%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRA014+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 07:18:44 AM UTC 2026
% Result : Theorem 11.22s 2.03s
% Output : CNFRefutation 11.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 79
% Number of leaves : 6
% Syntax : Number of formulae : 227 ( 23 unt; 0 def)
% Number of atoms : 761 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 710 ( 176 ~; 521 |; 9 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 77 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(red_clique,axiom,
! [X0,X1,X2] :
( ( red(X0,X2)
& red(X1,X2)
& red(X0,X1) )
=> goal ) ).
fof(green_clique,axiom,
! [X0,X1,X2] :
( ( green(X0,X2)
& green(X1,X2)
& green(X0,X1) )
=> goal ) ).
fof(ordering,axiom,
( 'less$uthan'(n5,n6)
& 'less$uthan'(n4,n5)
& 'less$uthan'(n3,n4)
& 'less$uthan'(n2,n3)
& 'less$uthan'(n1,n2) ) ).
fof(less_than_transitive,axiom,
! [X0,X1,X2] :
( ( 'less$uthan'(X1,X2)
& 'less$uthan'(X0,X1) )
=> 'less$uthan'(X0,X2) ) ).
fof(partition,axiom,
! [X0,X1] :
( 'less$uthan'(X0,X1)
=> ( green(X0,X1)
| red(X0,X1) ) ) ).
fof(goal_to_be_proved,conjecture,
goal ).
fof(negated_conjecture,negated_conjecture,
~ goal,
inference(negate_conjecture,[status(cth)],[goal_to_be_proved]) ).
cnf(c0,plain,
( goal
| ~ red(X0,X2)
| ~ red(X1,X2)
| ~ red(X0,X1) ),
inference(clausification,[status(esa)],[red_clique]) ).
cnf(c1,plain,
( goal
| ~ green(X0,X2)
| ~ green(X1,X2)
| ~ green(X0,X1) ),
inference(clausification,[status(esa)],[green_clique]) ).
cnf(c2,plain,
'less$uthan'(n1,n2),
inference(clausification,[status(esa)],[ordering]) ).
cnf(c3,plain,
'less$uthan'(n2,n3),
inference(clausification,[status(esa)],[ordering]) ).
cnf(c4,plain,
'less$uthan'(n3,n4),
inference(clausification,[status(esa)],[ordering]) ).
cnf(c5,plain,
'less$uthan'(n4,n5),
inference(clausification,[status(esa)],[ordering]) ).
cnf(c6,plain,
'less$uthan'(n5,n6),
inference(clausification,[status(esa)],[ordering]) ).
cnf(c7,plain,
( 'less$uthan'(X0,X2)
| ~ 'less$uthan'(X1,X2)
| ~ 'less$uthan'(X0,X1) ),
inference(clausification,[status(esa)],[less_than_transitive]) ).
cnf(c8,plain,
( green(X0,X1)
| red(X0,X1)
| ~ 'less$uthan'(X0,X1) ),
inference(clausification,[status(esa)],[partition]) ).
cnf(c9,plain,
~ goal,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'less$uthan'(X0,n3)
| 'less$uthan'(X0,n4) ),
inference(resolution,[status(thm)],[c7,c4]) ).
cnf(d1,plain,
'less$uthan'(n2,n4),
inference(resolution,[status(thm)],[d0,c3]) ).
cnf(d2,plain,
( green(n2,n4)
| red(n2,n4) ),
inference(resolution,[status(thm)],[d1,c8]) ).
cnf(d3,plain,
( ~ green(X2,X1)
| ~ green(X2,X0)
| ~ green(X0,X1) ),
inference(resolution,[status(thm)],[c9,c1]) ).
cnf(d4,plain,
( green(n4,n5)
| red(n4,n5) ),
inference(resolution,[status(thm)],[c8,c5]) ).
cnf(d5,plain,
( ~ green(X0,n4)
| ~ green(X0,n5)
| red(n4,n5) ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( ~ 'less$uthan'(X0,n4)
| 'less$uthan'(X0,n5) ),
inference(resolution,[status(thm)],[c7,c5]) ).
cnf(d7,plain,
'less$uthan'(n3,n5),
inference(resolution,[status(thm)],[d6,c4]) ).
cnf(d8,plain,
( ~ 'less$uthan'(X0,n3)
| 'less$uthan'(X0,n5) ),
inference(resolution,[status(thm)],[d7,c7]) ).
cnf(d9,plain,
'less$uthan'(n2,n5),
inference(resolution,[status(thm)],[d8,c3]) ).
cnf(d10,plain,
( green(n2,n5)
| red(n2,n5) ),
inference(resolution,[status(thm)],[d9,c8]) ).
cnf(d11,plain,
( ~ green(n2,n4)
| red(n4,n5)
| red(n2,n5) ),
inference(resolution,[status(thm)],[d10,d5]) ).
cnf(d12,plain,
( red(n2,n4)
| red(n4,n5)
| red(n2,n5) ),
inference(resolution,[status(thm)],[d11,d2]) ).
cnf(d13,plain,
( ~ 'less$uthan'(X0,n5)
| 'less$uthan'(X0,n6) ),
inference(resolution,[status(thm)],[c7,c6]) ).
cnf(d14,plain,
'less$uthan'(n4,n6),
inference(resolution,[status(thm)],[d13,c5]) ).
cnf(d15,plain,
( green(n4,n6)
| red(n4,n6) ),
inference(resolution,[status(thm)],[d14,c8]) ).
cnf(d16,plain,
( ~ green(X0,n4)
| ~ green(X0,n6)
| red(n4,n6) ),
inference(resolution,[status(thm)],[d15,d3]) ).
cnf(d17,plain,
( ~ 'less$uthan'(X0,n4)
| 'less$uthan'(X0,n6) ),
inference(resolution,[status(thm)],[d14,c7]) ).
cnf(d18,plain,
'less$uthan'(n2,n6),
inference(resolution,[status(thm)],[d17,d1]) ).
cnf(d19,plain,
( green(n2,n6)
| red(n2,n6) ),
inference(resolution,[status(thm)],[d18,c8]) ).
cnf(d20,plain,
( ~ green(n2,n4)
| red(n4,n6)
| red(n2,n6) ),
inference(resolution,[status(thm)],[d19,d16]) ).
cnf(d21,plain,
( red(n2,n4)
| red(n4,n6)
| red(n2,n6) ),
inference(resolution,[status(thm)],[d20,d2]) ).
cnf(d22,plain,
( ~ red(X2,X0)
| ~ red(X2,X1)
| ~ red(X0,X1) ),
inference(resolution,[status(thm)],[c9,c0]) ).
cnf(d23,plain,
( green(n5,n6)
| red(n5,n6) ),
inference(resolution,[status(thm)],[c8,c6]) ).
cnf(d24,plain,
( ~ green(X0,n5)
| ~ green(X0,n6)
| red(n5,n6) ),
inference(resolution,[status(thm)],[d23,d3]) ).
cnf(d25,plain,
( ~ green(n2,n5)
| red(n5,n6)
| red(n2,n6) ),
inference(resolution,[status(thm)],[d19,d24]) ).
cnf(d26,plain,
( red(n2,n5)
| red(n5,n6)
| red(n2,n6) ),
inference(resolution,[status(thm)],[d25,d10]) ).
cnf(d27,plain,
( ~ red(X0,n5)
| ~ red(X0,n6)
| red(n2,n6)
| red(n2,n5) ),
inference(resolution,[status(thm)],[d26,d22]) ).
cnf(d28,plain,
( red(n2,n6)
| red(n2,n4)
| red(n2,n6)
| red(n2,n5)
| ~ red(n4,n5) ),
inference(resolution,[status(thm)],[d27,d21]) ).
cnf(d29,plain,
( red(n2,n5)
| red(n2,n4)
| red(n2,n6)
| red(n2,n5)
| red(n2,n4) ),
inference(resolution,[status(thm)],[d28,d12]) ).
cnf(d30,plain,
( green(n1,n2)
| red(n1,n2) ),
inference(resolution,[status(thm)],[c8,c2]) ).
cnf(d31,plain,
( ~ 'less$uthan'(X0,n2)
| 'less$uthan'(X0,n3) ),
inference(resolution,[status(thm)],[c7,c3]) ).
cnf(d32,plain,
'less$uthan'(n1,n3),
inference(resolution,[status(thm)],[d31,c2]) ).
cnf(d33,plain,
'less$uthan'(n1,n4),
inference(resolution,[status(thm)],[d0,d32]) ).
cnf(d34,plain,
( green(n1,n4)
| red(n1,n4) ),
inference(resolution,[status(thm)],[d33,c8]) ).
cnf(d35,plain,
( ~ green(X0,n2)
| ~ green(X0,n4)
| red(n2,n4) ),
inference(resolution,[status(thm)],[d2,d3]) ).
cnf(d36,plain,
( red(n1,n4)
| ~ green(n1,n2)
| red(n2,n4) ),
inference(resolution,[status(thm)],[d35,d34]) ).
cnf(d37,plain,
( red(n1,n2)
| red(n2,n4)
| red(n1,n4) ),
inference(resolution,[status(thm)],[d36,d30]) ).
cnf(d38,plain,
'less$uthan'(n1,n5),
inference(resolution,[status(thm)],[d8,d32]) ).
cnf(d39,plain,
( green(n1,n5)
| red(n1,n5) ),
inference(resolution,[status(thm)],[d38,c8]) ).
cnf(d40,plain,
( ~ green(X0,n2)
| ~ green(X0,n5)
| red(n2,n5) ),
inference(resolution,[status(thm)],[d10,d3]) ).
cnf(d41,plain,
( red(n1,n5)
| ~ green(n1,n2)
| red(n2,n5) ),
inference(resolution,[status(thm)],[d40,d39]) ).
cnf(d42,plain,
( red(n1,n2)
| red(n2,n5)
| red(n1,n5) ),
inference(resolution,[status(thm)],[d41,d30]) ).
cnf(d43,plain,
( ~ red(X0,n4)
| ~ red(X0,n5)
| red(n2,n5)
| red(n2,n4) ),
inference(resolution,[status(thm)],[d12,d22]) ).
cnf(d44,plain,
( red(n2,n5)
| red(n1,n2)
| red(n2,n5)
| red(n2,n4)
| ~ red(n1,n4) ),
inference(resolution,[status(thm)],[d43,d42]) ).
cnf(d45,plain,
( red(n2,n4)
| red(n1,n2)
| red(n2,n5)
| red(n2,n4)
| red(n1,n2) ),
inference(resolution,[status(thm)],[d44,d37]) ).
cnf(d46,plain,
( green(n1,n3)
| red(n1,n3) ),
inference(resolution,[status(thm)],[d32,c8]) ).
cnf(d47,plain,
'less$uthan'(n3,n6),
inference(resolution,[status(thm)],[d7,d13]) ).
cnf(d48,plain,
( green(n3,n6)
| red(n3,n6) ),
inference(resolution,[status(thm)],[d47,c8]) ).
cnf(d49,plain,
( ~ green(X0,n3)
| ~ green(X0,n6)
| red(n3,n6) ),
inference(resolution,[status(thm)],[d48,d3]) ).
cnf(d50,plain,
'less$uthan'(n1,n6),
inference(resolution,[status(thm)],[d17,d33]) ).
cnf(d51,plain,
( green(n1,n6)
| red(n1,n6) ),
inference(resolution,[status(thm)],[d50,c8]) ).
cnf(d52,plain,
( ~ green(n1,n3)
| red(n3,n6)
| red(n1,n6) ),
inference(resolution,[status(thm)],[d51,d49]) ).
cnf(d53,plain,
( red(n1,n3)
| red(n3,n6)
| red(n1,n6) ),
inference(resolution,[status(thm)],[d52,d46]) ).
cnf(d54,plain,
( ~ red(X0,n2)
| ~ red(X0,n6)
| red(n2,n5)
| red(n2,n4) ),
inference(resolution,[status(thm)],[d29,d22]) ).
cnf(d55,plain,
( red(n3,n6)
| red(n1,n3)
| red(n2,n5)
| red(n2,n4)
| ~ red(n1,n2) ),
inference(resolution,[status(thm)],[d54,d53]) ).
cnf(d56,plain,
( red(n2,n5)
| red(n2,n4)
| red(n3,n6)
| red(n2,n5)
| red(n2,n4)
| red(n1,n3) ),
inference(resolution,[status(thm)],[d55,d45]) ).
cnf(d57,plain,
( green(n2,n3)
| red(n2,n3) ),
inference(resolution,[status(thm)],[c8,c3]) ).
cnf(d58,plain,
( green(n3,n4)
| red(n3,n4) ),
inference(resolution,[status(thm)],[c8,c4]) ).
cnf(d59,plain,
( ~ green(X0,n3)
| ~ green(X0,n4)
| red(n3,n4) ),
inference(resolution,[status(thm)],[d58,d3]) ).
cnf(d60,plain,
( ~ green(n2,n3)
| red(n3,n4)
| red(n2,n4) ),
inference(resolution,[status(thm)],[d2,d59]) ).
cnf(d61,plain,
( red(n2,n3)
| red(n3,n4)
| red(n2,n4) ),
inference(resolution,[status(thm)],[d60,d57]) ).
cnf(d62,plain,
( green(n3,n5)
| red(n3,n5) ),
inference(resolution,[status(thm)],[d7,c8]) ).
cnf(d63,plain,
( ~ green(X0,n3)
| ~ green(X0,n5)
| red(n3,n5) ),
inference(resolution,[status(thm)],[d62,d3]) ).
cnf(d64,plain,
( ~ green(n2,n3)
| red(n3,n5)
| red(n2,n5) ),
inference(resolution,[status(thm)],[d10,d63]) ).
cnf(d65,plain,
( red(n2,n3)
| red(n3,n5)
| red(n2,n5) ),
inference(resolution,[status(thm)],[d64,d57]) ).
cnf(d66,plain,
( red(n2,n5)
| red(n2,n3)
| red(n2,n5)
| red(n2,n4)
| ~ red(n3,n4) ),
inference(resolution,[status(thm)],[d43,d65]) ).
cnf(d67,plain,
( red(n2,n4)
| red(n2,n3)
| red(n2,n5)
| red(n2,n4)
| red(n2,n3) ),
inference(resolution,[status(thm)],[d66,d61]) ).
cnf(d68,plain,
( ~ green(n2,n3)
| red(n3,n6)
| red(n2,n6) ),
inference(resolution,[status(thm)],[d19,d49]) ).
cnf(d69,plain,
( red(n2,n3)
| red(n3,n6)
| red(n2,n6) ),
inference(resolution,[status(thm)],[d68,d57]) ).
cnf(d70,plain,
( ~ red(X0,n4)
| ~ red(X0,n6)
| red(n2,n6)
| red(n2,n4) ),
inference(resolution,[status(thm)],[d21,d22]) ).
cnf(d71,plain,
( red(n2,n6)
| red(n2,n3)
| red(n2,n6)
| red(n2,n4)
| ~ red(n3,n4) ),
inference(resolution,[status(thm)],[d70,d69]) ).
cnf(d72,plain,
( red(n2,n4)
| red(n2,n3)
| red(n2,n6)
| red(n2,n4)
| red(n2,n3) ),
inference(resolution,[status(thm)],[d71,d61]) ).
cnf(d73,plain,
( ~ green(X0,n2)
| ~ green(X0,n3)
| red(n2,n3) ),
inference(resolution,[status(thm)],[d57,d3]) ).
cnf(d74,plain,
( ~ green(n1,n2)
| red(n2,n3)
| red(n1,n3) ),
inference(resolution,[status(thm)],[d46,d73]) ).
cnf(d75,plain,
( red(n1,n2)
| red(n2,n3)
| red(n1,n3) ),
inference(resolution,[status(thm)],[d74,d30]) ).
cnf(d76,plain,
( ~ red(X0,n3)
| ~ red(X0,n4)
| red(n2,n4)
| red(n2,n3) ),
inference(resolution,[status(thm)],[d61,d22]) ).
cnf(d77,plain,
( red(n2,n4)
| red(n2,n3)
| ~ red(n1,n3)
| red(n2,n4)
| red(n1,n2) ),
inference(resolution,[status(thm)],[d37,d76]) ).
cnf(d78,plain,
( red(n2,n3)
| red(n1,n2)
| red(n2,n4)
| red(n2,n3)
| red(n1,n2) ),
inference(resolution,[status(thm)],[d77,d75]) ).
cnf(d79,plain,
( ~ red(X0,n2)
| ~ red(X0,n5)
| red(n2,n4)
| red(n2,n3) ),
inference(resolution,[status(thm)],[d67,d22]) ).
cnf(d80,plain,
( ~ green(n1,n5)
| red(n5,n6)
| red(n1,n6) ),
inference(resolution,[status(thm)],[d51,d24]) ).
cnf(d81,plain,
( red(n1,n5)
| red(n5,n6)
| red(n1,n6) ),
inference(resolution,[status(thm)],[d80,d39]) ).
cnf(d82,plain,
( ~ red(X0,n2)
| ~ red(X0,n6)
| red(n2,n4)
| red(n2,n3) ),
inference(resolution,[status(thm)],[d72,d22]) ).
cnf(d83,plain,
( red(n5,n6)
| red(n1,n5)
| red(n2,n4)
| red(n2,n3)
| ~ red(n1,n2) ),
inference(resolution,[status(thm)],[d82,d81]) ).
cnf(d84,plain,
( red(n2,n4)
| red(n2,n3)
| red(n5,n6)
| red(n2,n4)
| red(n2,n3)
| red(n1,n5) ),
inference(resolution,[status(thm)],[d83,d78]) ).
cnf(d85,plain,
( red(n2,n4)
| red(n2,n3)
| ~ red(n1,n2)
| red(n5,n6)
| red(n2,n4)
| red(n2,n3) ),
inference(resolution,[status(thm)],[d84,d79]) ).
cnf(d86,plain,
( red(n2,n4)
| red(n2,n3)
| red(n5,n6)
| red(n2,n4)
| red(n2,n3) ),
inference(resolution,[status(thm)],[d85,d78]) ).
cnf(d87,plain,
( ~ red(X0,n5)
| ~ red(X0,n6)
| red(n2,n4)
| red(n2,n3) ),
inference(resolution,[status(thm)],[d86,d22]) ).
cnf(d88,plain,
( red(n2,n4)
| red(n2,n3)
| red(n2,n4)
| red(n2,n3)
| ~ red(n2,n5) ),
inference(resolution,[status(thm)],[d87,d72]) ).
cnf(d89,plain,
( red(n2,n4)
| red(n2,n3)
| red(n2,n4)
| red(n2,n3) ),
inference(resolution,[status(thm)],[d88,d67]) ).
cnf(d90,plain,
( red(n2,n6)
| red(n2,n3)
| red(n2,n6)
| red(n2,n5)
| ~ red(n3,n5) ),
inference(resolution,[status(thm)],[d27,d69]) ).
cnf(d91,plain,
( red(n2,n5)
| red(n2,n3)
| red(n2,n6)
| red(n2,n5)
| red(n2,n3) ),
inference(resolution,[status(thm)],[d90,d65]) ).
cnf(d92,plain,
( ~ red(X0,n3)
| ~ red(X0,n5)
| red(n2,n5)
| red(n2,n3) ),
inference(resolution,[status(thm)],[d65,d22]) ).
cnf(d93,plain,
( red(n2,n5)
| red(n2,n3)
| ~ red(n1,n3)
| red(n2,n5)
| red(n1,n2) ),
inference(resolution,[status(thm)],[d42,d92]) ).
cnf(d94,plain,
( red(n2,n3)
| red(n1,n2)
| red(n2,n5)
| red(n2,n3)
| red(n1,n2) ),
inference(resolution,[status(thm)],[d93,d75]) ).
cnf(d95,plain,
( ~ green(n1,n4)
| red(n4,n6)
| red(n1,n6) ),
inference(resolution,[status(thm)],[d51,d16]) ).
cnf(d96,plain,
( red(n1,n4)
| red(n4,n6)
| red(n1,n6) ),
inference(resolution,[status(thm)],[d95,d34]) ).
cnf(d97,plain,
( ~ red(X0,n2)
| ~ red(X0,n6)
| red(n2,n5)
| red(n2,n3) ),
inference(resolution,[status(thm)],[d91,d22]) ).
cnf(d98,plain,
( red(n4,n6)
| red(n1,n4)
| red(n2,n5)
| red(n2,n3)
| ~ red(n1,n2) ),
inference(resolution,[status(thm)],[d97,d96]) ).
cnf(d99,plain,
( red(n2,n5)
| red(n2,n3)
| red(n4,n6)
| red(n2,n5)
| red(n2,n3)
| red(n1,n4) ),
inference(resolution,[status(thm)],[d98,d94]) ).
cnf(d100,plain,
( ~ red(X0,n2)
| ~ red(X0,n4)
| red(n2,n3) ),
inference(resolution,[status(thm)],[d89,d22]) ).
cnf(d101,plain,
( red(n4,n6)
| red(n2,n5)
| red(n2,n3)
| red(n2,n3)
| ~ red(n1,n2) ),
inference(resolution,[status(thm)],[d100,d99]) ).
cnf(d102,plain,
( red(n2,n5)
| red(n2,n3)
| red(n4,n6)
| red(n2,n5)
| red(n2,n3) ),
inference(resolution,[status(thm)],[d101,d94]) ).
cnf(d103,plain,
( ~ red(X0,n4)
| ~ red(X0,n6)
| red(n2,n5)
| red(n2,n3) ),
inference(resolution,[status(thm)],[d102,d22]) ).
cnf(d104,plain,
( red(n2,n5)
| red(n2,n3)
| red(n2,n5)
| red(n2,n3)
| ~ red(n2,n4) ),
inference(resolution,[status(thm)],[d103,d91]) ).
cnf(d105,plain,
( red(n2,n3)
| red(n2,n5)
| red(n2,n3) ),
inference(resolution,[status(thm)],[d104,d89]) ).
cnf(d106,plain,
( ~ green(X0,n2)
| ~ green(X0,n6)
| red(n2,n6) ),
inference(resolution,[status(thm)],[d19,d3]) ).
cnf(d107,plain,
( red(n1,n6)
| ~ green(n1,n2)
| red(n2,n6) ),
inference(resolution,[status(thm)],[d106,d51]) ).
cnf(d108,plain,
( red(n1,n2)
| red(n2,n6)
| red(n1,n6) ),
inference(resolution,[status(thm)],[d107,d30]) ).
cnf(d109,plain,
( ~ red(X0,n3)
| ~ red(X0,n6)
| red(n2,n6)
| red(n2,n3) ),
inference(resolution,[status(thm)],[d69,d22]) ).
cnf(d110,plain,
( red(n2,n6)
| red(n1,n2)
| red(n2,n6)
| red(n2,n3)
| ~ red(n1,n3) ),
inference(resolution,[status(thm)],[d109,d108]) ).
cnf(d111,plain,
( red(n2,n3)
| red(n1,n2)
| red(n2,n6)
| red(n2,n3)
| red(n1,n2) ),
inference(resolution,[status(thm)],[d110,d75]) ).
cnf(d112,plain,
( ~ green(n1,n4)
| red(n4,n5)
| red(n1,n5) ),
inference(resolution,[status(thm)],[d39,d5]) ).
cnf(d113,plain,
( red(n1,n4)
| red(n4,n5)
| red(n1,n5) ),
inference(resolution,[status(thm)],[d112,d34]) ).
cnf(d114,plain,
( ~ red(X0,n2)
| ~ red(X0,n5)
| red(n2,n3) ),
inference(resolution,[status(thm)],[d105,d22]) ).
cnf(d115,plain,
( red(n4,n5)
| red(n1,n4)
| red(n2,n3)
| ~ red(n1,n2) ),
inference(resolution,[status(thm)],[d114,d113]) ).
cnf(d116,plain,
( red(n2,n6)
| red(n2,n3)
| red(n4,n5)
| red(n2,n3)
| red(n1,n4) ),
inference(resolution,[status(thm)],[d115,d111]) ).
cnf(d117,plain,
( red(n2,n3)
| ~ red(n1,n2)
| red(n4,n5)
| red(n2,n6)
| red(n2,n3) ),
inference(resolution,[status(thm)],[d116,d100]) ).
cnf(d118,plain,
( red(n2,n6)
| red(n2,n3)
| red(n4,n5)
| red(n2,n6)
| red(n2,n3) ),
inference(resolution,[status(thm)],[d117,d111]) ).
cnf(d119,plain,
( ~ red(X0,n4)
| ~ red(X0,n5)
| red(n2,n6)
| red(n2,n3) ),
inference(resolution,[status(thm)],[d118,d22]) ).
cnf(d120,plain,
( red(n2,n3)
| red(n2,n6)
| red(n2,n3)
| ~ red(n2,n4) ),
inference(resolution,[status(thm)],[d119,d105]) ).
cnf(d121,plain,
( red(n2,n3)
| red(n2,n6)
| red(n2,n3) ),
inference(resolution,[status(thm)],[d120,d89]) ).
cnf(d122,plain,
( ~ green(n4,n5)
| red(n5,n6)
| red(n4,n6) ),
inference(resolution,[status(thm)],[d15,d24]) ).
cnf(d123,plain,
( red(n4,n5)
| red(n5,n6)
| red(n4,n6) ),
inference(resolution,[status(thm)],[d122,d4]) ).
cnf(d124,plain,
( ~ red(X0,n5)
| ~ red(X0,n6)
| red(n4,n6)
| red(n4,n5) ),
inference(resolution,[status(thm)],[d123,d22]) ).
cnf(d125,plain,
( red(n4,n6)
| red(n4,n5)
| ~ red(n2,n5)
| red(n2,n3) ),
inference(resolution,[status(thm)],[d121,d124]) ).
cnf(d126,plain,
( red(n2,n3)
| red(n4,n6)
| red(n4,n5)
| red(n2,n3) ),
inference(resolution,[status(thm)],[d125,d105]) ).
cnf(d127,plain,
( ~ red(X0,n4)
| ~ red(X0,n6)
| red(n4,n5)
| red(n2,n3) ),
inference(resolution,[status(thm)],[d126,d22]) ).
cnf(d128,plain,
( red(n2,n3)
| red(n4,n5)
| red(n2,n3)
| ~ red(n2,n4) ),
inference(resolution,[status(thm)],[d127,d121]) ).
cnf(d129,plain,
( red(n2,n3)
| red(n4,n5)
| red(n2,n3) ),
inference(resolution,[status(thm)],[d128,d89]) ).
cnf(d130,plain,
( ~ red(X0,n4)
| ~ red(X0,n5)
| red(n2,n3) ),
inference(resolution,[status(thm)],[d129,d22]) ).
cnf(d131,plain,
( red(n2,n3)
| red(n2,n3)
| ~ red(n2,n4) ),
inference(resolution,[status(thm)],[d130,d105]) ).
cnf(d132,plain,
( red(n2,n3)
| red(n2,n3) ),
inference(resolution,[status(thm)],[d131,d89]) ).
cnf(d133,plain,
( ~ red(X0,n2)
| ~ red(X0,n3) ),
inference(resolution,[status(thm)],[d132,d22]) ).
cnf(d134,plain,
( red(n3,n6)
| red(n2,n5)
| red(n2,n4)
| ~ red(n1,n2) ),
inference(resolution,[status(thm)],[d133,d56]) ).
cnf(d135,plain,
( red(n2,n5)
| red(n2,n4)
| red(n3,n6)
| red(n2,n5)
| red(n2,n4) ),
inference(resolution,[status(thm)],[d134,d45]) ).
cnf(d136,plain,
( ~ red(X0,n3)
| ~ red(X0,n6)
| red(n2,n5)
| red(n2,n4) ),
inference(resolution,[status(thm)],[d135,d22]) ).
cnf(d137,plain,
( red(n2,n5)
| red(n2,n4)
| red(n2,n5)
| red(n2,n4)
| ~ red(n2,n3) ),
inference(resolution,[status(thm)],[d136,d29]) ).
cnf(d138,plain,
( red(n2,n5)
| red(n2,n4) ),
inference(resolution,[status(thm)],[d132,d137]) ).
cnf(d139,plain,
( red(n2,n6)
| red(n1,n2)
| red(n2,n6)
| red(n2,n4)
| ~ red(n1,n4) ),
inference(resolution,[status(thm)],[d70,d108]) ).
cnf(d140,plain,
( red(n2,n4)
| red(n1,n2)
| red(n2,n6)
| red(n2,n4)
| red(n1,n2) ),
inference(resolution,[status(thm)],[d139,d37]) ).
cnf(d141,plain,
( ~ green(n1,n3)
| red(n3,n5)
| red(n1,n5) ),
inference(resolution,[status(thm)],[d39,d63]) ).
cnf(d142,plain,
( red(n1,n3)
| red(n3,n5)
| red(n1,n5) ),
inference(resolution,[status(thm)],[d141,d46]) ).
cnf(d143,plain,
( ~ green(n3,n5)
| red(n5,n6)
| red(n3,n6) ),
inference(resolution,[status(thm)],[d48,d24]) ).
cnf(d144,plain,
( red(n3,n5)
| red(n5,n6)
| red(n3,n6) ),
inference(resolution,[status(thm)],[d143,d62]) ).
cnf(d145,plain,
( ~ red(X0,n5)
| ~ red(X0,n6)
| red(n3,n6)
| red(n3,n5) ),
inference(resolution,[status(thm)],[d144,d22]) ).
cnf(d146,plain,
( red(n3,n6)
| red(n3,n5)
| ~ red(n1,n5)
| red(n3,n6)
| red(n1,n3) ),
inference(resolution,[status(thm)],[d53,d145]) ).
cnf(d147,plain,
( red(n3,n5)
| red(n1,n3)
| red(n3,n6)
| red(n3,n5)
| red(n1,n3) ),
inference(resolution,[status(thm)],[d146,d142]) ).
cnf(d148,plain,
( red(n3,n6)
| red(n3,n5)
| ~ red(n1,n2) ),
inference(resolution,[status(thm)],[d133,d147]) ).
cnf(d149,plain,
( red(n2,n6)
| red(n2,n4)
| red(n3,n6)
| red(n3,n5) ),
inference(resolution,[status(thm)],[d148,d140]) ).
cnf(d150,plain,
( red(n2,n6)
| red(n2,n4)
| ~ red(n3,n4)
| red(n3,n5)
| red(n2,n6)
| red(n2,n4) ),
inference(resolution,[status(thm)],[d149,d70]) ).
cnf(d151,plain,
( ~ green(n1,n3)
| red(n3,n4)
| red(n1,n4) ),
inference(resolution,[status(thm)],[d34,d59]) ).
cnf(d152,plain,
( red(n1,n3)
| red(n3,n4)
| red(n1,n4) ),
inference(resolution,[status(thm)],[d151,d46]) ).
cnf(d153,plain,
( ~ green(n3,n4)
| red(n4,n5)
| red(n3,n5) ),
inference(resolution,[status(thm)],[d62,d5]) ).
cnf(d154,plain,
( red(n3,n4)
| red(n4,n5)
| red(n3,n5) ),
inference(resolution,[status(thm)],[d153,d58]) ).
cnf(d155,plain,
( ~ red(X0,n4)
| ~ red(X0,n5)
| red(n3,n5)
| red(n3,n4) ),
inference(resolution,[status(thm)],[d154,d22]) ).
cnf(d156,plain,
( red(n3,n5)
| red(n3,n4)
| ~ red(n1,n4)
| red(n3,n5)
| red(n1,n3) ),
inference(resolution,[status(thm)],[d142,d155]) ).
cnf(d157,plain,
( red(n3,n4)
| red(n1,n3)
| red(n3,n5)
| red(n3,n4)
| red(n1,n3) ),
inference(resolution,[status(thm)],[d156,d152]) ).
cnf(d158,plain,
( red(n3,n6)
| ~ green(n3,n4)
| red(n4,n6) ),
inference(resolution,[status(thm)],[d16,d48]) ).
cnf(d159,plain,
( red(n3,n4)
| red(n4,n6)
| red(n3,n6) ),
inference(resolution,[status(thm)],[d158,d58]) ).
cnf(d160,plain,
( red(n3,n6)
| red(n3,n4)
| red(n3,n6)
| red(n3,n5)
| ~ red(n4,n5) ),
inference(resolution,[status(thm)],[d145,d159]) ).
cnf(d161,plain,
( red(n3,n5)
| red(n3,n4)
| red(n3,n6)
| red(n3,n5)
| red(n3,n4) ),
inference(resolution,[status(thm)],[d160,d154]) ).
cnf(d162,plain,
( ~ red(X0,n3)
| ~ red(X0,n6)
| red(n3,n5)
| red(n3,n4) ),
inference(resolution,[status(thm)],[d161,d22]) ).
cnf(d163,plain,
( red(n2,n6)
| red(n1,n2)
| red(n3,n5)
| red(n3,n4)
| ~ red(n1,n3) ),
inference(resolution,[status(thm)],[d162,d108]) ).
cnf(d164,plain,
( red(n3,n5)
| red(n3,n4)
| red(n3,n5)
| red(n3,n4)
| red(n2,n6)
| red(n1,n2) ),
inference(resolution,[status(thm)],[d163,d157]) ).
cnf(d165,plain,
( red(n3,n5)
| red(n3,n4)
| ~ red(n1,n2) ),
inference(resolution,[status(thm)],[d133,d157]) ).
cnf(d166,plain,
( red(n3,n5)
| red(n3,n4)
| red(n2,n6)
| red(n3,n5)
| red(n3,n4) ),
inference(resolution,[status(thm)],[d165,d164]) ).
cnf(d167,plain,
( ~ red(X0,n3)
| ~ red(X0,n5)
| red(n3,n4)
| red(n2,n6) ),
inference(resolution,[status(thm)],[d166,d22]) ).
cnf(d168,plain,
( red(n3,n4)
| red(n2,n6)
| ~ red(n2,n3)
| red(n2,n4) ),
inference(resolution,[status(thm)],[d138,d167]) ).
cnf(d169,plain,
( red(n3,n4)
| red(n2,n6)
| red(n2,n4) ),
inference(resolution,[status(thm)],[d132,d168]) ).
cnf(d170,plain,
( red(n3,n5)
| red(n2,n6)
| red(n2,n4)
| red(n2,n6)
| red(n2,n4) ),
inference(resolution,[status(thm)],[d169,d150]) ).
cnf(d171,plain,
( ~ red(X0,n3)
| ~ red(X0,n5)
| red(n2,n6)
| red(n2,n4) ),
inference(resolution,[status(thm)],[d170,d22]) ).
cnf(d172,plain,
( red(n2,n4)
| red(n2,n6)
| red(n2,n4)
| ~ red(n2,n3) ),
inference(resolution,[status(thm)],[d171,d138]) ).
cnf(d173,plain,
( red(n2,n6)
| red(n2,n4) ),
inference(resolution,[status(thm)],[d132,d172]) ).
cnf(d174,plain,
( red(n3,n6)
| red(n3,n5)
| ~ red(n2,n5)
| red(n2,n4) ),
inference(resolution,[status(thm)],[d173,d145]) ).
cnf(d175,plain,
( red(n2,n4)
| red(n3,n6)
| red(n3,n5)
| red(n2,n4) ),
inference(resolution,[status(thm)],[d174,d138]) ).
cnf(d176,plain,
( ~ red(X0,n3)
| ~ red(X0,n6)
| red(n3,n5)
| red(n2,n4) ),
inference(resolution,[status(thm)],[d175,d22]) ).
cnf(d177,plain,
( red(n2,n4)
| red(n3,n5)
| red(n2,n4)
| ~ red(n2,n3) ),
inference(resolution,[status(thm)],[d176,d173]) ).
cnf(d178,plain,
( red(n3,n5)
| red(n2,n4) ),
inference(resolution,[status(thm)],[d132,d177]) ).
cnf(d179,plain,
( ~ red(X0,n3)
| ~ red(X0,n5)
| red(n2,n4) ),
inference(resolution,[status(thm)],[d178,d22]) ).
cnf(d180,plain,
( red(n2,n4)
| red(n2,n4)
| ~ red(n2,n3) ),
inference(resolution,[status(thm)],[d179,d138]) ).
cnf(d181,plain,
red(n2,n4),
inference(resolution,[status(thm)],[d132,d180]) ).
cnf(d182,plain,
( red(n2,n6)
| red(n1,n2)
| red(n2,n6)
| red(n2,n5)
| ~ red(n1,n5) ),
inference(resolution,[status(thm)],[d27,d108]) ).
cnf(d183,plain,
( red(n2,n5)
| red(n1,n2)
| red(n2,n6)
| red(n2,n5)
| red(n1,n2) ),
inference(resolution,[status(thm)],[d182,d42]) ).
cnf(d184,plain,
( ~ red(X0,n4)
| ~ red(X0,n6)
| red(n3,n6)
| red(n3,n4) ),
inference(resolution,[status(thm)],[d159,d22]) ).
cnf(d185,plain,
( red(n3,n6)
| red(n3,n4)
| ~ red(n1,n4)
| red(n3,n6)
| red(n1,n3) ),
inference(resolution,[status(thm)],[d53,d184]) ).
cnf(d186,plain,
( red(n3,n4)
| red(n1,n3)
| red(n3,n6)
| red(n3,n4)
| red(n1,n3) ),
inference(resolution,[status(thm)],[d185,d152]) ).
cnf(d187,plain,
( red(n3,n6)
| red(n3,n4)
| ~ red(n1,n2) ),
inference(resolution,[status(thm)],[d133,d186]) ).
cnf(d188,plain,
( red(n2,n6)
| red(n2,n5)
| red(n3,n6)
| red(n3,n4) ),
inference(resolution,[status(thm)],[d187,d183]) ).
cnf(d189,plain,
( red(n2,n6)
| red(n2,n5)
| ~ red(n3,n5)
| red(n3,n4)
| red(n2,n6)
| red(n2,n5) ),
inference(resolution,[status(thm)],[d188,d27]) ).
cnf(d190,plain,
( red(n3,n4)
| red(n2,n6)
| red(n3,n4)
| red(n2,n6)
| red(n2,n5) ),
inference(resolution,[status(thm)],[d189,d166]) ).
cnf(d191,plain,
( ~ red(X0,n3)
| ~ red(X0,n4)
| red(n2,n6)
| red(n2,n5) ),
inference(resolution,[status(thm)],[d190,d22]) ).
cnf(d192,plain,
( red(n2,n6)
| red(n2,n5)
| ~ red(n2,n3) ),
inference(resolution,[status(thm)],[d181,d191]) ).
cnf(d193,plain,
( red(n2,n6)
| red(n2,n5) ),
inference(resolution,[status(thm)],[d132,d192]) ).
cnf(d194,plain,
( red(n3,n6)
| red(n3,n4)
| ~ red(n2,n4)
| red(n2,n5) ),
inference(resolution,[status(thm)],[d193,d184]) ).
cnf(d195,plain,
( red(n3,n6)
| red(n3,n4)
| red(n2,n5) ),
inference(resolution,[status(thm)],[d181,d194]) ).
cnf(d196,plain,
( ~ red(X0,n3)
| ~ red(X0,n6)
| red(n3,n4)
| red(n2,n5) ),
inference(resolution,[status(thm)],[d195,d22]) ).
cnf(d197,plain,
( red(n2,n5)
| red(n3,n4)
| red(n2,n5)
| ~ red(n2,n3) ),
inference(resolution,[status(thm)],[d196,d193]) ).
cnf(d198,plain,
( red(n3,n4)
| red(n2,n5) ),
inference(resolution,[status(thm)],[d132,d197]) ).
cnf(d199,plain,
( ~ red(X0,n3)
| ~ red(X0,n4)
| red(n2,n5) ),
inference(resolution,[status(thm)],[d198,d22]) ).
cnf(d200,plain,
( red(n2,n5)
| ~ red(n2,n3) ),
inference(resolution,[status(thm)],[d199,d181]) ).
cnf(d201,plain,
red(n2,n5),
inference(resolution,[status(thm)],[d132,d200]) ).
cnf(d202,plain,
( red(n3,n5)
| red(n3,n4)
| ~ red(n2,n4) ),
inference(resolution,[status(thm)],[d201,d155]) ).
cnf(d203,plain,
( red(n3,n5)
| red(n3,n4) ),
inference(resolution,[status(thm)],[d181,d202]) ).
cnf(d204,plain,
( ~ red(X0,n3)
| ~ red(X0,n5)
| red(n3,n4) ),
inference(resolution,[status(thm)],[d203,d22]) ).
cnf(d205,plain,
( red(n3,n4)
| ~ red(n2,n3) ),
inference(resolution,[status(thm)],[d204,d201]) ).
cnf(d206,plain,
red(n3,n4),
inference(resolution,[status(thm)],[d132,d205]) ).
cnf(d207,plain,
( ~ red(X0,n3)
| ~ red(X0,n4) ),
inference(resolution,[status(thm)],[d206,d22]) ).
cnf(d208,plain,
~ red(n2,n3),
inference(resolution,[status(thm)],[d207,d181]) ).
cnf(d209,plain,
$false,
inference(resolution,[status(thm)],[d132,d208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA014+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n008.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Fri Sep 25 13:49:25 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.22/2.03 % SZS status Theorem for theBenchmark.p
% 11.22/2.03 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------