%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM926+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 : n002.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 08:14:11 AM UTC 2026
% Result : Theorem 33.92s 19.59s
% Output : CNFRefutation 33.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 36 ( 18 unt; 0 def)
% Number of atoms : 61 ( 34 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 13 ~; 18 |; 1 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-3 aty)
% Number of variables : 26 ( 2 sgn 8 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(tsy_c_Groups_Oone__class_Oone_0_res,axiom,
! [X0] :
( 'zero$uneq$uone'(X0)
=> ti(X0,'one$uone'(X0)) = 'one$uone'(X0) ) ).
fof(tsy_v_t_____res,axiom,
ti(int,t) = t ).
fof(fact_0_tpos,axiom,
'ord$uless$ueq'(int,'one$uone'(int),t) ).
fof(fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,axiom,
( t = 'one$uone'(int)
=> ? [X0,X1] : 'plus$uplus'(int,'power$upower'(int,X0,'number$unumber$uof'(nat,bit0(bit1(pls)))),'power$upower'(int,X1,'number$unumber$uof'(nat,bit0(bit1(pls))))) = 'plus$uplus'(int,'times$utimes'(int,'number$unumber$uof'(int,bit0(bit0(bit1(pls)))),m),'one$uone'(int)) ) ).
fof(fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,axiom,
( 'ord$uless'(int,'one$uone'(int),t)
=> ? [X0,X1] : 'plus$uplus'(int,'power$upower'(int,X0,'number$unumber$uof'(nat,bit0(bit1(pls)))),'power$upower'(int,X1,'number$unumber$uof'(nat,bit0(bit1(pls))))) = 'plus$uplus'(int,'times$utimes'(int,'number$unumber$uof'(int,bit0(bit0(bit1(pls)))),m),'one$uone'(int)) ) ).
fof(fact_22_zless__le,axiom,
! [X0,X1] :
( 'ord$uless'(int,X0,X1)
<=> ( ti(int,X0) != ti(int,X1)
& 'ord$uless$ueq'(int,X0,X1) ) ) ).
fof(fact_23_zless__linear,axiom,
! [X0,X1] :
( 'ord$uless'(int,X1,X0)
| ti(int,X0) = ti(int,X1)
| 'ord$uless'(int,X0,X1) ) ).
fof(fact_25_zle__antisym,axiom,
! [X0,X1] :
( 'ord$uless$ueq'(int,X0,X1)
=> ( 'ord$uless$ueq'(int,X1,X0)
=> ti(int,X0) = ti(int,X1) ) ) ).
fof(fact_86_number__of__is__id,axiom,
! [X0] : 'number$unumber$uof'(int,X0) = ti(int,X0) ).
fof(arity_Int_Oint___Rings_Ozero__neq__one,axiom,
'zero$uneq$uone'(int) ).
fof(conj_0,conjecture,
? [X0,X1] : 'plus$uplus'(int,'power$upower'(int,X0,'number$unumber$uof'(nat,bit0(bit1(pls)))),'power$upower'(int,X1,'number$unumber$uof'(nat,bit0(bit1(pls))))) = 'plus$uplus'(int,'times$utimes'(int,'number$unumber$uof'(int,bit0(bit0(bit1(pls)))),m),'one$uone'(int)) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0,X1] : 'plus$uplus'(int,'power$upower'(int,X0,'number$unumber$uof'(nat,bit0(bit1(pls)))),'power$upower'(int,X1,'number$unumber$uof'(nat,bit0(bit1(pls))))) = 'plus$uplus'(int,'times$utimes'(int,'number$unumber$uof'(int,bit0(bit0(bit1(pls)))),m),'one$uone'(int)),
inference(negate_conjecture,[status(cth)],[conj_0]) ).
cnf(c6,plain,
( ti(X0,'one$uone'(X0)) = 'one$uone'(X0)
| ~ 'zero$uneq$uone'(X0) ),
inference(clausification,[status(esa)],[tsy_c_Groups_Oone__class_Oone_0_res]) ).
cnf(c82,plain,
ti(int,t) = t,
inference(clausification,[status(esa)],[tsy_v_t_____res]) ).
cnf(c83,plain,
'ord$uless$ueq'(int,'one$uone'(int),t),
inference(clausification,[status(esa)],[fact_0_tpos]) ).
cnf(c84,plain,
( 'plus$uplus'(int,'power$upower'(int,sK149,'number$unumber$uof'(nat,bit0(bit1(pls)))),'power$upower'(int,sK150,'number$unumber$uof'(nat,bit0(bit1(pls))))) = 'plus$uplus'(int,'times$utimes'(int,'number$unumber$uof'(int,bit0(bit0(bit1(pls)))),m),'one$uone'(int))
| t != 'one$uone'(int) ),
inference(clausification,[status(esa)],[fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06]) ).
cnf(c85,plain,
( 'plus$uplus'(int,'power$upower'(int,sK151,'number$unumber$uof'(nat,bit0(bit1(pls)))),'power$upower'(int,sK152,'number$unumber$uof'(nat,bit0(bit1(pls))))) = 'plus$uplus'(int,'times$utimes'(int,'number$unumber$uof'(int,bit0(bit0(bit1(pls)))),m),'one$uone'(int))
| ~ 'ord$uless'(int,'one$uone'(int),t) ),
inference(clausification,[status(esa)],[fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06]) ).
cnf(c105,plain,
( 'ord$uless$ueq'(int,X0,X1)
| ~ 'ord$uless'(int,X0,X1) ),
inference(clausification,[status(esa)],[fact_22_zless__le]) ).
cnf(c108,plain,
( 'ord$uless'(int,X1,X0)
| ti(int,X0) = ti(int,X1)
| 'ord$uless'(int,X0,X1) ),
inference(clausification,[status(esa)],[fact_23_zless__linear]) ).
cnf(c110,plain,
( ti(int,X0) = ti(int,X1)
| ~ 'ord$uless$ueq'(int,X1,X0)
| ~ 'ord$uless$ueq'(int,X0,X1) ),
inference(clausification,[status(esa)],[fact_25_zle__antisym]) ).
cnf(c198,plain,
'number$unumber$uof'(int,X0) = ti(int,X0),
inference(clausification,[status(esa)],[fact_86_number__of__is__id]) ).
cnf(c792,plain,
'zero$uneq$uone'(int),
inference(clausification,[status(esa)],[arity_Int_Oint___Rings_Ozero__neq__one]) ).
cnf(c861,plain,
'plus$uplus'(int,'power$upower'(int,X0,'number$unumber$uof'(nat,bit0(bit1(pls)))),'power$upower'(int,X1,'number$unumber$uof'(nat,bit0(bit1(pls))))) != 'plus$uplus'(int,'times$utimes'(int,'number$unumber$uof'(int,bit0(bit0(bit1(pls)))),m),'one$uone'(int)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
~ 'ord$uless'(int,'one$uone'(int),t),
inference(resolution,[status(thm)],[c861,c85]) ).
cnf(d1,plain,
( 'ord$uless'(int,t,'one$uone'(int))
| ti(int,'one$uone'(int)) = ti(int,t) ),
inference(resolution,[status(thm)],[c108,d0]) ).
cnf(d2,plain,
( 'ord$uless'(int,t,'one$uone'(int))
| ti(int,'one$uone'(int)) = t ),
inference(demodulation,[status(thm)],[d1,c82]) ).
cnf(d3,plain,
( 'ord$uless$ueq'(int,t,'one$uone'(int))
| ti(int,'one$uone'(int)) = t ),
inference(resolution,[status(thm)],[d2,c105]) ).
cnf(d4,plain,
( ti(int,'one$uone'(int)) = t
| ~ 'ord$uless$ueq'(int,'one$uone'(int),t)
| ti(int,'one$uone'(int)) = ti(int,t) ),
inference(resolution,[status(thm)],[c110,d3]) ).
cnf(d5,plain,
( ~ 'ord$uless$ueq'(int,'one$uone'(int),t)
| ti(int,'one$uone'(int)) = t
| ti(int,'one$uone'(int)) = t ),
inference(demodulation,[status(thm)],[d4,c82]) ).
cnf(d6,plain,
( ti(int,'one$uone'(int)) = t
| ti(int,'one$uone'(int)) = t ),
inference(resolution,[status(thm)],[c83,d5]) ).
cnf(d7,plain,
'number$unumber$uof'(int,'one$uone'(int)) = t,
inference(demodulation,[status(thm)],[d6,c198]) ).
cnf(d8,plain,
ti(int,'one$uone'(int)) = 'one$uone'(int),
inference(resolution,[status(thm)],[c792,c6]) ).
cnf(d9,plain,
'number$unumber$uof'(int,'one$uone'(int)) = 'one$uone'(int),
inference(demodulation,[status(thm)],[d8,c198]) ).
cnf(d10,plain,
t = 'one$uone'(int),
inference(demodulation,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
t != 'one$uone'(int),
inference(resolution,[status(thm)],[c861,c84]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[d11,d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM926+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
% 0.11/15.39 % Computer : n002.cluster.edu
% 0.11/15.39 % Model : x86_64 x86_64
% 0.11/15.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/15.39 % Memory : 8046.5625MB
% 0.11/15.39 % OS : Linux 6.8.0-71-generic
% 0.11/15.39 % CPULimit : 300
% 0.11/15.39 % WCLimit : 300
% 0.11/15.39 % DateTime : Sat Sep 26 04:23:50 UTC 2026
% 0.11/15.39 % CPUTime :
% 0.11/15.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 33.92/19.59 % SZS status Theorem for theBenchmark.p
% 33.92/19.59 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------