%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM926+1 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 08:14:09 AM UTC 2026
% Result : Theorem 14.66s 2.72s
% Output : CNFRefutation 14.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 25 ( 12 unt; 0 def)
% Number of atoms : 40 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 18 ~; 12 |; 0 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-2 aty)
% Number of variables : 28 ( 2 sgn 5 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
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') ) ).
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$uint') ) ).
fof(fact_29_zless__linear,axiom,
! [X0,X1] :
( 'ord$uless$uint'(X1,X0)
| X0 = X1
| 'ord$uless$uint'(X0,X1) ) ).
fof(fact_38_le__number__of__eq__not__less,axiom,
! [X0,X1] :
( 'ord$uless$ueq$uint'('number$unumber$uof$uint'(X0),'number$unumber$uof$uint'(X1))
<=> ~ 'ord$uless$uint'('number$unumber$uof$uint'(X1),'number$unumber$uof$uint'(X0)) ) ).
fof(fact_111_number__of__is__id,axiom,
! [X0] : 'number$unumber$uof$uint'(X0) = X0 ).
fof(conj_0,conjecture,
? [X0,X1] : 'plus$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$uint'),
inference(negate_conjecture,[status(cth)],[conj_0]) ).
cnf(c0,plain,
'ord$uless$ueq$uint'('one$uone$uint',t),
inference(clausification,[status(esa)],[fact_0_tpos]) ).
cnf(c1,plain,
( 'plus$uplus$uint'('power$upower$uint'(sK0,'number$unumber$uof$unat'(bit0(bit1(pls)))),'power$upower$uint'(sK1,'number$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$uint' ),
inference(clausification,[status(esa)],[fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06]) ).
cnf(c2,plain,
( 'plus$uplus$uint'('power$upower$uint'(sK2,'number$unumber$uof$unat'(bit0(bit1(pls)))),'power$upower$uint'(sK3,'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(c31,plain,
( 'ord$uless$uint'(X1,X0)
| X0 = X1
| 'ord$uless$uint'(X0,X1) ),
inference(clausification,[status(esa)],[fact_29_zless__linear]) ).
cnf(c41,plain,
( ~ 'ord$uless$uint'('number$unumber$uof$uint'(X1),'number$unumber$uof$uint'(X0))
| ~ 'ord$uless$ueq$uint'('number$unumber$uof$uint'(X0),'number$unumber$uof$uint'(X1)) ),
inference(clausification,[status(esa)],[fact_38_le__number__of__eq__not__less]) ).
cnf(c142,plain,
'number$unumber$uof$uint'(X0) = X0,
inference(clausification,[status(esa)],[fact_111_number__of__is__id]) ).
cnf(c162,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$uint',t),
inference(resolution,[status(thm)],[c162,c2]) ).
cnf(d1,plain,
( 'ord$uless$uint'(t,'one$uone$uint')
| t = 'one$uone$uint' ),
inference(resolution,[status(thm)],[c31,d0]) ).
cnf(d2,plain,
t != 'one$uone$uint',
inference(resolution,[status(thm)],[c162,c1]) ).
cnf(d3,plain,
'ord$uless$uint'(t,'one$uone$uint'),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( ~ 'ord$uless$uint'('number$unumber$uof$uint'(X1),'number$unumber$uof$uint'(X0))
| ~ 'ord$uless$ueq$uint'(X0,'number$unumber$uof$uint'(X1)) ),
inference(demodulation,[status(thm)],[c41,c142]) ).
cnf(d5,plain,
( ~ 'ord$uless$uint'('number$unumber$uof$uint'(X0),'number$unumber$uof$uint'(X1))
| ~ 'ord$uless$ueq$uint'(X1,X0) ),
inference(demodulation,[status(thm)],[d4,c142]) ).
cnf(d6,plain,
( ~ 'ord$uless$uint'(X0,'number$unumber$uof$uint'(X1))
| ~ 'ord$uless$ueq$uint'(X1,X0) ),
inference(demodulation,[status(thm)],[d5,c142]) ).
cnf(d7,plain,
( ~ 'ord$uless$uint'(X1,X0)
| ~ 'ord$uless$ueq$uint'(X0,X1) ),
inference(demodulation,[status(thm)],[d6,c142]) ).
cnf(d8,plain,
~ 'ord$uless$ueq$uint'('one$uone$uint',t),
inference(resolution,[status(thm)],[d7,d3]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[c0,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM926+1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.59 % Computer : n003.cluster.edu
% 0.09/0.59 % Model : x86_64 x86_64
% 0.09/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.59 % Memory : 8046.5625MB
% 0.09/0.59 % OS : Linux 6.8.0-71-generic
% 0.09/0.59 % CPULimit : 300
% 0.09/0.59 % WCLimit : 300
% 0.09/0.59 % DateTime : Sat Sep 26 04:21:39 UTC 2026
% 0.09/0.59 % CPUTime :
% 0.09/0.59 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.66/2.72 % SZS status Theorem for theBenchmark.p
% 14.66/2.72 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------