%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM924+1 : 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 16.98s 3.28s
% Output : CNFRefutation 16.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 30 ( 30 unt; 0 def)
% Number of atoms : 30 ( 15 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 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 : 12 ( 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_24_number__of__is__id,axiom,
! [X0] : 'number$unumber$uof$uint'(X0) = X0 ).
fof(fact_25_zmult__commute,axiom,
! [X0,X1] : 'times$utimes$uint'(X0,X1) = 'times$utimes$uint'(X1,X0) ).
fof(fact_65_nat__1__add__1,axiom,
'plus$uplus$unat'('one$uone$unat','one$uone$unat') = 'number$unumber$uof$unat'(bit0(bit1(pls))) ).
fof(fact_66_mult__Pls,axiom,
! [X0] : 'times$utimes$uint'(pls,X0) = pls ).
fof(fact_104_zadd__commute,axiom,
! [X0,X1] : 'plus$uplus$uint'(X0,X1) = 'plus$uplus$uint'(X1,X0) ).
fof(fact_105_zero__is__num__zero,axiom,
'zero$uzero$uint' = 'number$unumber$uof$uint'(pls) ).
fof(conj_0,conjecture,
'ord$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$uint'),
inference(negate_conjecture,[status(cth)],[conj_0]) ).
cnf(c2,plain,
'ord$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$uint')),
inference(clausification,[status(esa)],[fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096]) ).
cnf(c3,plain,
'plus$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$uint'),t),
inference(clausification,[status(esa)],[fact_3_t]) ).
cnf(c30,plain,
'number$unumber$uof$uint'(X0) = X0,
inference(clausification,[status(esa)],[fact_24_number__of__is__id]) ).
cnf(c31,plain,
'times$utimes$uint'(X0,X1) = 'times$utimes$uint'(X1,X0),
inference(clausification,[status(esa)],[fact_25_zmult__commute]) ).
cnf(c95,plain,
'plus$uplus$unat'('one$uone$unat','one$uone$unat') = 'number$unumber$uof$unat'(bit0(bit1(pls))),
inference(clausification,[status(esa)],[fact_65_nat__1__add__1]) ).
cnf(c96,plain,
'times$utimes$uint'(pls,X0) = pls,
inference(clausification,[status(esa)],[fact_66_mult__Pls]) ).
cnf(c156,plain,
'plus$uplus$uint'(X0,X1) = 'plus$uplus$uint'(X1,X0),
inference(clausification,[status(esa)],[fact_104_zadd__commute]) ).
cnf(c157,plain,
'zero$uzero$uint' = 'number$unumber$uof$uint'(pls),
inference(clausification,[status(esa)],[fact_105_zero__is__num__zero]) ).
cnf(c158,plain,
~ 'ord$uless$uint'('plus$uplus$uint'('power$upower$uint'(s,'number$unumber$uof$unat'(bit0(bit1(pls)))),'one$uone$uint'),'zero$uzero$uint'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'zero$uzero$uint' = pls,
inference(demodulation,[status(thm)],[c157,c30]) ).
cnf(d1,plain,
~ 'ord$uless$uint'('plus$uplus$uint'('power$upower$uint'(s,'number$unumber$uof$unat'(bit0(bit1(pls)))),'one$uone$uint'),pls),
inference(demodulation,[status(thm)],[c158,d0]) ).
cnf(d2,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)],[d1,c95]) ).
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'))),pls),
inference(demodulation,[status(thm)],[d2,c156]) ).
cnf(d4,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)],[c2,c3]) ).
cnf(d5,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)],[d4,c156]) ).
cnf(d6,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$uint')),
inference(demodulation,[status(thm)],[d5,c95]) ).
cnf(d7,plain,
'ord$uless$uint'('plus$uplus$uint'('one$uone$uint','power$upower$uint'(s,'plus$uplus$unat'('one$uone$unat','one$uone$unat'))),'times$utimes$uint'('zero$uzero$uint','plus$uplus$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls)))),m),'one$uone$uint'))),
inference(demodulation,[status(thm)],[d6,c31]) ).
cnf(d8,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'(pls,'plus$uplus$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls)))),m),'one$uone$uint'))),
inference(demodulation,[status(thm)],[d7,d0]) ).
cnf(d9,plain,
'ord$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)],[d8,c96]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[d9,d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM924+1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n008.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 04:18:24 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.98/3.28 % SZS status Theorem for theBenchmark.p
% 16.98/3.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------