%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUN082+1 : TPTP v9.2.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n027.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 13.73s 8.71s
% Output : CNFRefutation 13.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 17
% Syntax : Number of formulae : 135 ( 45 unt; 0 def)
% Number of atoms : 425 ( 0 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 512 ( 222 ~; 203 |; 87 &)
% ( 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 : 16 ( 16 usr; 1 con; 0-2 aty)
% Number of variables : 314 ( 27 sgn 122 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
? [X1] :
! [X2] :
( ( id(X2,X1)
& r1(X2) )
| ( ~ r1(X2)
& ~ id(X2,X1) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_8) ).
fof(axiom_7a,axiom,
! [X65,X66] :
( ! [X67] :
( ~ id(X67,X66)
| ~ r1(X67) )
| ~ r2(X65,X66) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_7a) ).
fof(axiom_6,axiom,
! [X15,X16] :
( ~ id(X15,X16)
| id(X16,X15) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_6) ).
fof(axiom_5a,axiom,
! [X57] :
? [X58] :
( ? [X59] :
( r1(X59)
& r4(X57,X59,X58) )
& ? [X60] :
( id(X58,X60)
& r1(X60) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_6a) ).
fof(axiom_7,axiom,
! [X17,X18,X19] :
( ~ id(X17,X18)
| id(X17,X19)
| ~ id(X18,X19) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_7) ).
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/sandbox/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/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_10) ).
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/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_2a) ).
fof(axiom_2,axiom,
! [X3] :
? [X4] :
! [X5] :
( ( id(X5,X4)
& r2(X3,X5) )
| ( ~ r2(X3,X5)
& ~ id(X5,X4) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_2) ).
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/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_9) ).
fof(axiom_5,axiom,
! [X14] : id(X14,X14),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_5) ).
fof(xtimesoneidzero,conjecture,
? [X63,X46] :
( ? [X47] :
( r4(X63,X47,X46)
& ? [X40] :
( r1(X40)
& r2(X40,X47) ) )
& ? [X41] :
( id(X46,X41)
& r1(X41) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xtimesoneidzero) ).
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/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_3) ).
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/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_4) ).
fof(c_0_17,plain,
? [X1] :
! [X2] :
( ( id(X2,X1)
& r1(X2) )
| ( ~ r1(X2)
& ~ id(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[axiom_1]) ).
fof(c_0_18,plain,
! [X20,X21] :
( ~ id(X20,X21)
| ( ~ r1(X20)
& ~ r1(X21) )
| ( r1(X20)
& r1(X21) ) ),
inference(fof_simplification,[status(thm)],[axiom_8]) ).
fof(c_0_19,plain,
! [X65,X66] :
( ! [X67] :
( ~ id(X67,X66)
| ~ r1(X67) )
| ~ r2(X65,X66) ),
inference(fof_simplification,[status(thm)],[axiom_7a]) ).
fof(c_0_20,plain,
! [X15,X16] :
( ~ id(X15,X16)
| id(X16,X15) ),
inference(fof_simplification,[status(thm)],[axiom_6]) ).
fof(c_0_21,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_17])])]) ).
fof(c_0_22,plain,
! [X196] :
( r1(esk16_1(X196))
& r4(X196,esk16_1(X196),esk15_1(X196))
& id(esk15_1(X196),esk17_1(X196))
& r1(esk17_1(X196)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_5a])]) ).
fof(c_0_23,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_18])]) ).
fof(c_0_24,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_25,plain,
! [X204,X205,X206] :
( ~ id(X206,X205)
| ~ r1(X206)
| ~ r2(X204,X205) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_19])]) ).
fof(c_0_26,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])])]) ).
fof(c_0_27,plain,
! [X17,X18,X19] :
( ~ id(X17,X18)
| id(X17,X19)
| ~ id(X18,X19) ),
inference(fof_simplification,[status(thm)],[axiom_7]) ).
fof(c_0_28,plain,
! [X154,X155] :
( ~ id(X154,X155)
| id(X155,X154) ),
inference(variable_rename,[status(thm)],[c_0_20]) ).
cnf(c_0_29,plain,
( id(X1,esk1_0)
| ~ r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,plain,
r1(esk17_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_31,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]) ).
cnf(c_0_32,plain,
( r1(X1)
| ~ r1(X2)
| ~ id(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,plain,
id(esk13_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,plain,
( ~ id(X1,X2)
| ~ r1(X1)
| ~ r2(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_35,plain,
( r2(esk19_1(X1),esk20_1(X1))
| id(X1,esk18_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_36,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_37,plain,
! [X156,X157,X158] :
( ~ id(X156,X157)
| id(X156,X158)
| ~ id(X157,X158) ),
inference(variable_rename,[status(thm)],[c_0_27]) ).
cnf(c_0_38,plain,
( id(X2,X1)
| ~ id(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_39,plain,
id(esk17_1(X1),esk1_0),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_40,plain,
id(esk15_1(X1),esk17_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_41,plain,
! [X171,X172,X173,X174,X175,X176] :
( ( r4(X171,X172,X173)
| ~ r4(X171,X172,X173)
| ~ id(X171,X174)
| ~ id(X172,X175)
| ~ id(X173,X176) )
& ( r4(X174,X175,X176)
| ~ r4(X171,X172,X173)
| ~ id(X171,X174)
| ~ id(X172,X175)
| ~ id(X173,X176) )
& ( r4(X171,X172,X173)
| ~ r4(X174,X175,X176)
| ~ id(X171,X174)
| ~ id(X172,X175)
| ~ id(X173,X176) )
& ( r4(X174,X175,X176)
| ~ r4(X174,X175,X176)
| ~ id(X171,X174)
| ~ id(X172,X175)
| ~ id(X173,X176) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_31])]) ).
fof(c_0_42,plain,
! [X183,X184] :
( id(esk10_2(X183,X184),esk9_2(X183,X184))
& r2(X184,esk11_2(X183,X184))
& r4(X183,esk11_2(X183,X184),esk10_2(X183,X184))
& r3(esk12_2(X183,X184),X183,esk9_2(X183,X184))
& r4(X183,X184,esk12_2(X183,X184)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_2a])]) ).
fof(c_0_43,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_44,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]) ).
cnf(c_0_45,plain,
( r1(esk13_1(X1))
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_46,plain,
( id(X1,esk18_1(X1))
| ~ r1(X2)
| ~ id(X2,esk20_1(X1)) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_47,plain,
( id(X1,esk20_1(X1))
| id(X1,esk18_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_48,plain,
! [X153] : id(X153,X153),
inference(variable_rename,[status(thm)],[axiom_5]) ).
fof(c_0_49,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_36])]) ).
cnf(c_0_50,plain,
( id(X1,X3)
| ~ id(X1,X2)
| ~ id(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_51,plain,
id(esk1_0,esk17_1(X1)),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_52,plain,
r1(esk15_1(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_40]),c_0_30])]) ).
cnf(c_0_53,plain,
( r4(X1,X2,X3)
| ~ r4(X4,X5,X6)
| ~ id(X4,X1)
| ~ id(X5,X2)
| ~ id(X6,X3) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_54,plain,
r4(X1,esk11_2(X1,X2),esk10_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
fof(c_0_55,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_43])])]) ).
fof(c_0_56,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_44])]) ).
cnf(c_0_57,plain,
( id(esk13_1(X1),esk1_0)
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_45]) ).
cnf(c_0_58,plain,
( id(X1,esk18_1(X1))
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_59,plain,
( r1(X1)
| ~ id(X1,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_60,plain,
id(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_61,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_49]) ).
cnf(c_0_62,plain,
r3(X1,esk14_1(X1),esk13_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_63,plain,
r4(X1,esk16_1(X1),esk15_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_64,plain,
( id(X1,esk17_1(X2))
| ~ id(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_65,plain,
id(esk15_1(X1),esk1_0),
inference(spm,[status(thm)],[c_0_29,c_0_52]) ).
cnf(c_0_66,plain,
id(X1,esk13_1(X1)),
inference(spm,[status(thm)],[c_0_38,c_0_33]) ).
cnf(c_0_67,plain,
( r4(X1,X2,X3)
| ~ id(esk10_2(X4,X5),X3)
| ~ id(esk11_2(X4,X5),X2)
| ~ id(X4,X1) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_68,plain,
id(esk10_2(X1,X2),esk9_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_69,plain,
( id(X2,esk2_1(X1))
| ~ r2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_70,plain,
r2(X1,esk11_2(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_71,plain,
( r2(X1,X2)
| ~ r2(X3,X4)
| ~ id(X3,X1)
| ~ id(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_72,plain,
( r2(X2,X1)
| ~ id(X1,esk2_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_73,plain,
( id(X1,X2)
| ~ id(X1,esk13_1(X2)) ),
inference(spm,[status(thm)],[c_0_50,c_0_33]) ).
cnf(c_0_74,plain,
( id(esk1_0,esk13_1(X1))
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_57]) ).
cnf(c_0_75,plain,
( id(esk18_1(X1),X1)
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_58]) ).
cnf(c_0_76,plain,
r1(esk1_0),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_77,plain,
( r3(X1,X2,X3)
| ~ id(esk13_1(X4),X3)
| ~ id(esk14_1(X4),X2)
| ~ id(X4,X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_78,plain,
r1(esk14_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_79,plain,
( r4(X1,X2,X3)
| ~ id(esk15_1(X4),X3)
| ~ id(esk16_1(X4),X2)
| ~ id(X4,X1) ),
inference(spm,[status(thm)],[c_0_53,c_0_63]) ).
cnf(c_0_80,plain,
id(esk15_1(X1),esk17_1(X2)),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_81,plain,
r1(esk16_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_82,plain,
( id(X1,esk13_1(X2))
| ~ id(X1,X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_66]) ).
fof(c_0_83,negated_conjecture,
~ ? [X63,X46] :
( ? [X47] :
( r4(X63,X47,X46)
& ? [X40] :
( r1(X40)
& r2(X40,X47) ) )
& ? [X41] :
( id(X46,X41)
& r1(X41) ) ),
inference(assume_negation,[status(cth)],[xtimesoneidzero]) ).
cnf(c_0_84,plain,
( r4(X1,X2,esk9_2(X3,X4))
| ~ id(esk11_2(X3,X4),X2)
| ~ id(X3,X1) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_85,plain,
id(esk11_2(X1,X2),esk2_1(X2)),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_86,plain,
( r2(X1,X2)
| ~ r2(X3,esk13_1(X2))
| ~ id(X3,X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_33]) ).
cnf(c_0_87,plain,
r2(X1,esk13_1(esk2_1(X1))),
inference(spm,[status(thm)],[c_0_72,c_0_33]) ).
cnf(c_0_88,plain,
( id(esk1_0,X1)
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_89,plain,
r1(esk18_1(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_75]),c_0_76])]) ).
fof(c_0_90,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]) ).
cnf(c_0_91,plain,
( r3(X1,X2,esk13_1(X3))
| ~ id(esk14_1(X3),X2)
| ~ id(X3,X1) ),
inference(spm,[status(thm)],[c_0_77,c_0_60]) ).
cnf(c_0_92,plain,
id(esk14_1(X1),esk1_0),
inference(spm,[status(thm)],[c_0_29,c_0_78]) ).
fof(c_0_93,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]) ).
cnf(c_0_94,plain,
( r4(X1,X2,esk17_1(X3))
| ~ id(esk16_1(X4),X2)
| ~ id(X4,X1) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_95,plain,
id(esk16_1(X1),esk1_0),
inference(spm,[status(thm)],[c_0_29,c_0_81]) ).
cnf(c_0_96,plain,
id(X1,esk13_1(esk13_1(X1))),
inference(spm,[status(thm)],[c_0_82,c_0_66]) ).
fof(c_0_97,negated_conjecture,
! [X207,X208,X209,X210,X211] :
( ~ r4(X207,X209,X208)
| ~ r1(X210)
| ~ r2(X210,X209)
| ~ id(X208,X211)
| ~ r1(X211) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_83])])]) ).
cnf(c_0_98,plain,
( r4(X1,esk2_1(X2),esk9_2(X3,X2))
| ~ id(X3,X1) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_99,plain,
( r2(X1,X2)
| ~ r2(X3,X2)
| ~ id(X3,X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_60]) ).
cnf(c_0_100,plain,
( r2(X1,esk2_1(X2))
| ~ id(X2,X1) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_101,plain,
id(esk1_0,esk18_1(esk1_0)),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_102,plain,
( id(X1,esk18_1(X2))
| ~ r1(X2)
| ~ id(X1,X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_58]) ).
fof(c_0_103,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_90])])]) ).
cnf(c_0_104,plain,
( r3(X1,esk1_0,esk13_1(X2))
| ~ id(X2,X1) ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
fof(c_0_105,plain,
! [X149,X150,X152] :
( ( ~ r4(X149,X150,X152)
| id(X152,esk4_2(X149,X150)) )
& ( ~ id(X152,esk4_2(X149,X150))
| id(X152,esk4_2(X149,X150)) )
& ( ~ r4(X149,X150,X152)
| r4(X149,X150,X152) )
& ( ~ id(X152,esk4_2(X149,X150))
| r4(X149,X150,X152) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_93])])]) ).
cnf(c_0_106,plain,
( r4(X1,esk1_0,esk17_1(X2))
| ~ id(X3,X1) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_107,plain,
id(esk13_1(esk13_1(X1)),X1),
inference(spm,[status(thm)],[c_0_38,c_0_96]) ).
cnf(c_0_108,negated_conjecture,
( ~ r4(X1,X2,X3)
| ~ r1(X4)
| ~ r2(X4,X2)
| ~ id(X3,X5)
| ~ r1(X5) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_109,plain,
r4(X1,esk2_1(X2),esk9_2(X1,X2)),
inference(spm,[status(thm)],[c_0_98,c_0_60]) ).
cnf(c_0_110,plain,
( r2(esk18_1(X1),X2)
| ~ r2(X1,X2)
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_99,c_0_58]) ).
cnf(c_0_111,plain,
r2(esk18_1(esk1_0),esk2_1(esk1_0)),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_112,plain,
( r1(X1)
| ~ r1(X2)
| ~ id(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_113,plain,
id(esk1_0,esk18_1(esk18_1(esk1_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_101]),c_0_89])]) ).
cnf(c_0_114,plain,
( id(X3,esk3_2(X1,X2))
| ~ r3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_115,plain,
r3(X1,esk1_0,esk13_1(X1)),
inference(spm,[status(thm)],[c_0_104,c_0_60]) ).
cnf(c_0_116,plain,
( id(X3,esk4_2(X1,X2))
| ~ r4(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_117,plain,
r4(X1,X2,esk12_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_118,plain,
r4(X1,esk1_0,esk17_1(X2)),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_119,negated_conjecture,
( ~ r2(X1,esk2_1(X2))
| ~ r1(X3)
| ~ r1(X1)
| ~ id(esk9_2(X4,X2),X3) ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_120,plain,
r2(esk18_1(esk18_1(esk1_0)),esk2_1(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_89])]) ).
cnf(c_0_121,plain,
r1(esk18_1(esk18_1(esk1_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_76])]) ).
cnf(c_0_122,plain,
r3(esk12_2(X1,X2),X1,esk9_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_123,plain,
id(esk13_1(X1),esk3_2(X1,esk1_0)),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_124,plain,
id(esk12_2(X1,X2),esk4_2(X1,X2)),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_125,plain,
id(esk17_1(X1),esk4_2(X2,esk1_0)),
inference(spm,[status(thm)],[c_0_116,c_0_118]) ).
cnf(c_0_126,negated_conjecture,
( ~ r1(X1)
| ~ id(esk9_2(X2,esk1_0),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_121])]) ).
cnf(c_0_127,plain,
id(esk9_2(X1,X2),esk3_2(esk12_2(X1,X2),X1)),
inference(spm,[status(thm)],[c_0_114,c_0_122]) ).
cnf(c_0_128,plain,
( r1(esk3_2(X1,esk1_0))
| ~ r1(esk13_1(X1)) ),
inference(spm,[status(thm)],[c_0_112,c_0_123]) ).
cnf(c_0_129,plain,
( r1(esk12_2(X1,X2))
| ~ r1(esk4_2(X1,X2)) ),
inference(spm,[status(thm)],[c_0_32,c_0_124]) ).
cnf(c_0_130,plain,
r1(esk4_2(X1,esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_125]),c_0_30])]) ).
cnf(c_0_131,negated_conjecture,
~ r1(esk3_2(esk12_2(X1,esk1_0),X1)),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_132,plain,
( r1(esk3_2(X1,esk1_0))
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_128,c_0_45]) ).
cnf(c_0_133,plain,
r1(esk12_2(X1,esk1_0)),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_134,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_133])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN082+1 : TPTP v9.2.1. Released v7.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.33 % Computer : n027.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 01:23:20 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 13.73/8.71 % Version : CSE_E---1.7
% 13.73/8.71 % Problem : theBenchmark.p
% 13.73/8.71 % SZS status Theorem for theBenchmark.p
% 13.73/8.71 % SZS output start CNFRefutation
% See solution above
% 13.73/8.77 % Total time : 6.382s
%------------------------------------------------------------------------------