%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM925+4 : 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 08:14:08 AM UTC 2026
% Result : Theorem 63.17s 24.16s
% Output : CNFRefutation 63.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 25 ( 17 unt; 0 def)
% Number of atoms : 37 ( 17 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 16 ~; 9 |; 0 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 11 con; 0-2 aty)
% Number of variables : 11 ( 3 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(gsy_c_hAPP_000tc__Int__Oint_000tc__Int__Oint,hypothesis,
! [X0,X1] :
( 'is$uint'(X1)
=> 'is$uint'('hAPP$uint$uint'(X0,X1)) ) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint,hypothesis,
! [X0,X1] : 'is$uint'('hAPP$unat$uint'(X0,X1)) ).
fof(fact_0_n1pos,axiom,
hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint','zero$uzero$uint'),'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','one$uone$uint'),'hAPP$unat$uint'('semiri1621563631at$uint',n)))) ).
fof(fact_22_zero__eq__power2,axiom,
! [X0] :
( 'is$uint'(X0)
=> ( 'hAPP$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)))) = 'zero$uzero$uint'
<=> X0 = 'zero$uzero$uint' ) ) ).
fof(fact_76_rel__simps_I2_J,axiom,
~ hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint',pls),pls)) ).
fof(fact_151_Pls__def,axiom,
pls = 'zero$uzero$uint' ).
fof(conj_0,conjecture,
'hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint','hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','one$uone$uint'),'hAPP$unat$uint'('semiri1621563631at$uint',n))),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,pls)))) != 'zero$uzero$uint' ).
fof(negated_conjecture,negated_conjecture,
~ ( 'hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint','hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','one$uone$uint'),'hAPP$unat$uint'('semiri1621563631at$uint',n))),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,pls)))) != 'zero$uzero$uint' ),
inference(negate_conjecture,[status(cth)],[conj_0]) ).
cnf(c33,plain,
( 'is$uint'('hAPP$uint$uint'(X1,X0))
| ~ 'is$uint'(X0) ),
inference(clausification,[status(esa)],[gsy_c_hAPP_000tc__Int__Oint_000tc__Int__Oint]) ).
cnf(c35,plain,
'is$uint'('hAPP$unat$uint'(X0,X1)),
inference(clausification,[status(esa)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint]) ).
cnf(c66,plain,
hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint','zero$uzero$uint'),'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','one$uone$uint'),'hAPP$unat$uint'('semiri1621563631at$uint',n)))),
inference(clausification,[status(esa)],[fact_0_n1pos]) ).
cnf(c97,plain,
( X0 = 'zero$uzero$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$uint'(bit1,pls)))) != 'zero$uzero$uint'
| ~ 'is$uint'(X0) ),
inference(clausification,[status(esa)],[fact_22_zero__eq__power2]) ).
cnf(c166,plain,
~ hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint',pls),pls)),
inference(clausification,[status(esa)],[fact_76_rel__simps_I2_J]) ).
cnf(c296,plain,
pls = 'zero$uzero$uint',
inference(clausification,[status(esa)],[fact_151_Pls__def]) ).
cnf(c7903,plain,
'hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint','hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','one$uone$uint'),'hAPP$unat$uint'('semiri1621563631at$uint',n))),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,pls)))) = 'zero$uzero$uint',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
~ hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint','zero$uzero$uint'),pls)),
inference(demodulation,[status(thm)],[c166,c296]) ).
cnf(d1,plain,
~ hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint','zero$uzero$uint'),'zero$uzero$uint')),
inference(demodulation,[status(thm)],[d0,c296]) ).
cnf(d2,plain,
( ~ 'is$uint'(X0)
| 'hAPP$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')))) != 'zero$uzero$uint'
| X0 = 'zero$uzero$uint' ),
inference(demodulation,[status(thm)],[c97,c296]) ).
cnf(d3,plain,
'hAPP$unat$uint'('hAPP$uint$ufun$unat$uint'('power$upower$uint','hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','one$uone$uint'),'hAPP$unat$uint'('semiri1621563631at$uint',n))),'hAPP$uint$unat'('number$unumber$uof$unat','hAPP$uint$uint'(bit0,'hAPP$uint$uint'(bit1,'zero$uzero$uint')))) = 'zero$uzero$uint',
inference(demodulation,[status(thm)],[c7903,c296]) ).
cnf(d4,plain,
( ~ 'is$uint'('hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','one$uone$uint'),'hAPP$unat$uint'('semiri1621563631at$uint',n)))
| 'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','one$uone$uint'),'hAPP$unat$uint'('semiri1621563631at$uint',n)) = 'zero$uzero$uint'
| 'zero$uzero$uint' != 'zero$uzero$uint' ),
inference(superposition,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
( ~ 'is$uint'('hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','one$uone$uint'),'hAPP$unat$uint'('semiri1621563631at$uint',n)))
| 'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','one$uone$uint'),'hAPP$unat$uint'('semiri1621563631at$uint',n)) = 'zero$uzero$uint' ),
inference(equality_resolution,[status(thm)],[d4]) ).
cnf(d6,plain,
( ~ 'is$uint'('hAPP$unat$uint'('semiri1621563631at$uint',n))
| 'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','one$uone$uint'),'hAPP$unat$uint'('semiri1621563631at$uint',n)) = 'zero$uzero$uint' ),
inference(resolution,[status(thm)],[d5,c33]) ).
cnf(d7,plain,
'hAPP$uint$uint'('hAPP$uint$ufun$uint$uint'('plus$uplus$uint','one$uone$uint'),'hAPP$unat$uint'('semiri1621563631at$uint',n)) = 'zero$uzero$uint',
inference(resolution,[status(thm)],[c35,d6]) ).
cnf(d8,plain,
hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint','zero$uzero$uint'),'zero$uzero$uint')),
inference(demodulation,[status(thm)],[c66,d7]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[d8,d1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM925+4 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/15.38 % Computer : n002.cluster.edu
% 0.10/15.38 % Model : x86_64 x86_64
% 0.10/15.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/15.38 % Memory : 8046.5625MB
% 0.10/15.38 % OS : Linux 6.8.0-71-generic
% 0.10/15.38 % CPULimit : 300
% 0.10/15.38 % WCLimit : 300
% 0.10/15.38 % DateTime : Sat Sep 26 04:21:54 UTC 2026
% 0.10/15.39 % CPUTime :
% 0.10/15.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 63.17/24.16 % SZS status Theorem for theBenchmark.p
% 63.17/24.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------