%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUN080+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 : n012.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 05:00:52 PM UTC 2026
% Result : Theorem 0.12s 1.52s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 19
% Syntax : Number of formulae : 163 ( 62 unt; 0 def)
% Number of atoms : 492 ( 0 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 585 ( 256 ~; 234 |; 95 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 1 con; 0-2 aty)
% Number of variables : 408 ( 24 sgn 139 !; 36 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_11,axiom,
! [X32,X33,X34,X35,X36,X37] :
( ~ id(X32,X35)
| ~ id(X33,X36)
| ~ id(X34,X37)
| ( ~ r4(X32,X33,X34)
& ~ r4(X35,X36,X37) )
| ( r4(X32,X33,X34)
& r4(X35,X36,X37) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_11) ).
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(xplustwoidy,conjecture,
? [X63,X46,X47] :
( id(X47,X46)
& ? [X40] :
( r3(X63,X40,X47)
& ? [X41] :
( r2(X41,X40)
& ? [X49] :
( r1(X49)
& r2(X49,X41) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xplustwoidy) ).
fof(axiom_4,axiom,
! [X10,X11] :
? [X12] :
! [X13] :
( ( id(X13,X12)
& r4(X10,X11,X13) )
| ( ~ r4(X10,X11,X13)
& ~ id(X13,X12) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_4) ).
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_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_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_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_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_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_6,axiom,
! [X15,X16] :
( ~ id(X15,X16)
| id(X16,X15) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_6) ).
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_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_2a,axiom,
! [X44,X45] :
? [X46] :
( ? [X47] :
( id(X47,X46)
& ? [X48] :
( r2(X45,X48)
& r4(X44,X48,X47) ) )
& ? [X49] :
( r3(X49,X44,X46)
& r4(X44,X45,X49) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_2a) ).
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(axiom_5a,axiom,
! [X57] :
? [X58] :
( ? [X59] :
( r1(X59)
& r4(X57,X59,X58) )
& ? [X60] :
( id(X58,X60)
& r1(X60) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_5a) ).
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_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_5,axiom,
! [X14] : id(X14,X14),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_5) ).
fof(i_0_19,plain,
! [X32,X33,X34,X35,X36,X37] :
( ~ id(X32,X35)
| ~ id(X33,X36)
| ~ id(X34,X37)
| ( ~ r4(X32,X33,X34)
& ~ r4(X35,X36,X37) )
| ( r4(X32,X33,X34)
& r4(X35,X36,X37) ) ),
inference(fof_simplification,[status(thm)],[axiom_11]) ).
fof(i_0_20,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(i_0_21,negated_conjecture,
~ ? [X63,X46,X47] :
( id(X47,X46)
& ? [X40] :
( r3(X63,X40,X47)
& ? [X41] :
( r2(X41,X40)
& ? [X49] :
( r1(X49)
& r2(X49,X41) ) ) ) ),
inference(assume_negation,[status(cth)],[xplustwoidy]) ).
fof(i_0_22,plain,
! [X10,X11] :
? [X12] :
! [X13] :
( ( id(X13,X12)
& r4(X10,X11,X13) )
| ( ~ r4(X10,X11,X13)
& ~ id(X13,X12) ) ),
inference(fof_simplification,[status(thm)],[axiom_4]) ).
fof(i_0_23,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(i_0_24,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(i_0_25,plain,
! [X50,X51] :
( ! [X52] :
( ! [X53] :
( ~ id(X53,X52)
| ~ r2(X50,X53) )
| ~ r2(X51,X52) )
| id(X50,X51) ),
inference(fof_simplification,[status(thm)],[axiom_3a]) ).
fof(i_0_26,plain,
! [X17,X18,X19] :
( ~ id(X17,X18)
| id(X17,X19)
| ~ id(X18,X19) ),
inference(fof_simplification,[status(thm)],[axiom_7]) ).
fof(i_0_27,plain,
! [X65,X66] :
( ! [X67] :
( ~ id(X67,X66)
| ~ r1(X67) )
| ~ r2(X65,X66) ),
inference(fof_simplification,[status(thm)],[axiom_7a]) ).
fof(i_0_28,plain,
! [X3] :
? [X4] :
! [X5] :
( ( id(X5,X4)
& r2(X3,X5) )
| ( ~ r2(X3,X5)
& ~ id(X5,X4) ) ),
inference(fof_simplification,[status(thm)],[axiom_2]) ).
fof(i_0_29,plain,
! [X15,X16] :
( ~ id(X15,X16)
| id(X16,X15) ),
inference(fof_simplification,[status(thm)],[axiom_6]) ).
fof(i_0_30,plain,
! [X20,X21] :
( ~ id(X20,X21)
| ( ~ r1(X20)
& ~ r1(X21) )
| ( r1(X20)
& r1(X21) ) ),
inference(fof_simplification,[status(thm)],[axiom_8]) ).
fof(i_0_31,plain,
? [X1] :
! [X2] :
( ( id(X2,X1)
& r1(X2) )
| ( ~ r1(X2)
& ~ id(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[axiom_1]) ).
fof(i_0_32,plain,
! [X172,X173,X174,X175,X176,X177] :
( ( r4(X172,X173,X174)
| ~ r4(X172,X173,X174)
| ~ id(X172,X175)
| ~ id(X173,X176)
| ~ id(X174,X177) )
& ( r4(X175,X176,X177)
| ~ r4(X172,X173,X174)
| ~ id(X172,X175)
| ~ id(X173,X176)
| ~ id(X174,X177) )
& ( r4(X172,X173,X174)
| ~ r4(X175,X176,X177)
| ~ id(X172,X175)
| ~ id(X173,X176)
| ~ id(X174,X177) )
& ( r4(X175,X176,X177)
| ~ r4(X175,X176,X177)
| ~ id(X172,X175)
| ~ id(X173,X176)
| ~ id(X174,X177) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[i_0_19])]) ).
fof(i_0_33,plain,
! [X166,X167,X168,X169,X170,X171] :
( ( r3(X166,X167,X168)
| ~ r3(X166,X167,X168)
| ~ id(X166,X169)
| ~ id(X167,X170)
| ~ id(X168,X171) )
& ( r3(X169,X170,X171)
| ~ r3(X166,X167,X168)
| ~ id(X166,X169)
| ~ id(X167,X170)
| ~ id(X168,X171) )
& ( r3(X166,X167,X168)
| ~ r3(X169,X170,X171)
| ~ id(X166,X169)
| ~ id(X167,X170)
| ~ id(X168,X171) )
& ( r3(X169,X170,X171)
| ~ r3(X169,X170,X171)
| ~ id(X166,X169)
| ~ id(X167,X170)
| ~ id(X168,X171) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[i_0_20])]) ).
fof(i_0_34,negated_conjecture,
! [X208,X209,X210,X211,X212,X213] :
( ~ id(X210,X209)
| ~ r3(X208,X211,X210)
| ~ r2(X212,X211)
| ~ r1(X213)
| ~ r2(X213,X212) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_21])])]) ).
fof(i_0_35,plain,
! [X150,X151,X153] :
( ( ~ r4(X150,X151,X153)
| id(X153,esk4_2(X150,X151)) )
& ( ~ id(X153,esk4_2(X150,X151))
| id(X153,esk4_2(X150,X151)) )
& ( ~ r4(X150,X151,X153)
| r4(X150,X151,X153) )
& ( ~ id(X153,esk4_2(X150,X151))
| r4(X150,X151,X153) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_22])])]) ).
fof(i_0_36,plain,
! [X146,X147,X149] :
( ( ~ r3(X146,X147,X149)
| id(X149,esk3_2(X146,X147)) )
& ( ~ id(X149,esk3_2(X146,X147))
| id(X149,esk3_2(X146,X147)) )
& ( ~ r3(X146,X147,X149)
| r3(X146,X147,X149) )
& ( ~ id(X149,esk3_2(X146,X147))
| r3(X146,X147,X149) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_23])])]) ).
fof(i_0_37,plain,
! [X184,X185] :
( id(esk10_2(X184,X185),esk9_2(X184,X185))
& r2(X185,esk11_2(X184,X185))
& r4(X184,esk11_2(X184,X185),esk10_2(X184,X185))
& r3(esk12_2(X184,X185),X184,esk9_2(X184,X185))
& r4(X184,X185,esk12_2(X184,X185)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_2a])]) ).
fof(i_0_38,plain,
! [X178,X179] :
( id(esk6_2(X178,X179),esk5_2(X178,X179))
& r2(X179,esk7_2(X178,X179))
& r3(X178,esk7_2(X178,X179),esk6_2(X178,X179))
& r2(esk8_2(X178,X179),esk5_2(X178,X179))
& r3(X178,X179,esk8_2(X178,X179)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_1a])]) ).
fof(i_0_39,plain,
! [X162,X163,X164,X165] :
( ( r2(X162,X163)
| ~ r2(X162,X163)
| ~ id(X162,X164)
| ~ id(X163,X165) )
& ( r2(X164,X165)
| ~ r2(X162,X163)
| ~ id(X162,X164)
| ~ id(X163,X165) )
& ( r2(X162,X163)
| ~ r2(X164,X165)
| ~ id(X162,X164)
| ~ id(X163,X165) )
& ( r2(X164,X165)
| ~ r2(X164,X165)
| ~ id(X162,X164)
| ~ id(X163,X165) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[i_0_24])]) ).
fof(i_0_40,plain,
! [X190,X191,X192,X193] :
( ~ id(X193,X192)
| ~ r2(X190,X193)
| ~ r2(X191,X192)
| id(X190,X191) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[i_0_25])]) ).
fof(i_0_41,plain,
! [X197] :
( r1(esk16_1(X197))
& r4(X197,esk16_1(X197),esk15_1(X197))
& id(esk15_1(X197),esk17_1(X197))
& r1(esk17_1(X197)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_5a])]) ).
fof(i_0_42,plain,
! [X194] :
( id(esk13_1(X194),X194)
& r1(esk14_1(X194))
& r3(X194,esk14_1(X194),esk13_1(X194)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_4a])]) ).
fof(i_0_43,plain,
! [X157,X158,X159] :
( ~ id(X157,X158)
| id(X157,X159)
| ~ id(X158,X159) ),
inference(variable_rename,[status(thm)],[i_0_26]) ).
fof(i_0_44,plain,
! [X205,X206,X207] :
( ~ id(X207,X206)
| ~ r1(X207)
| ~ r2(X205,X206) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[i_0_27])]) ).
fof(i_0_45,plain,
! [X201] :
( ( id(X201,esk20_1(X201))
| id(X201,esk18_1(X201)) )
& ( r2(esk19_1(X201),esk20_1(X201))
| id(X201,esk18_1(X201)) )
& ( id(X201,esk20_1(X201))
| r1(esk18_1(X201)) )
& ( r2(esk19_1(X201),esk20_1(X201))
| r1(esk18_1(X201)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_6a])])]) ).
fof(i_0_46,plain,
! [X143,X145] :
( ( ~ r2(X143,X145)
| id(X145,esk2_1(X143)) )
& ( ~ id(X145,esk2_1(X143))
| id(X145,esk2_1(X143)) )
& ( ~ r2(X143,X145)
| r2(X143,X145) )
& ( ~ id(X145,esk2_1(X143))
| r2(X143,X145) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_28])])]) ).
fof(i_0_47,plain,
! [X155,X156] :
( ~ id(X155,X156)
| id(X156,X155) ),
inference(variable_rename,[status(thm)],[i_0_29]) ).
fof(i_0_48,plain,
! [X160,X161] :
( ( r1(X160)
| ~ r1(X160)
| ~ id(X160,X161) )
& ( r1(X161)
| ~ r1(X160)
| ~ id(X160,X161) )
& ( r1(X160)
| ~ r1(X161)
| ~ id(X160,X161) )
& ( r1(X161)
| ~ r1(X161)
| ~ id(X160,X161) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[i_0_30])]) ).
fof(i_0_49,plain,
! [X142] :
( ( ~ r1(X142)
| id(X142,esk1_0) )
& ( ~ id(X142,esk1_0)
| id(X142,esk1_0) )
& ( ~ r1(X142)
| r1(X142) )
& ( ~ id(X142,esk1_0)
| r1(X142) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_31])])]) ).
fof(i_0_50,plain,
! [X154] : id(X154,X154),
inference(variable_rename,[status(thm)],[axiom_5]) ).
cnf(i_0_51,plain,
( r4(X1,X2,X3)
| ~ r4(X4,X5,X6)
| ~ id(X1,X4)
| ~ id(X2,X5)
| ~ id(X3,X6) ),
inference(split_conjunct,[status(thm)],[i_0_32]),
[final] ).
cnf(i_0_52,plain,
( r4(X1,X2,X3)
| ~ r4(X4,X5,X6)
| ~ id(X4,X1)
| ~ id(X5,X2)
| ~ id(X6,X3) ),
inference(split_conjunct,[status(thm)],[i_0_32]),
[final] ).
cnf(i_0_53,plain,
( r3(X1,X2,X3)
| ~ r3(X4,X5,X6)
| ~ id(X1,X4)
| ~ id(X2,X5)
| ~ id(X3,X6) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_54,plain,
( r3(X1,X2,X3)
| ~ r3(X4,X5,X6)
| ~ id(X4,X1)
| ~ id(X5,X2)
| ~ id(X6,X3) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_55,negated_conjecture,
( ~ id(X1,X2)
| ~ r3(X3,X4,X1)
| ~ r2(X5,X4)
| ~ r1(X6)
| ~ r2(X6,X5) ),
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_56,plain,
( id(X3,esk4_2(X1,X2))
| ~ r4(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_57,plain,
( id(X3,esk3_2(X1,X2))
| ~ r3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_36]),
[final] ).
cnf(i_0_58,plain,
( r4(X2,X3,X1)
| ~ id(X1,esk4_2(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_59,plain,
( r3(X2,X3,X1)
| ~ id(X1,esk3_2(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_36]),
[final] ).
cnf(i_0_60,plain,
r3(esk12_2(X1,X2),X1,esk9_2(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_61,plain,
r4(X1,esk11_2(X1,X2),esk10_2(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_62,plain,
r3(X1,esk7_2(X1,X2),esk6_2(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_63,plain,
( r2(X1,X2)
| ~ r2(X3,X4)
| ~ id(X1,X3)
| ~ id(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_39]),
[final] ).
cnf(i_0_64,plain,
( r2(X1,X2)
| ~ r2(X3,X4)
| ~ id(X3,X1)
| ~ id(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_39]),
[final] ).
cnf(i_0_65,plain,
( id(X3,X4)
| ~ id(X1,X2)
| ~ r2(X3,X1)
| ~ r2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_40]),
[final] ).
cnf(i_0_66,plain,
r4(X1,X2,esk12_2(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_67,plain,
r3(X1,X2,esk8_2(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_68,plain,
r4(X1,esk16_1(X1),esk15_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_69,plain,
r3(X1,esk14_1(X1),esk13_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_70,plain,
r2(esk8_2(X1,X2),esk5_2(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_71,plain,
id(esk10_2(X1,X2),esk9_2(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_72,plain,
id(esk6_2(X1,X2),esk5_2(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_73,plain,
( id(X1,X3)
| ~ id(X1,X2)
| ~ id(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_74,plain,
( ~ id(X1,X2)
| ~ r1(X1)
| ~ r2(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_75,plain,
( r2(esk19_1(X1),esk20_1(X1))
| id(X1,esk18_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_76,plain,
( r2(X2,X1)
| ~ id(X1,esk2_1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_77,plain,
( id(X2,esk2_1(X1))
| ~ r2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_78,plain,
( id(X1,esk20_1(X1))
| id(X1,esk18_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_79,plain,
r2(X1,esk11_2(X2,X1)),
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_80,plain,
r2(X1,esk7_2(X2,X1)),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_81,plain,
( r2(esk19_1(X1),esk20_1(X1))
| r1(esk18_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_82,plain,
( id(X2,X1)
| ~ id(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_83,plain,
( r1(X1)
| ~ r1(X2)
| ~ id(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_84,plain,
( r1(X1)
| ~ r1(X2)
| ~ id(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_85,plain,
( id(X1,esk20_1(X1))
| r1(esk18_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_86,plain,
id(esk15_1(X1),esk17_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_87,plain,
( r1(X1)
| ~ id(X1,esk1_0) ),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_88,plain,
id(esk13_1(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_89,plain,
( id(X1,esk1_0)
| ~ r1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_90,plain,
id(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_91,plain,
r1(esk17_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_92,plain,
r1(esk16_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_93,plain,
r1(esk14_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_94,plain,
r4(X1,X2,esk4_2(X1,X2)),
inference(scs_inference,[],[i_0_90,i_0_58]) ).
cnf(i_0_95,plain,
id(X1,X1),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_96,plain,
( ~ id(X1,esk4_2(X2,X3))
| r4(X2,X3,X1) ),
inference(rename_variables,[],[i_0_58]) ).
cnf(i_0_97,plain,
r3(X1,X2,esk3_2(X1,X2)),
inference(scs_inference,[],[i_0_90,i_0_95,i_0_58,i_0_59]) ).
cnf(i_0_98,plain,
id(X1,X1),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_99,plain,
( ~ id(X1,esk3_2(X2,X3))
| r3(X2,X3,X1) ),
inference(rename_variables,[],[i_0_59]) ).
cnf(i_0_100,plain,
r2(X1,esk2_1(X1)),
inference(scs_inference,[],[i_0_90,i_0_95,i_0_98,i_0_58,i_0_59,i_0_76]) ).
cnf(i_0_101,plain,
id(X1,X1),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_102,plain,
( ~ id(X1,esk2_1(X2))
| r2(X2,X1) ),
inference(rename_variables,[],[i_0_76]) ).
cnf(i_0_103,plain,
id(esk9_2(X1,X2),esk10_2(X1,X2)),
inference(scs_inference,[],[i_0_90,i_0_95,i_0_98,i_0_71,i_0_58,i_0_59,i_0_76,i_0_82]) ).
cnf(i_0_104,plain,
( ~ id(X1,X2)
| id(X2,X1) ),
inference(rename_variables,[],[i_0_82]) ).
cnf(i_0_105,plain,
r1(esk1_0),
inference(scs_inference,[],[i_0_90,i_0_95,i_0_98,i_0_101,i_0_71,i_0_58,i_0_59,i_0_76,i_0_82,i_0_87]) ).
cnf(i_0_106,plain,
id(X1,X1),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_107,plain,
( ~ id(X1,esk1_0)
| r1(X1) ),
inference(rename_variables,[],[i_0_87]) ).
cnf(i_0_108,plain,
~ r2(X1,esk17_1(X2)),
inference(scs_inference,[],[i_0_90,i_0_95,i_0_98,i_0_101,i_0_106,i_0_71,i_0_91,i_0_58,i_0_59,i_0_76,i_0_82,i_0_87,i_0_74]) ).
cnf(i_0_109,plain,
id(X1,X1),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_110,plain,
( ~ r1(X1)
| ~ id(X1,X2)
| ~ r2(X3,X2) ),
inference(rename_variables,[],[i_0_74]) ).
cnf(i_0_111,plain,
r1(esk15_1(X1)),
inference(scs_inference,[],[i_0_90,i_0_95,i_0_98,i_0_101,i_0_106,i_0_71,i_0_86,i_0_91,i_0_58,i_0_59,i_0_76,i_0_82,i_0_87,i_0_74,i_0_83]) ).
cnf(i_0_112,plain,
id(esk15_1(X1),esk17_1(X1)),
inference(rename_variables,[],[i_0_86]) ).
cnf(i_0_113,plain,
( ~ id(X1,X2)
| r1(X1)
| ~ r1(X2) ),
inference(rename_variables,[],[i_0_83]) ).
cnf(i_0_114,plain,
~ r2(esk15_1(X1),esk15_1(X1)),
inference(scs_inference,[],[i_0_90,i_0_95,i_0_98,i_0_101,i_0_106,i_0_71,i_0_86,i_0_112,i_0_91,i_0_58,i_0_59,i_0_76,i_0_82,i_0_87,i_0_74,i_0_83,i_0_64]) ).
cnf(i_0_115,plain,
id(esk15_1(X1),esk17_1(X1)),
inference(rename_variables,[],[i_0_86]) ).
cnf(i_0_116,plain,
( ~ id(X1,X2)
| ~ id(X3,X4)
| r2(X2,X4)
| ~ r2(X1,X3) ),
inference(rename_variables,[],[i_0_64]) ).
cnf(i_0_117,plain,
~ r1(esk8_2(X1,X2)),
inference(scs_inference,[],[i_0_60,i_0_90,i_0_95,i_0_98,i_0_101,i_0_106,i_0_109,i_0_70,i_0_71,i_0_86,i_0_112,i_0_79,i_0_91,i_0_58,i_0_59,i_0_76,i_0_82,i_0_87,i_0_74,i_0_83,i_0_64,i_0_55]) ).
cnf(i_0_118,plain,
id(X1,X1),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_119,plain,
r3(esk12_2(X1,X2),X1,esk9_2(X1,X2)),
inference(rename_variables,[],[i_0_60]) ).
cnf(i_0_120,plain,
r2(X1,esk11_2(X2,X1)),
inference(rename_variables,[],[i_0_79]) ).
cnf(i_0_121,plain,
( ~ r2(X1,X2)
| ~ id(X3,X4)
| ~ r3(X5,X6,X3)
| ~ r2(X2,X6)
| ~ r1(X1) ),
inference(rename_variables,[],[i_0_55]) ).
cnf(i_0_122,plain,
( r1(esk9_2(X1,X2))
| ~ r1(esk10_2(X1,X2)) ),
inference(scs_inference,[],[i_0_60,i_0_90,i_0_95,i_0_98,i_0_101,i_0_106,i_0_109,i_0_70,i_0_71,i_0_86,i_0_112,i_0_79,i_0_91,i_0_58,i_0_59,i_0_76,i_0_82,i_0_87,i_0_74,i_0_83,i_0_64,i_0_55,i_0_84]) ).
cnf(i_0_123,plain,
( ~ id(X1,X2)
| r1(X2)
| ~ r1(X1) ),
inference(rename_variables,[],[i_0_84]) ).
cnf(i_0_124,plain,
r2(esk13_1(esk8_2(X1,X2)),esk5_2(X1,X2)),
inference(scs_inference,[],[i_0_60,i_0_90,i_0_95,i_0_98,i_0_101,i_0_106,i_0_109,i_0_118,i_0_70,i_0_71,i_0_86,i_0_112,i_0_88,i_0_79,i_0_91,i_0_58,i_0_59,i_0_76,i_0_82,i_0_87,i_0_74,i_0_83,i_0_64,i_0_55,i_0_84,i_0_63]) ).
cnf(i_0_125,plain,
id(esk13_1(X1),X1),
inference(rename_variables,[],[i_0_88]) ).
cnf(i_0_126,plain,
id(X1,X1),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_127,plain,
( ~ id(X1,X2)
| ~ id(X3,X4)
| r2(X1,X3)
| ~ r2(X2,X4) ),
inference(rename_variables,[],[i_0_63]) ).
cnf(i_0_128,plain,
( id(X1,esk8_2(X2,X3))
| ~ id(esk11_2(X4,X1),esk5_2(X2,X3)) ),
inference(scs_inference,[],[i_0_60,i_0_90,i_0_95,i_0_98,i_0_101,i_0_106,i_0_109,i_0_118,i_0_70,i_0_71,i_0_86,i_0_112,i_0_88,i_0_79,i_0_120,i_0_91,i_0_58,i_0_59,i_0_76,i_0_82,i_0_87,i_0_74,i_0_83,i_0_64,i_0_55,i_0_84,i_0_63,i_0_65]) ).
cnf(i_0_129,plain,
( ~ r2(X1,X2)
| ~ r2(X3,X4)
| id(X1,X3)
| ~ id(X2,X4) ),
inference(rename_variables,[],[i_0_65]) ).
cnf(i_0_130,plain,
( r4(X1,X1,X1)
| ~ r4(X1,X1,X1) ),
inference(scs_inference,[],[i_0_60,i_0_90,i_0_95,i_0_98,i_0_101,i_0_106,i_0_109,i_0_118,i_0_126,i_0_70,i_0_71,i_0_86,i_0_112,i_0_88,i_0_79,i_0_120,i_0_91,i_0_58,i_0_59,i_0_76,i_0_82,i_0_87,i_0_74,i_0_83,i_0_64,i_0_55,i_0_84,i_0_63,i_0_65,i_0_51]) ).
cnf(i_0_131,plain,
( ~ id(X1,X2)
| ~ id(X3,X4)
| ~ id(X5,X6)
| r4(X1,X3,X5)
| ~ r4(X2,X4,X6) ),
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_132,plain,
( r4(esk9_2(X1,X2),esk9_2(X1,X2),esk9_2(X1,X2))
| ~ r4(esk10_2(X1,X2),esk10_2(X1,X2),esk10_2(X1,X2)) ),
inference(scs_inference,[],[i_0_60,i_0_90,i_0_95,i_0_98,i_0_101,i_0_106,i_0_109,i_0_118,i_0_126,i_0_70,i_0_71,i_0_86,i_0_112,i_0_88,i_0_79,i_0_120,i_0_91,i_0_58,i_0_59,i_0_76,i_0_82,i_0_87,i_0_74,i_0_83,i_0_64,i_0_55,i_0_84,i_0_63,i_0_65,i_0_51,i_0_52]) ).
cnf(i_0_133,plain,
( ~ id(X1,X2)
| ~ id(X3,X4)
| ~ id(X5,X6)
| r4(X2,X4,X6)
| ~ r4(X1,X3,X5) ),
inference(rename_variables,[],[i_0_52]) ).
cnf(i_0_134,plain,
id(X1,X1),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_135,plain,
id(X1,X1),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_136,plain,
id(X1,X1),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_137,plain,
id(X1,X1),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_138,plain,
( r3(esk10_2(X1,X2),esk10_2(X1,X2),esk10_2(X1,X2))
| ~ r3(esk10_2(X1,X2),esk10_2(X1,X2),esk10_2(X1,X2))
| ~ r4(esk10_2(X1,X2),esk10_2(X1,X2),esk10_2(X1,X2)) ),
inference(scs_inference,[],[i_0_60,i_0_90,i_0_95,i_0_98,i_0_101,i_0_106,i_0_109,i_0_118,i_0_126,i_0_134,i_0_70,i_0_71,i_0_86,i_0_112,i_0_88,i_0_79,i_0_120,i_0_91,i_0_58,i_0_59,i_0_76,i_0_82,i_0_87,i_0_74,i_0_83,i_0_64,i_0_55,i_0_63,i_0_51,i_0_52,i_0_53,i_0_54]) ).
cnf(i_0_139,plain,
r4(X1,X2,esk13_1(esk4_2(X1,X2))),
inference(scs_inference,[],[i_0_88,i_0_58]) ).
cnf(i_0_140,plain,
id(esk13_1(X1),X1),
inference(rename_variables,[],[i_0_88]) ).
cnf(i_0_141,plain,
( ~ id(X1,esk4_2(X2,X3))
| r4(X2,X3,X1) ),
inference(rename_variables,[],[i_0_58]) ).
cnf(i_0_142,plain,
r3(X1,X2,esk13_1(esk3_2(X1,X2))),
inference(scs_inference,[],[i_0_88,i_0_140,i_0_58,i_0_59]) ).
cnf(i_0_143,plain,
id(esk13_1(X1),X1),
inference(rename_variables,[],[i_0_88]) ).
cnf(i_0_144,plain,
( ~ id(X1,esk3_2(X2,X3))
| r3(X2,X3,X1) ),
inference(rename_variables,[],[i_0_59]) ).
cnf(i_0_145,plain,
r2(X1,esk13_1(esk2_1(X1))),
inference(scs_inference,[],[i_0_88,i_0_140,i_0_143,i_0_58,i_0_59,i_0_76]) ).
cnf(i_0_146,plain,
id(esk13_1(X1),X1),
inference(rename_variables,[],[i_0_88]) ).
cnf(i_0_147,plain,
( ~ id(X1,esk2_1(X2))
| r2(X2,X1) ),
inference(rename_variables,[],[i_0_76]) ).
cnf(i_0_148,plain,
r1(esk13_1(esk1_0)),
inference(scs_inference,[],[i_0_88,i_0_140,i_0_143,i_0_146,i_0_58,i_0_59,i_0_76,i_0_87]) ).
cnf(i_0_149,plain,
id(esk13_1(X1),X1),
inference(rename_variables,[],[i_0_88]) ).
cnf(i_0_150,plain,
( ~ id(X1,esk1_0)
| r1(X1) ),
inference(rename_variables,[],[i_0_87]) ).
cnf(i_0_151,plain,
id(esk5_2(X1,X2),esk6_2(X1,X2)),
inference(scs_inference,[],[i_0_72,i_0_88,i_0_140,i_0_143,i_0_146,i_0_58,i_0_59,i_0_76,i_0_87,i_0_82]) ).
cnf(i_0_152,plain,
( ~ id(X1,X2)
| id(X2,X1) ),
inference(rename_variables,[],[i_0_82]) ).
cnf(i_0_153,plain,
~ r2(X1,esk15_1(X2)),
inference(scs_inference,[],[i_0_111,i_0_72,i_0_90,i_0_88,i_0_140,i_0_143,i_0_146,i_0_58,i_0_59,i_0_76,i_0_87,i_0_82,i_0_74]) ).
cnf(i_0_154,plain,
id(X1,X1),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_155,plain,
( ~ r1(X1)
| ~ id(X1,X2)
| ~ r2(X3,X2) ),
inference(rename_variables,[],[i_0_74]) ).
cnf(i_0_156,plain,
r1(esk13_1(esk15_1(X1))),
inference(scs_inference,[],[i_0_111,i_0_72,i_0_90,i_0_88,i_0_140,i_0_143,i_0_146,i_0_149,i_0_58,i_0_59,i_0_76,i_0_87,i_0_82,i_0_74,i_0_83]) ).
cnf(i_0_157,plain,
id(esk13_1(X1),X1),
inference(rename_variables,[],[i_0_88]) ).
cnf(i_0_158,plain,
( ~ id(X1,X2)
| r1(X1)
| ~ r1(X2) ),
inference(rename_variables,[],[i_0_83]) ).
cnf(i_0_159,plain,
~ r1(esk13_1(esk8_2(X1,X2))),
inference(scs_inference,[],[i_0_117,i_0_111,i_0_72,i_0_90,i_0_88,i_0_140,i_0_143,i_0_146,i_0_149,i_0_157,i_0_58,i_0_59,i_0_76,i_0_87,i_0_82,i_0_74,i_0_83,i_0_84]) ).
cnf(i_0_160,plain,
id(esk13_1(X1),X1),
inference(rename_variables,[],[i_0_88]) ).
cnf(i_0_161,plain,
( ~ id(X1,X2)
| r1(X2)
| ~ r1(X1) ),
inference(rename_variables,[],[i_0_84]) ).
cnf(i_0_162,plain,
$false,
inference(scs_inference,[],[i_0_60,i_0_117,i_0_100,i_0_103,i_0_111,i_0_72,i_0_80,i_0_90,i_0_88,i_0_140,i_0_143,i_0_146,i_0_149,i_0_157,i_0_58,i_0_59,i_0_76,i_0_87,i_0_82,i_0_74,i_0_83,i_0_84,i_0_55]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : NUN080+1 : TPTP v9.2.1. Released v7.3.0.
% 0.00/0.07 % 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
% 0.06/0.26 % Computer : n012.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 300
% 0.06/0.26 % DateTime : Tue May 5 01:23:01 EDT 2026
% 0.06/0.26 % CPUTime :
% 0.06/0.26 % start to proof: theBenchmark
% 0.12/1.52 % Version : CSE_E---1.7
% 0.12/1.52 % Problem : theBenchmark.p
% 0.12/1.52 % SZS status Theorem for theBenchmark.p
% 0.12/1.52 % SZS output start CNFRefutation
% See solution above
% 0.20/1.64 % Total time : 1.261s
%------------------------------------------------------------------------------