%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM926+2 : 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 08:14:10 AM UTC 2026
% Result : Theorem 18.21s 4.46s
% Output : CNFRefutation 18.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 33 ( 15 unt; 0 def)
% Number of atoms : 79 ( 22 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 74 ( 28 ~; 30 |; 8 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-2 aty)
% Number of variables : 22 ( 2 sgn 6 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint,hypothesis,
'is$uint'('one$uone$uint') ).
fof(gsy_v_t____,axiom,
'is$uint'(t) ).
fof(fact_0_tpos,axiom,
'ord$uless$ueq$uint'('one$uone$uint',t) ).
fof(fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,axiom,
( t = 'one$uone$uint'
=> ? [X0,X1] :
( 'plus$uplus$uint'('power$upower$uint'(X0,'number$unumber$uof$unat'(bit0(bit1(pls)))),'power$upower$uint'(X1,'number$unumber$uof$unat'(bit0(bit1(pls))))) = 'plus$uplus$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls)))),m),'one$uone$uint')
& 'is$uint'(X1)
& 'is$uint'(X0) ) ) ).
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$uless$uint'('one$uone$uint',t)
=> ? [X0,X1] :
( 'plus$uplus$uint'('power$upower$uint'(X0,'number$unumber$uof$unat'(bit0(bit1(pls)))),'power$upower$uint'(X1,'number$unumber$uof$unat'(bit0(bit1(pls))))) = 'plus$uplus$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls)))),m),'one$uone$uint')
& 'is$uint'(X1)
& 'is$uint'(X0) ) ) ).
fof(fact_37_zless__le,axiom,
! [X0,X1] :
( ( 'is$uint'(X1)
& 'is$uint'(X0) )
=> ( 'ord$uless$uint'(X0,X1)
<=> ( X0 != X1
& 'ord$uless$ueq$uint'(X0,X1) ) ) ) ).
fof(fact_38_zless__linear,axiom,
! [X0,X1] :
( ( 'is$uint'(X1)
& 'is$uint'(X0) )
=> ( 'ord$uless$uint'(X1,X0)
| X0 = X1
| 'ord$uless$uint'(X0,X1) ) ) ).
fof(fact_40_zle__antisym,axiom,
! [X0,X1] :
( ( 'is$uint'(X1)
& 'is$uint'(X0) )
=> ( 'ord$uless$ueq$uint'(X0,X1)
=> ( 'ord$uless$ueq$uint'(X1,X0)
=> X0 = X1 ) ) ) ).
fof(conj_0,conjecture,
? [X0,X1] : 'plus$uplus$uint'('power$upower$uint'(X0,'number$unumber$uof$unat'(bit0(bit1(pls)))),'power$upower$uint'(X1,'number$unumber$uof$unat'(bit0(bit1(pls))))) = 'plus$uplus$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls)))),m),'one$uone$uint') ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0,X1] : 'plus$uplus$uint'('power$upower$uint'(X0,'number$unumber$uof$unat'(bit0(bit1(pls)))),'power$upower$uint'(X1,'number$unumber$uof$unat'(bit0(bit1(pls))))) = 'plus$uplus$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls)))),m),'one$uone$uint'),
inference(negate_conjecture,[status(cth)],[conj_0]) ).
cnf(c1,plain,
'is$uint'('one$uone$uint'),
inference(clausification,[status(esa)],[gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint]) ).
cnf(c17,plain,
'is$uint'(t),
inference(clausification,[status(esa)],[gsy_v_t____]) ).
cnf(c18,plain,
'ord$uless$ueq$uint'('one$uone$uint',t),
inference(clausification,[status(esa)],[fact_0_tpos]) ).
cnf(c21,plain,
( 'plus$uplus$uint'('power$upower$uint'(sK14,'number$unumber$uof$unat'(bit0(bit1(pls)))),'power$upower$uint'(sK15,'number$unumber$uof$unat'(bit0(bit1(pls))))) = 'plus$uplus$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls)))),m),'one$uone$uint')
| t != 'one$uone$uint' ),
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(c24,plain,
( 'plus$uplus$uint'('power$upower$uint'(sK16,'number$unumber$uof$unat'(bit0(bit1(pls)))),'power$upower$uint'(sK17,'number$unumber$uof$unat'(bit0(bit1(pls))))) = 'plus$uplus$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls)))),m),'one$uone$uint')
| ~ 'ord$uless$uint'('one$uone$uint',t) ),
inference(clausification,[status(esa)],[fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06]) ).
cnf(c60,plain,
( 'ord$uless$ueq$uint'(X0,X1)
| ~ 'ord$uless$uint'(X0,X1)
| ~ 'is$uint'(X1)
| ~ 'is$uint'(X0) ),
inference(clausification,[status(esa)],[fact_37_zless__le]) ).
cnf(c63,plain,
( ~ 'is$uint'(X0)
| ~ 'is$uint'(X1)
| 'ord$uless$uint'(X1,X0)
| X0 = X1
| 'ord$uless$uint'(X0,X1) ),
inference(clausification,[status(esa)],[fact_38_zless__linear]) ).
cnf(c65,plain,
( ~ 'is$uint'(X0)
| ~ 'is$uint'(X1)
| X0 = X1
| ~ 'ord$uless$ueq$uint'(X1,X0)
| ~ 'ord$uless$ueq$uint'(X0,X1) ),
inference(clausification,[status(esa)],[fact_40_zle__antisym]) ).
cnf(c967,plain,
'plus$uplus$uint'('power$upower$uint'(X0,'number$unumber$uof$unat'(bit0(bit1(pls)))),'power$upower$uint'(X1,'number$unumber$uof$unat'(bit0(bit1(pls))))) != 'plus$uplus$uint'('times$utimes$uint'('number$unumber$uof$uint'(bit0(bit0(bit1(pls)))),m),'one$uone$uint'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
~ 'ord$uless$uint'('one$uone$uint',t),
inference(resolution,[status(thm)],[c967,c24]) ).
cnf(d1,plain,
( 'ord$uless$uint'(t,'one$uone$uint')
| ~ 'is$uint'(t)
| ~ 'is$uint'('one$uone$uint')
| t = 'one$uone$uint' ),
inference(resolution,[status(thm)],[c63,d0]) ).
cnf(d2,plain,
( 'ord$uless$uint'(t,'one$uone$uint')
| ~ 'is$uint'(t)
| t = 'one$uone$uint' ),
inference(resolution,[status(thm)],[c1,d1]) ).
cnf(d3,plain,
( 'ord$uless$uint'(t,'one$uone$uint')
| t = 'one$uone$uint' ),
inference(resolution,[status(thm)],[c17,d2]) ).
cnf(d4,plain,
t != 'one$uone$uint',
inference(resolution,[status(thm)],[c967,c21]) ).
cnf(d5,plain,
'ord$uless$uint'(t,'one$uone$uint'),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( 'ord$uless$ueq$uint'(t,'one$uone$uint')
| ~ 'is$uint'('one$uone$uint')
| ~ 'is$uint'(t) ),
inference(resolution,[status(thm)],[d5,c60]) ).
cnf(d7,plain,
( 'ord$uless$ueq$uint'(t,'one$uone$uint')
| ~ 'is$uint'(t) ),
inference(resolution,[status(thm)],[c1,d6]) ).
cnf(d8,plain,
'ord$uless$ueq$uint'(t,'one$uone$uint'),
inference(resolution,[status(thm)],[c17,d7]) ).
cnf(d9,plain,
( ~ 'ord$uless$ueq$uint'('one$uone$uint',t)
| ~ 'is$uint'(t)
| ~ 'is$uint'('one$uone$uint')
| t = 'one$uone$uint' ),
inference(resolution,[status(thm)],[c65,d8]) ).
cnf(d10,plain,
( ~ 'ord$uless$ueq$uint'('one$uone$uint',t)
| ~ 'is$uint'(t)
| t = 'one$uone$uint' ),
inference(resolution,[status(thm)],[c1,d9]) ).
cnf(d11,plain,
( ~ 'ord$uless$ueq$uint'('one$uone$uint',t)
| t = 'one$uone$uint' ),
inference(resolution,[status(thm)],[c17,d10]) ).
cnf(d12,plain,
t = 'one$uone$uint',
inference(resolution,[status(thm)],[c18,d11]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[d4,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM926+2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 04:25:57 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.21/4.46 % SZS status Theorem for theBenchmark.p
% 18.21/4.46 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------