%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP731-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n015.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 06:44:49 AM UTC 2025
% Result : Unsatisfiable 63.30s 63.45s
% Output : CNFRefutation 63.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of clauses : 61 ( 61 unt; 0 nHn; 3 RR)
% Number of literals : 61 ( 60 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 : 13 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 135 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
op_k(asoc(a,b,c),d) != unit,
file('theBenchmark.p',goals) ).
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(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(c32,plain,
mult(X,i(mult(X,Y))) = i(Y),
inference(equational,[status(thm)],[c10,c13,c15]) ).
cnf(c34,axiom,
op_t(op_l(X,Y,Z),W) = op_l(op_t(X,W),Y,Z),
file('theBenchmark.p',c19) ).
cnf(c37,plain,
mult(X,mult(i(X),Y)) = Y,
inference(equational,[status(thm)],[c10,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(c49,plain,
rd(X,i(Y)) = rd(Y,i(X)),
inference(equational,[status(thm)],[c10,c48]) ).
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(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(c132,plain,
mult(mult(X,Y),i(Y)) = op_r(X,Y,i(Y)),
inference(equational,[status(thm)],[c3,c8,c125]) ).
cnf(c168,plain,
rd(X,i(op_r(Y,X,i(X)))) = mult(Y,X),
inference(equational,[status(thm)],[c6,c49,c132]) ).
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(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(c361,plain,
mult(X,rd(mult(i(X),Y),X)) = mult(Y,i(X)),
inference(equational,[status(thm)],[c37,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(c566,plain,
mult(X,asoc(X,Y,i(Y))) = op_r(X,Y,i(Y)),
inference(equational,[status(thm)],[c2,c3,c132,c559]) ).
cnf(c598,plain,
op_r(asoc(X,Y,Z),W,i(W)) = asoc(X,Y,Z),
inference(equational,[status(thm)],[c2,c28,c566]) ).
cnf(c605,plain,
rd(X,i(asoc(Y,Z,W))) = mult(asoc(Y,Z,W),X),
inference(equational,[status(thm)],[c168,c598]) ).
cnf(c608,plain,
mult(asoc(X,Y,Z),W) = mult(W,asoc(X,Y,Z)),
inference(equational,[status(thm)],[c10,c15,c361,c605]) ).
cnf(c610,plain,
op_k(asoc(X,Y,Z),W) = unit,
inference(equational,[status(thm)],[c3,c188,c441,c608]) ).
cnf(g1,plain,
op_k(asoc(a,b,c),d) = unit,
inference(equational,[status(thm)],[c610]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP731-1 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n015.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Jul 14 08:58:34 EDT 2025
% 0.11/0.32 % CPUTime :
% 63.30/63.45 % SZS status Unsatisfiable
% 63.30/63.45 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------