%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : AGT012+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 : n012.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 06:45:36 AM UTC 2026
% Result : Theorem 31.48s 8.33s
% Output : CNFRefutation 31.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 18
% Syntax : Number of formulae : 55 ( 32 unt; 0 def)
% Number of atoms : 106 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 95 ( 44 ~; 36 |; 9 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 16 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(a1_3,axiom,
! [X0,X1,X2,X3] :
( ( less(X2,X1)
& 'accept$upopulation'(X0,X3,X1) )
=> 'accept$upopulation'(X0,X3,X2) ) ).
fof(a2_9,axiom,
! [X0] :
( ( 'accept$upopulation'(X0,other,n0)
& 'accept$upopulation'(X0,native,n0)
& 'accept$upopulation'(X0,muslim,n1)
& 'accept$upopulation'(X0,christian,n24)
& 'accept$upopulation'(X0,atheist,n75) )
<=> 'accept$ucity'(X0,towna) ) ).
fof(deduced_93,axiom,
'accept$upopulation'(muslimcountrybhumanitarianorganization,other,n0) ).
fof(deduced_203,axiom,
'accept$upopulation'(muslimcountrybhumanitarianorganization,native,n0) ).
fof(deduced_204,axiom,
'accept$upopulation'(muslimcountrybhumanitarianorganization,muslim,n1) ).
fof(deduced_206,axiom,
'accept$upopulation'(muslimcountrybhumanitarianorganization,atheist,n78) ).
fof(deduced_366,axiom,
~ 'accept$ucity'(muslimcountrybhumanitarianorganization,towna) ).
fof(rdn75,axiom,
'rdn$utranslate'(n75,'rdn$upos'(rdn(rdnn(n5),rdnn(n7)))) ).
fof(rdn78,axiom,
'rdn$utranslate'(n78,'rdn$upos'(rdn(rdnn(n8),rdnn(n7)))) ).
fof(rdn_digit7,axiom,
'rdn$unon$uzero$udigit'(rdnn(n7)) ).
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_less78,axiom,
'rdn$upositive$uless'(rdnn(n7),rdnn(n8)) ).
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_low,axiom,
! [X0,X1,X2] :
( ( 'rdn$unon$uzero'(X1)
& 'rdn$upositive$uless'(rdnn(X0),rdnn(X2)) )
=> 'rdn$upositive$uless'(rdn(rdnn(X0),X1),rdn(rdnn(X2),X1)) ) ).
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$upos'(X2)) )
=> less(X0,X1) ) ).
fof(query_12,conjecture,
~ 'accept$upopulation'(muslimcountrybhumanitarianorganization,christian,n24) ).
fof(negated_conjecture,negated_conjecture,
~ ~ 'accept$upopulation'(muslimcountrybhumanitarianorganization,christian,n24),
inference(negate_conjecture,[status(cth)],[query_12]) ).
cnf(c5,plain,
( 'accept$upopulation'(X2,X3,X0)
| ~ 'accept$upopulation'(X2,X3,X1)
| ~ less(X0,X1) ),
inference(clausification,[status(esa)],[a1_3]) ).
cnf(c16,plain,
( ~ 'accept$upopulation'(X0,other,n0)
| 'accept$ucity'(X0,towna)
| ~ 'accept$upopulation'(X0,native,n0)
| ~ 'accept$upopulation'(X0,christian,n24)
| ~ 'accept$upopulation'(X0,atheist,n75)
| ~ 'accept$upopulation'(X0,muslim,n1) ),
inference(clausification,[status(esa)],[a2_9]) ).
cnf(c375,plain,
'accept$upopulation'(muslimcountrybhumanitarianorganization,other,n0),
inference(clausification,[status(esa)],[deduced_93]) ).
cnf(c485,plain,
'accept$upopulation'(muslimcountrybhumanitarianorganization,native,n0),
inference(clausification,[status(esa)],[deduced_203]) ).
cnf(c486,plain,
'accept$upopulation'(muslimcountrybhumanitarianorganization,muslim,n1),
inference(clausification,[status(esa)],[deduced_204]) ).
cnf(c488,plain,
'accept$upopulation'(muslimcountrybhumanitarianorganization,atheist,n78),
inference(clausification,[status(esa)],[deduced_206]) ).
cnf(c648,plain,
~ 'accept$ucity'(muslimcountrybhumanitarianorganization,towna),
inference(clausification,[status(esa)],[deduced_366]) ).
cnf(c665,plain,
'rdn$utranslate'(n75,'rdn$upos'(rdn(rdnn(n5),rdnn(n7)))),
inference(clausification,[status(esa)],[rdn75]) ).
cnf(c666,plain,
'rdn$utranslate'(n78,'rdn$upos'(rdn(rdnn(n8),rdnn(n7)))),
inference(clausification,[status(esa)],[rdn78]) ).
cnf(c674,plain,
'rdn$unon$uzero$udigit'(rdnn(n7)),
inference(clausification,[status(esa)],[rdn_digit7]) ).
cnf(c682,plain,
'rdn$upositive$uless'(rdnn(n5),rdnn(n6)),
inference(clausification,[status(esa)],[rdn_positive_less56]) ).
cnf(c683,plain,
'rdn$upositive$uless'(rdnn(n6),rdnn(n7)),
inference(clausification,[status(esa)],[rdn_positive_less67]) ).
cnf(c684,plain,
'rdn$upositive$uless'(rdnn(n7),rdnn(n8)),
inference(clausification,[status(esa)],[rdn_positive_less78]) ).
cnf(c686,plain,
( 'rdn$upositive$uless'(rdnn(X2),rdnn(X1))
| ~ 'rdn$upositive$uless'(rdnn(X2),rdnn(X0))
| ~ 'rdn$upositive$uless'(rdnn(X0),rdnn(X1)) ),
inference(clausification,[status(esa)],[rdn_positive_less_transitivity]) ).
cnf(c688,plain,
( 'rdn$upositive$uless'(rdn(rdnn(X1),X0),rdn(rdnn(X2),X0))
| ~ 'rdn$upositive$uless'(rdnn(X1),rdnn(X2))
| ~ 'rdn$unon$uzero'(X0) ),
inference(clausification,[status(esa)],[rdn_positive_less_multi_digit_low]) ).
cnf(c690,plain,
( 'rdn$unon$uzero'(rdnn(X0))
| ~ 'rdn$unon$uzero$udigit'(rdnn(X0)) ),
inference(clausification,[status(esa)],[rdn_non_zero_by_digit]) ).
cnf(c692,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(c702,plain,
'accept$upopulation'(muslimcountrybhumanitarianorganization,christian,n24),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'rdn$upositive$uless'(X1,rdn(rdnn(n8),rdnn(n7)))
| ~ 'rdn$utranslate'(X0,'rdn$upos'(X1))
| less(X0,n78) ),
inference(resolution,[status(thm)],[c692,c666]) ).
cnf(d1,plain,
( ~ 'rdn$unon$uzero'(rdnn(n7))
| ~ 'rdn$upositive$uless'(rdnn(X1),rdnn(n8))
| ~ 'rdn$utranslate'(X0,'rdn$upos'(rdn(rdnn(X1),rdnn(n7))))
| less(X0,n78) ),
inference(resolution,[status(thm)],[d0,c688]) ).
cnf(d2,plain,
'rdn$unon$uzero'(rdnn(n7)),
inference(resolution,[status(thm)],[c690,c674]) ).
cnf(d3,plain,
( ~ 'rdn$upositive$uless'(rdnn(X1),rdnn(n8))
| ~ 'rdn$utranslate'(X0,'rdn$upos'(rdn(rdnn(X1),rdnn(n7))))
| less(X0,n78) ),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( ~ 'rdn$upositive$uless'(rdnn(n5),rdnn(n8))
| less(n75,n78) ),
inference(resolution,[status(thm)],[d3,c665]) ).
cnf(d5,plain,
( 'accept$upopulation'(muslimcountrybhumanitarianorganization,atheist,X0)
| ~ less(X0,n78) ),
inference(resolution,[status(thm)],[c488,c5]) ).
cnf(d6,plain,
( ~ 'accept$upopulation'(muslimcountrybhumanitarianorganization,other,n0)
| ~ 'accept$upopulation'(muslimcountrybhumanitarianorganization,muslim,n1)
| ~ 'accept$upopulation'(muslimcountrybhumanitarianorganization,native,n0)
| ~ 'accept$upopulation'(muslimcountrybhumanitarianorganization,atheist,n75)
| 'accept$ucity'(muslimcountrybhumanitarianorganization,towna) ),
inference(resolution,[status(thm)],[c702,c16]) ).
cnf(d7,plain,
( ~ 'accept$upopulation'(muslimcountrybhumanitarianorganization,muslim,n1)
| ~ 'accept$upopulation'(muslimcountrybhumanitarianorganization,native,n0)
| ~ 'accept$upopulation'(muslimcountrybhumanitarianorganization,atheist,n75)
| 'accept$ucity'(muslimcountrybhumanitarianorganization,towna) ),
inference(resolution,[status(thm)],[c375,d6]) ).
cnf(d8,plain,
( ~ 'accept$upopulation'(muslimcountrybhumanitarianorganization,muslim,n1)
| ~ 'accept$upopulation'(muslimcountrybhumanitarianorganization,atheist,n75)
| 'accept$ucity'(muslimcountrybhumanitarianorganization,towna) ),
inference(resolution,[status(thm)],[c485,d7]) ).
cnf(d9,plain,
( ~ 'accept$upopulation'(muslimcountrybhumanitarianorganization,atheist,n75)
| 'accept$ucity'(muslimcountrybhumanitarianorganization,towna) ),
inference(resolution,[status(thm)],[c486,d8]) ).
cnf(d10,plain,
~ 'accept$upopulation'(muslimcountrybhumanitarianorganization,atheist,n75),
inference(resolution,[status(thm)],[c648,d9]) ).
cnf(d11,plain,
~ less(n75,n78),
inference(resolution,[status(thm)],[d10,d5]) ).
cnf(d12,plain,
~ 'rdn$upositive$uless'(rdnn(n5),rdnn(n8)),
inference(resolution,[status(thm)],[d11,d4]) ).
cnf(d13,plain,
( ~ 'rdn$upositive$uless'(rdnn(X0),rdnn(n7))
| 'rdn$upositive$uless'(rdnn(X0),rdnn(n8)) ),
inference(resolution,[status(thm)],[c686,c684]) ).
cnf(d14,plain,
( ~ 'rdn$upositive$uless'(rdnn(X0),rdnn(n6))
| 'rdn$upositive$uless'(rdnn(X0),rdnn(n7)) ),
inference(resolution,[status(thm)],[c686,c683]) ).
cnf(d15,plain,
'rdn$upositive$uless'(rdnn(n5),rdnn(n7)),
inference(resolution,[status(thm)],[d14,c682]) ).
cnf(d16,plain,
'rdn$upositive$uless'(rdnn(n5),rdnn(n8)),
inference(resolution,[status(thm)],[d15,d13]) ).
cnf(d17,plain,
$false,
inference(resolution,[status(thm)],[d16,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : AGT012+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
% 0.09/0.36 % Computer : n012.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 20:53:16 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 31.48/8.33 % SZS status Theorem for theBenchmark.p
% 31.48/8.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------