%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM924+3 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:14:06 AM UTC 2026
% Result : Theorem 99.13s 19.79s
% Output : CNFRefutation 99.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 53 ( 53 unt; 0 def)
% Number of atoms : 53 ( 29 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 8 con; 0-2 aty)
% Number of variables : 34 ( 1 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096,axiom,
hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint','hAPP$uint$uint'('times$utimes$uint'('hAPP$uint$uint'('plus$uplus$uint'('hAPP$uint$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls))))),m)),'one$uone$uint')),t)),'hAPP$uint$uint'('times$utimes$uint'('hAPP$uint$uint'('plus$uplus$uint'('hAPP$uint$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls))))),m)),'one$uone$uint')),'zero$uzero$uint'))) ).
fof(fact_3_t,axiom,
'hAPP$uint$uint'('plus$uplus$uint'('hAPP$unat$uint'('power$upower$uint'(s),'number$unumber$uof$unat'(bit0(bit1(pls))))),'one$uone$uint') = 'hAPP$uint$uint'('times$utimes$uint'('hAPP$uint$uint'('plus$uplus$uint'('hAPP$uint$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls))))),m)),'one$uone$uint')),t) ).
fof(fact_41_zmult__assoc,axiom,
! [X0,X1,X2] : 'hAPP$uint$uint'('times$utimes$uint'('hAPP$uint$uint'('times$utimes$uint'(X0),X1)),X2) = 'hAPP$uint$uint'('times$utimes$uint'(X0),'hAPP$uint$uint'('times$utimes$uint'(X1),X2)) ).
fof(fact_87_nat__1__add__1,axiom,
'hAPP$unat$unat'('plus$uplus$unat'('one$uone$unat'),'one$uone$unat') = 'number$unumber$uof$unat'(bit0(bit1(pls))) ).
fof(fact_134_zadd__commute,axiom,
! [X0,X1] : 'hAPP$uint$uint'('plus$uplus$uint'(X0),X1) = 'hAPP$uint$uint'('plus$uplus$uint'(X1),X0) ).
fof(fact_171_Bit0__Pls,axiom,
bit0(pls) = pls ).
fof(fact_172_Pls__def,axiom,
pls = 'zero$uzero$uint' ).
fof(fact_182_Bit0__def,axiom,
! [X0] : bit0(X0) = 'hAPP$uint$uint'('plus$uplus$uint'(X0),X0) ).
fof(fact_203_power2__eq__square,axiom,
! [X0] : 'hAPP$unat$uint'('power$upower$uint'(X0),'number$unumber$uof$unat'(bit0(bit1(pls)))) = 'hAPP$uint$uint'('times$utimes$uint'(X0),X0) ).
fof(fact_327_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
! [X0,X1,X2] : 'hAPP$uint$uint'('times$utimes$uint'(X0),'hAPP$uint$uint'('times$utimes$uint'(X1),X2)) = 'hAPP$uint$uint'('times$utimes$uint'(X1),'hAPP$uint$uint'('times$utimes$uint'(X0),X2)) ).
fof(fact_367_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
! [X0] : 'hAPP$uint$uint'('times$utimes$uint'(X0),'zero$uzero$uint') = 'zero$uzero$uint' ).
fof(fact_418_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
! [X0,X1] : 'hAPP$uint$uint'('plus$uplus$uint'(X0),'hAPP$uint$uint'('times$utimes$uint'(X1),X0)) = 'hAPP$uint$uint'('times$utimes$uint'('hAPP$uint$uint'('plus$uplus$uint'(X1),'one$uone$uint')),X0) ).
fof(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Int__Oint_000tc__HOL__Obool_U,axiom,
! [X0,X1,X2] : 'hAPP$uint$ubool'('cOMBC$uint$uint$ubool'(X0,X1),X2) = 'hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'(X0,X2),X1) ).
fof(conj_0,conjecture,
hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint','hAPP$uint$uint'('plus$uplus$uint'('hAPP$unat$uint'('power$upower$uint'(s),'number$unumber$uof$unat'(bit0(bit1(pls))))),'one$uone$uint')),'zero$uzero$uint')) ).
fof(negated_conjecture,negated_conjecture,
~ hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint','hAPP$uint$uint'('plus$uplus$uint'('hAPP$unat$uint'('power$upower$uint'(s),'number$unumber$uof$unat'(bit0(bit1(pls))))),'one$uone$uint')),'zero$uzero$uint')),
inference(negate_conjecture,[status(cth)],[conj_0]) ).
cnf(c27,plain,
hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint','hAPP$uint$uint'('times$utimes$uint'('hAPP$uint$uint'('plus$uplus$uint'('hAPP$uint$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls))))),m)),'one$uone$uint')),t)),'hAPP$uint$uint'('times$utimes$uint'('hAPP$uint$uint'('plus$uplus$uint'('hAPP$uint$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls))))),m)),'one$uone$uint')),'zero$uzero$uint'))),
inference(clausification,[status(esa)],[fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096]) ).
cnf(c28,plain,
'hAPP$uint$uint'('plus$uplus$uint'('hAPP$unat$uint'('power$upower$uint'(s),'number$unumber$uof$unat'(bit0(bit1(pls))))),'one$uone$uint') = 'hAPP$uint$uint'('times$utimes$uint'('hAPP$uint$uint'('plus$uplus$uint'('hAPP$uint$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls))))),m)),'one$uone$uint')),t),
inference(clausification,[status(esa)],[fact_3_t]) ).
cnf(c82,plain,
'hAPP$uint$uint'('times$utimes$uint'(X0),'hAPP$uint$uint'('times$utimes$uint'(X1),X2)) = 'hAPP$uint$uint'('times$utimes$uint'('hAPP$uint$uint'('times$utimes$uint'(X0),X1)),X2),
inference(clausification,[status(esa)],[fact_41_zmult__assoc]) ).
cnf(c157,plain,
'hAPP$unat$unat'('plus$uplus$unat'('one$uone$unat'),'one$uone$unat') = 'number$unumber$uof$unat'(bit0(bit1(pls))),
inference(clausification,[status(esa)],[fact_87_nat__1__add__1]) ).
cnf(c225,plain,
'hAPP$uint$uint'('plus$uplus$uint'(X0),X1) = 'hAPP$uint$uint'('plus$uplus$uint'(X1),X0),
inference(clausification,[status(esa)],[fact_134_zadd__commute]) ).
cnf(c276,plain,
bit0(pls) = pls,
inference(clausification,[status(esa)],[fact_171_Bit0__Pls]) ).
cnf(c277,plain,
pls = 'zero$uzero$uint',
inference(clausification,[status(esa)],[fact_172_Pls__def]) ).
cnf(c291,plain,
'hAPP$uint$uint'('plus$uplus$uint'(X0),X0) = bit0(X0),
inference(clausification,[status(esa)],[fact_182_Bit0__def]) ).
cnf(c312,plain,
'hAPP$uint$uint'('times$utimes$uint'(X0),X0) = 'hAPP$unat$uint'('power$upower$uint'(X0),'number$unumber$uof$unat'(bit0(bit1(pls)))),
inference(clausification,[status(esa)],[fact_203_power2__eq__square]) ).
cnf(c473,plain,
'hAPP$uint$uint'('times$utimes$uint'(X0),'hAPP$uint$uint'('times$utimes$uint'(X1),X2)) = 'hAPP$uint$uint'('times$utimes$uint'(X1),'hAPP$uint$uint'('times$utimes$uint'(X0),X2)),
inference(clausification,[status(esa)],[fact_327_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J]) ).
cnf(c517,plain,
'hAPP$uint$uint'('times$utimes$uint'(X0),'zero$uzero$uint') = 'zero$uzero$uint',
inference(clausification,[status(esa)],[fact_367_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J]) ).
cnf(c583,plain,
'hAPP$uint$uint'('times$utimes$uint'('hAPP$uint$uint'('plus$uplus$uint'(X0),'one$uone$uint')),X1) = 'hAPP$uint$uint'('plus$uplus$uint'(X1),'hAPP$uint$uint'('times$utimes$uint'(X0),X1)),
inference(clausification,[status(esa)],[fact_418_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J]) ).
cnf(c1716,plain,
'hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'(X0,X1),X2) = 'hAPP$uint$ubool'('cOMBC$uint$uint$ubool'(X0,X2),X1),
inference(clausification,[status(esa)],[help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Int__Oint_000tc__HOL__Obool_U]) ).
cnf(c1719,plain,
~ hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint','hAPP$uint$uint'('plus$uplus$uint'('hAPP$unat$uint'('power$upower$uint'(s),'number$unumber$uof$unat'(bit0(bit1(pls))))),'one$uone$uint')),'zero$uzero$uint')),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
bit0('zero$uzero$uint') = pls,
inference(demodulation,[status(thm)],[c276,c277]) ).
cnf(d1,plain,
bit0('zero$uzero$uint') = 'zero$uzero$uint',
inference(demodulation,[status(thm)],[d0,c277]) ).
cnf(d2,plain,
'hAPP$unat$unat'('plus$uplus$unat'('one$uone$unat'),'one$uone$unat') = 'number$unumber$uof$unat'(bit0(bit1('zero$uzero$uint'))),
inference(demodulation,[status(thm)],[c157,c277]) ).
cnf(d3,plain,
'hAPP$uint$uint'('times$utimes$uint'(X0),X0) = 'hAPP$unat$uint'('power$upower$uint'(X0),'number$unumber$uof$unat'(bit0(bit1('zero$uzero$uint')))),
inference(demodulation,[status(thm)],[c312,c277]) ).
cnf(d4,plain,
'hAPP$uint$uint'('times$utimes$uint'(X0),X0) = 'hAPP$unat$uint'('power$upower$uint'(X0),'hAPP$unat$unat'('plus$uplus$unat'('one$uone$unat'),'one$uone$unat')),
inference(demodulation,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint','hAPP$uint$uint'('plus$uplus$uint'('hAPP$unat$uint'('power$upower$uint'(s),'number$unumber$uof$unat'(bit0(bit1(pls))))),'one$uone$uint')),'hAPP$uint$uint'('times$utimes$uint'('hAPP$uint$uint'('plus$uplus$uint'('hAPP$uint$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls))))),m)),'one$uone$uint')),'zero$uzero$uint'))),
inference(demodulation,[status(thm)],[c27,c28]) ).
cnf(d6,plain,
hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint','hAPP$uint$uint'('plus$uplus$uint'('one$uone$uint'),'hAPP$unat$uint'('power$upower$uint'(s),'number$unumber$uof$unat'(bit0(bit1(pls)))))),'hAPP$uint$uint'('times$utimes$uint'('hAPP$uint$uint'('plus$uplus$uint'('hAPP$uint$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls))))),m)),'one$uone$uint')),'zero$uzero$uint'))),
inference(demodulation,[status(thm)],[d5,c225]) ).
cnf(d7,plain,
hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint','hAPP$uint$uint'('plus$uplus$uint'('one$uone$uint'),'hAPP$unat$uint'('power$upower$uint'(s),'number$unumber$uof$unat'(bit0(bit1('zero$uzero$uint')))))),'hAPP$uint$uint'('times$utimes$uint'('hAPP$uint$uint'('plus$uplus$uint'('hAPP$uint$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls))))),m)),'one$uone$uint')),'zero$uzero$uint'))),
inference(demodulation,[status(thm)],[d6,c277]) ).
cnf(d8,plain,
hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint','hAPP$uint$uint'('plus$uplus$uint'('one$uone$uint'),'hAPP$unat$uint'('power$upower$uint'(s),'hAPP$unat$unat'('plus$uplus$unat'('one$uone$unat'),'one$uone$unat')))),'hAPP$uint$uint'('times$utimes$uint'('hAPP$uint$uint'('plus$uplus$uint'('hAPP$uint$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls))))),m)),'one$uone$uint')),'zero$uzero$uint'))),
inference(demodulation,[status(thm)],[d7,d2]) ).
cnf(d9,plain,
hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint','hAPP$uint$uint'('plus$uplus$uint'('one$uone$uint'),'hAPP$uint$uint'('times$utimes$uint'(s),s))),'hAPP$uint$uint'('times$utimes$uint'('hAPP$uint$uint'('plus$uplus$uint'('hAPP$uint$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls))))),m)),'one$uone$uint')),'zero$uzero$uint'))),
inference(demodulation,[status(thm)],[d8,d4]) ).
cnf(d10,plain,
hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint','hAPP$uint$uint'('plus$uplus$uint'('one$uone$uint'),'hAPP$uint$uint'('times$utimes$uint'(s),s))),'hAPP$uint$uint'('plus$uplus$uint'('zero$uzero$uint'),'hAPP$uint$uint'('times$utimes$uint'('hAPP$uint$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls))))),m)),'zero$uzero$uint')))),
inference(demodulation,[status(thm)],[d9,c583]) ).
cnf(d11,plain,
hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint','hAPP$uint$uint'('plus$uplus$uint'('one$uone$uint'),'hAPP$uint$uint'('times$utimes$uint'(s),s))),'hAPP$uint$uint'('plus$uplus$uint'('zero$uzero$uint'),'hAPP$uint$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls))))),'hAPP$uint$uint'('times$utimes$uint'(m),'zero$uzero$uint'))))),
inference(demodulation,[status(thm)],[d10,c82]) ).
cnf(d12,plain,
hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint','hAPP$uint$uint'('plus$uplus$uint'('one$uone$uint'),'hAPP$uint$uint'('times$utimes$uint'(s),s))),'hAPP$uint$uint'('plus$uplus$uint'('zero$uzero$uint'),'hAPP$uint$uint'('times$utimes$uint'(m),'hAPP$uint$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls))))),'zero$uzero$uint'))))),
inference(demodulation,[status(thm)],[d11,c473]) ).
cnf(d13,plain,
hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint','hAPP$uint$uint'('plus$uplus$uint'('one$uone$uint'),'hAPP$uint$uint'('times$utimes$uint'(s),s))),'hAPP$uint$uint'('plus$uplus$uint'('zero$uzero$uint'),'hAPP$uint$uint'('times$utimes$uint'(m),'zero$uzero$uint')))),
inference(demodulation,[status(thm)],[d12,c517]) ).
cnf(d14,plain,
hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint','hAPP$uint$uint'('plus$uplus$uint'('one$uone$uint'),'hAPP$uint$uint'('times$utimes$uint'(s),s))),'hAPP$uint$uint'('plus$uplus$uint'('zero$uzero$uint'),'zero$uzero$uint'))),
inference(demodulation,[status(thm)],[d13,c517]) ).
cnf(d15,plain,
hBOOL('hAPP$uint$ubool'('cOMBC$uint$uint$ubool'('ord$uless$uint','hAPP$uint$uint'('plus$uplus$uint'('zero$uzero$uint'),'zero$uzero$uint')),'hAPP$uint$uint'('plus$uplus$uint'('one$uone$uint'),'hAPP$uint$uint'('times$utimes$uint'(s),s)))),
inference(demodulation,[status(thm)],[d14,c1716]) ).
cnf(d16,plain,
hBOOL('hAPP$uint$ubool'('cOMBC$uint$uint$ubool'('ord$uless$uint',bit0('zero$uzero$uint')),'hAPP$uint$uint'('plus$uplus$uint'('one$uone$uint'),'hAPP$uint$uint'('times$utimes$uint'(s),s)))),
inference(demodulation,[status(thm)],[d15,c291]) ).
cnf(d17,plain,
hBOOL('hAPP$uint$ubool'('cOMBC$uint$uint$ubool'('ord$uless$uint','zero$uzero$uint'),'hAPP$uint$uint'('plus$uplus$uint'('one$uone$uint'),'hAPP$uint$uint'('times$utimes$uint'(s),s)))),
inference(demodulation,[status(thm)],[d16,d1]) ).
cnf(d18,plain,
~ hBOOL('hAPP$uint$ubool'('cOMBC$uint$uint$ubool'('ord$uless$uint','zero$uzero$uint'),'hAPP$uint$uint'('plus$uplus$uint'('hAPP$unat$uint'('power$upower$uint'(s),'number$unumber$uof$unat'(bit0(bit1(pls))))),'one$uone$uint'))),
inference(demodulation,[status(thm)],[c1719,c1716]) ).
cnf(d19,plain,
~ hBOOL('hAPP$uint$ubool'('cOMBC$uint$uint$ubool'('ord$uless$uint','zero$uzero$uint'),'hAPP$uint$uint'('plus$uplus$uint'('one$uone$uint'),'hAPP$unat$uint'('power$upower$uint'(s),'number$unumber$uof$unat'(bit0(bit1(pls))))))),
inference(demodulation,[status(thm)],[d18,c225]) ).
cnf(d20,plain,
~ hBOOL('hAPP$uint$ubool'('cOMBC$uint$uint$ubool'('ord$uless$uint','zero$uzero$uint'),'hAPP$uint$uint'('plus$uplus$uint'('one$uone$uint'),'hAPP$unat$uint'('power$upower$uint'(s),'number$unumber$uof$unat'(bit0(bit1('zero$uzero$uint'))))))),
inference(demodulation,[status(thm)],[d19,c277]) ).
cnf(d21,plain,
~ hBOOL('hAPP$uint$ubool'('cOMBC$uint$uint$ubool'('ord$uless$uint','zero$uzero$uint'),'hAPP$uint$uint'('plus$uplus$uint'('one$uone$uint'),'hAPP$unat$uint'('power$upower$uint'(s),'hAPP$unat$unat'('plus$uplus$unat'('one$uone$unat'),'one$uone$unat'))))),
inference(demodulation,[status(thm)],[d20,d2]) ).
cnf(d22,plain,
~ hBOOL('hAPP$uint$ubool'('cOMBC$uint$uint$ubool'('ord$uless$uint','zero$uzero$uint'),'hAPP$uint$uint'('plus$uplus$uint'('one$uone$uint'),'hAPP$uint$uint'('times$utimes$uint'(s),s)))),
inference(demodulation,[status(thm)],[d21,d4]) ).
cnf(d23,plain,
$false,
inference(resolution,[status(thm)],[d22,d17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM924+3 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 26 04:17:54 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 99.13/19.79 % SZS status Theorem for theBenchmark.p
% 99.13/19.79 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------