%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM926+4 : 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 : n011.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 123.25s 18.41s
% Output : CNFRefutation 123.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 44 ( 19 unt; 0 def)
% Number of atoms : 100 ( 41 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 94 ( 38 ~; 40 |; 8 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 18 con; 0-2 aty)
% Number of variables : 28 ( 8 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,
hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('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$uint'
=> ? [X0,X1] :
( 'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint',X0),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,pls))))),'hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint',X1),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,pls))))) = 'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('times$utimes$uint','hAPP$uint$uint'('number$unumber$uof$uint','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit0,'hAPP$uint$uint'(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,
( hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint','one$uone$uint'),t))
=> ? [X0,X1] :
( 'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint',X0),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,pls))))),'hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint',X1),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,pls))))) = 'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('times$utimes$uint','hAPP$uint$uint'('number$unumber$uof$uint','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,pls))))),m)),'one$uone$uint')
& 'is$uint'(X1)
& 'is$uint'(X0) ) ) ).
fof(fact_65_zless__le,axiom,
! [X0,X1] :
( ( 'is$uint'(X1)
& 'is$uint'(X0) )
=> ( hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint',X0),X1))
<=> ( X0 != X1
& hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$ueq$uint',X0),X1)) ) ) ) ).
fof(fact_66_zless__linear,axiom,
! [X0,X1] :
( ( 'is$uint'(X1)
& 'is$uint'(X0) )
=> ( hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint',X1),X0))
| X0 = X1
| hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint',X0),X1)) ) ) ).
fof(fact_68_zle__antisym,axiom,
! [X0,X1] :
( ( 'is$uint'(X1)
& 'is$uint'(X0) )
=> ( hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$ueq$uint',X0),X1))
=> ( hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$ueq$uint',X1),X0))
=> X0 = X1 ) ) ) ).
fof(fact_644_Pls__def,axiom,
pls = 'zero$uzero$uint' ).
fof(conj_0,conjecture,
? [X0,X1] : 'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint',X0),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,pls))))),'hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint',X1),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,pls))))) = 'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('times$utimes$uint','hAPP$uint$uint'('number$unumber$uof$uint','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,pls))))),m)),'one$uone$uint') ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0,X1] : 'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint',X0),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,pls))))),'hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint',X1),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,pls))))) = 'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('times$utimes$uint','hAPP$uint$uint'('number$unumber$uof$uint','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,pls))))),m)),'one$uone$uint'),
inference(negate_conjecture,[status(cth)],[conj_0]) ).
cnf(c5,plain,
'is$uint'('one$uone$uint'),
inference(clausification,[status(esa)],[gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint]) ).
cnf(c58,plain,
'is$uint'(t),
inference(clausification,[status(esa)],[gsy_v_t____]) ).
cnf(c59,plain,
hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$ueq$uint','one$uone$uint'),t)),
inference(clausification,[status(esa)],[fact_0_tpos]) ).
cnf(c62,plain,
( 'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint',sK86),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,pls))))),'hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint',sK87),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,pls))))) = 'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('times$utimes$uint','hAPP$uint$uint'('number$unumber$uof$uint','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit0,'hAPP$uint$uint'(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(c65,plain,
( 'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint',sK88),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,pls))))),'hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint',sK89),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,pls))))) = 'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('times$utimes$uint','hAPP$uint$uint'('number$unumber$uof$uint','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,pls))))),m)),'one$uone$uint')
| ~ hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint','one$uone$uint'),t)) ),
inference(clausification,[status(esa)],[fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06]) ).
cnf(c129,plain,
( hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$ueq$uint',X0),X1))
| ~ hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint',X0),X1))
| ~ 'is$uint'(X1)
| ~ 'is$uint'(X0) ),
inference(clausification,[status(esa)],[fact_65_zless__le]) ).
cnf(c132,plain,
( ~ 'is$uint'(X1)
| hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint',X1),X0))
| ~ 'is$uint'(X0)
| X0 = X1
| hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint',X0),X1)) ),
inference(clausification,[status(esa)],[fact_66_zless__linear]) ).
cnf(c134,plain,
( ~ 'is$uint'(X1)
| ~ 'is$uint'(X0)
| X0 = X1
| ~ hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$ueq$uint',X1),X0))
| ~ hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$ueq$uint',X0),X1)) ),
inference(clausification,[status(esa)],[fact_68_zle__antisym]) ).
cnf(c855,plain,
pls = 'zero$uzero$uint',
inference(clausification,[status(esa)],[fact_644_Pls__def]) ).
cnf(c7817,plain,
'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint',X0),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,pls))))),'hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint',X1),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,pls))))) != 'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('times$utimes$uint','hAPP$uint$uint'('number$unumber$uof$uint','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,pls))))),m)),'one$uone$uint'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint','one$uone$uint'),t))
| 'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint',sK88),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,'zero$uzero$uint'))))),'hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint',sK89),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,pls))))) = 'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('times$utimes$uint','hAPP$uint$uint'('number$unumber$uof$uint','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,pls))))),m)),'one$uone$uint') ),
inference(demodulation,[status(thm)],[c65,c855]) ).
cnf(d1,plain,
( ~ hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint','one$uone$uint'),t))
| 'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint',sK88),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,'zero$uzero$uint'))))),'hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint',sK89),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,'zero$uzero$uint'))))) = 'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('times$utimes$uint','hAPP$uint$uint'('number$unumber$uof$uint','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,pls))))),m)),'one$uone$uint') ),
inference(demodulation,[status(thm)],[d0,c855]) ).
cnf(d2,plain,
( ~ hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint','one$uone$uint'),t))
| 'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint',sK88),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,'zero$uzero$uint'))))),'hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint',sK89),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,'zero$uzero$uint'))))) = 'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('times$utimes$uint','hAPP$uint$uint'('number$unumber$uof$uint','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,'zero$uzero$uint'))))),m)),'one$uone$uint') ),
inference(demodulation,[status(thm)],[d1,c855]) ).
cnf(d3,plain,
'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint',X0),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,'zero$uzero$uint'))))),'hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint',X1),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,pls))))) != 'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('times$utimes$uint','hAPP$uint$uint'('number$unumber$uof$uint','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,pls))))),m)),'one$uone$uint'),
inference(demodulation,[status(thm)],[c7817,c855]) ).
cnf(d4,plain,
'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint',X0),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,'zero$uzero$uint'))))),'hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint',X1),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,'zero$uzero$uint'))))) != 'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('times$utimes$uint','hAPP$uint$uint'('number$unumber$uof$uint','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,pls))))),m)),'one$uone$uint'),
inference(demodulation,[status(thm)],[d3,c855]) ).
cnf(d5,plain,
'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint',X0),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,'zero$uzero$uint'))))),'hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint',X1),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,'zero$uzero$uint'))))) != 'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('times$utimes$uint','hAPP$uint$uint'('number$unumber$uof$uint','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,'zero$uzero$uint'))))),m)),'one$uone$uint'),
inference(demodulation,[status(thm)],[d4,c855]) ).
cnf(d6,plain,
~ hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint','one$uone$uint'),t)),
inference(resolution,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
( hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint',t),'one$uone$uint'))
| ~ 'is$uint'('one$uone$uint')
| ~ 'is$uint'(t)
| 'one$uone$uint' = t ),
inference(resolution,[status(thm)],[c132,d6]) ).
cnf(d8,plain,
( hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint',t),'one$uone$uint'))
| ~ 'is$uint'(t)
| 'one$uone$uint' = t ),
inference(resolution,[status(thm)],[c5,d7]) ).
cnf(d9,plain,
( hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint',t),'one$uone$uint'))
| 'one$uone$uint' = t ),
inference(resolution,[status(thm)],[c58,d8]) ).
cnf(d10,plain,
( hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$ueq$uint',t),'one$uone$uint'))
| ~ 'is$uint'(t)
| ~ 'is$uint'('one$uone$uint')
| 'one$uone$uint' = t ),
inference(resolution,[status(thm)],[d9,c129]) ).
cnf(d11,plain,
( hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$ueq$uint',t),'one$uone$uint'))
| ~ 'is$uint'(t)
| 'one$uone$uint' = t ),
inference(resolution,[status(thm)],[c5,d10]) ).
cnf(d12,plain,
( hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$ueq$uint',t),'one$uone$uint'))
| 'one$uone$uint' = t ),
inference(resolution,[status(thm)],[c58,d11]) ).
cnf(d13,plain,
( 'one$uone$uint' = t
| ~ hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$ueq$uint','one$uone$uint'),t))
| ~ 'is$uint'(t)
| ~ 'is$uint'('one$uone$uint')
| 'one$uone$uint' = t ),
inference(resolution,[status(thm)],[c134,d12]) ).
cnf(d14,plain,
( ~ hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$ueq$uint','one$uone$uint'),t))
| ~ 'is$uint'(t)
| 'one$uone$uint' = t ),
inference(resolution,[status(thm)],[c5,d13]) ).
cnf(d15,plain,
( ~ hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$ueq$uint','one$uone$uint'),t))
| 'one$uone$uint' = t ),
inference(resolution,[status(thm)],[c58,d14]) ).
cnf(d16,plain,
'one$uone$uint' = t,
inference(resolution,[status(thm)],[c59,d15]) ).
cnf(d17,plain,
( t != 'one$uone$uint'
| 'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint',sK86),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,'zero$uzero$uint'))))),'hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint',sK87),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,pls))))) = 'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('times$utimes$uint','hAPP$uint$uint'('number$unumber$uof$uint','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,pls))))),m)),'one$uone$uint') ),
inference(demodulation,[status(thm)],[c62,c855]) ).
cnf(d18,plain,
( t != 'one$uone$uint'
| 'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint',sK86),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,'zero$uzero$uint'))))),'hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint',sK87),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,'zero$uzero$uint'))))) = 'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('times$utimes$uint','hAPP$uint$uint'('number$unumber$uof$uint','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,pls))))),m)),'one$uone$uint') ),
inference(demodulation,[status(thm)],[d17,c855]) ).
cnf(d19,plain,
( t != 'one$uone$uint'
| 'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint',sK86),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,'zero$uzero$uint'))))),'hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint',sK87),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,'zero$uzero$uint'))))) = 'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('times$utimes$uint','hAPP$uint$uint'('number$unumber$uof$uint','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,'zero$uzero$uint'))))),m)),'one$uone$uint') ),
inference(demodulation,[status(thm)],[d18,c855]) ).
cnf(d20,plain,
t != 'one$uone$uint',
inference(resolution,[status(thm)],[d5,d19]) ).
cnf(d21,plain,
'one$uone$uint' != 'one$uone$uint',
inference(demodulation,[status(thm)],[d20,d16]) ).
cnf(d22,plain,
$false,
inference(equality_resolution,[status(thm)],[d21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM926+4 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.36 % Computer : n011.cluster.edu
% 0.03/0.36 % Model : x86_64 x86_64
% 0.03/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.36 % Memory : 8046.5625MB
% 0.03/0.36 % OS : Linux 6.8.0-71-generic
% 0.03/0.36 % CPULimit : 300
% 0.03/0.36 % WCLimit : 300
% 0.03/0.36 % DateTime : Sat Sep 26 04:21:28 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 123.25/18.41 % SZS status Theorem for theBenchmark.p
% 123.25/18.41 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------