%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP660-12 : TPTP v9.0.0. Released v8.1.0.
% 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 06:44:37 AM UTC 2025
% Result : Unsatisfiable 61.25s 61.37s
% Output : CNFRefutation 61.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of clauses : 65 ( 65 unt; 0 nHn; 3 RR)
% Number of literals : 65 ( 64 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 143 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
mult(rd(x1,x1),x0) != x0,
file('theBenchmark.p',goal) ).
cnf(c1,axiom,
mult(X,ld(X,Y)) = Y,
file('theBenchmark.p',f01) ).
cnf(c2,axiom,
ld(X,mult(X,Y)) = Y,
file('theBenchmark.p',f02) ).
cnf(c3,axiom,
mult(rd(X,Y),Y) = X,
file('theBenchmark.p',f03) ).
cnf(c4,axiom,
rd(mult(X,Y),Y) = X,
file('theBenchmark.p',f04) ).
cnf(c5,plain,
rd(X,ld(Y,X)) = Y,
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c6,plain,
ld(rd(X,Y),X) = Y,
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c7,axiom,
mult(mult(mult(X,Y),Z),X) = mult(X,mult(Y,mult(Z,X))),
file('theBenchmark.p',f05) ).
cnf(c8,plain,
rd(mult(X,mult(Y,mult(Z,X))),X) = mult(mult(X,Y),Z),
inference(equational,[status(thm)],[c4,c7]) ).
cnf(c9,plain,
mult(mult(X,Y),rd(Z,X)) = rd(mult(X,mult(Y,Z)),X),
inference(equational,[status(thm)],[c3,c8]) ).
cnf(c10,plain,
mult(X,mult(ld(X,Y),mult(Z,X))) = mult(mult(Y,Z),X),
inference(equational,[status(thm)],[c1,c7]) ).
cnf(c12,plain,
mult(mult(X,rd(Y,Z)),Z) = mult(Z,mult(ld(Z,X),Y)),
inference(equational,[status(thm)],[c3,c10]) ).
cnf(c13,plain,
mult(mult(X,rd(Y,mult(Z,X))),Z) = rd(mult(X,Y),X),
inference(equational,[status(thm)],[c3,c8]) ).
cnf(c14,plain,
mult(X,rd(Y,mult(Z,X))) = rd(rd(mult(X,Y),X),Z),
inference(equational,[status(thm)],[c4,c13]) ).
cnf(c15,plain,
rd(mult(X,mult(ld(X,Y),Z)),X) = mult(Y,rd(Z,X)),
inference(equational,[status(thm)],[c4,c12]) ).
cnf(c16,plain,
mult(X,mult(Y,mult(ld(mult(X,Y),Z),X))) = mult(Z,X),
inference(equational,[status(thm)],[c1,c7]) ).
cnf(c17,plain,
mult(X,mult(ld(mult(Y,X),Z),Y)) = ld(Y,mult(Z,Y)),
inference(equational,[status(thm)],[c2,c16]) ).
cnf(c18,plain,
mult(ld(mult(X,Y),Z),X) = ld(Y,ld(X,mult(Z,X))),
inference(equational,[status(thm)],[c2,c17]) ).
cnf(c19,plain,
rd(ld(X,ld(Y,mult(Z,Y))),Y) = ld(mult(Y,X),Z),
inference(equational,[status(thm)],[c4,c18]) ).
cnf(c20,plain,
rd(ld(X,Y),Y) = ld(mult(Y,X),Y),
inference(equational,[status(thm)],[c2,c19]) ).
cnf(c21,plain,
ld(mult(X,rd(X,Y)),X) = rd(Y,X),
inference(equational,[status(thm)],[c6,c20]) ).
cnf(c22,plain,
mult(X,rd(X,Y)) = rd(X,rd(Y,X)),
inference(equational,[status(thm)],[c5,c21]) ).
cnf(c24,plain,
ld(X,rd(X,rd(Y,X))) = rd(X,Y),
inference(equational,[status(thm)],[c2,c22]) ).
cnf(c25,plain,
rd(X,mult(Y,X)) = ld(X,rd(X,Y)),
inference(equational,[status(thm)],[c4,c24]) ).
cnf(c26,plain,
ld(ld(X,Y),ld(X,mult(Z,X))) = mult(ld(Y,Z),X),
inference(equational,[status(thm)],[c1,c18]) ).
cnf(c27,plain,
mult(ld(X,Y),Y) = ld(ld(Y,X),Y),
inference(equational,[status(thm)],[c2,c26]) ).
cnf(c28,plain,
ld(ld(X,rd(X,Y)),X) = mult(Y,X),
inference(equational,[status(thm)],[c6,c27]) ).
cnf(c29,plain,
mult(ld(X,rd(Y,Z)),Z) = ld(ld(Z,X),ld(Z,Y)),
inference(equational,[status(thm)],[c3,c26]) ).
cnf(c30,plain,
mult(X,rd(ld(ld(Y,X),Z),Y)) = rd(mult(Y,Z),Y),
inference(equational,[status(thm)],[c1,c15]) ).
cnf(c32,plain,
ld(X,rd(rd(mult(X,Y),X),Z)) = rd(Y,mult(Z,X)),
inference(equational,[status(thm)],[c2,c14]) ).
cnf(c33,plain,
rd(ld(X,Y),mult(Z,X)) = ld(X,rd(rd(Y,X),Z)),
inference(equational,[status(thm)],[c1,c32]) ).
cnf(c34,plain,
rd(rd(mult(X,Y),X),rd(Z,X)) = mult(X,rd(Y,Z)),
inference(equational,[status(thm)],[c3,c14]) ).
cnf(c35,plain,
mult(X,rd(ld(X,Y),Z)) = rd(rd(Y,X),rd(Z,X)),
inference(equational,[status(thm)],[c1,c34]) ).
cnf(c39,plain,
mult(X,mult(ld(Y,Z),rd(Y,X))) = ld(rd(Y,X),mult(Z,rd(Y,X))),
inference(equational,[status(thm)],[c3,c17]) ).
cnf(c43,plain,
mult(X,mult(ld(X,rd(Y,rd(Z,X))),Z)) = mult(Y,X),
inference(equational,[status(thm)],[c3,c12]) ).
cnf(c44,plain,
mult(ld(X,rd(Y,rd(Z,X))),Z) = ld(X,mult(Y,X)),
inference(equational,[status(thm)],[c2,c43]) ).
cnf(c45,plain,
rd(ld(X,mult(Y,X)),Z) = ld(X,rd(Y,rd(Z,X))),
inference(equational,[status(thm)],[c4,c44]) ).
cnf(c46,plain,
ld(mult(X,Y),rd(mult(X,mult(Y,Z)),X)) = rd(Z,X),
inference(equational,[status(thm)],[c2,c9]) ).
cnf(c47,plain,
ld(mult(mult(X,Y),X),mult(X,Y)) = ld(Y,rd(Y,X)),
inference(equational,[status(thm)],[c4,c25,c46]) ).
cnf(c50,plain,
ld(ld(X,Y),rd(ld(X,Y),X)) = ld(mult(Y,X),Y),
inference(equational,[status(thm)],[c1,c47]) ).
cnf(c54,plain,
ld(X,rd(rd(Y,X),rd(Z,X))) = rd(ld(X,Y),Z),
inference(equational,[status(thm)],[c3,c33]) ).
cnf(c60,plain,
ld(ld(X,X),ld(mult(X,X),X)) = ld(mult(X,X),X),
inference(equational,[status(thm)],[c20,c50]) ).
cnf(c64,plain,
mult(ld(X,Y),mult(ld(ld(X,Y),Z),Y)) = mult(mult(Z,X),ld(X,Y)),
inference(equational,[status(thm)],[c1,c10]) ).
cnf(c71,plain,
mult(X,rd(ld(Y,Z),rd(X,Y))) = rd(mult(rd(X,Y),Z),rd(X,Y)),
inference(equational,[status(thm)],[c6,c30]) ).
cnf(c78,plain,
mult(ld(ld(X,Y),rd(Z,X)),Y) = ld(ld(X,Y),mult(Z,ld(X,Y))),
inference(equational,[status(thm)],[c5,c44]) ).
cnf(c103,plain,
ld(ld(X,ld(X,X)),ld(X,Y)) = ld(ld(X,X),mult(Y,ld(X,X))),
inference(equational,[status(thm)],[c29,c78]) ).
cnf(c110,plain,
rd(mult(rd(X,X),Y),rd(X,X)) = rd(rd(Y,X),rd(rd(X,X),X)),
inference(equational,[status(thm)],[c35,c71]) ).
cnf(c111,plain,
rd(rd(X,X),rd(rd(X,X),X)) = rd(X,rd(X,X)),
inference(equational,[status(thm)],[c3,c110]) ).
cnf(c112,plain,
rd(ld(X,X),rd(X,X)) = rd(X,X),
inference(equational,[status(thm)],[c24,c54,c111]) ).
cnf(c118,plain,
ld(ld(X,X),ld(X,X)) = ld(X,ld(ld(X,X),X)),
inference(equational,[status(thm)],[c27,c29,c44,c112]) ).
cnf(c125,plain,
ld(rd(X,rd(X,X)),rd(X,X)) = rd(rd(X,X),X),
inference(equational,[status(thm)],[c6,c111]) ).
cnf(c131,plain,
ld(rd(X,X),rd(Y,rd(X,rd(X,X)))) = mult(Y,rd(rd(X,X),X)),
inference(equational,[status(thm)],[c15,c39,c45]) ).
cnf(c132,plain,
rd(X,rd(X,X)) = X,
inference(equational,[status(thm)],[c3,c6,c22,c28,c131]) ).
cnf(c133,plain,
rd(X,X) = ld(X,X),
inference(equational,[status(thm)],[c6,c132]) ).
cnf(c134,plain,
ld(ld(X,X),X) = X,
inference(equational,[status(thm)],[c2,c27,c44,c132]) ).
cnf(c135,plain,
ld(mult(X,X),X) = ld(X,ld(X,X)),
inference(equational,[status(thm)],[c20,c125,c132,c133]) ).
cnf(c139,plain,
mult(X,ld(Y,ld(Y,Y))) = ld(ld(Y,Y),rd(X,Y)),
inference(equational,[status(thm)],[c20,c131,c132,c133,c135]) ).
cnf(c141,plain,
mult(ld(X,Y),ld(Y,Y)) = ld(ld(ld(Y,Y),X),Y),
inference(equational,[status(thm)],[c6,c29,c132,c133]) ).
cnf(c166,plain,
rd(rd(ld(X,Y),X),ld(mult(Y,X),Y)) = ld(X,Y),
inference(equational,[status(thm)],[c5,c50]) ).
cnf(c167,plain,
ld(ld(X,X),ld(X,ld(X,X))) = ld(X,ld(X,X)),
inference(equational,[status(thm)],[c20,c27,c60,c103,c118,c134,c135,c141,c166]) ).
cnf(c183,plain,
mult(mult(X,ld(Y,X)),ld(ld(Y,X),Z)) = rd(mult(X,mult(mult(Z,Y),ld(Y,X))),X),
inference(equational,[status(thm)],[c8,c64]) ).
cnf(c184,plain,
rd(X,ld(Y,Y)) = X,
inference(equational,[status(thm)],[c1,c4,c20,c135,c139,c167,c183]) ).
cnf(c186,plain,
mult(ld(X,X),Y) = Y,
inference(equational,[status(thm)],[c28,c134,c184]) ).
cnf(g1,plain,
mult(rd(x1,x1),x0) = x0,
inference(equational,[status(thm)],[c133,c186]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP660-12 : TPTP v9.0.0. Released v8.1.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.32 % Computer : n015.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Jul 14 08:46:05 EDT 2025
% 0.12/0.32 % CPUTime :
% 61.25/61.37 % SZS status Unsatisfiable
% 61.25/61.37 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------