%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM924+2 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 39.14s 5.39s
% Output : CNFRefutation 39.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 32 unt; 0 def)
% Number of atoms : 32 ( 15 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Maximal term depth : 8 ( 3 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 13 ( 1 sgn 6 !; 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,
'ord$uless$uint'('times$utimes$uint'('plus$uplus$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls)))),m),'one$uone$uint'),t),'times$utimes$uint'('plus$uplus$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls)))),m),'one$uone$uint'),'zero$uzero$uint')) ).
fof(fact_3_t,axiom,
'plus$uplus$uint'('power$upower$uint'(s,'number$unumber$uof$unat'(bit0(bit1(pls)))),'one$uone$uint') = 'times$utimes$uint'('plus$uplus$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls)))),m),'one$uone$uint'),t) ).
fof(fact_35_zmult__commute,axiom,
! [X0,X1] : 'times$utimes$uint'(X0,X1) = 'times$utimes$uint'(X1,X0) ).
fof(fact_87_nat__1__add__1,axiom,
'plus$uplus$unat'('one$uone$unat','one$uone$unat') = 'number$unumber$uof$unat'(bit0(bit1(pls))) ).
fof(fact_88_mult__Pls,axiom,
! [X0] : 'times$utimes$uint'(pls,X0) = pls ).
fof(fact_132_zadd__commute,axiom,
! [X0,X1] : 'plus$uplus$uint'(X0,X1) = 'plus$uplus$uint'(X1,X0) ).
fof(fact_170_Pls__def,axiom,
pls = 'zero$uzero$uint' ).
fof(fact_201_power2__eq__square,axiom,
! [X0] : 'power$upower$uint'(X0,'number$unumber$uof$unat'(bit0(bit1(pls)))) = 'times$utimes$uint'(X0,X0) ).
fof(conj_0,conjecture,
'ord$uless$uint'('plus$uplus$uint'('power$upower$uint'(s,'number$unumber$uof$unat'(bit0(bit1(pls)))),'one$uone$uint'),'zero$uzero$uint') ).
fof(negated_conjecture,negated_conjecture,
~ 'ord$uless$uint'('plus$uplus$uint'('power$upower$uint'(s,'number$unumber$uof$unat'(bit0(bit1(pls)))),'one$uone$uint'),'zero$uzero$uint'),
inference(negate_conjecture,[status(cth)],[conj_0]) ).
cnf(c19,plain,
'ord$uless$uint'('times$utimes$uint'('plus$uplus$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls)))),m),'one$uone$uint'),t),'times$utimes$uint'('plus$uplus$uint'('times$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(c20,plain,
'plus$uplus$uint'('power$upower$uint'(s,'number$unumber$uof$unat'(bit0(bit1(pls)))),'one$uone$uint') = 'times$utimes$uint'('plus$uplus$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls)))),m),'one$uone$uint'),t),
inference(clausification,[status(esa)],[fact_3_t]) ).
cnf(c65,plain,
'times$utimes$uint'(X0,X1) = 'times$utimes$uint'(X1,X0),
inference(clausification,[status(esa)],[fact_35_zmult__commute]) ).
cnf(c149,plain,
'plus$uplus$unat'('one$uone$unat','one$uone$unat') = 'number$unumber$uof$unat'(bit0(bit1(pls))),
inference(clausification,[status(esa)],[fact_87_nat__1__add__1]) ).
cnf(c150,plain,
'times$utimes$uint'(pls,X0) = pls,
inference(clausification,[status(esa)],[fact_88_mult__Pls]) ).
cnf(c220,plain,
'plus$uplus$uint'(X0,X1) = 'plus$uplus$uint'(X1,X0),
inference(clausification,[status(esa)],[fact_132_zadd__commute]) ).
cnf(c272,plain,
pls = 'zero$uzero$uint',
inference(clausification,[status(esa)],[fact_170_Pls__def]) ).
cnf(c307,plain,
'power$upower$uint'(X0,'number$unumber$uof$unat'(bit0(bit1(pls)))) = 'times$utimes$uint'(X0,X0),
inference(clausification,[status(esa)],[fact_201_power2__eq__square]) ).
cnf(c958,plain,
~ 'ord$uless$uint'('plus$uplus$uint'('power$upower$uint'(s,'number$unumber$uof$unat'(bit0(bit1(pls)))),'one$uone$uint'),'zero$uzero$uint'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'power$upower$uint'(X0,'plus$uplus$unat'('one$uone$unat','one$uone$unat')) = 'times$utimes$uint'(X0,X0),
inference(demodulation,[status(thm)],[c307,c149]) ).
cnf(d1,plain,
'ord$uless$uint'('plus$uplus$uint'('power$upower$uint'(s,'number$unumber$uof$unat'(bit0(bit1(pls)))),'one$uone$uint'),'times$utimes$uint'('plus$uplus$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls)))),m),'one$uone$uint'),'zero$uzero$uint')),
inference(demodulation,[status(thm)],[c19,c20]) ).
cnf(d2,plain,
'ord$uless$uint'('plus$uplus$uint'('one$uone$uint','power$upower$uint'(s,'number$unumber$uof$unat'(bit0(bit1(pls))))),'times$utimes$uint'('plus$uplus$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls)))),m),'one$uone$uint'),'zero$uzero$uint')),
inference(demodulation,[status(thm)],[d1,c220]) ).
cnf(d3,plain,
'ord$uless$uint'('plus$uplus$uint'('one$uone$uint','power$upower$uint'(s,'plus$uplus$unat'('one$uone$unat','one$uone$unat'))),'times$utimes$uint'('plus$uplus$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls)))),m),'one$uone$uint'),'zero$uzero$uint')),
inference(demodulation,[status(thm)],[d2,c149]) ).
cnf(d4,plain,
'ord$uless$uint'('plus$uplus$uint'('one$uone$uint','times$utimes$uint'(s,s)),'times$utimes$uint'('plus$uplus$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls)))),m),'one$uone$uint'),'zero$uzero$uint')),
inference(demodulation,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
'ord$uless$uint'('plus$uplus$uint'('one$uone$uint','times$utimes$uint'(s,s)),'times$utimes$uint'('zero$uzero$uint','plus$uplus$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls)))),m),'one$uone$uint'))),
inference(demodulation,[status(thm)],[d4,c65]) ).
cnf(d6,plain,
'ord$uless$uint'('plus$uplus$uint'('one$uone$uint','times$utimes$uint'(s,s)),'times$utimes$uint'(pls,'plus$uplus$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls)))),m),'one$uone$uint'))),
inference(demodulation,[status(thm)],[d5,c272]) ).
cnf(d7,plain,
'ord$uless$uint'('plus$uplus$uint'('one$uone$uint','times$utimes$uint'(s,s)),pls),
inference(demodulation,[status(thm)],[d6,c150]) ).
cnf(d8,plain,
~ 'ord$uless$uint'('plus$uplus$uint'('power$upower$uint'(s,'number$unumber$uof$unat'(bit0(bit1(pls)))),'one$uone$uint'),pls),
inference(demodulation,[status(thm)],[c958,c272]) ).
cnf(d9,plain,
~ 'ord$uless$uint'('plus$uplus$uint'('power$upower$uint'(s,'plus$uplus$unat'('one$uone$unat','one$uone$unat')),'one$uone$uint'),pls),
inference(demodulation,[status(thm)],[d8,c149]) ).
cnf(d10,plain,
~ 'ord$uless$uint'('plus$uplus$uint'('one$uone$uint','power$upower$uint'(s,'plus$uplus$unat'('one$uone$unat','one$uone$unat'))),pls),
inference(demodulation,[status(thm)],[d9,c220]) ).
cnf(d11,plain,
~ 'ord$uless$uint'('plus$uplus$uint'('one$uone$uint','times$utimes$uint'(s,s)),pls),
inference(demodulation,[status(thm)],[d10,d0]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[d11,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM924+2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n006.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 26 04:17:11 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 39.14/5.39 % SZS status Theorem for theBenchmark.p
% 39.14/5.39 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------