%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : NUN135-1.006 : TPTP v9.3.0. Released v9.3.0.
% 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 May 5 06:48:44 PM UTC 2026
% Result : Unsatisfiable 0.54s 0.80s
% Output : CNFRefutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 31 ( 30 unt; 0 def)
% Number of atoms : 33 ( 32 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 : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-4 aty)
% Number of variables : 61 ( 8 sgn 1 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
perfectp(X) != true,
file('theBenchmark.p',goal) ).
fof(e,plain,
! [X] :
( true0 != false0
& eq(X,X) = true0
& eq(perfectp(X),true) = false0 ),
inference(encode_existential,[status(esa)],[g0]) ).
cnf(g1,plain,
true0 != false0,
inference(split_conjunct,[status(thm)],[e]) ).
cnf(c2,plain,
eq(X,X) = true0,
inference(split_conjunct,[status(thm)],[e]) ).
cnf(c3,axiom,
minus(X,zero) = X,
file('theBenchmark.p',rule1) ).
cnf(c4,axiom,
'<='(zero,X) = true,
file('theBenchmark.p',rule3) ).
cnf(c5,axiom,
if(false,X,Y) = Y,
file('theBenchmark.p',rule7) ).
cnf(c6,axiom,
if(true,X,Y) = X,
file('theBenchmark.p',rule6) ).
cnf(c7,plain,
eq(perfectp(X),true) = false0,
inference(split_conjunct,[status(thm)],[e]) ).
cnf(c9,axiom,
'<='(s(X),zero) = false,
file('theBenchmark.p',rule4) ).
cnf(c10,axiom,
f(zero,X,zero,Y) = true,
file('theBenchmark.p',rule10) ).
cnf(c11,axiom,
'<='(s(X),s(Y)) = '<='(X,Y),
file('theBenchmark.p',rule5) ).
cnf(c12,axiom,
minus(s(X),s(Y)) = minus(X,Y),
file('theBenchmark.p',rule2) ).
cnf(c14,axiom,
perfectp(s(X)) = f(X,s(zero),s(X),s(X)),
file('theBenchmark.p',rule9) ).
cnf(c15,axiom,
f(s(X),zero,Y,Z) = f(X,Z,minus(Y,s(X)),Z),
file('theBenchmark.p',rule12) ).
cnf(c16,plain,
eq(f(X,s(zero),s(X),s(X)),true) = false0,
inference(equational,[status(thm)],[c7,c14]) ).
cnf(c17,axiom,
f(s(X),s(Y),Z,W) = if('<='(X,Y),f(s(X),minus(Y,X),Z,W),f(X,W,Z,W)),
file('theBenchmark.p',rule13) ).
cnf(c18,plain,
if('<='(X,Y),f(s(X),minus(Y,X),Z,W),f(X,W,Z,W)) = f(s(X),s(Y),Z,W),
inference(equational,[status(thm)],[c17]) ).
cnf(c19,plain,
f(s(zero),s(X),Y,Z) = f(s(zero),X,Y,Z),
inference(equational,[status(thm)],[c3,c4,c6,c18]) ).
cnf(c20,plain,
f(s(s(X)),s(zero),Y,Z) = f(s(X),Z,Y,Z),
inference(equational,[status(thm)],[c5,c9,c18]) ).
cnf(c21,plain,
eq(f(s(X),s(s(s(X))),s(s(s(X))),s(s(s(X)))),true) = false0,
inference(equational,[status(thm)],[c16,c20]) ).
cnf(c22,plain,
if('<='(X,Y),f(s(s(X)),minus(Y,X),Z,W),f(s(X),W,Z,W)) = f(s(s(X)),s(s(Y)),Z,W),
inference(equational,[status(thm)],[c11,c12,c18]) ).
cnf(c23,plain,
f(s(s(zero)),s(s(X)),Y,Z) = f(s(s(zero)),X,Y,Z),
inference(equational,[status(thm)],[c3,c4,c6,c22]) ).
cnf(c24,plain,
f(s(s(s(X))),s(s(zero)),Y,Z) = f(s(s(X)),Z,Y,Z),
inference(equational,[status(thm)],[c5,c9,c22]) ).
cnf(c26,plain,
if('<='(X,Y),f(s(s(s(X))),minus(Y,X),Z,W),f(s(s(X)),W,Z,W)) = f(s(s(s(X))),s(s(s(Y))),Z,W),
inference(equational,[status(thm)],[c11,c12,c22]) ).
cnf(c27,plain,
f(s(s(s(zero))),s(s(s(X))),Y,Z) = f(s(s(s(zero))),X,Y,Z),
inference(equational,[status(thm)],[c3,c4,c6,c26]) ).
cnf(c36,plain,
if('<='(X,Y),f(s(s(s(s(X)))),minus(Y,X),Z,W),f(s(s(s(X))),W,Z,W)) = f(s(s(s(s(X)))),s(s(s(s(Y)))),Z,W),
inference(equational,[status(thm)],[c11,c12,c26]) ).
cnf(c37,plain,
f(s(s(s(s(zero)))),s(s(s(s(X)))),Y,Z) = f(s(s(s(s(zero)))),X,Y,Z),
inference(equational,[status(thm)],[c3,c4,c6,c36]) ).
cnf(c38,plain,
true0 = false0,
inference(equational,[status(thm)],[c2,c3,c10,c12,c15,c19,c21,c23,c24,c27,c37]) ).
cnf(g2,plain,
true0 = false0,
inference(equational,[status(thm)],[c38]) ).
cnf(g3,plain,
$false,
inference(resolution,[status(thm)],[g1,g2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN135-1.006 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_Leo-III %s %d THM
% 0.15/0.33 % Computer : n015.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 04:50:01 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.54/0.80 % SZS status Unsatisfiable
% 0.54/0.80 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------