%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUN085+1 : TPTP v9.2.1. Released v7.3.0.
% 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 : n024.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 05:00:53 PM UTC 2026
% Result : Theorem 14.24s 8.83s
% Output : CNFRefutation 14.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of formulae : 164 ( 41 unt; 0 def)
% Number of atoms : 467 ( 0 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 555 ( 252 ~; 239 |; 64 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 6 con; 0-2 aty)
% Number of variables : 301 ( 20 sgn 110 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_6,axiom,
! [X15,X16] :
( ~ id(X15,X16)
| id(X16,X15) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_6) ).
fof(zeroplusoneidzero,conjecture,
! [X63] :
( ! [X46] :
( ! [X47] :
( ~ r1(X47)
| ~ r3(X47,X46,X63) )
| ! [X40] :
( ~ r1(X40)
| ~ r2(X40,X46) ) )
| ! [X41] :
( ~ id(X63,X41)
| ~ r1(X41) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zeroplusoneidzero) ).
fof(axiom_2,axiom,
! [X3] :
? [X4] :
! [X5] :
( ( id(X5,X4)
& r2(X3,X5) )
| ( ~ r2(X3,X5)
& ~ id(X5,X4) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_2) ).
fof(axiom_1,axiom,
? [X1] :
! [X2] :
( ( id(X2,X1)
& r1(X2) )
| ( ~ r1(X2)
& ~ id(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_1) ).
fof(axiom_8,axiom,
! [X20,X21] :
( ~ id(X20,X21)
| ( ~ r1(X20)
& ~ r1(X21) )
| ( r1(X20)
& r1(X21) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_8) ).
fof(axiom_3,axiom,
! [X6,X7] :
? [X8] :
! [X9] :
( ( id(X9,X8)
& r3(X6,X7,X9) )
| ( ~ r3(X6,X7,X9)
& ~ id(X9,X8) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_3) ).
fof(axiom_7a,axiom,
! [X65,X66] :
( ! [X67] :
( ~ id(X67,X66)
| ~ r1(X67) )
| ~ r2(X65,X66) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_7a) ).
fof(axiom_5,axiom,
! [X14] : id(X14,X14),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_5) ).
fof(axiom_9,axiom,
! [X22,X23,X24,X25] :
( ~ id(X22,X24)
| ~ id(X23,X25)
| ( ~ r2(X22,X23)
& ~ r2(X24,X25) )
| ( r2(X22,X23)
& r2(X24,X25) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_9) ).
fof(axiom_7,axiom,
! [X17,X18,X19] :
( ~ id(X17,X18)
| id(X17,X19)
| ~ id(X18,X19) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_7) ).
fof(axiom_4a,axiom,
! [X54] :
? [X55] :
( id(X55,X54)
& ? [X56] :
( r1(X56)
& r3(X54,X56,X55) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_4a) ).
fof(axiom_10,axiom,
! [X26,X27,X28,X29,X30,X31] :
( ~ id(X26,X29)
| ~ id(X27,X30)
| ~ id(X28,X31)
| ( ~ r3(X26,X27,X28)
& ~ r3(X29,X30,X31) )
| ( r3(X26,X27,X28)
& r3(X29,X30,X31) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_10) ).
fof(axiom_6a,axiom,
! [X61] :
( ? [X62] :
( id(X61,X62)
& r1(X62) )
| ? [X63,X64] :
( id(X61,X64)
& r2(X63,X64) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_6a) ).
fof(axiom_3a,axiom,
! [X50,X51] :
( ! [X52] :
( ! [X53] :
( ~ id(X53,X52)
| ~ r2(X50,X53) )
| ~ r2(X51,X52) )
| id(X50,X51) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_3a) ).
fof(axiom_1a,axiom,
! [X38,X39] :
? [X40] :
( ? [X41] :
( id(X41,X40)
& ? [X42] :
( r2(X39,X42)
& r3(X38,X42,X41) ) )
& ? [X43] :
( r2(X43,X40)
& r3(X38,X39,X43) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_1a) ).
fof(c_0_15,plain,
! [X15,X16] :
( ~ id(X15,X16)
| id(X16,X15) ),
inference(fof_simplification,[status(thm)],[axiom_6]) ).
fof(c_0_16,negated_conjecture,
~ ! [X63] :
( ! [X46] :
( ! [X47] :
( ~ r1(X47)
| ~ r3(X47,X46,X63) )
| ! [X40] :
( ~ r1(X40)
| ~ r2(X40,X46) ) )
| ! [X41] :
( ~ id(X63,X41)
| ~ r1(X41) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[zeroplusoneidzero])]) ).
fof(c_0_17,plain,
! [X3] :
? [X4] :
! [X5] :
( ( id(X5,X4)
& r2(X3,X5) )
| ( ~ r2(X3,X5)
& ~ id(X5,X4) ) ),
inference(fof_simplification,[status(thm)],[axiom_2]) ).
fof(c_0_18,plain,
? [X1] :
! [X2] :
( ( id(X2,X1)
& r1(X2) )
| ( ~ r1(X2)
& ~ id(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[axiom_1]) ).
fof(c_0_19,plain,
! [X20,X21] :
( ~ id(X20,X21)
| ( ~ r1(X20)
& ~ r1(X21) )
| ( r1(X20)
& r1(X21) ) ),
inference(fof_simplification,[status(thm)],[axiom_8]) ).
fof(c_0_20,plain,
! [X6,X7] :
? [X8] :
! [X9] :
( ( id(X9,X8)
& r3(X6,X7,X9) )
| ( ~ r3(X6,X7,X9)
& ~ id(X9,X8) ) ),
inference(fof_simplification,[status(thm)],[axiom_3]) ).
fof(c_0_21,plain,
! [X154,X155] :
( ~ id(X154,X155)
| id(X155,X154) ),
inference(variable_rename,[status(thm)],[c_0_15]) ).
fof(c_0_22,negated_conjecture,
( r1(esk23_0)
& r3(esk23_0,esk22_0,esk21_0)
& r1(esk24_0)
& r2(esk24_0,esk22_0)
& id(esk21_0,esk25_0)
& r1(esk25_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
fof(c_0_23,plain,
! [X65,X66] :
( ! [X67] :
( ~ id(X67,X66)
| ~ r1(X67) )
| ~ r2(X65,X66) ),
inference(fof_simplification,[status(thm)],[axiom_7a]) ).
fof(c_0_24,plain,
! [X142,X144] :
( ( ~ r2(X142,X144)
| id(X144,esk2_1(X142)) )
& ( ~ id(X144,esk2_1(X142))
| id(X144,esk2_1(X142)) )
& ( ~ r2(X142,X144)
| r2(X142,X144) )
& ( ~ id(X144,esk2_1(X142))
| r2(X142,X144) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_17])])]) ).
fof(c_0_25,plain,
! [X153] : id(X153,X153),
inference(variable_rename,[status(thm)],[axiom_5]) ).
fof(c_0_26,plain,
! [X141] :
( ( ~ r1(X141)
| id(X141,esk1_0) )
& ( ~ id(X141,esk1_0)
| id(X141,esk1_0) )
& ( ~ r1(X141)
| r1(X141) )
& ( ~ id(X141,esk1_0)
| r1(X141) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_18])])]) ).
fof(c_0_27,plain,
! [X159,X160] :
( ( r1(X159)
| ~ r1(X159)
| ~ id(X159,X160) )
& ( r1(X160)
| ~ r1(X159)
| ~ id(X159,X160) )
& ( r1(X159)
| ~ r1(X160)
| ~ id(X159,X160) )
& ( r1(X160)
| ~ r1(X160)
| ~ id(X159,X160) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_19])]) ).
fof(c_0_28,plain,
! [X145,X146,X148] :
( ( ~ r3(X145,X146,X148)
| id(X148,esk3_2(X145,X146)) )
& ( ~ id(X148,esk3_2(X145,X146))
| id(X148,esk3_2(X145,X146)) )
& ( ~ r3(X145,X146,X148)
| r3(X145,X146,X148) )
& ( ~ id(X148,esk3_2(X145,X146))
| r3(X145,X146,X148) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_20])])]) ).
cnf(c_0_29,plain,
( id(X2,X1)
| ~ id(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,negated_conjecture,
id(esk21_0,esk25_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_31,plain,
! [X204,X205,X206] :
( ~ id(X206,X205)
| ~ r1(X206)
| ~ r2(X204,X205) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_23])]) ).
cnf(c_0_32,plain,
( r2(X2,X1)
| ~ id(X1,esk2_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,plain,
id(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_34,plain,
! [X22,X23,X24,X25] :
( ~ id(X22,X24)
| ~ id(X23,X25)
| ( ~ r2(X22,X23)
& ~ r2(X24,X25) )
| ( r2(X22,X23)
& r2(X24,X25) ) ),
inference(fof_simplification,[status(thm)],[axiom_9]) ).
fof(c_0_35,plain,
! [X17,X18,X19] :
( ~ id(X17,X18)
| id(X17,X19)
| ~ id(X18,X19) ),
inference(fof_simplification,[status(thm)],[axiom_7]) ).
cnf(c_0_36,plain,
( id(X1,esk1_0)
| ~ r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_37,negated_conjecture,
r1(esk24_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_38,plain,
( r1(X1)
| ~ r1(X2)
| ~ id(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_39,plain,
( id(X3,esk3_2(X1,X2))
| ~ r3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_40,negated_conjecture,
id(esk25_0,esk21_0),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_41,negated_conjecture,
r1(esk25_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_42,plain,
( ~ id(X1,X2)
| ~ r1(X1)
| ~ r2(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_43,plain,
r2(X1,esk2_1(X1)),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
fof(c_0_44,plain,
! [X161,X162,X163,X164] :
( ( r2(X161,X162)
| ~ r2(X161,X162)
| ~ id(X161,X163)
| ~ id(X162,X164) )
& ( r2(X163,X164)
| ~ r2(X161,X162)
| ~ id(X161,X163)
| ~ id(X162,X164) )
& ( r2(X161,X162)
| ~ r2(X163,X164)
| ~ id(X161,X163)
| ~ id(X162,X164) )
& ( r2(X163,X164)
| ~ r2(X163,X164)
| ~ id(X161,X163)
| ~ id(X162,X164) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_34])]) ).
fof(c_0_45,plain,
! [X193] :
( id(esk13_1(X193),X193)
& r1(esk14_1(X193))
& r3(X193,esk14_1(X193),esk13_1(X193)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_4a])]) ).
fof(c_0_46,plain,
! [X26,X27,X28,X29,X30,X31] :
( ~ id(X26,X29)
| ~ id(X27,X30)
| ~ id(X28,X31)
| ( ~ r3(X26,X27,X28)
& ~ r3(X29,X30,X31) )
| ( r3(X26,X27,X28)
& r3(X29,X30,X31) ) ),
inference(fof_simplification,[status(thm)],[axiom_10]) ).
fof(c_0_47,plain,
! [X156,X157,X158] :
( ~ id(X156,X157)
| id(X156,X158)
| ~ id(X157,X158) ),
inference(variable_rename,[status(thm)],[c_0_35]) ).
cnf(c_0_48,negated_conjecture,
id(esk24_0,esk1_0),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_49,plain,
( r1(esk3_2(X1,X2))
| ~ r3(X1,X2,X3)
| ~ r1(X3) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_50,negated_conjecture,
r3(esk23_0,esk22_0,esk21_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_51,negated_conjecture,
r1(esk21_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_40]),c_0_41])]) ).
cnf(c_0_52,plain,
( ~ r1(X1)
| ~ id(X1,esk2_1(X2)) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_53,plain,
( id(X2,esk2_1(X1))
| ~ r2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_54,plain,
( r2(X1,X2)
| ~ r2(X3,X4)
| ~ id(X3,X1)
| ~ id(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_55,negated_conjecture,
r2(esk24_0,esk22_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_56,plain,
id(esk13_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_57,plain,
( r1(X1)
| ~ r1(X2)
| ~ id(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_58,plain,
! [X165,X166,X167,X168,X169,X170] :
( ( r3(X165,X166,X167)
| ~ r3(X165,X166,X167)
| ~ id(X165,X168)
| ~ id(X166,X169)
| ~ id(X167,X170) )
& ( r3(X168,X169,X170)
| ~ r3(X165,X166,X167)
| ~ id(X165,X168)
| ~ id(X166,X169)
| ~ id(X167,X170) )
& ( r3(X165,X166,X167)
| ~ r3(X168,X169,X170)
| ~ id(X165,X168)
| ~ id(X166,X169)
| ~ id(X167,X170) )
& ( r3(X168,X169,X170)
| ~ r3(X168,X169,X170)
| ~ id(X165,X168)
| ~ id(X166,X169)
| ~ id(X167,X170) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_46])]) ).
cnf(c_0_59,negated_conjecture,
id(esk25_0,esk1_0),
inference(spm,[status(thm)],[c_0_36,c_0_41]) ).
cnf(c_0_60,plain,
( id(X1,X3)
| ~ id(X1,X2)
| ~ id(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_61,negated_conjecture,
id(esk1_0,esk24_0),
inference(spm,[status(thm)],[c_0_29,c_0_48]) ).
cnf(c_0_62,negated_conjecture,
r1(esk3_2(esk23_0,esk22_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51])]) ).
fof(c_0_63,plain,
! [X200] :
( ( id(X200,esk20_1(X200))
| id(X200,esk18_1(X200)) )
& ( r2(esk19_1(X200),esk20_1(X200))
| id(X200,esk18_1(X200)) )
& ( id(X200,esk20_1(X200))
| r1(esk18_1(X200)) )
& ( r2(esk19_1(X200),esk20_1(X200))
| r1(esk18_1(X200)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_6a])])]) ).
cnf(c_0_64,plain,
( ~ r2(X1,X2)
| ~ r1(X2) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_65,negated_conjecture,
( r2(X1,X2)
| ~ id(esk22_0,X2)
| ~ id(esk24_0,X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_66,plain,
id(X1,esk13_1(X1)),
inference(spm,[status(thm)],[c_0_29,c_0_56]) ).
cnf(c_0_67,plain,
( r1(X1)
| ~ r3(X2,X3,X1)
| ~ r1(esk3_2(X2,X3)) ),
inference(spm,[status(thm)],[c_0_57,c_0_39]) ).
cnf(c_0_68,plain,
( r3(X1,X2,X3)
| ~ r3(X4,X5,X6)
| ~ id(X4,X1)
| ~ id(X5,X2)
| ~ id(X6,X3) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_69,negated_conjecture,
id(esk1_0,esk25_0),
inference(spm,[status(thm)],[c_0_29,c_0_59]) ).
cnf(c_0_70,negated_conjecture,
( id(X1,esk24_0)
| ~ id(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_71,negated_conjecture,
id(esk3_2(esk23_0,esk22_0),esk1_0),
inference(spm,[status(thm)],[c_0_36,c_0_62]) ).
fof(c_0_72,plain,
! [X50,X51] :
( ! [X52] :
( ! [X53] :
( ~ id(X53,X52)
| ~ r2(X50,X53) )
| ~ r2(X51,X52) )
| id(X50,X51) ),
inference(fof_simplification,[status(thm)],[axiom_3a]) ).
cnf(c_0_73,plain,
( r2(esk19_1(X1),esk20_1(X1))
| r1(esk18_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_74,negated_conjecture,
( ~ r1(X1)
| ~ id(esk22_0,X1)
| ~ id(esk24_0,X2) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_75,plain,
( id(X1,esk13_1(X2))
| ~ id(X1,X2) ),
inference(spm,[status(thm)],[c_0_60,c_0_66]) ).
cnf(c_0_76,negated_conjecture,
( r1(X1)
| ~ r3(esk23_0,esk22_0,X1) ),
inference(spm,[status(thm)],[c_0_67,c_0_62]) ).
cnf(c_0_77,negated_conjecture,
( r3(X1,X2,X3)
| ~ id(esk21_0,X3)
| ~ id(esk22_0,X2)
| ~ id(esk23_0,X1) ),
inference(spm,[status(thm)],[c_0_68,c_0_50]) ).
cnf(c_0_78,negated_conjecture,
( id(X1,esk25_0)
| ~ id(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_60,c_0_69]) ).
cnf(c_0_79,negated_conjecture,
id(esk3_2(esk23_0,esk22_0),esk24_0),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
fof(c_0_80,plain,
! [X189,X190,X191,X192] :
( ~ id(X192,X191)
| ~ r2(X189,X192)
| ~ r2(X190,X191)
| id(X189,X190) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_72])]) ).
cnf(c_0_81,plain,
( r1(esk18_1(X1))
| ~ r1(X2)
| ~ id(X2,esk20_1(X1)) ),
inference(spm,[status(thm)],[c_0_42,c_0_73]) ).
cnf(c_0_82,plain,
( id(X1,esk20_1(X1))
| r1(esk18_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_83,negated_conjecture,
( ~ r1(esk13_1(X1))
| ~ id(esk24_0,X2)
| ~ id(esk22_0,X1) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_84,negated_conjecture,
( r1(X1)
| ~ id(esk21_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_33]),c_0_33])]) ).
cnf(c_0_85,negated_conjecture,
id(esk3_2(esk23_0,esk22_0),esk25_0),
inference(spm,[status(thm)],[c_0_78,c_0_71]) ).
cnf(c_0_86,plain,
( r3(X2,X3,X1)
| ~ id(X1,esk3_2(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_87,negated_conjecture,
id(esk24_0,esk3_2(esk23_0,esk22_0)),
inference(spm,[status(thm)],[c_0_29,c_0_79]) ).
cnf(c_0_88,plain,
( id(X3,X4)
| ~ id(X1,X2)
| ~ r2(X3,X1)
| ~ r2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
fof(c_0_89,plain,
! [X177,X178] :
( id(esk6_2(X177,X178),esk5_2(X177,X178))
& r2(X178,esk7_2(X177,X178))
& r3(X177,esk7_2(X177,X178),esk6_2(X177,X178))
& r2(esk8_2(X177,X178),esk5_2(X177,X178))
& r3(X177,X178,esk8_2(X177,X178)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_1a])]) ).
cnf(c_0_90,negated_conjecture,
r1(esk23_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_91,plain,
( r1(esk18_1(X1))
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_92,plain,
( r2(esk19_1(X1),esk20_1(X1))
| id(X1,esk18_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_93,negated_conjecture,
( ~ id(esk21_0,esk13_1(X1))
| ~ id(esk24_0,X2)
| ~ id(esk22_0,X1) ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_94,negated_conjecture,
id(esk24_0,esk25_0),
inference(spm,[status(thm)],[c_0_78,c_0_48]) ).
cnf(c_0_95,plain,
( r1(esk13_1(X1))
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_56]) ).
cnf(c_0_96,negated_conjecture,
( id(X1,esk25_0)
| ~ id(X1,esk3_2(esk23_0,esk22_0)) ),
inference(spm,[status(thm)],[c_0_60,c_0_85]) ).
cnf(c_0_97,negated_conjecture,
r3(esk23_0,esk22_0,esk24_0),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_98,plain,
( r1(esk18_1(X1))
| id(X2,esk19_1(X1))
| ~ r2(X2,X3)
| ~ id(X3,esk20_1(X1)) ),
inference(spm,[status(thm)],[c_0_88,c_0_73]) ).
cnf(c_0_99,plain,
id(esk6_2(X1,X2),esk5_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_100,plain,
r2(esk8_2(X1,X2),esk5_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_101,negated_conjecture,
( id(X1,esk21_0)
| ~ id(X1,esk25_0) ),
inference(spm,[status(thm)],[c_0_60,c_0_40]) ).
cnf(c_0_102,negated_conjecture,
id(esk23_0,esk1_0),
inference(spm,[status(thm)],[c_0_36,c_0_90]) ).
cnf(c_0_103,plain,
( id(esk18_1(X1),esk1_0)
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_91]) ).
cnf(c_0_104,plain,
( id(X1,esk20_1(X1))
| id(X1,esk18_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_105,plain,
( id(X1,esk18_1(X1))
| ~ r1(esk20_1(X1)) ),
inference(spm,[status(thm)],[c_0_64,c_0_92]) ).
cnf(c_0_106,negated_conjecture,
( ~ id(esk24_0,X1)
| ~ id(esk22_0,X2)
| ~ id(esk21_0,X2) ),
inference(spm,[status(thm)],[c_0_93,c_0_75]) ).
cnf(c_0_107,negated_conjecture,
( id(X1,esk25_0)
| ~ id(X1,esk24_0) ),
inference(spm,[status(thm)],[c_0_60,c_0_94]) ).
cnf(c_0_108,plain,
( id(esk13_1(X1),esk1_0)
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_95]) ).
cnf(c_0_109,negated_conjecture,
( id(X1,esk25_0)
| ~ r3(esk23_0,esk22_0,X1) ),
inference(spm,[status(thm)],[c_0_96,c_0_39]) ).
cnf(c_0_110,negated_conjecture,
( r3(X1,X2,X3)
| ~ id(esk24_0,X3)
| ~ id(esk22_0,X2)
| ~ id(esk23_0,X1) ),
inference(spm,[status(thm)],[c_0_68,c_0_97]) ).
cnf(c_0_111,plain,
( r1(esk18_1(X1))
| id(X2,esk19_1(X1))
| ~ r2(X2,X1) ),
inference(spm,[status(thm)],[c_0_98,c_0_82]) ).
cnf(c_0_112,plain,
( id(X1,esk5_2(X2,X3))
| ~ id(X1,esk6_2(X2,X3)) ),
inference(spm,[status(thm)],[c_0_60,c_0_99]) ).
cnf(c_0_113,plain,
~ r1(esk5_2(X1,X2)),
inference(spm,[status(thm)],[c_0_64,c_0_100]) ).
cnf(c_0_114,negated_conjecture,
( id(esk21_0,X1)
| ~ id(X1,esk25_0) ),
inference(spm,[status(thm)],[c_0_29,c_0_101]) ).
cnf(c_0_115,negated_conjecture,
id(esk23_0,esk25_0),
inference(spm,[status(thm)],[c_0_78,c_0_102]) ).
cnf(c_0_116,negated_conjecture,
( id(esk18_1(X1),esk25_0)
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_78,c_0_103]) ).
cnf(c_0_117,plain,
( id(X1,esk18_1(X1))
| ~ r1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_104]),c_0_105]) ).
cnf(c_0_118,negated_conjecture,
( id(X1,esk24_0)
| ~ r2(X1,X2)
| ~ id(X2,esk22_0) ),
inference(spm,[status(thm)],[c_0_88,c_0_55]) ).
cnf(c_0_119,negated_conjecture,
( ~ id(esk22_0,X1)
| ~ id(esk21_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_33])]) ).
cnf(c_0_120,negated_conjecture,
( id(esk13_1(X1),esk25_0)
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_78,c_0_108]) ).
cnf(c_0_121,plain,
( r2(X1,X2)
| r1(esk18_1(X3))
| ~ id(esk20_1(X3),X2)
| ~ id(esk19_1(X3),X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_73]) ).
cnf(c_0_122,plain,
( r1(esk18_1(X1))
| id(esk20_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_82]) ).
cnf(c_0_123,negated_conjecture,
( id(X1,esk25_0)
| ~ id(esk24_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_33]),c_0_33])]) ).
cnf(c_0_124,negated_conjecture,
( r1(esk18_1(esk22_0))
| id(esk24_0,esk19_1(esk22_0)) ),
inference(spm,[status(thm)],[c_0_111,c_0_55]) ).
cnf(c_0_125,plain,
( ~ r1(X1)
| ~ id(X1,esk6_2(X2,X3)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_112]),c_0_113]) ).
cnf(c_0_126,plain,
( id(esk3_2(X1,X2),X3)
| ~ r3(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_29,c_0_39]) ).
cnf(c_0_127,negated_conjecture,
id(esk21_0,esk23_0),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_128,negated_conjecture,
( id(X1,esk25_0)
| ~ r1(X2)
| ~ id(X1,esk18_1(X2)) ),
inference(spm,[status(thm)],[c_0_60,c_0_116]) ).
cnf(c_0_129,plain,
( id(X1,esk18_1(X2))
| ~ r1(X2)
| ~ id(X1,X2) ),
inference(spm,[status(thm)],[c_0_60,c_0_117]) ).
cnf(c_0_130,negated_conjecture,
( id(esk19_1(X1),esk24_0)
| id(X1,esk18_1(X1))
| ~ id(esk20_1(X1),esk22_0) ),
inference(spm,[status(thm)],[c_0_118,c_0_92]) ).
cnf(c_0_131,plain,
( id(X1,esk18_1(X1))
| id(esk20_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_104]) ).
cnf(c_0_132,negated_conjecture,
( ~ id(esk21_0,esk13_1(X1))
| ~ id(esk22_0,X1) ),
inference(spm,[status(thm)],[c_0_119,c_0_75]) ).
cnf(c_0_133,negated_conjecture,
( id(esk21_0,esk13_1(X1))
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_114,c_0_120]) ).
cnf(c_0_134,plain,
( r2(X1,X2)
| r1(esk18_1(X2))
| ~ id(esk19_1(X2),X1) ),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_135,negated_conjecture,
( r1(esk18_1(esk22_0))
| id(esk19_1(esk22_0),esk25_0) ),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_136,plain,
( ~ r3(X1,X2,esk6_2(X3,X4))
| ~ r1(esk3_2(X1,X2)) ),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_137,plain,
r3(X1,esk7_2(X1,X2),esk6_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_138,negated_conjecture,
( id(X1,esk23_0)
| ~ id(X1,esk21_0) ),
inference(spm,[status(thm)],[c_0_60,c_0_127]) ).
cnf(c_0_139,plain,
( id(esk2_1(X1),X2)
| ~ r2(X1,X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_53]) ).
cnf(c_0_140,plain,
( r2(X1,X2)
| id(X3,esk18_1(X3))
| ~ id(esk20_1(X3),X2)
| ~ id(esk19_1(X3),X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_92]) ).
cnf(c_0_141,negated_conjecture,
( id(X1,esk25_0)
| ~ r1(X2)
| ~ id(X1,X2) ),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_142,negated_conjecture,
( id(esk22_0,esk18_1(esk22_0))
| id(esk19_1(esk22_0),esk24_0) ),
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_143,negated_conjecture,
( ~ r1(X1)
| ~ id(esk22_0,X1) ),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_144,negated_conjecture,
( r2(esk25_0,esk22_0)
| r1(esk18_1(esk22_0)) ),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_145,plain,
~ r1(esk3_2(X1,esk7_2(X1,X2))),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_146,negated_conjecture,
( r1(X1)
| ~ id(X1,esk21_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_138]),c_0_90])]) ).
cnf(c_0_147,plain,
( id(X1,X2)
| ~ r2(X3,X2)
| ~ id(X1,esk2_1(X3)) ),
inference(spm,[status(thm)],[c_0_60,c_0_139]) ).
cnf(c_0_148,plain,
( r2(X1,X2)
| id(X2,esk18_1(X2))
| ~ id(esk19_1(X2),X1) ),
inference(spm,[status(thm)],[c_0_140,c_0_131]) ).
cnf(c_0_149,negated_conjecture,
( id(esk22_0,esk18_1(esk22_0))
| id(esk19_1(esk22_0),esk25_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_37])]) ).
cnf(c_0_150,negated_conjecture,
( r2(esk25_0,esk22_0)
| ~ id(esk22_0,esk18_1(esk22_0)) ),
inference(spm,[status(thm)],[c_0_143,c_0_144]) ).
cnf(c_0_151,negated_conjecture,
~ id(esk3_2(X1,esk7_2(X1,X2)),esk21_0),
inference(spm,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_152,plain,
( r3(X1,X2,X3)
| ~ r3(X4,X5,X6)
| ~ id(X1,X4)
| ~ id(X2,X5)
| ~ id(X3,X6) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_153,plain,
( id(X1,X2)
| ~ r2(X3,X2)
| ~ r2(X3,X1) ),
inference(spm,[status(thm)],[c_0_147,c_0_53]) ).
cnf(c_0_154,negated_conjecture,
r2(esk25_0,esk22_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_150]) ).
cnf(c_0_155,negated_conjecture,
~ r3(X1,esk7_2(X1,X2),esk21_0),
inference(spm,[status(thm)],[c_0_151,c_0_126]) ).
cnf(c_0_156,negated_conjecture,
( r3(X1,X2,X3)
| ~ id(X3,esk21_0)
| ~ id(X2,esk22_0)
| ~ id(X1,esk23_0) ),
inference(spm,[status(thm)],[c_0_152,c_0_50]) ).
cnf(c_0_157,negated_conjecture,
( id(X1,esk22_0)
| ~ r2(esk25_0,X1) ),
inference(spm,[status(thm)],[c_0_153,c_0_154]) ).
cnf(c_0_158,plain,
r2(X1,esk7_2(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_159,negated_conjecture,
( ~ id(esk7_2(X1,X2),esk22_0)
| ~ id(X1,esk23_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_33])]) ).
cnf(c_0_160,negated_conjecture,
id(esk7_2(X1,esk25_0),esk22_0),
inference(spm,[status(thm)],[c_0_157,c_0_158]) ).
cnf(c_0_161,negated_conjecture,
id(esk1_0,esk23_0),
inference(spm,[status(thm)],[c_0_29,c_0_102]) ).
cnf(c_0_162,negated_conjecture,
~ id(X1,esk23_0),
inference(spm,[status(thm)],[c_0_159,c_0_160]) ).
cnf(c_0_163,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_161,c_0_162]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : NUN085+1 : TPTP v9.2.1. Released v7.3.0.
% 0.00/0.09 % 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
% 0.08/0.27 % Computer : n024.cluster.edu
% 0.08/0.27 % Model : x86_64 x86_64
% 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27 % Memory : 8042.1875MB
% 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27 % CPULimit : 300
% 0.08/0.27 % WCLimit : 300
% 0.08/0.27 % DateTime : Mon May 4 20:23:42 EDT 2026
% 0.08/0.27 % CPUTime :
% 0.08/0.28 % start to proof: theBenchmark
% 14.24/8.83 % Version : CSE_E---1.7
% 14.24/8.83 % Problem : theBenchmark.p
% 14.24/8.83 % SZS status Theorem for theBenchmark.p
% 14.24/8.83 % SZS output start CNFRefutation
% See solution above
% 14.33/8.90 % Total time : 6.368s
%------------------------------------------------------------------------------