%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM925+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 : 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 08:14:08 AM UTC 2026
% Result : Theorem 26.31s 4.12s
% Output : CNFRefutation 26.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 14 unt; 0 def)
% Number of atoms : 24 ( 17 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 9 ~; 4 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-2 aty)
% Number of variables : 4 ( 0 sgn 1 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_0_n1pos,axiom,
hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint','zero$uzero$uint'),'hAPP$uint$uint'('plus$uplus$uint'('one$uone$uint'),'hAPP$unat$uint'('semiri1621563631at$uint',n)))) ).
fof(fact_10_zero__eq__power2,axiom,
! [X0] :
( 'hAPP$unat$uint'('power$upower$uint'(X0),'number$unumber$uof$unat'(bit0(bit1(pls)))) = 'zero$uzero$uint'
<=> X0 = 'zero$uzero$uint' ) ).
fof(fact_48_rel__simps_I2_J,axiom,
~ hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint',pls),pls)) ).
fof(fact_98_Pls__def,axiom,
pls = 'zero$uzero$uint' ).
fof(conj_0,conjecture,
'hAPP$unat$uint'('power$upower$uint'('hAPP$uint$uint'('plus$uplus$uint'('one$uone$uint'),'hAPP$unat$uint'('semiri1621563631at$uint',n))),'number$unumber$uof$unat'(bit0(bit1(pls)))) != 'zero$uzero$uint' ).
fof(negated_conjecture,negated_conjecture,
~ ( 'hAPP$unat$uint'('power$upower$uint'('hAPP$uint$uint'('plus$uplus$uint'('one$uone$uint'),'hAPP$unat$uint'('semiri1621563631at$uint',n))),'number$unumber$uof$unat'(bit0(bit1(pls)))) != 'zero$uzero$uint' ),
inference(negate_conjecture,[status(cth)],[conj_0]) ).
cnf(c5,plain,
hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint','zero$uzero$uint'),'hAPP$uint$uint'('plus$uplus$uint'('one$uone$uint'),'hAPP$unat$uint'('semiri1621563631at$uint',n)))),
inference(clausification,[status(esa)],[fact_0_n1pos]) ).
cnf(c19,plain,
( X0 = 'zero$uzero$uint'
| 'hAPP$unat$uint'('power$upower$uint'(X0),'number$unumber$uof$unat'(bit0(bit1(pls)))) != 'zero$uzero$uint' ),
inference(clausification,[status(esa)],[fact_10_zero__eq__power2]) ).
cnf(c68,plain,
~ hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint',pls),pls)),
inference(clausification,[status(esa)],[fact_48_rel__simps_I2_J]) ).
cnf(c154,plain,
pls = 'zero$uzero$uint',
inference(clausification,[status(esa)],[fact_98_Pls__def]) ).
cnf(c987,plain,
'hAPP$unat$uint'('power$upower$uint'('hAPP$uint$uint'('plus$uplus$uint'('one$uone$uint'),'hAPP$unat$uint'('semiri1621563631at$uint',n))),'number$unumber$uof$unat'(bit0(bit1(pls)))) = 'zero$uzero$uint',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'hAPP$unat$uint'('power$upower$uint'(X0),'number$unumber$uof$unat'(bit0(bit1(pls)))) != 'zero$uzero$uint'
| X0 = pls ),
inference(demodulation,[status(thm)],[c19,c154]) ).
cnf(d1,plain,
( 'hAPP$unat$uint'('power$upower$uint'(X0),'number$unumber$uof$unat'(bit0(bit1(pls)))) != pls
| X0 = pls ),
inference(demodulation,[status(thm)],[d0,c154]) ).
cnf(d2,plain,
'hAPP$unat$uint'('power$upower$uint'('hAPP$uint$uint'('plus$uplus$uint'('one$uone$uint'),'hAPP$unat$uint'('semiri1621563631at$uint',n))),'number$unumber$uof$unat'(bit0(bit1(pls)))) = pls,
inference(demodulation,[status(thm)],[c987,c154]) ).
cnf(d3,plain,
( 'hAPP$uint$uint'('plus$uplus$uint'('one$uone$uint'),'hAPP$unat$uint'('semiri1621563631at$uint',n)) = pls
| pls != pls ),
inference(superposition,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
'hAPP$uint$uint'('plus$uplus$uint'('one$uone$uint'),'hAPP$unat$uint'('semiri1621563631at$uint',n)) = pls,
inference(equality_resolution,[status(thm)],[d3]) ).
cnf(d5,plain,
hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint',pls),'hAPP$uint$uint'('plus$uplus$uint'('one$uone$uint'),'hAPP$unat$uint'('semiri1621563631at$uint',n)))),
inference(demodulation,[status(thm)],[c5,c154]) ).
cnf(d6,plain,
hBOOL('hAPP$uint$ubool'('hAPP$ui1948725293t$ubool'('ord$uless$uint',pls),pls)),
inference(demodulation,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[d6,c68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM925+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
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 04:19:53 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.31/4.12 % SZS status Theorem for theBenchmark.p
% 26.31/4.12 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------