%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP684-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n007.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 06:44:42 AM UTC 2025
% Result : Unsatisfiable 1.02s 1.21s
% Output : CNFRefutation 1.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of clauses : 40 ( 40 unt; 0 nHn; 3 RR)
% Number of literals : 40 ( 39 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 77 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
rd(mult(a,mult(b,c)),mult(b,c)) != rd(mult(a,c),c),
file('theBenchmark.p',goals) ).
cnf(c1,axiom,
ld(X,mult(X,X)) = X,
file('theBenchmark.p',c01) ).
cnf(c2,axiom,
rd(mult(X,X),X) = X,
file('theBenchmark.p',c02) ).
cnf(c3,axiom,
mult(X,ld(X,Y)) = ld(X,mult(X,Y)),
file('theBenchmark.p',c03) ).
cnf(c4,plain,
ld(X,mult(X,Y)) = mult(X,ld(X,Y)),
inference(equational,[status(thm)],[c3]) ).
cnf(c5,plain,
mult(X,ld(X,X)) = X,
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c6,axiom,
mult(rd(X,Y),Y) = rd(mult(X,Y),Y),
file('theBenchmark.p',c04) ).
cnf(c7,plain,
rd(mult(mult(X,X),X),X) = mult(X,X),
inference(equational,[status(thm)],[c2,c6]) ).
cnf(c8,axiom,
ld(X,mult(X,ld(Y,Y))) = rd(mult(rd(X,X),Y),Y),
file('theBenchmark.p',c07) ).
cnf(c9,plain,
mult(X,ld(X,ld(Y,Y))) = rd(mult(rd(X,X),Y),Y),
inference(equational,[status(thm)],[c4,c8]) ).
cnf(c10,plain,
ld(X,X) = rd(X,X),
inference(equational,[status(thm)],[c2,c4,c5,c6,c9]) ).
cnf(c11,plain,
mult(X,rd(X,X)) = X,
inference(equational,[status(thm)],[c5,c10]) ).
cnf(c12,plain,
mult(X,ld(X,rd(X,X))) = rd(X,X),
inference(equational,[status(thm)],[c4,c10,c11]) ).
cnf(c13,plain,
mult(X,ld(X,rd(Y,Y))) = rd(mult(rd(X,X),Y),Y),
inference(equational,[status(thm)],[c9,c10]) ).
cnf(c18,axiom,
ld(ld(X,Y),mult(ld(X,Y),mult(Z,W))) = mult(ld(X,mult(X,Z)),W),
file('theBenchmark.p',c05) ).
cnf(c19,plain,
mult(ld(X,Y),ld(ld(X,Y),mult(Z,W))) = mult(mult(X,ld(X,Z)),W),
inference(equational,[status(thm)],[c4,c18]) ).
cnf(c20,plain,
mult(X,ld(X,mult(Y,Z))) = mult(mult(X,ld(X,Y)),Z),
inference(equational,[status(thm)],[c1,c4,c10,c11,c19]) ).
cnf(c21,plain,
mult(X,mult(X,ld(X,Y))) = mult(X,Y),
inference(equational,[status(thm)],[c4,c10,c11,c20]) ).
cnf(c24,plain,
mult(X,rd(mult(rd(X,X),Y),Y)) = mult(X,rd(Y,Y)),
inference(equational,[status(thm)],[c9,c10,c21]) ).
cnf(c25,plain,
mult(X,rd(rd(X,X),rd(X,X))) = X,
inference(equational,[status(thm)],[c2,c11,c24]) ).
cnf(c27,plain,
mult(X,ld(X,rd(mult(Y,Z),Z))) = mult(mult(X,ld(X,rd(Y,Z))),Z),
inference(equational,[status(thm)],[c6,c20]) ).
cnf(c28,plain,
mult(X,ld(X,Y)) = rd(mult(mult(rd(X,X),Y),Y),Y),
inference(equational,[status(thm)],[c2,c6,c13,c27]) ).
cnf(c29,plain,
mult(rd(X,X),rd(X,X)) = rd(X,X),
inference(equational,[status(thm)],[c7,c12,c28]) ).
cnf(c34,axiom,
rd(mult(mult(X,Y),rd(Z,W)),rd(Z,W)) = mult(X,rd(mult(Y,W),W)),
file('theBenchmark.p',c06) ).
cnf(c35,plain,
rd(mult(mult(X,Y),Z),Z) = mult(X,rd(mult(Y,Z),Z)),
inference(equational,[status(thm)],[c2,c34]) ).
cnf(c36,plain,
mult(X,rd(Y,Y)) = rd(mult(X,Y),Y),
inference(equational,[status(thm)],[c5,c10,c24,c35]) ).
cnf(c37,plain,
rd(X,rd(X,X)) = X,
inference(equational,[status(thm)],[c2,c25,c36]) ).
cnf(c38,plain,
rd(mult(X,rd(Y,Z)),rd(Y,Z)) = rd(mult(X,Z),Z),
inference(equational,[status(thm)],[c5,c10,c24,c34,c36]) ).
cnf(c39,plain,
rd(rd(mult(X,Y),Y),Y) = rd(X,Y),
inference(equational,[status(thm)],[c2,c6,c38]) ).
cnf(c42,plain,
rd(rd(mult(X,Y),Y),rd(Y,Y)) = rd(mult(X,Y),Y),
inference(equational,[status(thm)],[c36,c38]) ).
cnf(c44,plain,
rd(rd(X,Y),rd(Y,Y)) = rd(X,Y),
inference(equational,[status(thm)],[c6,c39,c42]) ).
cnf(c45,plain,
rd(mult(X,mult(Y,Y)),mult(Y,Y)) = rd(mult(X,Y),Y),
inference(equational,[status(thm)],[c2,c7,c35,c38]) ).
cnf(c52,plain,
rd(rd(mult(X,Y),Y),mult(Y,Y)) = rd(X,mult(Y,Y)),
inference(equational,[status(thm)],[c39,c45]) ).
cnf(c53,plain,
rd(mult(X,Y),Y) = rd(X,rd(Y,Y)),
inference(equational,[status(thm)],[c29,c36,c42,c52]) ).
cnf(c57,plain,
mult(X,rd(Y,rd(Z,Z))) = rd(mult(X,Y),rd(Z,Z)),
inference(equational,[status(thm)],[c35,c53]) ).
cnf(c58,plain,
rd(mult(X,Y),rd(Y,Y)) = mult(X,Y),
inference(equational,[status(thm)],[c37,c57]) ).
cnf(c83,plain,
rd(X,rd(rd(Y,Z),rd(Y,Z))) = rd(X,rd(Z,Z)),
inference(equational,[status(thm)],[c38,c53]) ).
cnf(c105,plain,
rd(X,rd(mult(Y,Z),mult(Y,Z))) = rd(X,rd(Z,Z)),
inference(equational,[status(thm)],[c44,c58,c83]) ).
cnf(g1,plain,
rd(mult(a,mult(b,c)),mult(b,c)) = rd(mult(a,c),c),
inference(equational,[status(thm)],[c53,c105]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP684-1 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.32 % Computer : n007.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 08:52:34 EDT 2025
% 0.12/0.32 % CPUTime :
% 1.02/1.21 % SZS status Unsatisfiable
% 1.02/1.21 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------