%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP669-1 : 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 06:44:40 AM UTC 2025
% Result : Unsatisfiable 68.60s 68.68s
% Output : CNFRefutation 68.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 10
% Syntax : Number of clauses : 79 ( 79 unt; 0 nHn; 3 RR)
% Number of literals : 79 ( 78 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 171 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
mult(mult(a,b),mult(c,mult(a,b))) != mult(mult(mult(a,mult(b,c)),a),b),
file('theBenchmark.p',goals) ).
cnf(c1,axiom,
mult(X,unit) = X,
file('theBenchmark.p',c05) ).
cnf(c2,axiom,
mult(unit,X) = X,
file('theBenchmark.p',c06) ).
cnf(c3,axiom,
mult(rd(X,Y),Y) = X,
file('theBenchmark.p',c03) ).
cnf(c4,plain,
rd(X,unit) = X,
inference(equational,[status(thm)],[c1,c3]) ).
cnf(c5,axiom,
rd(mult(X,Y),Y) = X,
file('theBenchmark.p',c04) ).
cnf(c6,plain,
rd(X,X) = unit,
inference(equational,[status(thm)],[c2,c5]) ).
cnf(c7,axiom,
mult(X,ld(X,Y)) = Y,
file('theBenchmark.p',c01) ).
cnf(c9,axiom,
ld(X,mult(X,Y)) = Y,
file('theBenchmark.p',c02) ).
cnf(c10,plain,
ld(X,X) = unit,
inference(equational,[status(thm)],[c1,c9]) ).
cnf(c11,plain,
ld(rd(X,Y),X) = Y,
inference(equational,[status(thm)],[c3,c9]) ).
cnf(c12,plain,
rd(X,ld(Y,X)) = Y,
inference(equational,[status(thm)],[c5,c7]) ).
cnf(c13,axiom,
mult(X,mult(Y,mult(X,Z))) = mult(mult(mult(X,Y),X),Z),
file('theBenchmark.p',c07) ).
cnf(c14,plain,
mult(mult(mult(X,Y),X),Z) = mult(X,mult(Y,mult(X,Z))),
inference(equational,[status(thm)],[c13]) ).
cnf(c15,plain,
mult(mult(X,Y),X) = mult(X,mult(Y,X)),
inference(equational,[status(thm)],[c1,c14]) ).
cnf(c16,plain,
mult(mult(X,X),Y) = mult(X,mult(X,Y)),
inference(equational,[status(thm)],[c1,c2,c14]) ).
cnf(c17,axiom,
mult(X,mult(Y,mult(Z,Y))) = mult(mult(mult(X,Y),Z),Y),
file('theBenchmark.p',c08) ).
cnf(c18,plain,
mult(mult(mult(X,Y),Z),Y) = mult(X,mult(Y,mult(Z,Y))),
inference(equational,[status(thm)],[c17]) ).
cnf(c19,plain,
mult(mult(X,Y),Y) = mult(X,mult(Y,Y)),
inference(equational,[status(thm)],[c1,c2,c18]) ).
cnf(c20,axiom,
mult(mult(X,Y),mult(Z,X)) = mult(mult(X,mult(Y,Z)),X),
file('theBenchmark.p',c09) ).
cnf(c21,plain,
mult(mult(X,Y),mult(Z,X)) = mult(X,mult(mult(Y,Z),X)),
inference(equational,[status(thm)],[c15,c20]) ).
cnf(c22,plain,
rd(mult(X,mult(X,Y)),Y) = mult(X,X),
inference(equational,[status(thm)],[c5,c16]) ).
cnf(c24,plain,
mult(X,mult(ld(X,Y),X)) = mult(Y,X),
inference(equational,[status(thm)],[c7,c15]) ).
cnf(c26,plain,
rd(mult(X,mult(Y,X)),X) = mult(X,Y),
inference(equational,[status(thm)],[c5,c15]) ).
cnf(c27,plain,
mult(X,rd(Y,X)) = rd(mult(X,Y),X),
inference(equational,[status(thm)],[c3,c26]) ).
cnf(c28,plain,
mult(rd(X,Y),mult(Y,Y)) = mult(X,Y),
inference(equational,[status(thm)],[c3,c19]) ).
cnf(c29,plain,
ld(rd(X,Y),mult(X,Y)) = mult(Y,Y),
inference(equational,[status(thm)],[c9,c28]) ).
cnf(c30,plain,
ld(rd(unit,X),X) = mult(X,X),
inference(equational,[status(thm)],[c2,c29]) ).
cnf(c31,plain,
rd(X,mult(X,X)) = rd(unit,X),
inference(equational,[status(thm)],[c12,c30]) ).
cnf(c32,plain,
rd(mult(X,Y),mult(Y,Y)) = rd(X,Y),
inference(equational,[status(thm)],[c5,c28]) ).
cnf(c35,plain,
rd(mult(X,Y),ld(X,Y)) = mult(X,X),
inference(equational,[status(thm)],[c7,c22]) ).
cnf(c36,plain,
rd(X,ld(X,unit)) = mult(X,X),
inference(equational,[status(thm)],[c1,c35]) ).
cnf(c37,plain,
ld(mult(X,X),X) = ld(X,unit),
inference(equational,[status(thm)],[c11,c36]) ).
cnf(c43,plain,
mult(mult(X,mult(Y,X)),Z) = mult(X,mult(Y,mult(X,Z))),
inference(equational,[status(thm)],[c14,c15]) ).
cnf(c44,plain,
ld(X,rd(mult(X,Y),X)) = rd(Y,X),
inference(equational,[status(thm)],[c9,c27]) ).
cnf(c45,plain,
rd(unit,X) = ld(X,unit),
inference(equational,[status(thm)],[c5,c31,c32,c37,c44]) ).
cnf(c55,plain,
ld(mult(X,Y),mult(X,mult(Y,X))) = X,
inference(equational,[status(thm)],[c9,c15]) ).
cnf(c60,plain,
mult(rd(X,Y),mult(Y,mult(Z,Y))) = mult(mult(X,Z),Y),
inference(equational,[status(thm)],[c3,c18]) ).
cnf(c61,plain,
mult(mult(X,rd(Y,Z)),Z) = mult(rd(X,Z),mult(Z,Y)),
inference(equational,[status(thm)],[c3,c60]) ).
cnf(c62,plain,
mult(ld(X,unit),mult(X,Y)) = Y,
inference(equational,[status(thm)],[c2,c3,c45,c61]) ).
cnf(c63,plain,
rd(X,mult(Y,X)) = ld(Y,unit),
inference(equational,[status(thm)],[c5,c62]) ).
cnf(c64,plain,
ld(ld(X,unit),Y) = mult(X,Y),
inference(equational,[status(thm)],[c9,c62]) ).
cnf(c65,plain,
mult(ld(X,unit),Y) = ld(X,Y),
inference(equational,[status(thm)],[c7,c62]) ).
cnf(c67,plain,
ld(rd(X,Y),unit) = rd(Y,X),
inference(equational,[status(thm)],[c3,c63]) ).
cnf(c69,plain,
mult(mult(X,Y),ld(Y,unit)) = X,
inference(equational,[status(thm)],[c3,c60,c62]) ).
cnf(c70,plain,
ld(mult(X,Y),X) = ld(Y,unit),
inference(equational,[status(thm)],[c62,c65,c69]) ).
cnf(c71,plain,
rd(X,ld(Y,unit)) = mult(X,Y),
inference(equational,[status(thm)],[c5,c69]) ).
cnf(c72,plain,
mult(X,ld(Y,unit)) = rd(X,Y),
inference(equational,[status(thm)],[c3,c69]) ).
cnf(c73,plain,
ld(X,rd(X,Y)) = ld(Y,unit),
inference(equational,[status(thm)],[c62,c65,c72]) ).
cnf(c74,plain,
rd(ld(X,unit),Y) = ld(mult(Y,X),unit),
inference(equational,[status(thm)],[c63,c69]) ).
cnf(c75,plain,
ld(ld(X,Y),unit) = ld(Y,X),
inference(equational,[status(thm)],[c65,c71,c74]) ).
cnf(c76,plain,
mult(X,rd(Y,Z)) = rd(X,rd(Z,Y)),
inference(equational,[status(thm)],[c67,c71]) ).
cnf(c80,plain,
mult(rd(X,Y),Z) = ld(rd(Y,X),Z),
inference(equational,[status(thm)],[c64,c67]) ).
cnf(c81,plain,
ld(mult(X,Y),unit) = ld(Y,ld(X,unit)),
inference(equational,[status(thm)],[c65,c72,c74]) ).
cnf(c82,plain,
mult(ld(X,Y),Z) = ld(ld(Y,X),Z),
inference(equational,[status(thm)],[c65,c75]) ).
cnf(c83,plain,
mult(X,ld(Y,Z)) = rd(X,ld(Z,Y)),
inference(equational,[status(thm)],[c72,c75]) ).
cnf(c84,plain,
rd(X,ld(X,Y)) = ld(rd(Y,X),X),
inference(equational,[status(thm)],[c24,c65,c73,c80,c83]) ).
cnf(c88,plain,
ld(rd(ld(X,Y),Z),Y) = ld(rd(Y,Z),mult(X,Y)),
inference(equational,[status(thm)],[c24,c60,c80,c83]) ).
cnf(c89,plain,
ld(ld(X,Y),Y) = ld(Y,mult(X,Y)),
inference(equational,[status(thm)],[c4,c88]) ).
cnf(c94,plain,
rd(mult(X,mult(Y,mult(Z,Y))),Y) = mult(mult(X,Y),Z),
inference(equational,[status(thm)],[c5,c18]) ).
cnf(c95,plain,
rd(mult(X,mult(Y,Z)),Y) = rd(mult(X,Y),rd(Y,Z)),
inference(equational,[status(thm)],[c3,c76,c94]) ).
cnf(c97,plain,
rd(mult(X,mult(Y,Z)),Z) = rd(mult(X,Z),ld(Y,Z)),
inference(equational,[status(thm)],[c5,c24,c82,c84,c89,c95]) ).
cnf(c98,plain,
rd(X,ld(mult(X,Y),ld(Z,X))) = mult(mult(Z,X),Y),
inference(equational,[status(thm)],[c7,c14,c82,c83]) ).
cnf(c101,plain,
rd(mult(X,Y),ld(Z,Y)) = rd(Y,ld(Z,ld(X,Y))),
inference(equational,[status(thm)],[c7,c83,c98]) ).
cnf(c102,plain,
rd(X,ld(mult(X,Y),Z)) = ld(ld(X,rd(Z,X)),Y),
inference(equational,[status(thm)],[c11,c80,c82,c98]) ).
cnf(c106,plain,
ld(rd(rd(rd(X,Y),Z),X),X) = mult(mult(X,Z),Y),
inference(equational,[status(thm)],[c3,c21,c76,c80,c83,c84]) ).
cnf(c107,plain,
rd(rd(rd(X,Y),Z),X) = rd(X,mult(mult(X,Z),Y)),
inference(equational,[status(thm)],[c12,c106]) ).
cnf(c109,plain,
rd(X,mult(X,mult(Y,X))) = ld(Y,ld(X,unit)),
inference(equational,[status(thm)],[c6,c15,c45,c74,c81,c107]) ).
cnf(c110,plain,
ld(ld(X,Y),ld(X,unit)) = ld(Y,unit),
inference(equational,[status(thm)],[c24,c63,c109]) ).
cnf(c131,plain,
ld(rd(X,Y),mult(mult(X,Z),Y)) = mult(Y,mult(Z,Y)),
inference(equational,[status(thm)],[c9,c60]) ).
cnf(c186,plain,
mult(mult(X,Y),mult(X,mult(Z,X))) = mult(X,mult(mult(Y,mult(X,Z)),X)),
inference(equational,[status(thm)],[c14,c15,c18]) ).
cnf(c188,plain,
ld(mult(X,Y),ld(Y,unit)) = ld(Y,ld(X,ld(Y,unit))),
inference(equational,[status(thm)],[c55,c81,c110]) ).
cnf(c238,plain,
ld(ld(X,ld(Y,ld(X,unit))),Z) = mult(X,mult(Y,mult(X,Z))),
inference(equational,[status(thm)],[c10,c15,c43,c74,c81,c94,c97,c101,c102,c186]) ).
cnf(c245,plain,
ld(mult(X,Y),mult(X,mult(mult(Y,Z),X))) = mult(Z,X),
inference(equational,[status(thm)],[c9,c21]) ).
cnf(c246,plain,
ld(mult(X,Y),mult(X,mult(Z,X))) = ld(ld(Z,Y),X),
inference(equational,[status(thm)],[c7,c82,c245]) ).
cnf(c247,plain,
rd(mult(X,mult(mult(Y,Z),X)),mult(Z,X)) = mult(X,Y),
inference(equational,[status(thm)],[c5,c21]) ).
cnf(c320,plain,
mult(mult(X,Y),mult(Z,mult(X,Y))) = mult(X,mult(Y,mult(mult(Z,X),Y))),
inference(equational,[status(thm)],[c18,c21,c43,c70,c81,c131,c188,c238,c246,c247]) ).
cnf(g1,plain,
mult(mult(a,b),mult(c,mult(a,b))) = mult(mult(mult(a,mult(b,c)),a),b),
inference(equational,[status(thm)],[c14,c21,c320]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP669-1 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n015.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Jul 14 08:50:04 EDT 2025
% 0.11/0.33 % CPUTime :
% 68.60/68.68 % SZS status Unsatisfiable
% 68.60/68.68 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------