%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM924+7 : 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 : n001.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 65.88s 9.67s
% Output : CNFRefutation 65.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 48 ( 48 unt; 0 def)
% Number of atoms : 48 ( 29 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 1 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 8 con; 0-5 aty)
% Number of variables : 27 ( 1 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(tsy_c_Int_OBit1_res,hypothesis,
! [X0] : ti(int,bit1(X0)) = bit1(X0) ).
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,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),'ord$uless'(int),hAPP(int,int,'times$utimes'(int,hAPP(int,int,'plus$uplus'(int,hAPP(int,int,'times$utimes'(int,'number$unumber$uof'(int,bit0(bit0(bit1(pls))))),m)),'one$uone'(int))),t)),hAPP(int,int,'times$utimes'(int,hAPP(int,int,'plus$uplus'(int,hAPP(int,int,'times$utimes'(int,'number$unumber$uof'(int,bit0(bit0(bit1(pls))))),m)),'one$uone'(int))),'zero$uzero'(int)))) ).
fof(fact_3_t,axiom,
hAPP(int,int,'plus$uplus'(int,hAPP(nat,int,'power$upower'(int,s),'number$unumber$uof'(nat,bit0(bit1(pls))))),'one$uone'(int)) = hAPP(int,int,'times$utimes'(int,hAPP(int,int,'plus$uplus'(int,hAPP(int,int,'times$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$uof'(int,X0) = ti(int,X0) ).
fof(fact_23_zmult__commute,axiom,
! [X0,X1] : hAPP(int,int,'times$utimes'(int,X0),X1) = hAPP(int,int,'times$utimes'(int,X1),X0) ).
fof(fact_62_mult__Pls,axiom,
! [X0] : hAPP(int,int,'times$utimes'(int,pls),X0) = pls ).
fof(fact_98_zadd__commute,axiom,
! [X0,X1] : hAPP(int,int,'plus$uplus'(int,X0),X1) = hAPP(int,int,'plus$uplus'(int,X1),X0) ).
fof(fact_111_one__is__num__one,axiom,
'one$uone'(int) = 'number$unumber$uof'(int,bit1(pls)) ).
fof(fact_122_Pls__def,axiom,
pls = 'zero$uzero'(int) ).
fof(fact_466__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096,axiom,
hAPP(int,int,'minus$uminus'(int,hAPP(nat,int,'power$upower'(int,s),'number$unumber$uof'(nat,bit0(bit1(pls))))),'number$unumber$uof'(int,min)) = hAPP(int,int,'plus$uplus'(int,hAPP(nat,int,'power$upower'(int,s),'number$unumber$uof'(nat,bit0(bit1(pls))))),'one$uone'(int)) ).
fof(help_COMBC_1_1_U,axiom,
! [X0,X1,X2,X3,X4,X5] : hAPP(X0,X1,combc(X0,X2,X1,X3,X4),X5) = hAPP(X2,X1,hAPP(X0,fun(X2,X1),X3,X5),X4) ).
fof(conj_0,conjecture,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),'ord$uless'(int),hAPP(int,int,'plus$uplus'(int,hAPP(nat,int,'power$upower'(int,s),'number$unumber$uof'(nat,bit0(bit1(pls))))),'one$uone'(int))),'zero$uzero'(int))) ).
fof(negated_conjecture,negated_conjecture,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),'ord$uless'(int),hAPP(int,int,'plus$uplus'(int,hAPP(nat,int,'power$upower'(int,s),'number$unumber$uof'(nat,bit0(bit1(pls))))),'one$uone'(int))),'zero$uzero'(int))),
inference(negate_conjecture,[status(cth)],[conj_0]) ).
cnf(c52,plain,
ti(int,bit1(X0)) = bit1(X0),
inference(clausification,[status(esa)],[tsy_c_Int_OBit1_res]) ).
cnf(c53,plain,
ti(int,min) = min,
inference(clausification,[status(esa)],[tsy_c_Int_OMin_res]) ).
cnf(c100,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),'ord$uless'(int),hAPP(int,int,'times$utimes'(int,hAPP(int,int,'plus$uplus'(int,hAPP(int,int,'times$utimes'(int,'number$unumber$uof'(int,bit0(bit0(bit1(pls))))),m)),'one$uone'(int))),t)),hAPP(int,int,'times$utimes'(int,hAPP(int,int,'plus$uplus'(int,hAPP(int,int,'times$utimes'(int,'number$unumber$uof'(int,bit0(bit0(bit1(pls))))),m)),'one$uone'(int))),'zero$uzero'(int)))),
inference(clausification,[status(esa)],[fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096]) ).
cnf(c101,plain,
hAPP(int,int,'plus$uplus'(int,hAPP(nat,int,'power$upower'(int,s),'number$unumber$uof'(nat,bit0(bit1(pls))))),'one$uone'(int)) = hAPP(int,int,'times$utimes'(int,hAPP(int,int,'plus$uplus'(int,hAPP(int,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(c126,plain,
'number$unumber$uof'(int,X0) = ti(int,X0),
inference(clausification,[status(esa)],[fact_22_number__of__is__id]) ).
cnf(c127,plain,
hAPP(int,int,'times$utimes'(int,X0),X1) = hAPP(int,int,'times$utimes'(int,X1),X0),
inference(clausification,[status(esa)],[fact_23_zmult__commute]) ).
cnf(c189,plain,
hAPP(int,int,'times$utimes'(int,pls),X0) = pls,
inference(clausification,[status(esa)],[fact_62_mult__Pls]) ).
cnf(c247,plain,
hAPP(int,int,'plus$uplus'(int,X0),X1) = hAPP(int,int,'plus$uplus'(int,X1),X0),
inference(clausification,[status(esa)],[fact_98_zadd__commute]) ).
cnf(c264,plain,
'one$uone'(int) = 'number$unumber$uof'(int,bit1(pls)),
inference(clausification,[status(esa)],[fact_111_one__is__num__one]) ).
cnf(c280,plain,
pls = 'zero$uzero'(int),
inference(clausification,[status(esa)],[fact_122_Pls__def]) ).
cnf(c749,plain,
hAPP(int,int,'minus$uminus'(int,hAPP(nat,int,'power$upower'(int,s),'number$unumber$uof'(nat,bit0(bit1(pls))))),'number$unumber$uof'(int,min)) = hAPP(int,int,'plus$uplus'(int,hAPP(nat,int,'power$upower'(int,s),'number$unumber$uof'(nat,bit0(bit1(pls))))),'one$uone'(int)),
inference(clausification,[status(esa)],[fact_466__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096]) ).
cnf(c1708,plain,
hAPP(X0,X1,combc(X0,X2,X1,X3,X4),X5) = hAPP(X2,X1,hAPP(X0,fun(X2,X1),X3,X5),X4),
inference(clausification,[status(esa)],[help_COMBC_1_1_U]) ).
cnf(c1713,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),'ord$uless'(int),hAPP(int,int,'plus$uplus'(int,hAPP(nat,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$uof'(int,bit1(X0)) = bit1(X0),
inference(demodulation,[status(thm)],[c52,c126]) ).
cnf(d1,plain,
'one$uone'(int) = bit1(pls),
inference(demodulation,[status(thm)],[c264,d0]) ).
cnf(d2,plain,
'number$unumber$uof'(int,min) = min,
inference(demodulation,[status(thm)],[c53,c126]) ).
cnf(d3,plain,
hAPP(int,int,'minus$uminus'(int,hAPP(nat,int,'power$upower'(int,s),'number$unumber$uof'(nat,bit0('one$uone'(int))))),'number$unumber$uof'(int,min)) = hAPP(int,int,'plus$uplus'(int,hAPP(nat,int,'power$upower'(int,s),'number$unumber$uof'(nat,bit0(bit1(pls))))),'one$uone'(int)),
inference(demodulation,[status(thm)],[c749,d1]) ).
cnf(d4,plain,
hAPP(int,int,'minus$uminus'(int,hAPP(nat,int,'power$upower'(int,s),'number$unumber$uof'(nat,bit0('one$uone'(int))))),min) = hAPP(int,int,'plus$uplus'(int,hAPP(nat,int,'power$upower'(int,s),'number$unumber$uof'(nat,bit0(bit1(pls))))),'one$uone'(int)),
inference(demodulation,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
hAPP(int,int,'minus$uminus'(int,hAPP(nat,int,'power$upower'(int,s),'number$unumber$uof'(nat,bit0('one$uone'(int))))),min) = hAPP(int,int,'plus$uplus'(int,'one$uone'(int)),hAPP(nat,int,'power$upower'(int,s),'number$unumber$uof'(nat,bit0(bit1(pls))))),
inference(demodulation,[status(thm)],[d4,c247]) ).
cnf(d6,plain,
hAPP(int,int,'minus$uminus'(int,hAPP(nat,int,'power$upower'(int,s),'number$unumber$uof'(nat,bit0('one$uone'(int))))),min) = hAPP(int,int,'plus$uplus'(int,'one$uone'(int)),hAPP(nat,int,'power$upower'(int,s),'number$unumber$uof'(nat,bit0('one$uone'(int))))),
inference(demodulation,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),'ord$uless'(int),hAPP(int,int,'plus$uplus'(int,hAPP(nat,int,'power$upower'(int,s),'number$unumber$uof'(nat,bit0(bit1(pls))))),'one$uone'(int))),pls)),
inference(demodulation,[status(thm)],[c1713,c280]) ).
cnf(d8,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),'ord$uless'(int),hAPP(int,int,'plus$uplus'(int,hAPP(nat,int,'power$upower'(int,s),'number$unumber$uof'(nat,bit0('one$uone'(int))))),'one$uone'(int))),pls)),
inference(demodulation,[status(thm)],[d7,d1]) ).
cnf(d9,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),'ord$uless'(int),hAPP(int,int,'plus$uplus'(int,'one$uone'(int)),hAPP(nat,int,'power$upower'(int,s),'number$unumber$uof'(nat,bit0('one$uone'(int)))))),pls)),
inference(demodulation,[status(thm)],[d8,c247]) ).
cnf(d10,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),'ord$uless'(int),hAPP(int,int,'minus$uminus'(int,hAPP(nat,int,'power$upower'(int,s),'number$unumber$uof'(nat,bit0('one$uone'(int))))),min)),pls)),
inference(demodulation,[status(thm)],[d9,d6]) ).
cnf(d11,plain,
~ hBOOL(hAPP(int,bool,combc(int,int,bool,'ord$uless'(int),pls),hAPP(int,int,'minus$uminus'(int,hAPP(nat,int,'power$upower'(int,s),'number$unumber$uof'(nat,bit0('one$uone'(int))))),min))),
inference(demodulation,[status(thm)],[d10,c1708]) ).
cnf(d12,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),'ord$uless'(int),hAPP(int,int,'plus$uplus'(int,hAPP(nat,int,'power$upower'(int,s),'number$unumber$uof'(nat,bit0(bit1(pls))))),'one$uone'(int))),hAPP(int,int,'times$utimes'(int,hAPP(int,int,'plus$uplus'(int,hAPP(int,int,'times$utimes'(int,'number$unumber$uof'(int,bit0(bit0(bit1(pls))))),m)),'one$uone'(int))),'zero$uzero'(int)))),
inference(demodulation,[status(thm)],[c100,c101]) ).
cnf(d13,plain,
hBOOL(hAPP(int,bool,combc(int,int,bool,'ord$uless'(int),hAPP(int,int,'times$utimes'(int,hAPP(int,int,'plus$uplus'(int,hAPP(int,int,'times$utimes'(int,'number$unumber$uof'(int,bit0(bit0(bit1(pls))))),m)),'one$uone'(int))),'zero$uzero'(int))),hAPP(int,int,'plus$uplus'(int,hAPP(nat,int,'power$upower'(int,s),'number$unumber$uof'(nat,bit0(bit1(pls))))),'one$uone'(int)))),
inference(demodulation,[status(thm)],[d12,c1708]) ).
cnf(d14,plain,
hBOOL(hAPP(int,bool,combc(int,int,bool,'ord$uless'(int),hAPP(int,int,'times$utimes'(int,'zero$uzero'(int)),hAPP(int,int,'plus$uplus'(int,hAPP(int,int,'times$utimes'(int,'number$unumber$uof'(int,bit0(bit0(bit1(pls))))),m)),'one$uone'(int)))),hAPP(int,int,'plus$uplus'(int,hAPP(nat,int,'power$upower'(int,s),'number$unumber$uof'(nat,bit0(bit1(pls))))),'one$uone'(int)))),
inference(demodulation,[status(thm)],[d13,c127]) ).
cnf(d15,plain,
hBOOL(hAPP(int,bool,combc(int,int,bool,'ord$uless'(int),hAPP(int,int,'times$utimes'(int,pls),hAPP(int,int,'plus$uplus'(int,hAPP(int,int,'times$utimes'(int,'number$unumber$uof'(int,bit0(bit0(bit1(pls))))),m)),'one$uone'(int)))),hAPP(int,int,'plus$uplus'(int,hAPP(nat,int,'power$upower'(int,s),'number$unumber$uof'(nat,bit0(bit1(pls))))),'one$uone'(int)))),
inference(demodulation,[status(thm)],[d14,c280]) ).
cnf(d16,plain,
hBOOL(hAPP(int,bool,combc(int,int,bool,'ord$uless'(int),pls),hAPP(int,int,'plus$uplus'(int,hAPP(nat,int,'power$upower'(int,s),'number$unumber$uof'(nat,bit0(bit1(pls))))),'one$uone'(int)))),
inference(demodulation,[status(thm)],[d15,c189]) ).
cnf(d17,plain,
hBOOL(hAPP(int,bool,combc(int,int,bool,'ord$uless'(int),pls),hAPP(int,int,'plus$uplus'(int,'one$uone'(int)),hAPP(nat,int,'power$upower'(int,s),'number$unumber$uof'(nat,bit0(bit1(pls))))))),
inference(demodulation,[status(thm)],[d16,c247]) ).
cnf(d18,plain,
hBOOL(hAPP(int,bool,combc(int,int,bool,'ord$uless'(int),pls),hAPP(int,int,'plus$uplus'(int,'one$uone'(int)),hAPP(nat,int,'power$upower'(int,s),'number$unumber$uof'(nat,bit0('one$uone'(int))))))),
inference(demodulation,[status(thm)],[d17,d1]) ).
cnf(d19,plain,
hBOOL(hAPP(int,bool,combc(int,int,bool,'ord$uless'(int),pls),hAPP(int,int,'minus$uminus'(int,hAPP(nat,int,'power$upower'(int,s),'number$unumber$uof'(nat,bit0('one$uone'(int))))),min))),
inference(demodulation,[status(thm)],[d18,d6]) ).
cnf(d20,plain,
$false,
inference(resolution,[status(thm)],[d19,d11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM924+7 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n001.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % 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 04:24:13 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 65.88/9.67 % SZS status Theorem for theBenchmark.p
% 65.88/9.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------