%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP729-1 : TPTP v9.0.0. Released v4.0.0.
% 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 06:44:48 AM UTC 2025
% Result : Unsatisfiable 63.03s 63.10s
% Output : CNFRefutation 63.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% 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 : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 68 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
asoc(a,b,op_k(c,d)) != unit,
file('theBenchmark.p',goals) ).
cnf(c1,axiom,
mult(unit,X) = X,
file('theBenchmark.p',c01) ).
cnf(c2,axiom,
mult(X,unit) = X,
file('theBenchmark.p',c02) ).
cnf(c3,axiom,
mult(X,i(X)) = unit,
file('theBenchmark.p',c03) ).
cnf(c5,axiom,
mult(i(X),X) = unit,
file('theBenchmark.p',c04) ).
cnf(c6,axiom,
rd(mult(X,Y),Y) = X,
file('theBenchmark.p',c07) ).
cnf(c9,plain,
rd(unit,X) = i(X),
inference(equational,[status(thm)],[c5,c6]) ).
cnf(c10,plain,
i(i(X)) = X,
inference(equational,[status(thm)],[c3,c6,c9]) ).
cnf(c11,axiom,
mult(rd(X,Y),Y) = X,
file('theBenchmark.p',c08) ).
cnf(c12,axiom,
i(mult(X,Y)) = mult(i(X),i(Y)),
file('theBenchmark.p',c05) ).
cnf(c13,plain,
mult(i(X),i(Y)) = i(mult(X,Y)),
inference(equational,[status(thm)],[c12]) ).
cnf(c15,axiom,
mult(i(X),mult(X,Y)) = Y,
file('theBenchmark.p',c06) ).
cnf(c16,plain,
rd(X,mult(Y,X)) = i(Y),
inference(equational,[status(thm)],[c6,c15]) ).
cnf(c17,plain,
i(rd(X,Y)) = rd(Y,X),
inference(equational,[status(thm)],[c11,c16]) ).
cnf(c30,axiom,
asoc(X,Y,asoc(Z,W,V)) = unit,
file('theBenchmark.p',c22) ).
cnf(c32,plain,
mult(X,i(mult(X,Y))) = i(Y),
inference(equational,[status(thm)],[c10,c13,c15]) ).
cnf(c38,axiom,
mult(X,Y) = mult(mult(Y,X),op_k(X,Y)),
file('theBenchmark.p',c11) ).
cnf(c39,plain,
mult(mult(X,Y),op_k(Y,X)) = mult(Y,X),
inference(equational,[status(thm)],[c38]) ).
cnf(c47,plain,
mult(rd(X,Y),i(X)) = i(Y),
inference(equational,[status(thm)],[c11,c32]) ).
cnf(c48,plain,
rd(i(X),i(Y)) = rd(Y,X),
inference(equational,[status(thm)],[c16,c17,c47]) ).
cnf(c70,axiom,
mult(mult(X,mult(Y,X)),Z) = mult(X,mult(Y,mult(X,Z))),
file('theBenchmark.p',c09) ).
cnf(c93,plain,
mult(i(X),rd(Y,Z)) = i(mult(X,rd(Z,Y))),
inference(equational,[status(thm)],[c13,c17]) ).
cnf(c98,plain,
mult(i(mult(X,Y)),mult(Y,X)) = op_k(Y,X),
inference(equational,[status(thm)],[c15,c39]) ).
cnf(c221,plain,
mult(i(mult(X,rd(Y,X))),Y) = op_k(rd(Y,X),X),
inference(equational,[status(thm)],[c11,c98]) ).
cnf(c332,plain,
mult(X,mult(rd(Y,X),mult(X,Z))) = mult(mult(X,Y),Z),
inference(equational,[status(thm)],[c11,c70]) ).
cnf(c333,plain,
mult(mult(X,Y),i(X)) = mult(X,rd(Y,X)),
inference(equational,[status(thm)],[c2,c3,c332]) ).
cnf(c336,plain,
mult(i(mult(X,Y)),X) = i(mult(X,rd(Y,X))),
inference(equational,[status(thm)],[c10,c13,c48,c93,c333]) ).
cnf(c558,axiom,
mult(mult(X,Y),Z) = mult(mult(X,mult(Y,Z)),asoc(X,Y,Z)),
file('theBenchmark.p',c10) ).
cnf(c559,plain,
mult(mult(X,mult(Y,Z)),asoc(X,Y,Z)) = mult(mult(X,Y),Z),
inference(equational,[status(thm)],[c558]) ).
cnf(c563,plain,
asoc(i(mult(X,Y)),X,Y) = op_k(rd(Y,X),X),
inference(equational,[status(thm)],[c1,c5,c221,c336,c559]) ).
cnf(c570,plain,
asoc(X,Y,op_k(rd(Z,W),W)) = unit,
inference(equational,[status(thm)],[c30,c563]) ).
cnf(c571,plain,
asoc(X,Y,op_k(Z,W)) = unit,
inference(equational,[status(thm)],[c6,c570]) ).
cnf(g1,plain,
asoc(a,b,op_k(c,d)) = unit,
inference(equational,[status(thm)],[c571]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRP729-1 : TPTP v9.0.0. Released v4.0.0.
% 0.00/0.09 % Command : run_Leo-III %s %d THM
% 0.09/0.30 % Computer : n013.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Mon Jul 14 08:58:19 EDT 2025
% 0.09/0.30 % CPUTime :
% 63.03/63.10 % SZS status Unsatisfiable
% 63.03/63.10 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------