%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP670-1 : 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 06:44:40 AM UTC 2025
% Result : Unsatisfiable 81.57s 81.76s
% Output : CNFRefutation 81.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of clauses : 47 ( 47 unt; 0 nHn; 3 RR)
% Number of literals : 47 ( 46 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 111 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
mult(mult(a,b),mult(mult(c,b),c)) != mult(mult(a,mult(mult(b,c),b)),c),
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(c5,axiom,
rd(mult(X,Y),Y) = X,
file('theBenchmark.p',c04) ).
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(c11,plain,
ld(rd(X,Y),X) = Y,
inference(equational,[status(thm)],[c3,c9]) ).
cnf(c13,axiom,
mult(i(X),mult(X,Y)) = Y,
file('theBenchmark.p',c07) ).
cnf(c18,plain,
mult(i(X),Y) = ld(X,Y),
inference(equational,[status(thm)],[c7,c13]) ).
cnf(c20,plain,
ld(i(X),Y) = mult(X,Y),
inference(equational,[status(thm)],[c9,c13]) ).
cnf(c22,plain,
rd(X,mult(Y,X)) = i(Y),
inference(equational,[status(thm)],[c5,c13]) ).
cnf(c23,plain,
i(rd(X,Y)) = rd(Y,X),
inference(equational,[status(thm)],[c3,c22]) ).
cnf(c24,axiom,
mult(mult(X,Y),i(Y)) = X,
file('theBenchmark.p',c08) ).
cnf(c25,plain,
rd(X,i(Y)) = mult(X,Y),
inference(equational,[status(thm)],[c5,c24]) ).
cnf(c26,plain,
mult(X,i(Y)) = rd(X,Y),
inference(equational,[status(thm)],[c3,c24]) ).
cnf(c27,plain,
ld(mult(X,Y),X) = i(Y),
inference(equational,[status(thm)],[c13,c18,c24]) ).
cnf(c28,plain,
i(ld(X,Y)) = ld(Y,X),
inference(equational,[status(thm)],[c7,c27]) ).
cnf(c29,plain,
ld(X,i(Y)) = i(mult(Y,X)),
inference(equational,[status(thm)],[c13,c27]) ).
cnf(c30,plain,
rd(i(X),Y) = i(mult(Y,X)),
inference(equational,[status(thm)],[c22,c24]) ).
cnf(c33,plain,
mult(rd(X,Y),Z) = ld(rd(Y,X),Z),
inference(equational,[status(thm)],[c20,c23]) ).
cnf(c34,plain,
mult(X,rd(Y,Z)) = rd(X,rd(Z,Y)),
inference(equational,[status(thm)],[c23,c26]) ).
cnf(c35,plain,
mult(ld(X,Y),Z) = ld(ld(Y,X),Z),
inference(equational,[status(thm)],[c18,c28]) ).
cnf(c36,plain,
mult(X,ld(Y,Z)) = rd(X,ld(Z,Y)),
inference(equational,[status(thm)],[c26,c28]) ).
cnf(c39,plain,
rd(rd(X,Y),rd(Z,W)) = ld(rd(Y,X),rd(W,Z)),
inference(equational,[status(thm)],[c33,c34]) ).
cnf(c40,plain,
rd(ld(X,Y),ld(Z,W)) = ld(ld(Y,X),ld(W,Z)),
inference(equational,[status(thm)],[c35,c36]) ).
cnf(c43,axiom,
mult(mult(X,Y),mult(Z,mult(X,Y))) = mult(mult(mult(X,mult(Y,Z)),X),Y),
file('theBenchmark.p',c09) ).
cnf(c44,plain,
mult(mult(mult(X,mult(Y,Z)),X),Y) = mult(mult(X,Y),mult(Z,mult(X,Y))),
inference(equational,[status(thm)],[c43]) ).
cnf(c45,plain,
mult(mult(X,Y),X) = mult(X,mult(Y,X)),
inference(equational,[status(thm)],[c1,c2,c44]) ).
cnf(c46,plain,
rd(X,ld(X,Y)) = ld(rd(Y,X),X),
inference(equational,[status(thm)],[c18,c26,c33,c36,c45]) ).
cnf(c137,plain,
ld(ld(rd(mult(X,Y),Z),Z),X) = ld(ld(X,Z),rd(Y,ld(X,Z))),
inference(equational,[status(thm)],[c18,c23,c29,c33,c35,c36,c44,c46]) ).
cnf(c139,plain,
rd(ld(rd(ld(X,Y),Z),Z),Y) = ld(rd(Y,Z),rd(X,rd(Y,Z))),
inference(equational,[status(thm)],[c18,c23,c26,c29,c33,c34,c35,c36,c44]) ).
cnf(c142,plain,
ld(ld(X,rd(rd(Y,Z),X)),Z) = ld(rd(Y,mult(X,Z)),mult(X,Z)),
inference(equational,[status(thm)],[c18,c26,c33,c34,c35,c36,c44,c46]) ).
cnf(c178,plain,
rd(ld(rd(mult(X,Y),Z),Z),Y) = ld(rd(Y,Z),ld(X,rd(Z,Y))),
inference(equational,[status(thm)],[c20,c28,c30,c33,c139]) ).
cnf(c185,plain,
ld(rd(X,rd(Y,Z)),rd(Y,Z)) = ld(rd(Z,Y),ld(X,rd(Y,Z))),
inference(equational,[status(thm)],[c23,c25,c26,c29,c36,c142,c178]) ).
cnf(c186,plain,
ld(ld(rd(rd(X,Y),Z),Z),X) = ld(ld(X,Z),ld(Y,ld(Z,X))),
inference(equational,[status(thm)],[c26,c28,c30,c35,c137]) ).
cnf(c221,plain,
ld(rd(ld(X,Y),mult(Z,Y)),mult(Z,Y)) = mult(mult(Z,mult(X,Z)),Y),
inference(equational,[status(thm)],[c7,c35,c36,c44,c45,c46]) ).
cnf(c223,plain,
ld(rd(X,Y),rd(mult(X,Z),rd(X,Y))) = rd(mult(Y,mult(Z,Y)),X),
inference(equational,[status(thm)],[c13,c26,c33,c34,c44,c45]) ).
cnf(c257,plain,
ld(ld(X,rd(Y,Z)),rd(Z,Y)) = ld(rd(Y,Z),rd(X,rd(Y,Z))),
inference(equational,[status(thm)],[c28,c185]) ).
cnf(c264,plain,
ld(ld(X,ld(Y,Z)),ld(Z,Y)) = ld(Z,ld(rd(rd(Z,X),Y),Y)),
inference(equational,[status(thm)],[c28,c186]) ).
cnf(c338,plain,
ld(rd(X,Y),ld(rd(Z,X),rd(Y,X))) = rd(ld(rd(Z,Y),Y),X),
inference(equational,[status(thm)],[c18,c26,c36,c39,c46,c223]) ).
cnf(c343,plain,
ld(X,ld(rd(rd(X,ld(Y,Z)),Y),Y)) = ld(ld(rd(Z,X),X),Y),
inference(equational,[status(thm)],[c18,c26,c35,c40,c221,c264]) ).
cnf(c345,plain,
ld(ld(rd(X,Y),Y),rd(X,Z)) = ld(Y,rd(ld(rd(Y,X),X),Z)),
inference(equational,[status(thm)],[c11,c39,c257,c338,c343]) ).
cnf(c346,plain,
ld(rd(ld(rd(X,Y),Y),Z),X) = ld(rd(Y,Z),ld(rd(Y,X),X)),
inference(equational,[status(thm)],[c28,c345]) ).
cnf(c523,plain,
mult(mult(X,mult(Y,mult(Z,Y))),Z) = mult(mult(X,Y),mult(Z,mult(Y,Z))),
inference(equational,[status(thm)],[c20,c25,c29,c30,c45,c346]) ).
cnf(g1,plain,
mult(mult(a,b),mult(mult(c,b),c)) = mult(mult(a,mult(mult(b,c),b)),c),
inference(equational,[status(thm)],[c45,c523]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP670-1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n013.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 08:50:19 EDT 2025
% 0.11/0.33 % CPUTime :
% 81.57/81.76 % SZS status Unsatisfiable
% 81.57/81.76 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------