%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM924+6 : 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 : n017.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 08:14:07 AM UTC 2026
% Result : Theorem 6.05s 5.52s
% Output : CNFRefutation 6.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 34 ( 34 unt; 0 def)
% Number of atoms : 34 ( 19 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 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-3 aty)
% Number of variables : 12 ( 1 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(tsy_c_Int_OMin_res,axiom,
ti(int,min) = min ).
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$uless'(int,'times$utimes'(int,'plus$uplus'(int,'times$utimes'(int,'number$unumber$uof'(int,bit0(bit0(bit1(pls)))),m),'one$uone'(int)),t),'times$utimes'(int,'plus$uplus'(int,'times$utimes'(int,'number$unumber$uof'(int,bit0(bit0(bit1(pls)))),m),'one$uone'(int)),'zero$uzero'(int))) ).
fof(fact_3_t,axiom,
'plus$uplus'(int,'power$upower'(int,s,'number$unumber$uof'(nat,bit0(bit1(pls)))),'one$uone'(int)) = 'times$utimes'(int,'plus$uplus'(int,'times$utimes'(int,'number$unumber$uof'(int,bit0(bit0(bit1(pls)))),m),'one$uone'(int)),t) ).
fof(fact_22_number__of__is__id,axiom,
! [X0] : 'number$unumber$uof'(int,X0) = ti(int,X0) ).
fof(fact_23_zmult__commute,axiom,
! [X0,X1] : 'times$utimes'(int,X0,X1) = 'times$utimes'(int,X1,X0) ).
fof(fact_62_mult__Pls,axiom,
! [X0] : 'times$utimes'(int,pls,X0) = pls ).
fof(fact_96_zadd__commute,axiom,
! [X0,X1] : 'plus$uplus'(int,X0,X1) = 'plus$uplus'(int,X1,X0) ).
fof(fact_120_Pls__def,axiom,
pls = 'zero$uzero'(int) ).
fof(fact_324__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096,axiom,
'minus$uminus'(int,'power$upower'(int,s,'number$unumber$uof'(nat,bit0(bit1(pls)))),'number$unumber$uof'(int,min)) = 'plus$uplus'(int,'power$upower'(int,s,'number$unumber$uof'(nat,bit0(bit1(pls)))),'one$uone'(int)) ).
fof(conj_0,conjecture,
'ord$uless'(int,'plus$uplus'(int,'power$upower'(int,s,'number$unumber$uof'(nat,bit0(bit1(pls)))),'one$uone'(int)),'zero$uzero'(int)) ).
fof(negated_conjecture,negated_conjecture,
~ 'ord$uless'(int,'plus$uplus'(int,'power$upower'(int,s,'number$unumber$uof'(nat,bit0(bit1(pls)))),'one$uone'(int)),'zero$uzero'(int)),
inference(negate_conjecture,[status(cth)],[conj_0]) ).
cnf(c46,plain,
ti(int,min) = min,
inference(clausification,[status(esa)],[tsy_c_Int_OMin_res]) ).
cnf(c80,plain,
'ord$uless'(int,'times$utimes'(int,'plus$uplus'(int,'times$utimes'(int,'number$unumber$uof'(int,bit0(bit0(bit1(pls)))),m),'one$uone'(int)),t),'times$utimes'(int,'plus$uplus'(int,'times$utimes'(int,'number$unumber$uof'(int,bit0(bit0(bit1(pls)))),m),'one$uone'(int)),'zero$uzero'(int))),
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(c81,plain,
'plus$uplus'(int,'power$upower'(int,s,'number$unumber$uof'(nat,bit0(bit1(pls)))),'one$uone'(int)) = 'times$utimes'(int,'plus$uplus'(int,'times$utimes'(int,'number$unumber$uof'(int,bit0(bit0(bit1(pls)))),m),'one$uone'(int)),t),
inference(clausification,[status(esa)],[fact_3_t]) ).
cnf(c106,plain,
'number$unumber$uof'(int,X0) = ti(int,X0),
inference(clausification,[status(esa)],[fact_22_number__of__is__id]) ).
cnf(c107,plain,
'times$utimes'(int,X0,X1) = 'times$utimes'(int,X1,X0),
inference(clausification,[status(esa)],[fact_23_zmult__commute]) ).
cnf(c169,plain,
'times$utimes'(int,pls,X0) = pls,
inference(clausification,[status(esa)],[fact_62_mult__Pls]) ).
cnf(c224,plain,
'plus$uplus'(int,X0,X1) = 'plus$uplus'(int,X1,X0),
inference(clausification,[status(esa)],[fact_96_zadd__commute]) ).
cnf(c257,plain,
pls = 'zero$uzero'(int),
inference(clausification,[status(esa)],[fact_120_Pls__def]) ).
cnf(c533,plain,
'minus$uminus'(int,'power$upower'(int,s,'number$unumber$uof'(nat,bit0(bit1(pls)))),'number$unumber$uof'(int,min)) = 'plus$uplus'(int,'power$upower'(int,s,'number$unumber$uof'(nat,bit0(bit1(pls)))),'one$uone'(int)),
inference(clausification,[status(esa)],[fact_324__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096]) ).
cnf(c857,plain,
~ 'ord$uless'(int,'plus$uplus'(int,'power$upower'(int,s,'number$unumber$uof'(nat,bit0(bit1(pls)))),'one$uone'(int)),'zero$uzero'(int)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'number$unumber$uof'(int,min) = min,
inference(demodulation,[status(thm)],[c46,c106]) ).
cnf(d1,plain,
'minus$uminus'(int,'power$upower'(int,s,'number$unumber$uof'(nat,bit0(bit1(pls)))),min) = 'plus$uplus'(int,'power$upower'(int,s,'number$unumber$uof'(nat,bit0(bit1(pls)))),'one$uone'(int)),
inference(demodulation,[status(thm)],[c533,d0]) ).
cnf(d2,plain,
'minus$uminus'(int,'power$upower'(int,s,'number$unumber$uof'(nat,bit0(bit1(pls)))),min) = 'plus$uplus'(int,'one$uone'(int),'power$upower'(int,s,'number$unumber$uof'(nat,bit0(bit1(pls))))),
inference(demodulation,[status(thm)],[d1,c224]) ).
cnf(d3,plain,
'ord$uless'(int,'plus$uplus'(int,'power$upower'(int,s,'number$unumber$uof'(nat,bit0(bit1(pls)))),'one$uone'(int)),'times$utimes'(int,'plus$uplus'(int,'times$utimes'(int,'number$unumber$uof'(int,bit0(bit0(bit1(pls)))),m),'one$uone'(int)),'zero$uzero'(int))),
inference(demodulation,[status(thm)],[c80,c81]) ).
cnf(d4,plain,
'ord$uless'(int,'plus$uplus'(int,'one$uone'(int),'power$upower'(int,s,'number$unumber$uof'(nat,bit0(bit1(pls))))),'times$utimes'(int,'plus$uplus'(int,'times$utimes'(int,'number$unumber$uof'(int,bit0(bit0(bit1(pls)))),m),'one$uone'(int)),'zero$uzero'(int))),
inference(demodulation,[status(thm)],[d3,c224]) ).
cnf(d5,plain,
'ord$uless'(int,'minus$uminus'(int,'power$upower'(int,s,'number$unumber$uof'(nat,bit0(bit1(pls)))),min),'times$utimes'(int,'plus$uplus'(int,'times$utimes'(int,'number$unumber$uof'(int,bit0(bit0(bit1(pls)))),m),'one$uone'(int)),'zero$uzero'(int))),
inference(demodulation,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
'ord$uless'(int,'minus$uminus'(int,'power$upower'(int,s,'number$unumber$uof'(nat,bit0(bit1(pls)))),min),'times$utimes'(int,'zero$uzero'(int),'plus$uplus'(int,'times$utimes'(int,'number$unumber$uof'(int,bit0(bit0(bit1(pls)))),m),'one$uone'(int)))),
inference(demodulation,[status(thm)],[d5,c107]) ).
cnf(d7,plain,
'ord$uless'(int,'minus$uminus'(int,'power$upower'(int,s,'number$unumber$uof'(nat,bit0(bit1(pls)))),min),'times$utimes'(int,pls,'plus$uplus'(int,'times$utimes'(int,'number$unumber$uof'(int,bit0(bit0(bit1(pls)))),m),'one$uone'(int)))),
inference(demodulation,[status(thm)],[d6,c257]) ).
cnf(d8,plain,
'ord$uless'(int,'minus$uminus'(int,'power$upower'(int,s,'number$unumber$uof'(nat,bit0(bit1(pls)))),min),pls),
inference(demodulation,[status(thm)],[d7,c169]) ).
cnf(d9,plain,
~ 'ord$uless'(int,'plus$uplus'(int,'power$upower'(int,s,'number$unumber$uof'(nat,bit0(bit1(pls)))),'one$uone'(int)),pls),
inference(demodulation,[status(thm)],[c857,c257]) ).
cnf(d10,plain,
~ 'ord$uless'(int,'plus$uplus'(int,'one$uone'(int),'power$upower'(int,s,'number$unumber$uof'(nat,bit0(bit1(pls))))),pls),
inference(demodulation,[status(thm)],[d9,c224]) ).
cnf(d11,plain,
~ 'ord$uless'(int,'minus$uminus'(int,'power$upower'(int,s,'number$unumber$uof'(nat,bit0(bit1(pls)))),min),pls),
inference(demodulation,[status(thm)],[d10,d2]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[d11,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM924+6 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 04:13:50 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.05/5.52 % SZS status Theorem for theBenchmark.p
% 6.05/5.52 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------