%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP700-10 : TPTP v9.0.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n004.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 06:44:44 AM UTC 2025
% Result : Unsatisfiable 0.80s 0.99s
% Output : CNFRefutation 0.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 23 unt; 0 def)
% Number of atoms : 26 ( 25 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 5 ( 3 ~; 0 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 1 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
tuple(mult(X1,x0),mult(x0,X1)) != tuple(unit,unit),
file('theBenchmark.p',goal) ).
fof(e,plain,
! [X1] :
( true != false
& eq(X1,X1) = true
& eq(tuple(mult(X1,x0),mult(x0,X1)),tuple(unit,unit)) = false ),
inference(encode_existential,[status(esa)],[g0]) ).
cnf(g1,plain,
true != false,
inference(split_conjunct,[status(thm)],[e]) ).
cnf(c1,plain,
eq(X,X) = true,
inference(split_conjunct,[status(thm)],[e]) ).
cnf(c2,axiom,
mult(X,unit) = X,
file('theBenchmark.p',f05) ).
cnf(c3,axiom,
mult(unit,X) = X,
file('theBenchmark.p',f06) ).
cnf(c4,axiom,
mult(rd(X,Y),Y) = X,
file('theBenchmark.p',f03) ).
cnf(c6,axiom,
rd(mult(X,Y),Y) = X,
file('theBenchmark.p',f04) ).
cnf(c8,axiom,
mult(X,ld(X,Y)) = Y,
file('theBenchmark.p',f01) ).
cnf(c10,axiom,
ld(X,mult(X,Y)) = Y,
file('theBenchmark.p',f02) ).
cnf(c11,plain,
ld(X,X) = unit,
inference(equational,[status(thm)],[c2,c10]) ).
cnf(c13,plain,
rd(X,ld(Y,X)) = Y,
inference(equational,[status(thm)],[c6,c8]) ).
cnf(c21,axiom,
mult(mult(X,Y),mult(Y,mult(Z,Y))) = mult(mult(X,mult(Y,mult(Y,Z))),Y),
file('theBenchmark.p',f08) ).
cnf(c22,plain,
mult(mult(X,mult(Y,mult(Y,Z))),Y) = mult(mult(X,Y),mult(Y,mult(Z,Y))),
inference(equational,[status(thm)],[c21]) ).
cnf(c23,plain,
mult(mult(X,mult(X,Y)),X) = mult(X,mult(X,mult(Y,X))),
inference(equational,[status(thm)],[c3,c22]) ).
cnf(c32,plain,
rd(mult(X,mult(X,mult(Y,X))),X) = mult(X,mult(X,Y)),
inference(equational,[status(thm)],[c6,c23]) ).
cnf(c33,plain,
rd(mult(X,mult(X,Y)),X) = mult(X,mult(X,rd(Y,X))),
inference(equational,[status(thm)],[c4,c32]) ).
cnf(c34,plain,
mult(X,mult(X,rd(unit,X))) = X,
inference(equational,[status(thm)],[c2,c6,c33]) ).
cnf(c35,plain,
mult(X,rd(unit,X)) = unit,
inference(equational,[status(thm)],[c10,c11,c34]) ).
cnf(c37,plain,
mult(ld(X,unit),X) = unit,
inference(equational,[status(thm)],[c13,c35]) ).
cnf(c55,plain,
eq(tuple(mult(X,x0),mult(x0,X)),tuple(unit,unit)) = false,
inference(split_conjunct,[status(thm)],[e]) ).
cnf(c56,plain,
true = false,
inference(equational,[status(thm)],[c1,c8,c37,c55]) ).
cnf(g2,plain,
true = false,
inference(equational,[status(thm)],[c56]) ).
cnf(g3,plain,
$false,
inference(resolution,[status(thm)],[g1,g2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP700-10 : TPTP v9.0.0. Released v8.1.0.
% 0.10/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n004.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 08:54:04 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.80/0.99 % SZS status Unsatisfiable
% 0.80/0.99 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------