%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRA014+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 : Thu Sep 24 12:31:31 PM UTC 2026
% Result : Theorem 0.07s 0.37s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 57
% Number of leaves : 6
% Syntax : Number of formulae : 175 ( 15 unt; 0 def)
% Number of atoms : 554 ( 0 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 540 ( 161 ~; 366 |; 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 : 132 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goal_to_be_proved,conjecture,
goal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_to_be_proved) ).
fof(green_clique,axiom,
! [X1,X2,X3] :
( ( green(X1,X3)
& green(X2,X3)
& green(X1,X2) )
=> goal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',green_clique) ).
fof(partition,axiom,
! [X1,X2] :
( less_than(X1,X2)
=> ( green(X1,X2)
| red(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partition) ).
fof(less_than_transitive,axiom,
! [X1,X2,X3] :
( ( less_than(X2,X3)
& less_than(X1,X2) )
=> less_than(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_than_transitive) ).
fof(ordering,axiom,
( less_than(n5,n6)
& less_than(n4,n5)
& less_than(n3,n4)
& less_than(n2,n3)
& less_than(n1,n2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordering) ).
fof(red_clique,axiom,
! [X1,X2,X3] :
( ( red(X1,X3)
& red(X2,X3)
& red(X1,X2) )
=> goal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',red_clique) ).
fof(c_0_6,negated_conjecture,
~ goal,
inference(assume_negation,[status(cth)],[goal_to_be_proved]) ).
fof(c_0_7,negated_conjecture,
~ goal,
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_8,plain,
! [X7,X8,X9] :
( goal
| ~ green(X7,X9)
| ~ green(X8,X9)
| ~ green(X7,X8) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[green_clique])])]) ).
fof(c_0_9,negated_conjecture,
~ goal,
inference(fof_nnf,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
( ~ green(X1,X3)
| ~ green(X2,X3)
| ~ green(X1,X2)
| goal ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,negated_conjecture,
~ goal,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X10,X11] :
( green(X10,X11)
| red(X10,X11)
| ~ less_than(X10,X11) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[partition])])]) ).
cnf(c_0_13,plain,
( ~ green(X3,X1)
| ~ green(X3,X2)
| ~ green(X1,X2) ),
inference(sr,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
( ~ less_than(X1,X2)
| green(X1,X2)
| red(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,plain,
( ~ green(X3,X1)
| ~ green(X3,X2)
| ~ less_than(X1,X2)
| red(X1,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_16,plain,
! [X12,X13,X14] :
( less_than(X12,X14)
| ~ less_than(X13,X14)
| ~ less_than(X12,X13) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[less_than_transitive])])]) ).
cnf(c_0_17,plain,
( ~ green(X1,X3)
| ~ less_than(X1,X2)
| ~ less_than(X3,X2)
| red(X3,X2)
| red(X1,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_18,plain,
( ~ less_than(X2,X3)
| ~ less_than(X1,X2)
| less_than(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_19,plain,
less_than(n5,n6),
inference(split_conjunct,[status(thm)],[ordering]) ).
cnf(c_0_20,plain,
( ~ less_than(X1,X2)
| ~ less_than(X2,X3)
| red(X1,X3)
| red(X2,X3)
| red(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_14]),c_0_18]) ).
cnf(c_0_21,plain,
( ~ less_than(X1,n5)
| less_than(X1,n6) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
( ~ less_than(X1,X2)
| ~ less_than(X2,n5)
| red(X1,X2)
| red(X2,n6)
| red(X1,n6) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,plain,
less_than(n4,n5),
inference(split_conjunct,[status(thm)],[ordering]) ).
cnf(c_0_24,plain,
less_than(n3,n4),
inference(split_conjunct,[status(thm)],[ordering]) ).
cnf(c_0_25,plain,
( ~ less_than(X1,X2)
| ~ less_than(X2,n5)
| less_than(X1,n6) ),
inference(spm,[status(thm)],[c_0_18,c_0_21]) ).
fof(c_0_26,plain,
! [X4,X5,X6] :
( goal
| ~ red(X4,X6)
| ~ red(X5,X6)
| ~ red(X4,X5) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[red_clique])])]) ).
cnf(c_0_27,plain,
( ~ less_than(X1,n4)
| red(X1,n6)
| red(X1,n4)
| red(n4,n6) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
( ~ less_than(X1,n3)
| less_than(X1,n4) ),
inference(spm,[status(thm)],[c_0_18,c_0_24]) ).
cnf(c_0_29,plain,
( ~ less_than(X1,n4)
| less_than(X1,n6) ),
inference(spm,[status(thm)],[c_0_25,c_0_23]) ).
cnf(c_0_30,plain,
( ~ less_than(X1,n4)
| less_than(X1,n5) ),
inference(spm,[status(thm)],[c_0_18,c_0_23]) ).
cnf(c_0_31,plain,
( ~ less_than(X1,n4)
| red(X1,n4)
| red(X1,n5)
| red(n4,n5) ),
inference(spm,[status(thm)],[c_0_20,c_0_23]) ).
cnf(c_0_32,plain,
( ~ red(X1,X3)
| ~ red(X2,X3)
| ~ red(X1,X2)
| goal ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
( ~ less_than(X1,n3)
| red(X1,n4)
| red(X1,n6)
| red(n4,n6) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,plain,
less_than(n2,n3),
inference(split_conjunct,[status(thm)],[ordering]) ).
cnf(c_0_35,plain,
( ~ less_than(X1,X2)
| ~ less_than(X2,n4)
| red(X1,X2)
| red(X2,n6)
| red(X1,n6) ),
inference(spm,[status(thm)],[c_0_20,c_0_29]) ).
cnf(c_0_36,plain,
( ~ less_than(X1,X2)
| ~ less_than(X2,n4)
| less_than(X1,n5) ),
inference(spm,[status(thm)],[c_0_18,c_0_30]) ).
cnf(c_0_37,plain,
( ~ less_than(X1,n3)
| red(X1,n5)
| red(X1,n4)
| red(n4,n5) ),
inference(spm,[status(thm)],[c_0_31,c_0_28]) ).
cnf(c_0_38,plain,
( ~ less_than(X1,X2)
| ~ less_than(X2,n4)
| red(X1,X2)
| red(X2,n5)
| red(X1,n5) ),
inference(spm,[status(thm)],[c_0_20,c_0_30]) ).
cnf(c_0_39,plain,
( ~ red(X3,X1)
| ~ red(X3,X2)
| ~ red(X1,X2) ),
inference(sr,[status(thm)],[c_0_32,c_0_11]) ).
cnf(c_0_40,plain,
( red(n4,n6)
| red(n2,n6)
| red(n2,n4) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_41,plain,
( ~ less_than(X1,n3)
| red(X1,n6)
| red(X1,n3)
| red(n3,n6) ),
inference(spm,[status(thm)],[c_0_35,c_0_24]) ).
cnf(c_0_42,plain,
( ~ less_than(X1,n3)
| red(X1,n3)
| red(X1,n4)
| red(n3,n4) ),
inference(spm,[status(thm)],[c_0_20,c_0_24]) ).
cnf(c_0_43,plain,
( ~ less_than(X1,X2)
| ~ less_than(X2,n3)
| less_than(X1,n5) ),
inference(spm,[status(thm)],[c_0_36,c_0_28]) ).
cnf(c_0_44,plain,
( ~ less_than(X1,X2)
| ~ less_than(X2,n3)
| red(X1,X2)
| red(X2,n4)
| red(X1,n4) ),
inference(spm,[status(thm)],[c_0_20,c_0_28]) ).
cnf(c_0_45,plain,
( red(n4,n5)
| red(n2,n4)
| red(n2,n5) ),
inference(spm,[status(thm)],[c_0_37,c_0_34]) ).
cnf(c_0_46,plain,
( ~ less_than(X1,n3)
| red(X1,n5)
| red(X1,n3)
| red(n3,n5) ),
inference(spm,[status(thm)],[c_0_38,c_0_24]) ).
cnf(c_0_47,plain,
( ~ red(X1,n4)
| ~ red(X1,n6)
| red(n2,n4)
| red(n2,n6) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_48,plain,
( red(n3,n6)
| red(n2,n3)
| red(n2,n6) ),
inference(spm,[status(thm)],[c_0_41,c_0_34]) ).
cnf(c_0_49,plain,
( red(n3,n4)
| red(n2,n4)
| red(n2,n3) ),
inference(spm,[status(thm)],[c_0_42,c_0_34]) ).
cnf(c_0_50,plain,
( ~ less_than(X1,n5)
| red(X1,n5)
| red(X1,n6)
| red(n5,n6) ),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_51,plain,
( ~ less_than(X1,n2)
| less_than(X1,n5) ),
inference(spm,[status(thm)],[c_0_43,c_0_34]) ).
cnf(c_0_52,plain,
( ~ less_than(X1,n2)
| red(X1,n4)
| red(X1,n2)
| red(n2,n4) ),
inference(spm,[status(thm)],[c_0_44,c_0_34]) ).
cnf(c_0_53,plain,
less_than(n1,n2),
inference(split_conjunct,[status(thm)],[ordering]) ).
cnf(c_0_54,plain,
( ~ less_than(X1,n2)
| red(X1,n2)
| red(X1,n3)
| red(n2,n3) ),
inference(spm,[status(thm)],[c_0_20,c_0_34]) ).
cnf(c_0_55,plain,
( ~ less_than(X1,n3)
| less_than(X1,n5) ),
inference(spm,[status(thm)],[c_0_36,c_0_24]) ).
cnf(c_0_56,plain,
( ~ red(X1,n4)
| ~ red(X1,n5)
| red(n2,n5)
| red(n2,n4) ),
inference(spm,[status(thm)],[c_0_39,c_0_45]) ).
cnf(c_0_57,plain,
( red(n3,n5)
| red(n2,n3)
| red(n2,n5) ),
inference(spm,[status(thm)],[c_0_46,c_0_34]) ).
cnf(c_0_58,plain,
( red(n2,n6)
| red(n2,n4)
| red(n2,n3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
cnf(c_0_59,plain,
( ~ less_than(X1,n2)
| red(X1,n6)
| red(X1,n5)
| red(n5,n6) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_60,plain,
( ~ red(X1,n3)
| ~ red(X1,n4)
| red(n2,n3)
| red(n2,n4) ),
inference(spm,[status(thm)],[c_0_39,c_0_49]) ).
cnf(c_0_61,plain,
( red(n2,n4)
| red(n1,n2)
| red(n1,n4) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_62,plain,
( red(n2,n3)
| red(n1,n3)
| red(n1,n2) ),
inference(spm,[status(thm)],[c_0_54,c_0_53]) ).
cnf(c_0_63,plain,
( ~ less_than(X1,n3)
| red(X1,n6)
| red(X1,n5)
| red(n5,n6) ),
inference(spm,[status(thm)],[c_0_50,c_0_55]) ).
cnf(c_0_64,plain,
( red(n2,n4)
| red(n2,n5)
| red(n2,n3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_49]) ).
cnf(c_0_65,plain,
( ~ red(X1,n2)
| ~ red(X1,n6)
| red(n2,n3)
| red(n2,n4) ),
inference(spm,[status(thm)],[c_0_39,c_0_58]) ).
cnf(c_0_66,plain,
( red(n5,n6)
| red(n1,n5)
| red(n1,n6) ),
inference(spm,[status(thm)],[c_0_59,c_0_53]) ).
cnf(c_0_67,plain,
( red(n2,n4)
| red(n2,n3)
| red(n1,n2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]) ).
cnf(c_0_68,plain,
( red(n5,n6)
| red(n2,n5)
| red(n2,n6) ),
inference(spm,[status(thm)],[c_0_63,c_0_34]) ).
cnf(c_0_69,plain,
( ~ red(X1,n2)
| ~ red(X1,n5)
| red(n2,n3)
| red(n2,n4) ),
inference(spm,[status(thm)],[c_0_39,c_0_64]) ).
cnf(c_0_70,plain,
( red(n2,n4)
| red(n2,n3)
| red(n1,n5)
| red(n5,n6) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]) ).
cnf(c_0_71,plain,
( ~ red(X1,n5)
| ~ red(X1,n6)
| red(n2,n6)
| red(n2,n5) ),
inference(spm,[status(thm)],[c_0_39,c_0_68]) ).
cnf(c_0_72,plain,
( ~ less_than(X1,X2)
| ~ less_than(X2,n3)
| less_than(X1,n4) ),
inference(spm,[status(thm)],[c_0_18,c_0_28]) ).
cnf(c_0_73,plain,
( ~ less_than(X1,X2)
| ~ less_than(X2,n3)
| red(X1,X2)
| red(X2,n5)
| red(X1,n5) ),
inference(spm,[status(thm)],[c_0_20,c_0_55]) ).
cnf(c_0_74,plain,
( red(n2,n4)
| red(n2,n3)
| red(n5,n6) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_67]) ).
cnf(c_0_75,plain,
( ~ red(n3,n5)
| red(n2,n5)
| red(n2,n6)
| red(n2,n3) ),
inference(spm,[status(thm)],[c_0_71,c_0_48]) ).
cnf(c_0_76,plain,
( ~ less_than(X1,n2)
| less_than(X1,n4) ),
inference(spm,[status(thm)],[c_0_72,c_0_34]) ).
cnf(c_0_77,plain,
( ~ less_than(X1,n2)
| red(X1,n5)
| red(X1,n2)
| red(n2,n5) ),
inference(spm,[status(thm)],[c_0_73,c_0_34]) ).
cnf(c_0_78,plain,
( ~ red(X1,n5)
| ~ red(X1,n6)
| red(n2,n3)
| red(n2,n4) ),
inference(spm,[status(thm)],[c_0_39,c_0_74]) ).
cnf(c_0_79,plain,
( red(n2,n3)
| red(n2,n6)
| red(n2,n5) ),
inference(spm,[status(thm)],[c_0_75,c_0_57]) ).
cnf(c_0_80,plain,
( ~ less_than(X1,n2)
| red(X1,n4)
| red(X1,n6)
| red(n4,n6) ),
inference(spm,[status(thm)],[c_0_27,c_0_76]) ).
cnf(c_0_81,plain,
( ~ red(X1,n3)
| ~ red(X1,n5)
| red(n2,n5)
| red(n2,n3) ),
inference(spm,[status(thm)],[c_0_39,c_0_57]) ).
cnf(c_0_82,plain,
( red(n2,n5)
| red(n1,n2)
| red(n1,n5) ),
inference(spm,[status(thm)],[c_0_77,c_0_53]) ).
cnf(c_0_83,plain,
( red(n2,n4)
| red(n2,n3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_58]),c_0_64]) ).
cnf(c_0_84,plain,
( ~ red(X1,n2)
| ~ red(X1,n6)
| red(n2,n5)
| red(n2,n3) ),
inference(spm,[status(thm)],[c_0_39,c_0_79]) ).
cnf(c_0_85,plain,
( red(n4,n6)
| red(n1,n6)
| red(n1,n4) ),
inference(spm,[status(thm)],[c_0_80,c_0_53]) ).
cnf(c_0_86,plain,
( red(n2,n3)
| red(n2,n5)
| red(n1,n2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_62]) ).
cnf(c_0_87,plain,
( ~ red(X1,n2)
| ~ red(X1,n4)
| red(n2,n3) ),
inference(spm,[status(thm)],[c_0_39,c_0_83]) ).
cnf(c_0_88,plain,
( red(n2,n3)
| red(n2,n5)
| red(n1,n4)
| red(n4,n6) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86]) ).
cnf(c_0_89,plain,
( ~ less_than(X1,X2)
| ~ less_than(X2,n4)
| less_than(X1,n6) ),
inference(spm,[status(thm)],[c_0_25,c_0_30]) ).
cnf(c_0_90,plain,
( red(n2,n3)
| red(n4,n6)
| red(n2,n5) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_86]) ).
cnf(c_0_91,plain,
( ~ less_than(X1,n3)
| less_than(X1,n6) ),
inference(spm,[status(thm)],[c_0_89,c_0_24]) ).
cnf(c_0_92,plain,
( ~ red(X1,n4)
| ~ red(X1,n6)
| red(n2,n5)
| red(n2,n3) ),
inference(spm,[status(thm)],[c_0_39,c_0_90]) ).
cnf(c_0_93,plain,
( ~ less_than(X1,X2)
| ~ less_than(X2,n3)
| red(X1,X2)
| red(X2,n6)
| red(X1,n6) ),
inference(spm,[status(thm)],[c_0_20,c_0_91]) ).
cnf(c_0_94,plain,
( red(n2,n3)
| red(n2,n5) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_79]),c_0_83]) ).
cnf(c_0_95,plain,
( ~ less_than(X1,n2)
| red(X1,n5)
| red(X1,n4)
| red(n4,n5) ),
inference(spm,[status(thm)],[c_0_31,c_0_76]) ).
cnf(c_0_96,plain,
( ~ less_than(X1,n2)
| red(X1,n6)
| red(X1,n2)
| red(n2,n6) ),
inference(spm,[status(thm)],[c_0_93,c_0_34]) ).
cnf(c_0_97,plain,
( ~ red(X1,n2)
| ~ red(X1,n5)
| red(n2,n3) ),
inference(spm,[status(thm)],[c_0_39,c_0_94]) ).
cnf(c_0_98,plain,
( red(n4,n5)
| red(n1,n4)
| red(n1,n5) ),
inference(spm,[status(thm)],[c_0_95,c_0_53]) ).
cnf(c_0_99,plain,
( ~ red(X1,n3)
| ~ red(X1,n6)
| red(n2,n6)
| red(n2,n3) ),
inference(spm,[status(thm)],[c_0_39,c_0_48]) ).
cnf(c_0_100,plain,
( red(n2,n6)
| red(n1,n2)
| red(n1,n6) ),
inference(spm,[status(thm)],[c_0_96,c_0_53]) ).
cnf(c_0_101,plain,
( ~ red(n1,n2)
| red(n2,n3)
| red(n4,n5) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_87]) ).
cnf(c_0_102,plain,
( red(n2,n3)
| red(n2,n6)
| red(n1,n2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_62]) ).
cnf(c_0_103,plain,
( red(n4,n5)
| red(n2,n3)
| red(n2,n6) ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_104,plain,
( red(n5,n6)
| red(n4,n6)
| red(n4,n5) ),
inference(spm,[status(thm)],[c_0_50,c_0_23]) ).
cnf(c_0_105,plain,
( ~ red(X1,n4)
| ~ red(X1,n5)
| red(n2,n6)
| red(n2,n3) ),
inference(spm,[status(thm)],[c_0_39,c_0_103]) ).
cnf(c_0_106,plain,
( ~ red(X1,n5)
| ~ red(X1,n6)
| red(n4,n5)
| red(n4,n6) ),
inference(spm,[status(thm)],[c_0_39,c_0_104]) ).
cnf(c_0_107,plain,
( red(n2,n3)
| red(n2,n6) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_94]),c_0_83]) ).
cnf(c_0_108,plain,
( red(n4,n6)
| red(n4,n5)
| red(n2,n3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_94]) ).
cnf(c_0_109,plain,
( ~ red(X1,n4)
| ~ red(X1,n6)
| red(n2,n3)
| red(n4,n5) ),
inference(spm,[status(thm)],[c_0_39,c_0_108]) ).
cnf(c_0_110,plain,
( ~ less_than(X1,n4)
| red(X1,n6)
| red(X1,n5)
| red(n5,n6) ),
inference(spm,[status(thm)],[c_0_50,c_0_30]) ).
cnf(c_0_111,plain,
( red(n4,n5)
| red(n2,n3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_107]),c_0_83]) ).
cnf(c_0_112,plain,
( ~ less_than(X1,n2)
| less_than(X1,n3) ),
inference(spm,[status(thm)],[c_0_18,c_0_34]) ).
cnf(c_0_113,plain,
( red(n5,n6)
| red(n3,n5)
| red(n3,n6) ),
inference(spm,[status(thm)],[c_0_110,c_0_24]) ).
cnf(c_0_114,plain,
( ~ red(X1,n4)
| ~ red(X1,n5)
| red(n2,n3) ),
inference(spm,[status(thm)],[c_0_39,c_0_111]) ).
cnf(c_0_115,plain,
( red(n4,n5)
| red(n3,n5)
| red(n3,n4) ),
inference(spm,[status(thm)],[c_0_31,c_0_24]) ).
cnf(c_0_116,plain,
( ~ less_than(X1,n2)
| red(X1,n3)
| red(X1,n5)
| red(n3,n5) ),
inference(spm,[status(thm)],[c_0_46,c_0_112]) ).
cnf(c_0_117,plain,
( ~ less_than(X1,n2)
| red(X1,n4)
| red(X1,n3)
| red(n3,n4) ),
inference(spm,[status(thm)],[c_0_42,c_0_112]) ).
cnf(c_0_118,plain,
( ~ red(X1,n5)
| ~ red(X1,n6)
| red(n3,n6)
| red(n3,n5) ),
inference(spm,[status(thm)],[c_0_39,c_0_113]) ).
cnf(c_0_119,plain,
( red(n4,n6)
| red(n3,n4)
| red(n3,n6) ),
inference(spm,[status(thm)],[c_0_27,c_0_24]) ).
cnf(c_0_120,plain,
( red(n2,n5)
| red(n2,n6)
| red(n2,n4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_40]),c_0_45]) ).
cnf(c_0_121,plain,
( ~ less_than(X1,n2)
| red(X1,n3)
| red(X1,n6)
| red(n3,n6) ),
inference(spm,[status(thm)],[c_0_41,c_0_112]) ).
cnf(c_0_122,plain,
red(n2,n3),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_94]),c_0_83]) ).
cnf(c_0_123,plain,
( ~ red(X1,n4)
| ~ red(X1,n5)
| red(n3,n4)
| red(n3,n5) ),
inference(spm,[status(thm)],[c_0_39,c_0_115]) ).
cnf(c_0_124,plain,
( red(n3,n5)
| red(n1,n5)
| red(n1,n3) ),
inference(spm,[status(thm)],[c_0_116,c_0_53]) ).
cnf(c_0_125,plain,
( red(n3,n4)
| red(n1,n3)
| red(n1,n4) ),
inference(spm,[status(thm)],[c_0_117,c_0_53]) ).
cnf(c_0_126,plain,
( red(n3,n5)
| red(n3,n6)
| red(n3,n4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_115]) ).
cnf(c_0_127,plain,
( ~ red(X1,n2)
| ~ red(X1,n6)
| red(n2,n4)
| red(n2,n5) ),
inference(spm,[status(thm)],[c_0_39,c_0_120]) ).
cnf(c_0_128,plain,
( red(n3,n6)
| red(n1,n6)
| red(n1,n3) ),
inference(spm,[status(thm)],[c_0_121,c_0_53]) ).
cnf(c_0_129,plain,
( red(n2,n4)
| red(n2,n5)
| red(n1,n2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_82]),c_0_61]) ).
cnf(c_0_130,plain,
( ~ red(X1,n2)
| ~ red(X1,n3) ),
inference(spm,[status(thm)],[c_0_39,c_0_122]) ).
cnf(c_0_131,plain,
( red(n3,n5)
| red(n3,n4)
| red(n1,n3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_125]) ).
cnf(c_0_132,plain,
( ~ red(X1,n3)
| ~ red(X1,n6)
| red(n3,n4)
| red(n3,n5) ),
inference(spm,[status(thm)],[c_0_39,c_0_126]) ).
cnf(c_0_133,plain,
( red(n2,n5)
| red(n2,n4)
| red(n1,n3)
| red(n3,n6) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_129]) ).
cnf(c_0_134,plain,
( ~ red(n1,n5)
| red(n3,n5)
| red(n3,n6)
| red(n1,n3) ),
inference(spm,[status(thm)],[c_0_118,c_0_128]) ).
cnf(c_0_135,plain,
( ~ red(n1,n2)
| red(n3,n4)
| red(n3,n5) ),
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_136,plain,
( red(n3,n5)
| red(n3,n4)
| red(n1,n2)
| red(n2,n6) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_100]),c_0_131]) ).
cnf(c_0_137,plain,
( red(n3,n6)
| red(n2,n4)
| red(n2,n5) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_133]),c_0_129]) ).
cnf(c_0_138,plain,
( red(n1,n3)
| red(n3,n6)
| red(n3,n5) ),
inference(spm,[status(thm)],[c_0_134,c_0_124]) ).
cnf(c_0_139,plain,
( ~ red(n1,n4)
| red(n2,n6)
| red(n2,n4)
| red(n1,n2) ),
inference(spm,[status(thm)],[c_0_47,c_0_100]) ).
cnf(c_0_140,plain,
( red(n3,n5)
| red(n3,n4)
| red(n2,n6) ),
inference(spm,[status(thm)],[c_0_135,c_0_136]) ).
cnf(c_0_141,plain,
( ~ red(X1,n3)
| ~ red(X1,n6)
| red(n2,n5)
| red(n2,n4) ),
inference(spm,[status(thm)],[c_0_39,c_0_137]) ).
cnf(c_0_142,plain,
( ~ red(n1,n2)
| red(n3,n5)
| red(n3,n6) ),
inference(spm,[status(thm)],[c_0_130,c_0_138]) ).
cnf(c_0_143,plain,
( red(n1,n2)
| red(n2,n4)
| red(n2,n6) ),
inference(spm,[status(thm)],[c_0_139,c_0_61]) ).
cnf(c_0_144,plain,
( ~ red(X1,n3)
| ~ red(X1,n5)
| red(n2,n6)
| red(n3,n4) ),
inference(spm,[status(thm)],[c_0_39,c_0_140]) ).
cnf(c_0_145,plain,
( red(n2,n4)
| red(n2,n5) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_120]),c_0_122])]) ).
cnf(c_0_146,plain,
( red(n3,n6)
| red(n3,n5)
| red(n2,n6)
| red(n2,n4) ),
inference(spm,[status(thm)],[c_0_142,c_0_143]) ).
cnf(c_0_147,plain,
( red(n3,n4)
| red(n2,n6)
| red(n2,n4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_122])]) ).
cnf(c_0_148,plain,
( red(n2,n6)
| red(n2,n4)
| red(n3,n5) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_146]),c_0_147]) ).
cnf(c_0_149,plain,
( ~ red(X1,n3)
| ~ red(X1,n5)
| red(n2,n4)
| red(n2,n6) ),
inference(spm,[status(thm)],[c_0_39,c_0_148]) ).
cnf(c_0_150,plain,
( ~ red(X1,n4)
| ~ red(X1,n6)
| red(n3,n6)
| red(n3,n4) ),
inference(spm,[status(thm)],[c_0_39,c_0_119]) ).
cnf(c_0_151,plain,
( red(n2,n6)
| red(n2,n4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_145]),c_0_122])]) ).
cnf(c_0_152,plain,
( red(n3,n4)
| red(n3,n6)
| red(n1,n3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_128]),c_0_125]) ).
cnf(c_0_153,plain,
( ~ red(n1,n5)
| red(n2,n5)
| red(n2,n6)
| red(n1,n2) ),
inference(spm,[status(thm)],[c_0_71,c_0_100]) ).
cnf(c_0_154,plain,
( red(n3,n5)
| red(n3,n6)
| red(n2,n4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_151]),c_0_145]) ).
cnf(c_0_155,plain,
( ~ red(n1,n2)
| red(n3,n6)
| red(n3,n4) ),
inference(spm,[status(thm)],[c_0_130,c_0_152]) ).
cnf(c_0_156,plain,
( red(n1,n2)
| red(n2,n6)
| red(n2,n5) ),
inference(spm,[status(thm)],[c_0_153,c_0_82]) ).
cnf(c_0_157,plain,
( ~ red(X1,n3)
| ~ red(X1,n6)
| red(n2,n4)
| red(n3,n5) ),
inference(spm,[status(thm)],[c_0_39,c_0_154]) ).
cnf(c_0_158,plain,
( red(n3,n4)
| red(n3,n6)
| red(n2,n5)
| red(n2,n6) ),
inference(spm,[status(thm)],[c_0_155,c_0_156]) ).
cnf(c_0_159,plain,
( red(n3,n5)
| red(n2,n4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_151]),c_0_122])]) ).
cnf(c_0_160,plain,
( red(n2,n5)
| red(n2,n6)
| red(n3,n4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_158]),c_0_140]) ).
cnf(c_0_161,plain,
( ~ red(X1,n3)
| ~ red(X1,n5)
| red(n2,n4) ),
inference(spm,[status(thm)],[c_0_39,c_0_159]) ).
cnf(c_0_162,plain,
( ~ red(X1,n3)
| ~ red(X1,n4)
| red(n2,n6)
| red(n2,n5) ),
inference(spm,[status(thm)],[c_0_39,c_0_160]) ).
cnf(c_0_163,plain,
red(n2,n4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_145]),c_0_122])]) ).
cnf(c_0_164,plain,
( red(n2,n5)
| red(n2,n6) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_163]),c_0_122])]) ).
cnf(c_0_165,plain,
( red(n3,n4)
| red(n3,n6)
| red(n2,n5) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_164]),c_0_163])]) ).
cnf(c_0_166,plain,
( ~ red(X1,n3)
| ~ red(X1,n6)
| red(n2,n5)
| red(n3,n4) ),
inference(spm,[status(thm)],[c_0_39,c_0_165]) ).
cnf(c_0_167,plain,
( red(n3,n4)
| red(n2,n5) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_164]),c_0_122])]) ).
cnf(c_0_168,plain,
( ~ red(X1,n3)
| ~ red(X1,n4)
| red(n2,n5) ),
inference(spm,[status(thm)],[c_0_39,c_0_167]) ).
cnf(c_0_169,plain,
red(n2,n5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_163]),c_0_122])]) ).
cnf(c_0_170,plain,
( red(n3,n5)
| red(n3,n4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_169]),c_0_163])]) ).
cnf(c_0_171,plain,
( ~ red(X1,n3)
| ~ red(X1,n5)
| red(n3,n4) ),
inference(spm,[status(thm)],[c_0_39,c_0_170]) ).
cnf(c_0_172,plain,
red(n3,n4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_169]),c_0_122])]) ).
cnf(c_0_173,plain,
( ~ red(X1,n3)
| ~ red(X1,n4) ),
inference(spm,[status(thm)],[c_0_39,c_0_172]) ).
cnf(c_0_174,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_163]),c_0_122])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRA014+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sun Sep 20 18:23:53 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.37 % Version: 3.5.1
% 0.07/0.37 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.07/0.37 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.37 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.07/0.37 % Starting new_bool_3 with 300s (1) cores
% 0.07/0.37 % Starting new_bool_1 with 300s (1) cores
% 0.07/0.37 % Starting sh5l with 300s (1) cores
% 0.07/0.37 % new_bool_3 with pid 618593 completed with status 9
% 0.07/0.37 % new_bool_1 with pid 618594 completed with status 9
% 0.07/0.37 % sh5l with pid 618595 completed with status 0
% 0.07/0.37 % Result found by sh5l
% 0.07/0.37 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.07/0.37 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.37 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.07/0.37 % Starting new_bool_3 with 300s (1) cores
% 0.07/0.37 % Starting new_bool_1 with 300s (1) cores
% 0.07/0.37 % Starting sh5l with 300s (1) cores
% 0.07/0.37 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.07/0.37 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.07/0.37 % Search class: FGUNF-FFSS00-SFFFFFNN
% 0.07/0.37 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.37 % Starting SubtermCWHack with 31s (1) cores
% 0.07/0.37 % SubtermCWHack with pid 618602 completed with status 0
% 0.07/0.37 % Result found by SubtermCWHack
% 0.07/0.37 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.07/0.37 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.37 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.07/0.37 % Starting new_bool_3 with 300s (1) cores
% 0.07/0.37 % Starting new_bool_1 with 300s (1) cores
% 0.07/0.37 % Starting sh5l with 300s (1) cores
% 0.07/0.37 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.07/0.37 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.07/0.37 % Search class: FGUNF-FFSS00-SFFFFFNN
% 0.07/0.37 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.37 % Starting SubtermCWHack with 31s (1) cores
% 0.07/0.37 % Preprocessing time : 0.001 s
% 0.07/0.37
% 0.07/0.37 % Proof found!
% 0.07/0.37 % SZS status Theorem
% 0.07/0.37 % SZS output start CNFRefutation
% See solution above
% 0.07/0.37 % Parsed axioms : 6
% 0.07/0.37 % Removed by relevancy pruning/SinE : 0
% 0.07/0.37 % Initial clauses : 10
% 0.07/0.37 % Removed in clause preprocessing : 0
% 0.07/0.37 % Initial clauses in saturation : 10
% 0.07/0.37 % Processed clauses : 584
% 0.07/0.37 % ...of these trivial : 0
% 0.07/0.37 % ...subsumed : 185
% 0.07/0.37 % ...remaining for further processing : 399
% 0.07/0.37 % Other redundant clauses eliminated : 0
% 0.07/0.37 % Clauses deleted for lack of memory : 0
% 0.07/0.37 % Backward-subsumed : 199
% 0.07/0.37 % Backward-rewritten : 84
% 0.07/0.37 % Generated clauses : 1684
% 0.07/0.37 % ...of the previous two non-redundant : 1496
% 0.07/0.37 % ...aggressively subsumed : 0
% 0.07/0.37 % Contextual simplify-reflections : 73
% 0.07/0.37 % Paramodulations : 1684
% 0.07/0.37 % Factorizations : 0
% 0.07/0.37 % NegExts : 0
% 0.07/0.37 % Equation resolutions : 0
% 0.07/0.37 % Disequality decompositions : 0
% 0.07/0.37 % Total rewrite steps : 100
% 0.07/0.37 % ...of those cached : 96
% 0.07/0.37 % Propositional unsat checks : 0
% 0.07/0.37 % Propositional check models : 0
% 0.07/0.37 % Propositional check unsatisfiable : 0
% 0.07/0.37 % Propositional clauses : 0
% 0.07/0.37 % Propositional clauses after purity: 0
% 0.07/0.37 % Propositional unsat core size : 0
% 0.07/0.37 % Propositional preprocessing time : 0.000
% 0.07/0.37 % Propositional encoding time : 0.000
% 0.07/0.37 % Propositional solver time : 0.000
% 0.07/0.37 % Success case prop preproc time : 0.000
% 0.07/0.37 % Success case prop encoding time : 0.000
% 0.07/0.37 % Success case prop solver time : 0.000
% 0.07/0.37 % Current number of processed clauses : 116
% 0.07/0.37 % Positive orientable unit clauses : 9
% 0.07/0.37 % Positive unorientable unit clauses: 0
% 0.07/0.37 % Negative unit clauses : 3
% 0.07/0.37 % Non-unit-clauses : 104
% 0.07/0.37 % Current number of unprocessed clauses: 749
% 0.07/0.37 % ...number of literals in the above : 4297
% 0.07/0.37 % Current number of archived formulas : 0
% 0.07/0.37 % Current number of archived clauses : 283
% 0.07/0.37 % Clause-clause subsumption calls (NU) : 8904
% 0.07/0.37 % Rec. Clause-clause subsumption calls : 2502
% 0.07/0.37 % Non-unit clause-clause subsumptions : 445
% 0.07/0.37 % Unit Clause-clause subsumption calls : 163
% 0.07/0.37 % Rewrite failures with RHS unbound : 0
% 0.07/0.37 % BW rewrite match attempts : 4
% 0.07/0.37 % BW rewrite match successes : 4
% 0.07/0.37 % Condensation attempts : 0
% 0.07/0.37 % Condensation successes : 0
% 0.07/0.37 % Termbank termtop insertions : 24733
% 0.07/0.37 % Search garbage collected termcells : 88
% 0.07/0.37
% 0.07/0.37 % -------------------------------------------------
% 0.07/0.37 % User time : 0.031 s
% 0.07/0.37 % System time : 0.000 s
% 0.07/0.37 % Total time : 0.031 s
% 0.07/0.37 % Maximum resident set size: 3632 pages
% 0.07/0.37
% 0.07/0.37 % -------------------------------------------------
% 0.07/0.37 % User time : 0.052 s
% 0.07/0.37 % System time : 0.017 s
% 0.07/0.37 % Total time : 0.069 s
% 0.07/0.37 % Maximum resident set size: 4608 pages
% 0.07/0.37 % E exiting
%------------------------------------------------------------------------------