%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP728-1 : TPTP v9.0.0. Released v4.0.0.
% 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 06:44:48 AM UTC 2025
% Result : Unsatisfiable 63.22s 63.36s
% Output : CNFRefutation 63.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 20
% Syntax : Number of clauses : 91 ( 91 unt; 0 nHn; 3 RR)
% Number of literals : 91 ( 90 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 : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 218 ( 33 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
op_k(op_k(a,b),c) != 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(c8,plain,
rd(X,unit) = X,
inference(equational,[status(thm)],[c2,c6]) ).
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(c18,axiom,
op_t(X,Y) = mult(i(Y),mult(X,Y)),
file('theBenchmark.p',c14) ).
cnf(c19,plain,
mult(i(X),mult(Y,X)) = op_t(Y,X),
inference(equational,[status(thm)],[c18]) ).
cnf(c23,plain,
op_t(X,i(X)) = X,
inference(equational,[status(thm)],[c2,c3,c10,c19]) ).
cnf(c24,plain,
op_t(i(X),X) = i(X),
inference(equational,[status(thm)],[c2,c5,c19]) ).
cnf(c25,plain,
mult(X,op_t(Y,X)) = mult(Y,X),
inference(equational,[status(thm)],[c10,c15,c19]) ).
cnf(c28,axiom,
asoc(asoc(X,Y,Z),W,V) = unit,
file('theBenchmark.p',c21) ).
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(c33,axiom,
op_t(op_r(X,Y,Z),W) = op_r(op_t(X,W),Y,Z),
file('theBenchmark.p',c18) ).
cnf(c34,axiom,
op_t(op_l(X,Y,Z),W) = op_l(op_t(X,W),Y,Z),
file('theBenchmark.p',c19) ).
cnf(c35,plain,
i(mult(i(X),Y)) = mult(X,i(Y)),
inference(equational,[status(thm)],[c10,c13]) ).
cnf(c36,plain,
i(mult(X,i(Y))) = mult(i(X),Y),
inference(equational,[status(thm)],[c10,c13]) ).
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(c51,plain,
mult(X,i(mult(Y,X))) = op_t(i(Y),i(X)),
inference(equational,[status(thm)],[c10,c13,c19]) ).
cnf(c58,plain,
mult(X,mult(Y,i(X))) = op_t(Y,i(X)),
inference(equational,[status(thm)],[c10,c19]) ).
cnf(c59,plain,
op_t(i(X),i(Y)) = i(op_t(X,Y)),
inference(equational,[status(thm)],[c10,c35,c51,c58]) ).
cnf(c60,plain,
op_t(rd(X,Y),i(X)) = mult(X,i(Y)),
inference(equational,[status(thm)],[c11,c17,c51]) ).
cnf(c66,axiom,
op_r(op_r(X,Y,Z),W,V) = op_r(op_r(X,W,V),Y,Z),
file('theBenchmark.p',c15) ).
cnf(c70,axiom,
mult(mult(X,mult(Y,X)),Z) = mult(X,mult(Y,mult(X,Z))),
file('theBenchmark.p',c09) ).
cnf(c77,plain,
mult(X,op_k(Y,rd(X,Y))) = mult(Y,rd(X,Y)),
inference(equational,[status(thm)],[c11,c39]) ).
cnf(c85,plain,
mult(rd(X,Y),rd(Y,X)) = unit,
inference(equational,[status(thm)],[c5,c17]) ).
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(c124,axiom,
op_r(X,Y,Z) = rd(mult(mult(X,Y),Z),mult(Y,Z)),
file('theBenchmark.p',c13) ).
cnf(c125,plain,
rd(mult(mult(X,Y),Z),mult(Y,Z)) = op_r(X,Y,Z),
inference(equational,[status(thm)],[c124]) ).
cnf(c130,plain,
op_r(X,i(X),Y) = X,
inference(equational,[status(thm)],[c1,c3,c10,c16,c125]) ).
cnf(c133,plain,
mult(mult(X,i(Y)),Y) = op_r(X,i(Y),Y),
inference(equational,[status(thm)],[c5,c8,c125]) ).
cnf(c134,plain,
op_r(X,Y,i(mult(X,Y))) = op_t(X,Y),
inference(equational,[status(thm)],[c3,c9,c10,c51,c59,c125]) ).
cnf(c142,plain,
rd(op_r(X,i(Y),Y),Y) = mult(X,i(Y)),
inference(equational,[status(thm)],[c6,c133]) ).
cnf(c144,plain,
rd(X,op_r(Y,i(X),X)) = mult(i(Y),X),
inference(equational,[status(thm)],[c16,c36,c133]) ).
cnf(c155,plain,
op_r(X,i(mult(X,Y)),Y) = op_t(X,i(mult(X,Y))),
inference(equational,[status(thm)],[c10,c32,c134]) ).
cnf(c160,plain,
op_r(rd(X,Y),i(X),Y) = mult(X,i(Y)),
inference(equational,[status(thm)],[c11,c60,c155]) ).
cnf(c171,plain,
op_r(op_r(X,Y,Z),i(X),W) = op_r(X,Y,Z),
inference(equational,[status(thm)],[c66,c130]) ).
cnf(c178,plain,
mult(X,op_k(mult(Y,X),i(Y))) = mult(mult(Y,X),i(Y)),
inference(equational,[status(thm)],[c15,c39]) ).
cnf(c180,plain,
mult(op_r(X,Y,Z),i(X)) = rd(op_r(X,Y,Z),X),
inference(equational,[status(thm)],[c142,c171]) ).
cnf(c188,plain,
mult(mult(X,Y),i(mult(Y,X))) = i(op_k(Y,X)),
inference(equational,[status(thm)],[c32,c39]) ).
cnf(c189,plain,
i(op_k(i(X),i(Y))) = op_k(X,Y),
inference(equational,[status(thm)],[c10,c13,c98,c188]) ).
cnf(c190,plain,
op_k(i(X),i(Y)) = i(op_k(X,Y)),
inference(equational,[status(thm)],[c10,c189]) ).
cnf(c221,plain,
mult(i(mult(X,rd(Y,X))),Y) = op_k(rd(Y,X),X),
inference(equational,[status(thm)],[c11,c98]) ).
cnf(c238,plain,
mult(X,op_r(op_t(Y,X),Z,W)) = mult(op_r(Y,Z,W),X),
inference(equational,[status(thm)],[c25,c33]) ).
cnf(c243,plain,
mult(i(X),op_r(X,Y,Z)) = rd(op_r(X,Y,Z),X),
inference(equational,[status(thm)],[c23,c180,c238]) ).
cnf(c246,plain,
op_k(op_r(X,Y,Z),i(X)) = unit,
inference(equational,[status(thm)],[c17,c85,c98,c180,c243]) ).
cnf(c264,plain,
mult(X,op_l(op_t(Y,X),Z,W)) = mult(op_l(Y,Z,W),X),
inference(equational,[status(thm)],[c25,c34]) ).
cnf(c276,plain,
mult(op_l(i(X),Y,Z),X) = mult(X,op_l(i(X),Y,Z)),
inference(equational,[status(thm)],[c24,c264]) ).
cnf(c294,plain,
i(op_k(X,rd(Y,Z))) = op_k(i(X),rd(Z,Y)),
inference(equational,[status(thm)],[c17,c190]) ).
cnf(c330,plain,
mult(X,i(mult(Y,rd(X,Y)))) = op_k(i(Y),rd(Y,X)),
inference(equational,[status(thm)],[c32,c77,c294]) ).
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(c416,axiom,
op_l(X,Y,Z) = mult(i(mult(Z,Y)),mult(Z,mult(Y,X))),
file('theBenchmark.p',c12) ).
cnf(c417,plain,
mult(i(mult(X,Y)),mult(X,mult(Y,Z))) = op_l(Z,Y,X),
inference(equational,[status(thm)],[c416]) ).
cnf(c425,plain,
i(mult(X,rd(Y,X))) = op_l(i(Y),Y,X),
inference(equational,[status(thm)],[c2,c3,c336,c417]) ).
cnf(c439,plain,
mult(X,op_l(i(X),X,Y)) = op_k(rd(X,Y),Y),
inference(equational,[status(thm)],[c11,c98,c276,c425]) ).
cnf(c440,plain,
op_k(i(X),rd(X,Y)) = op_k(rd(Y,X),X),
inference(equational,[status(thm)],[c330,c425,c439]) ).
cnf(c441,plain,
i(op_k(X,Y)) = op_k(Y,X),
inference(equational,[status(thm)],[c6,c16,c190,c440]) ).
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(c567,plain,
mult(X,asoc(X,i(Y),Y)) = op_r(X,i(Y),Y),
inference(equational,[status(thm)],[c2,c5,c133,c559]) ).
cnf(c572,plain,
asoc(op_k(rd(X,Y),Y),Z,W) = unit,
inference(equational,[status(thm)],[c28,c563]) ).
cnf(c573,plain,
asoc(op_k(X,Y),Z,W) = unit,
inference(equational,[status(thm)],[c6,c572]) ).
cnf(c582,plain,
rd(op_r(X,i(Y),Y),X) = asoc(X,i(Y),Y),
inference(equational,[status(thm)],[c2,c178,c180,c246,c567]) ).
cnf(c593,plain,
mult(asoc(X,i(Y),Y),X) = op_r(X,i(Y),Y),
inference(equational,[status(thm)],[c11,c582]) ).
cnf(c599,plain,
op_r(op_k(X,Y),i(Z),Z) = op_k(X,Y),
inference(equational,[status(thm)],[c1,c573,c593]) ).
cnf(c600,plain,
mult(op_k(X,Y),Z) = rd(Z,op_k(Y,X)),
inference(equational,[status(thm)],[c144,c441,c599]) ).
cnf(c618,plain,
mult(mult(X,Y),asoc(Z,W,V)) = mult(X,mult(Y,asoc(Z,W,V))),
inference(equational,[status(thm)],[c2,c30,c559]) ).
cnf(c619,plain,
op_r(X,Y,asoc(Z,W,V)) = X,
inference(equational,[status(thm)],[c6,c125,c618]) ).
cnf(c622,plain,
op_r(X,Y,op_k(rd(Z,W),W)) = X,
inference(equational,[status(thm)],[c563,c619]) ).
cnf(c623,plain,
op_r(X,Y,op_k(Z,W)) = X,
inference(equational,[status(thm)],[c6,c622]) ).
cnf(c624,plain,
mult(X,op_k(Y,Z)) = rd(X,op_k(Z,Y)),
inference(equational,[status(thm)],[c160,c441,c623]) ).
cnf(c626,plain,
op_k(op_k(X,Y),Z) = unit,
inference(equational,[status(thm)],[c17,c85,c188,c441,c600,c624]) ).
cnf(g1,plain,
op_k(op_k(a,b),c) = unit,
inference(equational,[status(thm)],[c626]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP728-1 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % 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 08:58:19 EDT 2025
% 0.12/0.34 % CPUTime :
% 63.22/63.36 % SZS status Unsatisfiable
% 63.22/63.36 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------