%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRA014+1 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:22:57 PM UTC 2026
% Result : Theorem 1.37s 1.74s
% Output : CNFRefutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 64
% Number of leaves : 6
% Syntax : Number of formulae : 191 ( 13 unt; 0 def)
% Number of atoms : 544 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 521 ( 168 ~; 340 |; 9 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 111 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(less_than_transitive,axiom,
! [X1,X2,X3] :
( ( less_than(X1,X2)
& less_than(X2,X3) )
=> less_than(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_than_transitive) ).
fof(ordering,axiom,
( less_than(n1,n2)
& less_than(n2,n3)
& less_than(n3,n4)
& less_than(n4,n5)
& less_than(n5,n6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordering) ).
fof(partition,axiom,
! [X1,X2] :
( less_than(X1,X2)
=> ( red(X1,X2)
| green(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partition) ).
fof(green_clique,axiom,
! [X1,X2,X3] :
( ( green(X1,X2)
& green(X2,X3)
& green(X1,X3) )
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',green_clique) ).
fof(goal_to_be_proved,conjecture,
goal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_to_be_proved) ).
fof(red_clique,axiom,
! [X1,X2,X3] :
( ( red(X1,X2)
& red(X2,X3)
& red(X1,X3) )
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',red_clique) ).
fof(c_0_6,plain,
! [X21,X22,X23] :
( ~ less_than(X21,X22)
| ~ less_than(X22,X23)
| less_than(X21,X23) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[less_than_transitive])]) ).
cnf(c_0_7,plain,
( less_than(X1,X3)
| ~ less_than(X1,X2)
| ~ less_than(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_8,plain,
less_than(n4,n5),
inference(split_conjunct,[status(thm)],[ordering]) ).
cnf(c_0_9,plain,
less_than(n5,n6),
inference(split_conjunct,[status(thm)],[ordering]) ).
fof(c_0_10,plain,
! [X24,X25] :
( ~ less_than(X24,X25)
| red(X24,X25)
| green(X24,X25) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[partition])]) ).
cnf(c_0_11,plain,
( less_than(X1,n5)
| ~ less_than(X1,n4) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,plain,
( less_than(X1,n6)
| ~ less_than(X1,n5) ),
inference(spm,[status(thm)],[c_0_7,c_0_9]) ).
fof(c_0_13,plain,
! [X18,X19,X20] :
( ~ green(X18,X19)
| ~ green(X19,X20)
| ~ green(X18,X20)
| goal ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[green_clique])]) ).
fof(c_0_14,negated_conjecture,
~ goal,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[goal_to_be_proved])]) ).
cnf(c_0_15,plain,
( red(X1,X2)
| green(X1,X2)
| ~ less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( less_than(X1,n5)
| ~ less_than(X2,n4)
| ~ less_than(X1,X2) ),
inference(spm,[status(thm)],[c_0_7,c_0_11]) ).
cnf(c_0_17,plain,
less_than(n3,n4),
inference(split_conjunct,[status(thm)],[ordering]) ).
cnf(c_0_18,plain,
( less_than(X1,n6)
| ~ less_than(X2,n5)
| ~ less_than(X1,X2) ),
inference(spm,[status(thm)],[c_0_7,c_0_12]) ).
cnf(c_0_19,plain,
( goal
| ~ green(X1,X2)
| ~ green(X2,X3)
| ~ green(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
~ goal,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
( green(X1,n6)
| red(X1,n6)
| ~ less_than(X1,n5) ),
inference(spm,[status(thm)],[c_0_15,c_0_12]) ).
cnf(c_0_22,plain,
( less_than(X1,n5)
| ~ less_than(X1,n3) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,plain,
( less_than(X1,n6)
| ~ less_than(X1,n4) ),
inference(spm,[status(thm)],[c_0_18,c_0_8]) ).
cnf(c_0_24,plain,
( less_than(X1,n4)
| ~ less_than(X1,n3) ),
inference(spm,[status(thm)],[c_0_7,c_0_17]) ).
cnf(c_0_25,plain,
( ~ green(X1,X2)
| ~ green(X3,X2)
| ~ green(X3,X1) ),
inference(sr,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,plain,
( green(n4,n6)
| red(n4,n6) ),
inference(spm,[status(thm)],[c_0_21,c_0_8]) ).
cnf(c_0_27,plain,
( green(X1,n6)
| red(X1,n6)
| ~ less_than(X1,n3) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,plain,
less_than(n2,n3),
inference(split_conjunct,[status(thm)],[ordering]) ).
cnf(c_0_29,plain,
( green(X1,n6)
| red(X1,n6)
| ~ less_than(X1,n4) ),
inference(spm,[status(thm)],[c_0_15,c_0_23]) ).
cnf(c_0_30,plain,
( less_than(X1,n4)
| ~ less_than(X2,n3)
| ~ less_than(X1,X2) ),
inference(spm,[status(thm)],[c_0_7,c_0_24]) ).
cnf(c_0_31,plain,
( green(n4,n5)
| red(n4,n5) ),
inference(spm,[status(thm)],[c_0_15,c_0_8]) ).
cnf(c_0_32,plain,
( green(X1,n5)
| red(X1,n5)
| ~ less_than(X1,n3) ),
inference(spm,[status(thm)],[c_0_15,c_0_22]) ).
cnf(c_0_33,plain,
( green(X1,n5)
| red(X1,n5)
| ~ less_than(X1,n4) ),
inference(spm,[status(thm)],[c_0_15,c_0_11]) ).
fof(c_0_34,plain,
! [X15,X16,X17] :
( ~ red(X15,X16)
| ~ red(X16,X17)
| ~ red(X15,X17)
| goal ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[red_clique])]) ).
cnf(c_0_35,plain,
( red(n4,n6)
| ~ green(X1,n6)
| ~ green(X1,n4) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_36,plain,
( green(n2,n6)
| red(n2,n6) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_37,plain,
( green(X1,n4)
| red(X1,n4)
| ~ less_than(X1,n3) ),
inference(spm,[status(thm)],[c_0_15,c_0_24]) ).
cnf(c_0_38,plain,
( green(n3,n6)
| red(n3,n6) ),
inference(spm,[status(thm)],[c_0_29,c_0_17]) ).
cnf(c_0_39,plain,
( green(n3,n4)
| red(n3,n4) ),
inference(spm,[status(thm)],[c_0_15,c_0_17]) ).
cnf(c_0_40,plain,
( less_than(X1,n5)
| ~ less_than(X2,n3)
| ~ less_than(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_24]) ).
cnf(c_0_41,plain,
( less_than(X1,n4)
| ~ less_than(X1,n2) ),
inference(spm,[status(thm)],[c_0_30,c_0_28]) ).
cnf(c_0_42,plain,
( less_than(X1,n3)
| ~ less_than(X1,n2) ),
inference(spm,[status(thm)],[c_0_7,c_0_28]) ).
cnf(c_0_43,plain,
( red(n4,n5)
| ~ green(X1,n5)
| ~ green(X1,n4) ),
inference(spm,[status(thm)],[c_0_25,c_0_31]) ).
cnf(c_0_44,plain,
( green(n2,n5)
| red(n2,n5) ),
inference(spm,[status(thm)],[c_0_32,c_0_28]) ).
cnf(c_0_45,plain,
( green(n3,n5)
| red(n3,n5) ),
inference(spm,[status(thm)],[c_0_33,c_0_17]) ).
cnf(c_0_46,plain,
( goal
| ~ red(X1,X2)
| ~ red(X2,X3)
| ~ red(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_47,plain,
( red(n2,n6)
| red(n4,n6)
| ~ green(n2,n4) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_48,plain,
( green(n2,n4)
| red(n2,n4) ),
inference(spm,[status(thm)],[c_0_37,c_0_28]) ).
cnf(c_0_49,plain,
( red(n3,n6)
| ~ green(X1,n6)
| ~ green(X1,n3) ),
inference(spm,[status(thm)],[c_0_25,c_0_38]) ).
cnf(c_0_50,plain,
( red(n3,n4)
| ~ green(X1,n4)
| ~ green(X1,n3) ),
inference(spm,[status(thm)],[c_0_25,c_0_39]) ).
cnf(c_0_51,plain,
( less_than(X1,n5)
| ~ less_than(X1,n2) ),
inference(spm,[status(thm)],[c_0_40,c_0_28]) ).
cnf(c_0_52,plain,
( green(X1,n4)
| red(X1,n4)
| ~ less_than(X1,n2) ),
inference(spm,[status(thm)],[c_0_15,c_0_41]) ).
cnf(c_0_53,plain,
less_than(n1,n2),
inference(split_conjunct,[status(thm)],[ordering]) ).
cnf(c_0_54,plain,
( green(n2,n3)
| red(n2,n3) ),
inference(spm,[status(thm)],[c_0_15,c_0_28]) ).
cnf(c_0_55,plain,
( green(X1,n3)
| red(X1,n3)
| ~ less_than(X1,n2) ),
inference(spm,[status(thm)],[c_0_15,c_0_42]) ).
cnf(c_0_56,plain,
( red(n2,n5)
| red(n4,n5)
| ~ green(n2,n4) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_57,plain,
( red(n3,n5)
| ~ green(X1,n5)
| ~ green(X1,n3) ),
inference(spm,[status(thm)],[c_0_25,c_0_45]) ).
cnf(c_0_58,plain,
( ~ red(X1,X2)
| ~ red(X3,X2)
| ~ red(X3,X1) ),
inference(sr,[status(thm)],[c_0_46,c_0_20]) ).
cnf(c_0_59,plain,
( red(n2,n4)
| red(n4,n6)
| red(n2,n6) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_60,plain,
( red(n2,n6)
| red(n3,n6)
| ~ green(n2,n3) ),
inference(spm,[status(thm)],[c_0_49,c_0_36]) ).
cnf(c_0_61,plain,
( red(n2,n4)
| red(n3,n4)
| ~ green(n2,n3) ),
inference(spm,[status(thm)],[c_0_50,c_0_48]) ).
cnf(c_0_62,plain,
( green(n5,n6)
| red(n5,n6) ),
inference(spm,[status(thm)],[c_0_15,c_0_9]) ).
cnf(c_0_63,plain,
( green(X1,n6)
| red(X1,n6)
| ~ less_than(X1,n2) ),
inference(spm,[status(thm)],[c_0_21,c_0_51]) ).
cnf(c_0_64,plain,
( red(n2,n4)
| ~ green(X1,n4)
| ~ green(X1,n2) ),
inference(spm,[status(thm)],[c_0_25,c_0_48]) ).
cnf(c_0_65,plain,
( green(n1,n4)
| red(n1,n4) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_66,plain,
( red(n2,n3)
| ~ green(X1,n3)
| ~ green(X1,n2) ),
inference(spm,[status(thm)],[c_0_25,c_0_54]) ).
cnf(c_0_67,plain,
( green(n1,n3)
| red(n1,n3) ),
inference(spm,[status(thm)],[c_0_55,c_0_53]) ).
cnf(c_0_68,plain,
( red(n2,n4)
| red(n4,n5)
| red(n2,n5) ),
inference(spm,[status(thm)],[c_0_56,c_0_48]) ).
cnf(c_0_69,plain,
( red(n2,n5)
| red(n3,n5)
| ~ green(n2,n3) ),
inference(spm,[status(thm)],[c_0_57,c_0_44]) ).
cnf(c_0_70,plain,
( red(n2,n6)
| red(n2,n4)
| ~ red(X1,n6)
| ~ red(X1,n4) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_71,plain,
( red(n2,n3)
| red(n3,n6)
| red(n2,n6) ),
inference(spm,[status(thm)],[c_0_60,c_0_54]) ).
cnf(c_0_72,plain,
( red(n2,n3)
| red(n3,n4)
| red(n2,n4) ),
inference(spm,[status(thm)],[c_0_61,c_0_54]) ).
cnf(c_0_73,plain,
( red(n5,n6)
| ~ green(X1,n6)
| ~ green(X1,n5) ),
inference(spm,[status(thm)],[c_0_25,c_0_62]) ).
cnf(c_0_74,plain,
( green(n1,n6)
| red(n1,n6) ),
inference(spm,[status(thm)],[c_0_63,c_0_53]) ).
cnf(c_0_75,plain,
( green(X1,n5)
| red(X1,n5)
| ~ less_than(X1,n2) ),
inference(spm,[status(thm)],[c_0_33,c_0_41]) ).
cnf(c_0_76,plain,
( red(n1,n4)
| red(n2,n4)
| ~ green(n1,n2) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_77,plain,
( green(n1,n2)
| red(n1,n2) ),
inference(spm,[status(thm)],[c_0_15,c_0_53]) ).
cnf(c_0_78,plain,
( red(n1,n3)
| red(n2,n3)
| ~ green(n1,n2) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_79,plain,
( red(n2,n5)
| red(n2,n4)
| ~ red(X1,n5)
| ~ red(X1,n4) ),
inference(spm,[status(thm)],[c_0_58,c_0_68]) ).
cnf(c_0_80,plain,
( red(n2,n3)
| red(n3,n5)
| red(n2,n5) ),
inference(spm,[status(thm)],[c_0_69,c_0_54]) ).
cnf(c_0_81,plain,
( red(n2,n3)
| red(n2,n4)
| red(n2,n6) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]) ).
cnf(c_0_82,plain,
( red(n1,n6)
| red(n5,n6)
| ~ green(n1,n5) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_83,plain,
( green(n1,n5)
| red(n1,n5) ),
inference(spm,[status(thm)],[c_0_75,c_0_53]) ).
cnf(c_0_84,plain,
( red(n2,n4)
| red(n2,n3)
| ~ red(X1,n4)
| ~ red(X1,n3) ),
inference(spm,[status(thm)],[c_0_58,c_0_72]) ).
cnf(c_0_85,plain,
( red(n1,n2)
| red(n2,n4)
| red(n1,n4) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_86,plain,
( red(n1,n2)
| red(n2,n3)
| red(n1,n3) ),
inference(spm,[status(thm)],[c_0_78,c_0_77]) ).
cnf(c_0_87,plain,
( red(n2,n3)
| red(n2,n4)
| red(n2,n5) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_72]) ).
cnf(c_0_88,plain,
( red(n2,n4)
| red(n2,n3)
| ~ red(X1,n6)
| ~ red(X1,n2) ),
inference(spm,[status(thm)],[c_0_58,c_0_81]) ).
cnf(c_0_89,plain,
( red(n1,n5)
| red(n5,n6)
| red(n1,n6) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_90,plain,
( red(n1,n2)
| red(n2,n3)
| red(n2,n4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86]) ).
cnf(c_0_91,plain,
( red(n2,n6)
| red(n5,n6)
| ~ green(n2,n5) ),
inference(spm,[status(thm)],[c_0_73,c_0_36]) ).
cnf(c_0_92,plain,
( red(n2,n4)
| red(n2,n3)
| ~ red(X1,n5)
| ~ red(X1,n2) ),
inference(spm,[status(thm)],[c_0_58,c_0_87]) ).
cnf(c_0_93,plain,
( red(n5,n6)
| red(n1,n5)
| red(n2,n3)
| red(n2,n4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_90]) ).
cnf(c_0_94,plain,
( red(n2,n5)
| red(n5,n6)
| red(n2,n6) ),
inference(spm,[status(thm)],[c_0_91,c_0_44]) ).
cnf(c_0_95,plain,
( red(n2,n5)
| ~ green(X1,n5)
| ~ green(X1,n2) ),
inference(spm,[status(thm)],[c_0_25,c_0_44]) ).
cnf(c_0_96,plain,
( red(n5,n6)
| red(n2,n3)
| red(n2,n4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_90]) ).
cnf(c_0_97,plain,
( red(n2,n6)
| red(n2,n5)
| ~ red(X1,n6)
| ~ red(X1,n5) ),
inference(spm,[status(thm)],[c_0_58,c_0_94]) ).
cnf(c_0_98,plain,
( red(n1,n5)
| red(n2,n5)
| ~ green(n1,n2) ),
inference(spm,[status(thm)],[c_0_95,c_0_83]) ).
cnf(c_0_99,plain,
( red(n2,n4)
| red(n2,n3)
| ~ red(X1,n6)
| ~ red(X1,n5) ),
inference(spm,[status(thm)],[c_0_58,c_0_96]) ).
cnf(c_0_100,plain,
( red(n2,n3)
| red(n2,n5)
| red(n2,n6) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_71]),c_0_80]) ).
cnf(c_0_101,plain,
( red(n1,n6)
| red(n4,n6)
| ~ green(n1,n4) ),
inference(spm,[status(thm)],[c_0_35,c_0_74]) ).
cnf(c_0_102,plain,
( red(n2,n5)
| red(n2,n3)
| ~ red(X1,n5)
| ~ red(X1,n3) ),
inference(spm,[status(thm)],[c_0_58,c_0_80]) ).
cnf(c_0_103,plain,
( red(n1,n2)
| red(n2,n5)
| red(n1,n5) ),
inference(spm,[status(thm)],[c_0_98,c_0_77]) ).
cnf(c_0_104,plain,
( red(n2,n3)
| red(n2,n4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_81]),c_0_87]) ).
cnf(c_0_105,plain,
( red(n2,n5)
| red(n2,n3)
| ~ red(X1,n6)
| ~ red(X1,n2) ),
inference(spm,[status(thm)],[c_0_58,c_0_100]) ).
cnf(c_0_106,plain,
( red(n1,n4)
| red(n4,n6)
| red(n1,n6) ),
inference(spm,[status(thm)],[c_0_101,c_0_65]) ).
cnf(c_0_107,plain,
( red(n1,n2)
| red(n2,n3)
| red(n2,n5) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_86]) ).
cnf(c_0_108,plain,
( red(n2,n3)
| ~ red(X1,n4)
| ~ red(X1,n2) ),
inference(spm,[status(thm)],[c_0_58,c_0_104]) ).
cnf(c_0_109,plain,
( red(n4,n6)
| red(n1,n4)
| red(n2,n3)
| red(n2,n5) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107]) ).
cnf(c_0_110,plain,
( red(n2,n5)
| red(n4,n6)
| red(n2,n3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_107]) ).
cnf(c_0_111,plain,
( red(n2,n3)
| red(n2,n5)
| ~ red(X1,n6)
| ~ red(X1,n4) ),
inference(spm,[status(thm)],[c_0_58,c_0_110]) ).
cnf(c_0_112,plain,
( red(n2,n6)
| ~ green(X1,n6)
| ~ green(X1,n2) ),
inference(spm,[status(thm)],[c_0_25,c_0_36]) ).
cnf(c_0_113,plain,
( red(n2,n5)
| red(n2,n3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_100]),c_0_104]) ).
cnf(c_0_114,plain,
( red(n1,n5)
| red(n4,n5)
| ~ green(n1,n4) ),
inference(spm,[status(thm)],[c_0_43,c_0_83]) ).
cnf(c_0_115,plain,
( red(n1,n6)
| red(n2,n6)
| ~ green(n1,n2) ),
inference(spm,[status(thm)],[c_0_112,c_0_74]) ).
cnf(c_0_116,plain,
( red(n2,n3)
| ~ red(X1,n5)
| ~ red(X1,n2) ),
inference(spm,[status(thm)],[c_0_58,c_0_113]) ).
cnf(c_0_117,plain,
( red(n1,n4)
| red(n4,n5)
| red(n1,n5) ),
inference(spm,[status(thm)],[c_0_114,c_0_65]) ).
cnf(c_0_118,plain,
( red(n2,n6)
| red(n2,n3)
| ~ red(X1,n6)
| ~ red(X1,n3) ),
inference(spm,[status(thm)],[c_0_58,c_0_71]) ).
cnf(c_0_119,plain,
( red(n1,n2)
| red(n2,n6)
| red(n1,n6) ),
inference(spm,[status(thm)],[c_0_115,c_0_77]) ).
cnf(c_0_120,plain,
( red(n4,n5)
| red(n2,n3)
| ~ red(n1,n2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_108]) ).
cnf(c_0_121,plain,
( red(n1,n2)
| red(n2,n3)
| red(n2,n6) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_86]) ).
cnf(c_0_122,plain,
( red(n4,n6)
| red(n5,n6)
| ~ green(n4,n5) ),
inference(spm,[status(thm)],[c_0_73,c_0_26]) ).
cnf(c_0_123,plain,
( red(n2,n6)
| red(n2,n3)
| red(n4,n5) ),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_124,plain,
( red(n4,n5)
| red(n5,n6)
| red(n4,n6) ),
inference(spm,[status(thm)],[c_0_122,c_0_31]) ).
cnf(c_0_125,plain,
( red(n2,n3)
| red(n2,n6)
| ~ red(X1,n5)
| ~ red(X1,n4) ),
inference(spm,[status(thm)],[c_0_58,c_0_123]) ).
cnf(c_0_126,plain,
( red(n4,n6)
| red(n4,n5)
| ~ red(X1,n6)
| ~ red(X1,n5) ),
inference(spm,[status(thm)],[c_0_58,c_0_124]) ).
cnf(c_0_127,plain,
( red(n2,n6)
| red(n2,n3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_113]),c_0_104]) ).
cnf(c_0_128,plain,
( red(n2,n3)
| red(n4,n5)
| red(n4,n6) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_113]) ).
cnf(c_0_129,plain,
( red(n4,n5)
| red(n2,n3)
| ~ red(X1,n6)
| ~ red(X1,n4) ),
inference(spm,[status(thm)],[c_0_58,c_0_128]) ).
cnf(c_0_130,plain,
( red(n2,n3)
| red(n4,n5) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_127]),c_0_104]) ).
cnf(c_0_131,plain,
( red(n2,n3)
| ~ red(X1,n5)
| ~ red(X1,n4) ),
inference(spm,[status(thm)],[c_0_58,c_0_130]) ).
cnf(c_0_132,plain,
( red(n2,n4)
| red(n2,n5)
| red(n2,n6) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_59]),c_0_68]) ).
cnf(c_0_133,plain,
( red(n1,n6)
| red(n3,n6)
| ~ green(n1,n3) ),
inference(spm,[status(thm)],[c_0_49,c_0_74]) ).
cnf(c_0_134,plain,
red(n2,n3),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_113]),c_0_104]) ).
cnf(c_0_135,plain,
( red(n2,n5)
| red(n2,n4)
| ~ red(X1,n6)
| ~ red(X1,n2) ),
inference(spm,[status(thm)],[c_0_58,c_0_132]) ).
cnf(c_0_136,plain,
( red(n1,n3)
| red(n3,n6)
| red(n1,n6) ),
inference(spm,[status(thm)],[c_0_133,c_0_67]) ).
cnf(c_0_137,plain,
( red(n1,n2)
| red(n2,n4)
| red(n2,n5) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_103]),c_0_85]) ).
cnf(c_0_138,plain,
( ~ red(X1,n3)
| ~ red(X1,n2) ),
inference(spm,[status(thm)],[c_0_58,c_0_134]) ).
cnf(c_0_139,plain,
( red(n3,n6)
| red(n1,n3)
| red(n2,n4)
| red(n2,n5) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_137]) ).
cnf(c_0_140,plain,
( red(n2,n5)
| red(n2,n4)
| red(n3,n6) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_137]) ).
cnf(c_0_141,plain,
( red(n2,n4)
| red(n2,n5)
| ~ red(X1,n6)
| ~ red(X1,n3) ),
inference(spm,[status(thm)],[c_0_58,c_0_140]) ).
cnf(c_0_142,plain,
( red(n2,n5)
| red(n2,n4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_132]),c_0_134])]) ).
cnf(c_0_143,plain,
( red(n1,n5)
| red(n3,n5)
| ~ green(n1,n3) ),
inference(spm,[status(thm)],[c_0_57,c_0_83]) ).
cnf(c_0_144,plain,
( red(n3,n6)
| red(n5,n6)
| ~ green(n3,n5) ),
inference(spm,[status(thm)],[c_0_73,c_0_38]) ).
cnf(c_0_145,plain,
( red(n2,n4)
| ~ red(X1,n5)
| ~ red(X1,n2) ),
inference(spm,[status(thm)],[c_0_58,c_0_142]) ).
cnf(c_0_146,plain,
( red(n1,n3)
| red(n3,n5)
| red(n1,n5) ),
inference(spm,[status(thm)],[c_0_143,c_0_67]) ).
cnf(c_0_147,plain,
( red(n3,n5)
| red(n5,n6)
| red(n3,n6) ),
inference(spm,[status(thm)],[c_0_144,c_0_45]) ).
cnf(c_0_148,plain,
( red(n3,n6)
| red(n4,n6)
| ~ green(n3,n4) ),
inference(spm,[status(thm)],[c_0_35,c_0_38]) ).
cnf(c_0_149,plain,
( red(n3,n5)
| red(n4,n5)
| ~ green(n3,n4) ),
inference(spm,[status(thm)],[c_0_43,c_0_45]) ).
cnf(c_0_150,plain,
( red(n3,n5)
| red(n2,n4)
| ~ red(n1,n2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_138]) ).
cnf(c_0_151,plain,
( red(n1,n2)
| red(n2,n4)
| red(n2,n6) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_119]),c_0_85]) ).
cnf(c_0_152,plain,
( red(n3,n6)
| red(n3,n5)
| ~ red(X1,n6)
| ~ red(X1,n5) ),
inference(spm,[status(thm)],[c_0_58,c_0_147]) ).
cnf(c_0_153,plain,
( red(n3,n4)
| red(n4,n6)
| red(n3,n6) ),
inference(spm,[status(thm)],[c_0_148,c_0_39]) ).
cnf(c_0_154,plain,
( red(n3,n4)
| red(n4,n5)
| red(n3,n5) ),
inference(spm,[status(thm)],[c_0_149,c_0_39]) ).
cnf(c_0_155,plain,
( red(n2,n6)
| red(n2,n4)
| red(n3,n5) ),
inference(spm,[status(thm)],[c_0_150,c_0_151]) ).
cnf(c_0_156,plain,
( red(n3,n4)
| red(n3,n5)
| red(n3,n6) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_154]) ).
cnf(c_0_157,plain,
( red(n2,n4)
| red(n2,n6)
| ~ red(X1,n5)
| ~ red(X1,n3) ),
inference(spm,[status(thm)],[c_0_58,c_0_155]) ).
cnf(c_0_158,plain,
( red(n3,n5)
| red(n3,n4)
| ~ red(X1,n6)
| ~ red(X1,n3) ),
inference(spm,[status(thm)],[c_0_58,c_0_156]) ).
cnf(c_0_159,plain,
( red(n2,n6)
| red(n2,n4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_142]),c_0_134])]) ).
cnf(c_0_160,plain,
( red(n2,n4)
| red(n3,n4)
| red(n3,n5) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_159]),c_0_134])]) ).
cnf(c_0_161,plain,
( red(n3,n4)
| red(n2,n4)
| ~ red(X1,n5)
| ~ red(X1,n3) ),
inference(spm,[status(thm)],[c_0_58,c_0_160]) ).
cnf(c_0_162,plain,
( red(n2,n4)
| red(n3,n4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_142]),c_0_134])]) ).
cnf(c_0_163,plain,
( red(n2,n4)
| ~ red(X1,n4)
| ~ red(X1,n3) ),
inference(spm,[status(thm)],[c_0_58,c_0_162]) ).
cnf(c_0_164,plain,
( red(n2,n4)
| ~ red(n1,n3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_85]),c_0_138]) ).
cnf(c_0_165,plain,
( red(n1,n3)
| red(n3,n5)
| red(n3,n6) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_136]),c_0_146]) ).
cnf(c_0_166,plain,
( red(n3,n6)
| red(n3,n5)
| red(n2,n4) ),
inference(spm,[status(thm)],[c_0_164,c_0_165]) ).
cnf(c_0_167,plain,
( red(n2,n4)
| red(n3,n5)
| ~ red(X1,n6)
| ~ red(X1,n3) ),
inference(spm,[status(thm)],[c_0_58,c_0_166]) ).
cnf(c_0_168,plain,
( red(n3,n5)
| red(n2,n4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_159]),c_0_134])]) ).
cnf(c_0_169,plain,
( red(n2,n4)
| ~ red(X1,n5)
| ~ red(X1,n3) ),
inference(spm,[status(thm)],[c_0_58,c_0_168]) ).
cnf(c_0_170,plain,
red(n2,n4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_142]),c_0_134])]) ).
cnf(c_0_171,plain,
( red(n1,n4)
| red(n3,n4)
| ~ green(n1,n3) ),
inference(spm,[status(thm)],[c_0_50,c_0_65]) ).
cnf(c_0_172,plain,
( ~ red(X1,n4)
| ~ red(X1,n2) ),
inference(spm,[status(thm)],[c_0_58,c_0_170]) ).
cnf(c_0_173,plain,
( red(n1,n3)
| red(n3,n4)
| red(n1,n4) ),
inference(spm,[status(thm)],[c_0_171,c_0_67]) ).
cnf(c_0_174,plain,
( red(n3,n4)
| ~ red(n1,n2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_173]),c_0_138]) ).
cnf(c_0_175,plain,
( red(n1,n2)
| red(n2,n5)
| red(n2,n6) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_119]),c_0_103]) ).
cnf(c_0_176,plain,
( red(n2,n6)
| red(n2,n5)
| red(n3,n4) ),
inference(spm,[status(thm)],[c_0_174,c_0_175]) ).
cnf(c_0_177,plain,
( red(n2,n5)
| red(n2,n6)
| ~ red(X1,n4)
| ~ red(X1,n3) ),
inference(spm,[status(thm)],[c_0_58,c_0_176]) ).
cnf(c_0_178,plain,
( red(n3,n6)
| red(n3,n4)
| ~ red(X1,n6)
| ~ red(X1,n4) ),
inference(spm,[status(thm)],[c_0_58,c_0_153]) ).
cnf(c_0_179,plain,
( red(n2,n6)
| red(n2,n5) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_170]),c_0_134])]) ).
cnf(c_0_180,plain,
( red(n2,n5)
| red(n3,n4)
| red(n3,n6) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_179]),c_0_170])]) ).
cnf(c_0_181,plain,
( red(n3,n4)
| red(n2,n5)
| ~ red(X1,n6)
| ~ red(X1,n3) ),
inference(spm,[status(thm)],[c_0_58,c_0_180]) ).
cnf(c_0_182,plain,
( red(n2,n5)
| red(n3,n4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_179]),c_0_134])]) ).
cnf(c_0_183,plain,
( red(n2,n5)
| ~ red(X1,n4)
| ~ red(X1,n3) ),
inference(spm,[status(thm)],[c_0_58,c_0_182]) ).
cnf(c_0_184,plain,
( red(n3,n5)
| red(n3,n4)
| ~ red(X1,n5)
| ~ red(X1,n4) ),
inference(spm,[status(thm)],[c_0_58,c_0_154]) ).
cnf(c_0_185,plain,
red(n2,n5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_170]),c_0_134])]) ).
cnf(c_0_186,plain,
( red(n3,n4)
| red(n3,n5) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_185]),c_0_170])]) ).
cnf(c_0_187,plain,
( red(n3,n4)
| ~ red(X1,n5)
| ~ red(X1,n3) ),
inference(spm,[status(thm)],[c_0_58,c_0_186]) ).
cnf(c_0_188,plain,
red(n3,n4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_185]),c_0_134])]) ).
cnf(c_0_189,plain,
( ~ red(X1,n4)
| ~ red(X1,n3) ),
inference(spm,[status(thm)],[c_0_58,c_0_188]) ).
cnf(c_0_190,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_170]),c_0_134])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA014+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n029.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 18:06:29 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.37/1.74 % Version : CSE_E---1.7
% 1.37/1.74 % Problem : theBenchmark.p
% 1.37/1.74 % SZS status Theorem for theBenchmark.p
% 1.37/1.74 % SZS output start CNFRefutation
% See solution above
% 1.37/1.75 % Total time : 1.372s
%------------------------------------------------------------------------------