%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP710-11 : 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 06:44:47 AM UTC 2025
% Result : Unsatisfiable 0.44s 0.61s
% Output : CNFRefutation 0.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 29 unt; 0 def)
% Number of atoms : 32 ( 31 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 40 ( 7 sgn 1 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
mult(X5,x4) != x3,
file('theBenchmark.p',goal) ).
fof(e,plain,
! [X5] :
( true != false
& eq(X5,X5) = true
& eq(mult(X5,x4),x3) = 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',f01) ).
cnf(c3,axiom,
mult(unit,X) = X,
file('theBenchmark.p',f02) ).
cnf(c4,axiom,
mult(X,i(X)) = unit,
file('theBenchmark.p',f04) ).
cnf(c6,axiom,
mult(i(X),X) = unit,
file('theBenchmark.p',f05) ).
cnf(c7,plain,
eq(mult(X,x4),x3) = false,
inference(split_conjunct,[status(thm)],[e]) ).
cnf(c10,axiom,
mult(X,mult(Y,mult(Y,Z))) = mult(mult(mult(X,Y),Y),Z),
file('theBenchmark.p',f03) ).
cnf(c11,plain,
mult(mult(mult(X,Y),Y),Z) = mult(X,mult(Y,mult(Y,Z))),
inference(equational,[status(thm)],[c10]) ).
cnf(c12,plain,
mult(mult(X,Y),Y) = mult(X,mult(Y,Y)),
inference(equational,[status(thm)],[c2,c11]) ).
cnf(c13,plain,
mult(mult(X,X),Y) = mult(X,mult(X,Y)),
inference(equational,[status(thm)],[c3,c11]) ).
cnf(c17,plain,
mult(X,mult(i(X),i(X))) = i(X),
inference(equational,[status(thm)],[c3,c4,c12]) ).
cnf(c19,plain,
mult(i(X),mult(X,mult(X,Y))) = mult(X,Y),
inference(equational,[status(thm)],[c3,c6,c11]) ).
cnf(c21,plain,
mult(X,mult(X,i(mult(X,X)))) = unit,
inference(equational,[status(thm)],[c4,c13]) ).
cnf(c22,plain,
mult(X,i(mult(X,X))) = i(X),
inference(equational,[status(thm)],[c2,c19,c21]) ).
cnf(c27,plain,
mult(mult(X,mult(Y,Y)),Z) = mult(X,mult(Y,mult(Y,Z))),
inference(equational,[status(thm)],[c11,c12]) ).
cnf(c28,plain,
eq(mult(X,mult(Y,mult(Y,x4))),x3) = false,
inference(equational,[status(thm)],[c7,c11]) ).
cnf(c29,plain,
eq(mult(X,i(x4)),x3) = false,
inference(equational,[status(thm)],[c2,c6,c28]) ).
cnf(c36,plain,
eq(mult(X,mult(i(x4),i(x4))),x3) = false,
inference(equational,[status(thm)],[c12,c29]) ).
cnf(c38,plain,
mult(i(mult(X,X)),mult(X,mult(X,Y))) = Y,
inference(equational,[status(thm)],[c3,c6,c27]) ).
cnf(c39,plain,
mult(i(X),i(X)) = i(mult(X,X)),
inference(equational,[status(thm)],[c2,c4,c17,c38]) ).
cnf(c45,plain,
eq(mult(X,i(mult(x4,x4))),x3) = false,
inference(equational,[status(thm)],[c36,c39]) ).
cnf(c47,plain,
mult(mult(X,mult(Y,mult(Y,Z))),Z) = mult(X,mult(Y,mult(Y,mult(Z,Z)))),
inference(equational,[status(thm)],[c11,c12,c27]) ).
cnf(c48,plain,
mult(mult(X,Y),i(Y)) = X,
inference(equational,[status(thm)],[c2,c4,c22,c39,c47]) ).
cnf(c49,plain,
eq(X,x3) = false,
inference(equational,[status(thm)],[c45,c48]) ).
cnf(c50,plain,
true = false,
inference(equational,[status(thm)],[c1,c49]) ).
cnf(g2,plain,
true = false,
inference(equational,[status(thm)],[c50]) ).
cnf(g3,plain,
$false,
inference(resolution,[status(thm)],[g1,g2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP710-11 : TPTP v9.0.0. Released v8.1.0.
% 0.11/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 14 08:55:34 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.44/0.61 % SZS status Unsatisfiable
% 0.44/0.61 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------