inference(equational,[status(thm)],[c3,c5]) ).
cnf(c12,plain,
multiply(multiply(X,Y,Z),W,Y) = multiply(X,Y,multiply(Z,W,Y)),
inference(equational,[status(thm)],[c1,c5]) ).
cnf(c13,plain,
multiply(X,Y,multiply(Z,multiply(X,Y,Z),W)) = multiply(X,Y,Z),
inference(equational,[status(thm)],[c2,c5]) ).
cnf(c18,plain,
multiply(X,Y,multiply(Z,W,multiply(X,Y,W))) = multiply(X,Y,W),
inference(equational,[status(thm)],[c9,c13]) ).
cnf(c19,plain,
multiply(X,multiply(Y,Z,X),Z) = multiply(Y,Z,X),
inference(equational,[status(thm)],[c1,c13,c18]) ).
cnf(c21,plain,
multiply(X,Y,multiply(Z,W,multiply(X,Y,Z))) = multiply(X,Y,Z),
inference(equational,[status(thm)],[c7,c13]) ).
cnf(c22,plain,
multiply(X,multiply(Y,Z,X),Y) = multiply(Y,Z,X),
inference(equational,[status(thm)],[c1,c13,c21]) ).
cnf(c24,plain,
multiply(X,multiply(Y,X,Z),Z) = multiply(Y,X,Z),
inference(equational,[status(thm)],[c19,c22]) ).
cnf(c47,plain,
multiply(multiply(X,Y,multiply(Z,W,X)),V,W) = multiply(multiply(X,Y,Z),W,multiply(X,V,W)),
inference(equational,[status(thm)],[c11,c12]) ).
cnf(c50,plain,
multiply(multiply(X,Y,Z),W,Z) = multiply(multiply(X,Y,Z),Z,multiply(X,W,Z)),
inference(equational,[status(thm)],[c2,c47]) ).
cnf(c51,plain,
multiply(multiply(X,Y,Z),X,Z) = multiply(X,Y,Z),
inference(equational,[status(thm)],[c2,c11,c50]) ).
cnf(c52,plain,
multiply(multiply(inverse(X),Y,Z),X,Z) = Z,
inference(equational,[status(thm)],[c1,c4,c50]) ).
cnf(c53,plain,
multiply(multiply(X,inverse(Y),Z),Y,Z) = Z,
inference(equational,[status(thm)],[c24,c52]) ).
cnf(c54,plain,
multiply(X,inverse(X),Y) = Y,
inference(equational,[status(thm)],[c51,c53]) ).
cnf(g1,plain,
multiply(a,inverse(a),b) = b,
inference(equational,[status(thm)],[c54]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.15 % Problem : BOO002-2 : TPTP v9.0.0. Released v1.1.0.
% 0.05/0.15 % Command : run_Leo-III %s %d THM
% 0.12/0.36 % Computer : n013.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8042.1875MB
% 0.12/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Mon Jul 14 04:21:49 EDT 2025
% 0.12/0.37 % CPUTime :
% 0.78/1.00 % SZS status Unsatisfiable
% 0.78/1.00 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------