%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : AGT026+2 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 06:45:39 AM UTC 2026
% Result : Theorem 91.26s 38.56s
% Output : CNFRefutation 91.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 30
% Syntax : Number of formulae : 105 ( 62 unt; 0 def)
% Number of atoms : 185 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 158 ( 78 ~; 65 |; 8 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 22 con; 0-2 aty)
% Number of variables : 85 ( 18 sgn 20 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(a1_3,axiom,
! [X0,X1,X2,X3] :
( ( less(X2,X1)
& 'accept$upopulation'(X0,X3,X1) )
=> 'accept$upopulation'(X0,X3,X2) ) ).
fof(a2_7,axiom,
! [X0] :
( ( 'accept$upopulation'(X0,other,n0)
& 'accept$upopulation'(X0,native,n85)
& 'accept$upopulation'(X0,muslim,n0)
& 'accept$upopulation'(X0,christian,n3)
& 'accept$upopulation'(X0,atheist,n12) )
<=> 'accept$ucity'(X0,coastvillage) ) ).
fof(deduced_13,axiom,
~ 'accept$ucity'(countryamedicalorganization,coastvillage) ).
fof(deduced_16,axiom,
'accept$upopulation'(countryamedicalorganization,muslim,n65) ).
fof(deduced_211,axiom,
'accept$upopulation'(countryamedicalorganization,christian,n20) ).
fof(deduced_212,axiom,
'accept$upopulation'(countryamedicalorganization,atheist,n78) ).
fof(deduced_220,axiom,
'accept$upopulation'(countryamedicalorganization,other,n0) ).
fof(rdn0,axiom,
'rdn$utranslate'(n0,'rdn$upos'(rdnn(n0))) ).
fof(rdn3,axiom,
'rdn$utranslate'(n3,'rdn$upos'(rdnn(n3))) ).
fof(rdn12,axiom,
'rdn$utranslate'(n12,'rdn$upos'(rdn(rdnn(n2),rdnn(n1)))) ).
fof(rdn20,axiom,
'rdn$utranslate'(n20,'rdn$upos'(rdn(rdnn(n0),rdnn(n2)))) ).
fof(rdn65,axiom,
'rdn$utranslate'(n65,'rdn$upos'(rdn(rdnn(n5),rdnn(n6)))) ).
fof(rdn78,axiom,
'rdn$utranslate'(n78,'rdn$upos'(rdn(rdnn(n8),rdnn(n7)))) ).
fof(rdn85,axiom,
'rdn$utranslate'(n85,'rdn$upos'(rdn(rdnn(n5),rdnn(n8)))) ).
fof(rdn100,axiom,
'rdn$utranslate'(n100,'rdn$upos'(rdn(rdnn(n0),rdn(rdnn(n0),rdnn(n1))))) ).
fof(rdn_digit1,axiom,
'rdn$unon$uzero$udigit'(rdnn(n1)) ).
fof(rdn_digit2,axiom,
'rdn$unon$uzero$udigit'(rdnn(n2)) ).
fof(rdn_digit6,axiom,
'rdn$unon$uzero$udigit'(rdnn(n6)) ).
fof(rdn_positive_less12,axiom,
'rdn$upositive$uless'(rdnn(n1),rdnn(n2)) ).
fof(rdn_positive_less23,axiom,
'rdn$upositive$uless'(rdnn(n2),rdnn(n3)) ).
fof(rdn_positive_less34,axiom,
'rdn$upositive$uless'(rdnn(n3),rdnn(n4)) ).
fof(rdn_positive_less45,axiom,
'rdn$upositive$uless'(rdnn(n4),rdnn(n5)) ).
fof(rdn_positive_less56,axiom,
'rdn$upositive$uless'(rdnn(n5),rdnn(n6)) ).
fof(rdn_positive_less67,axiom,
'rdn$upositive$uless'(rdnn(n6),rdnn(n7)) ).
fof(rdn_positive_less_transitivity,axiom,
! [X0,X1,X2] :
( ( 'rdn$upositive$uless'(rdnn(X1),rdnn(X2))
& 'rdn$upositive$uless'(rdnn(X0),rdnn(X1)) )
=> 'rdn$upositive$uless'(rdnn(X0),rdnn(X2)) ) ).
fof(rdn_positive_less_multi_digit_high,axiom,
! [X0,X1,X2,X3] :
( 'rdn$upositive$uless'(X1,X3)
=> 'rdn$upositive$uless'(rdn(rdnn(X0),X1),rdn(rdnn(X2),X3)) ) ).
fof(rdn_extra_digits_positive_less,axiom,
! [X0,X1,X2] :
( 'rdn$unon$uzero'(X2)
=> 'rdn$upositive$uless'(rdnn(X0),rdn(rdnn(X1),X2)) ) ).
fof(rdn_non_zero_by_digit,axiom,
! [X0] :
( 'rdn$unon$uzero$udigit'(rdnn(X0))
=> 'rdn$unon$uzero'(rdnn(X0)) ) ).
fof(less_entry_point_pos_pos,axiom,
! [X0,X1,X2,X3] :
( ( 'rdn$upositive$uless'(X2,X3)
& 'rdn$utranslate'(X1,'rdn$upos'(X3))
& 'rdn$utranslate'(X0,'rdn$upos'(X2)) )
=> less(X0,X1) ) ).
fof(query_26,conjecture,
? [X0,X1] : ~ 'accept$upopulation'(X0,X1,n100) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0,X1] : ~ 'accept$upopulation'(X0,X1,n100),
inference(negate_conjecture,[status(cth)],[query_26]) ).
cnf(c5,plain,
( 'accept$upopulation'(X2,X3,X0)
| ~ 'accept$upopulation'(X2,X3,X1)
| ~ less(X0,X1) ),
inference(clausification,[status(esa)],[a1_3]) ).
cnf(c9,plain,
( ~ 'accept$upopulation'(X0,christian,n3)
| ~ 'accept$upopulation'(X0,native,n85)
| 'accept$ucity'(X0,coastvillage)
| ~ 'accept$upopulation'(X0,other,n0)
| ~ 'accept$upopulation'(X0,atheist,n12)
| ~ 'accept$upopulation'(X0,muslim,n0) ),
inference(clausification,[status(esa)],[a2_7]) ).
cnf(c302,plain,
~ 'accept$ucity'(countryamedicalorganization,coastvillage),
inference(clausification,[status(esa)],[deduced_13]) ).
cnf(c305,plain,
'accept$upopulation'(countryamedicalorganization,muslim,n65),
inference(clausification,[status(esa)],[deduced_16]) ).
cnf(c500,plain,
'accept$upopulation'(countryamedicalorganization,christian,n20),
inference(clausification,[status(esa)],[deduced_211]) ).
cnf(c501,plain,
'accept$upopulation'(countryamedicalorganization,atheist,n78),
inference(clausification,[status(esa)],[deduced_212]) ).
cnf(c509,plain,
'accept$upopulation'(countryamedicalorganization,other,n0),
inference(clausification,[status(esa)],[deduced_220]) ).
cnf(c657,plain,
'rdn$utranslate'(n0,'rdn$upos'(rdnn(n0))),
inference(clausification,[status(esa)],[rdn0]) ).
cnf(c660,plain,
'rdn$utranslate'(n3,'rdn$upos'(rdnn(n3))),
inference(clausification,[status(esa)],[rdn3]) ).
cnf(c667,plain,
'rdn$utranslate'(n12,'rdn$upos'(rdn(rdnn(n2),rdnn(n1)))),
inference(clausification,[status(esa)],[rdn12]) ).
cnf(c668,plain,
'rdn$utranslate'(n20,'rdn$upos'(rdn(rdnn(n0),rdnn(n2)))),
inference(clausification,[status(esa)],[rdn20]) ).
cnf(c671,plain,
'rdn$utranslate'(n65,'rdn$upos'(rdn(rdnn(n5),rdnn(n6)))),
inference(clausification,[status(esa)],[rdn65]) ).
cnf(c673,plain,
'rdn$utranslate'(n78,'rdn$upos'(rdn(rdnn(n8),rdnn(n7)))),
inference(clausification,[status(esa)],[rdn78]) ).
cnf(c674,plain,
'rdn$utranslate'(n85,'rdn$upos'(rdn(rdnn(n5),rdnn(n8)))),
inference(clausification,[status(esa)],[rdn85]) ).
cnf(c675,plain,
'rdn$utranslate'(n100,'rdn$upos'(rdn(rdnn(n0),rdn(rdnn(n0),rdnn(n1))))),
inference(clausification,[status(esa)],[rdn100]) ).
cnf(c676,plain,
'rdn$unon$uzero$udigit'(rdnn(n1)),
inference(clausification,[status(esa)],[rdn_digit1]) ).
cnf(c677,plain,
'rdn$unon$uzero$udigit'(rdnn(n2)),
inference(clausification,[status(esa)],[rdn_digit2]) ).
cnf(c681,plain,
'rdn$unon$uzero$udigit'(rdnn(n6)),
inference(clausification,[status(esa)],[rdn_digit6]) ).
cnf(c686,plain,
'rdn$upositive$uless'(rdnn(n1),rdnn(n2)),
inference(clausification,[status(esa)],[rdn_positive_less12]) ).
cnf(c687,plain,
'rdn$upositive$uless'(rdnn(n2),rdnn(n3)),
inference(clausification,[status(esa)],[rdn_positive_less23]) ).
cnf(c688,plain,
'rdn$upositive$uless'(rdnn(n3),rdnn(n4)),
inference(clausification,[status(esa)],[rdn_positive_less34]) ).
cnf(c689,plain,
'rdn$upositive$uless'(rdnn(n4),rdnn(n5)),
inference(clausification,[status(esa)],[rdn_positive_less45]) ).
cnf(c690,plain,
'rdn$upositive$uless'(rdnn(n5),rdnn(n6)),
inference(clausification,[status(esa)],[rdn_positive_less56]) ).
cnf(c691,plain,
'rdn$upositive$uless'(rdnn(n6),rdnn(n7)),
inference(clausification,[status(esa)],[rdn_positive_less67]) ).
cnf(c694,plain,
( 'rdn$upositive$uless'(rdnn(X2),rdnn(X1))
| ~ 'rdn$upositive$uless'(rdnn(X2),rdnn(X0))
| ~ 'rdn$upositive$uless'(rdnn(X0),rdnn(X1)) ),
inference(clausification,[status(esa)],[rdn_positive_less_transitivity]) ).
cnf(c695,plain,
( 'rdn$upositive$uless'(rdn(rdnn(X2),X0),rdn(rdnn(X3),X1))
| ~ 'rdn$upositive$uless'(X0,X1) ),
inference(clausification,[status(esa)],[rdn_positive_less_multi_digit_high]) ).
cnf(c697,plain,
( 'rdn$upositive$uless'(rdnn(X1),rdn(rdnn(X2),X0))
| ~ 'rdn$unon$uzero'(X0) ),
inference(clausification,[status(esa)],[rdn_extra_digits_positive_less]) ).
cnf(c698,plain,
( 'rdn$unon$uzero'(rdnn(X0))
| ~ 'rdn$unon$uzero$udigit'(rdnn(X0)) ),
inference(clausification,[status(esa)],[rdn_non_zero_by_digit]) ).
cnf(c700,plain,
( less(X3,X0)
| ~ 'rdn$utranslate'(X3,'rdn$upos'(X2))
| ~ 'rdn$upositive$uless'(X2,X1)
| ~ 'rdn$utranslate'(X0,'rdn$upos'(X1)) ),
inference(clausification,[status(esa)],[less_entry_point_pos_pos]) ).
cnf(c710,plain,
'accept$upopulation'(X0,X1,n100),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'accept$upopulation'(countryamedicalorganization,atheist,X0)
| ~ less(X0,n78) ),
inference(resolution,[status(thm)],[c501,c5]) ).
cnf(d1,plain,
( 'accept$upopulation'(X1,X2,X0)
| ~ less(X0,n100) ),
inference(resolution,[status(thm)],[c710,c5]) ).
cnf(d2,plain,
( 'accept$upopulation'(countryamedicalorganization,muslim,X0)
| ~ less(X0,n65) ),
inference(resolution,[status(thm)],[c305,c5]) ).
cnf(d3,plain,
( 'accept$upopulation'(countryamedicalorganization,christian,X0)
| ~ less(X0,n20) ),
inference(resolution,[status(thm)],[c500,c5]) ).
cnf(d4,plain,
( ~ 'accept$upopulation'(countryamedicalorganization,other,n0)
| ~ 'accept$upopulation'(countryamedicalorganization,muslim,n0)
| ~ 'accept$upopulation'(countryamedicalorganization,native,n85)
| ~ 'accept$upopulation'(countryamedicalorganization,atheist,n12)
| 'accept$ucity'(countryamedicalorganization,coastvillage)
| ~ less(n3,n20) ),
inference(resolution,[status(thm)],[d3,c9]) ).
cnf(d5,plain,
( ~ 'accept$upopulation'(countryamedicalorganization,other,n0)
| ~ 'accept$upopulation'(countryamedicalorganization,muslim,n0)
| ~ 'accept$upopulation'(countryamedicalorganization,native,n85)
| ~ 'accept$upopulation'(countryamedicalorganization,atheist,n12)
| ~ less(n3,n20) ),
inference(resolution,[status(thm)],[c302,d4]) ).
cnf(d6,plain,
( ~ 'accept$upopulation'(countryamedicalorganization,muslim,n0)
| ~ 'accept$upopulation'(countryamedicalorganization,native,n85)
| ~ 'accept$upopulation'(countryamedicalorganization,atheist,n12)
| ~ less(n3,n20) ),
inference(resolution,[status(thm)],[c509,d5]) ).
cnf(d7,plain,
( ~ less(n0,n65)
| ~ 'accept$upopulation'(countryamedicalorganization,native,n85)
| ~ 'accept$upopulation'(countryamedicalorganization,atheist,n12)
| ~ less(n3,n20) ),
inference(resolution,[status(thm)],[d6,d2]) ).
cnf(d8,plain,
( ~ 'rdn$upositive$uless'(X1,rdn(rdnn(n5),rdnn(n6)))
| ~ 'rdn$utranslate'(X0,'rdn$upos'(X1))
| less(X0,n65) ),
inference(resolution,[status(thm)],[c700,c671]) ).
cnf(d9,plain,
( ~ 'rdn$unon$uzero'(rdnn(n6))
| ~ 'rdn$utranslate'(X0,'rdn$upos'(rdnn(X1)))
| less(X0,n65) ),
inference(resolution,[status(thm)],[d8,c697]) ).
cnf(d10,plain,
'rdn$unon$uzero'(rdnn(n6)),
inference(resolution,[status(thm)],[c698,c681]) ).
cnf(d11,plain,
( ~ 'rdn$utranslate'(X0,'rdn$upos'(rdnn(X1)))
| less(X0,n65) ),
inference(resolution,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
less(n0,n65),
inference(resolution,[status(thm)],[d11,c657]) ).
cnf(d13,plain,
( ~ 'accept$upopulation'(countryamedicalorganization,native,n85)
| ~ 'accept$upopulation'(countryamedicalorganization,atheist,n12)
| ~ less(n3,n20) ),
inference(resolution,[status(thm)],[d12,d7]) ).
cnf(d14,plain,
( ~ 'rdn$upositive$uless'(X1,rdn(rdnn(n0),rdnn(n2)))
| ~ 'rdn$utranslate'(X0,'rdn$upos'(X1))
| less(X0,n20) ),
inference(resolution,[status(thm)],[c700,c668]) ).
cnf(d15,plain,
( ~ 'rdn$unon$uzero'(rdnn(n2))
| ~ 'rdn$utranslate'(X0,'rdn$upos'(rdnn(X1)))
| less(X0,n20) ),
inference(resolution,[status(thm)],[d14,c697]) ).
cnf(d16,plain,
'rdn$unon$uzero'(rdnn(n2)),
inference(resolution,[status(thm)],[c698,c677]) ).
cnf(d17,plain,
( ~ 'rdn$utranslate'(X0,'rdn$upos'(rdnn(X1)))
| less(X0,n20) ),
inference(resolution,[status(thm)],[d16,d15]) ).
cnf(d18,plain,
less(n3,n20),
inference(resolution,[status(thm)],[d17,c660]) ).
cnf(d19,plain,
( ~ 'accept$upopulation'(countryamedicalorganization,native,n85)
| ~ 'accept$upopulation'(countryamedicalorganization,atheist,n12) ),
inference(resolution,[status(thm)],[d18,d13]) ).
cnf(d20,plain,
( ~ less(n85,n100)
| ~ 'accept$upopulation'(countryamedicalorganization,atheist,n12) ),
inference(resolution,[status(thm)],[d19,d1]) ).
cnf(d21,plain,
( ~ 'rdn$upositive$uless'(X1,rdn(rdnn(n0),rdn(rdnn(n0),rdnn(n1))))
| ~ 'rdn$utranslate'(X0,'rdn$upos'(X1))
| less(X0,n100) ),
inference(resolution,[status(thm)],[c700,c675]) ).
cnf(d22,plain,
( ~ 'rdn$upositive$uless'(X2,rdn(rdnn(n0),rdnn(n1)))
| ~ 'rdn$utranslate'(X0,'rdn$upos'(rdn(rdnn(X1),X2)))
| less(X0,n100) ),
inference(resolution,[status(thm)],[d21,c695]) ).
cnf(d23,plain,
( ~ 'rdn$unon$uzero'(rdnn(n1))
| ~ 'rdn$utranslate'(X0,'rdn$upos'(rdn(rdnn(X1),rdnn(X2))))
| less(X0,n100) ),
inference(resolution,[status(thm)],[d22,c697]) ).
cnf(d24,plain,
'rdn$unon$uzero'(rdnn(n1)),
inference(resolution,[status(thm)],[c698,c676]) ).
cnf(d25,plain,
( ~ 'rdn$utranslate'(X0,'rdn$upos'(rdn(rdnn(X1),rdnn(X2))))
| less(X0,n100) ),
inference(resolution,[status(thm)],[d24,d23]) ).
cnf(d26,plain,
less(n85,n100),
inference(resolution,[status(thm)],[d25,c674]) ).
cnf(d27,plain,
~ 'accept$upopulation'(countryamedicalorganization,atheist,n12),
inference(resolution,[status(thm)],[d26,d20]) ).
cnf(d28,plain,
~ less(n12,n78),
inference(resolution,[status(thm)],[d27,d0]) ).
cnf(d29,plain,
( ~ 'rdn$upositive$uless'(X1,rdn(rdnn(n8),rdnn(n7)))
| ~ 'rdn$utranslate'(X0,'rdn$upos'(X1))
| less(X0,n78) ),
inference(resolution,[status(thm)],[c700,c673]) ).
cnf(d30,plain,
( ~ 'rdn$upositive$uless'(X2,rdnn(n7))
| ~ 'rdn$utranslate'(X0,'rdn$upos'(rdn(rdnn(X1),X2)))
| less(X0,n78) ),
inference(resolution,[status(thm)],[d29,c695]) ).
cnf(d31,plain,
( ~ 'rdn$upositive$uless'(rdnn(n1),rdnn(n7))
| less(n12,n78) ),
inference(resolution,[status(thm)],[d30,c667]) ).
cnf(d32,plain,
( ~ 'rdn$upositive$uless'(rdnn(X0),rdnn(n6))
| 'rdn$upositive$uless'(rdnn(X0),rdnn(n7)) ),
inference(resolution,[status(thm)],[c694,c691]) ).
cnf(d33,plain,
( ~ 'rdn$upositive$uless'(rdnn(X0),rdnn(n5))
| 'rdn$upositive$uless'(rdnn(X0),rdnn(n6)) ),
inference(resolution,[status(thm)],[c694,c690]) ).
cnf(d34,plain,
( ~ 'rdn$upositive$uless'(rdnn(X0),rdnn(n4))
| 'rdn$upositive$uless'(rdnn(X0),rdnn(n5)) ),
inference(resolution,[status(thm)],[c694,c689]) ).
cnf(d35,plain,
( ~ 'rdn$upositive$uless'(rdnn(X0),rdnn(n3))
| 'rdn$upositive$uless'(rdnn(X0),rdnn(n4)) ),
inference(resolution,[status(thm)],[c694,c688]) ).
cnf(d36,plain,
( ~ 'rdn$upositive$uless'(rdnn(X0),rdnn(n2))
| 'rdn$upositive$uless'(rdnn(X0),rdnn(n3)) ),
inference(resolution,[status(thm)],[c694,c687]) ).
cnf(d37,plain,
'rdn$upositive$uless'(rdnn(n1),rdnn(n3)),
inference(resolution,[status(thm)],[d36,c686]) ).
cnf(d38,plain,
'rdn$upositive$uless'(rdnn(n1),rdnn(n4)),
inference(resolution,[status(thm)],[d37,d35]) ).
cnf(d39,plain,
'rdn$upositive$uless'(rdnn(n1),rdnn(n5)),
inference(resolution,[status(thm)],[d38,d34]) ).
cnf(d40,plain,
'rdn$upositive$uless'(rdnn(n1),rdnn(n6)),
inference(resolution,[status(thm)],[d39,d33]) ).
cnf(d41,plain,
'rdn$upositive$uless'(rdnn(n1),rdnn(n7)),
inference(resolution,[status(thm)],[d40,d32]) ).
cnf(d42,plain,
less(n12,n78),
inference(resolution,[status(thm)],[d41,d31]) ).
cnf(d43,plain,
$false,
inference(resolution,[status(thm)],[d42,d28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : AGT026+2 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.39 % Computer : n005.cluster.edu
% 0.10/5.39 % Model : x86_64 x86_64
% 0.10/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.39 % Memory : 8046.5625MB
% 0.10/5.39 % OS : Linux 6.8.0-71-generic
% 0.10/5.39 % CPULimit : 300
% 0.10/5.39 % WCLimit : 300
% 0.10/5.39 % DateTime : Sat Sep 26 20:55:52 UTC 2026
% 0.10/5.40 % CPUTime :
% 0.10/5.40 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 91.26/38.56 % SZS status Theorem for theBenchmark.p
% 91.26/38.56 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------