%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUN077+2 : 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 : n026.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 05:00:51 PM UTC 2026
% Result : Theorem 125.38s 80.11s
% Output : CNFRefutation 125.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of formulae : 113 ( 57 unt; 0 def)
% Number of atoms : 383 ( 94 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 483 ( 213 ~; 186 |; 84 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 1 con; 0-2 aty)
% Number of variables : 352 ( 14 sgn 66 !; 51 ?)
% Comments :
%------------------------------------------------------------------------------
fof(twotimesthreeeqsix,conjecture,
? [X39] :
( ? [X22] :
( X39 = X22
& ? [X23] :
( r2(X23,X22)
& ? [X16] :
( r2(X16,X23)
& ? [X17] :
( r2(X17,X16)
& ? [X19] :
( r2(X19,X17)
& ? [X42] :
( r2(X42,X19)
& ? [X29] :
( r1(X29)
& r2(X29,X42) ) ) ) ) ) ) )
& ? [X25] :
( ? [X34] :
( r2(X34,X25)
& ? [X40] :
( r2(X40,X34)
& ? [X24] :
( r1(X24)
& r2(X24,X40) ) ) )
& ? [X31] :
( r4(X31,X25,X39)
& ? [X28] :
( r2(X28,X31)
& ? [X18] :
( r1(X18)
& r2(X18,X28) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',twotimesthreeeqsix) ).
fof(axiom_1,axiom,
? [X1] :
! [X2] :
( ( ~ r1(X2)
& X2 != X1 )
| ( r1(X2)
& X2 = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_1) ).
fof(axiom_2a,axiom,
! [X20,X21] :
? [X22] :
( ? [X23] :
( ? [X24] :
( r2(X21,X24)
& r4(X20,X24,X23) )
& X23 = X22 )
& ? [X25] :
( r3(X25,X20,X22)
& r4(X20,X21,X25) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_2a) ).
fof(axiom_2,axiom,
! [X3] :
? [X4] :
! [X5] :
( ( ~ r2(X3,X5)
& X5 != X4 )
| ( r2(X3,X5)
& X5 = X4 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_2) ).
fof(axiom_5a,axiom,
! [X33] :
? [X34] :
( ? [X35] :
( r1(X35)
& r4(X33,X35,X34) )
& ? [X36] :
( r1(X36)
& X34 = X36 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_5a) ).
fof(axiom_3,axiom,
! [X6,X7] :
? [X8] :
! [X9] :
( ( ~ r3(X6,X7,X9)
& X9 != X8 )
| ( r3(X6,X7,X9)
& X9 = X8 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_3) ).
fof(axiom_1a,axiom,
! [X14,X15] :
? [X16] :
( ? [X17] :
( ? [X18] :
( r2(X15,X18)
& r3(X14,X18,X17) )
& X17 = X16 )
& ? [X19] :
( r2(X19,X16)
& r3(X14,X15,X19) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_1a) ).
fof(axiom_4,axiom,
! [X10,X11] :
? [X12] :
! [X13] :
( ( ~ r4(X10,X11,X13)
& X13 != X12 )
| ( r4(X10,X11,X13)
& X13 = X12 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_4) ).
fof(axiom_3a,axiom,
! [X26,X27] :
( ! [X28] :
( ! [X29] :
( ~ r2(X26,X29)
| X29 != X28 )
| ~ r2(X27,X28) )
| X26 = X27 ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_3a) ).
fof(axiom_4a,axiom,
! [X30] :
? [X31] :
( ? [X32] :
( r1(X32)
& r3(X30,X32,X31) )
& X31 = X30 ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_4a) ).
fof(c_0_10,negated_conjecture,
~ ? [X39] :
( ? [X22] :
( X39 = X22
& ? [X23] :
( r2(X23,X22)
& ? [X16] :
( r2(X16,X23)
& ? [X17] :
( r2(X17,X16)
& ? [X19] :
( r2(X19,X17)
& ? [X42] :
( r2(X42,X19)
& ? [X29] :
( r1(X29)
& r2(X29,X42) ) ) ) ) ) ) )
& ? [X25] :
( ? [X34] :
( r2(X34,X25)
& ? [X40] :
( r2(X40,X34)
& ? [X24] :
( r1(X24)
& r2(X24,X40) ) ) )
& ? [X31] :
( r4(X31,X25,X39)
& ? [X28] :
( r2(X28,X31)
& ? [X18] :
( r1(X18)
& r2(X18,X28) ) ) ) ) ),
inference(assume_negation,[status(cth)],[twotimesthreeeqsix]) ).
fof(c_0_11,negated_conjecture,
! [X145,X146,X147,X148,X149,X150,X151,X152,X153,X154,X155,X156,X157,X158,X159] :
( X145 != X146
| ~ r2(X147,X146)
| ~ r2(X148,X147)
| ~ r2(X149,X148)
| ~ r2(X150,X149)
| ~ r2(X151,X150)
| ~ r1(X152)
| ~ r2(X152,X151)
| ~ r2(X154,X153)
| ~ r2(X155,X154)
| ~ r1(X156)
| ~ r2(X156,X155)
| ~ r4(X157,X153,X145)
| ~ r2(X158,X157)
| ~ r1(X159)
| ~ r2(X159,X158) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_12,plain,
? [X1] :
! [X2] :
( ( ~ r1(X2)
& X2 != X1 )
| ( r1(X2)
& X2 = X1 ) ),
inference(fof_simplification,[status(thm)],[axiom_1]) ).
cnf(c_0_13,negated_conjecture,
( X1 != X2
| ~ r2(X3,X2)
| ~ r2(X4,X3)
| ~ r2(X5,X4)
| ~ r2(X6,X5)
| ~ r2(X7,X6)
| ~ r1(X8)
| ~ r2(X8,X7)
| ~ r2(X9,X10)
| ~ r2(X11,X9)
| ~ r1(X12)
| ~ r2(X12,X11)
| ~ r4(X13,X10,X1)
| ~ r2(X14,X13)
| ~ r1(X15)
| ~ r2(X15,X14) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_14,plain,
! [X121,X122] :
( r2(X122,esk11_2(X121,X122))
& r4(X121,esk11_2(X121,X122),esk10_2(X121,X122))
& esk10_2(X121,X122) = esk9_2(X121,X122)
& r3(esk12_2(X121,X122),X121,esk9_2(X121,X122))
& r4(X121,X122,esk12_2(X121,X122)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_2a])]) ).
fof(c_0_15,plain,
! [X103] :
( ( r1(X103)
| ~ r1(X103) )
& ( X103 = esk1_0
| ~ r1(X103) )
& ( r1(X103)
| X103 != esk1_0 )
& ( X103 = esk1_0
| X103 != esk1_0 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_12])])]) ).
cnf(c_0_16,negated_conjecture,
( ~ r4(X1,X2,X3)
| ~ r2(X4,X5)
| ~ r2(X5,X1)
| ~ r2(X6,X7)
| ~ r2(X7,X8)
| ~ r2(X8,X2)
| ~ r2(X9,X10)
| ~ r2(X10,X11)
| ~ r2(X11,X12)
| ~ r2(X12,X13)
| ~ r2(X13,X14)
| ~ r2(X14,X3)
| ~ r1(X4)
| ~ r1(X6)
| ~ r1(X9) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
r4(X1,X2,esk12_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
( r1(X1)
| X1 != esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,negated_conjecture,
( ~ r2(X1,esk12_2(X2,X3))
| ~ r2(X4,X5)
| ~ r2(X5,X2)
| ~ r2(X6,X7)
| ~ r2(X7,X8)
| ~ r2(X8,X3)
| ~ r2(X9,X10)
| ~ r2(X10,X11)
| ~ r2(X11,X12)
| ~ r2(X12,X13)
| ~ r2(X13,X1)
| ~ r1(X4)
| ~ r1(X6)
| ~ r1(X9) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
r1(esk1_0),
inference(er,[status(thm)],[c_0_18]) ).
fof(c_0_21,plain,
! [X3] :
? [X4] :
! [X5] :
( ( ~ r2(X3,X5)
& X5 != X4 )
| ( r2(X3,X5)
& X5 = X4 ) ),
inference(fof_simplification,[status(thm)],[axiom_2]) ).
fof(c_0_22,plain,
! [X134] :
( r1(esk16_1(X134))
& r4(X134,esk16_1(X134),esk15_1(X134))
& r1(esk17_1(X134))
& esk15_1(X134) = esk17_1(X134) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_5a])]) ).
cnf(c_0_23,negated_conjecture,
( ~ r2(X1,esk12_2(X2,X3))
| ~ r2(esk1_0,X4)
| ~ r2(X4,X2)
| ~ r2(X5,X6)
| ~ r2(X6,X7)
| ~ r2(X7,X3)
| ~ r2(X8,X9)
| ~ r2(X9,X10)
| ~ r2(X10,X11)
| ~ r2(X11,X12)
| ~ r2(X12,X1)
| ~ r1(X5)
| ~ r1(X8) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_24,plain,
! [X104,X106] :
( ( r2(X104,X106)
| ~ r2(X104,X106) )
& ( X106 = esk2_1(X104)
| ~ r2(X104,X106) )
& ( r2(X104,X106)
| X106 != esk2_1(X104) )
& ( X106 = esk2_1(X104)
| X106 != esk2_1(X104) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_21])])]) ).
fof(c_0_25,plain,
! [X6,X7] :
? [X8] :
! [X9] :
( ( ~ r3(X6,X7,X9)
& X9 != X8 )
| ( r3(X6,X7,X9)
& X9 = X8 ) ),
inference(fof_simplification,[status(thm)],[axiom_3]) ).
cnf(c_0_26,plain,
r1(esk17_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
esk15_1(X1) = esk17_1(X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,negated_conjecture,
( ~ r2(X1,esk12_2(X2,X3))
| ~ r2(esk1_0,X4)
| ~ r2(esk1_0,X5)
| ~ r2(X4,X2)
| ~ r2(X5,X6)
| ~ r2(X6,X3)
| ~ r2(X7,X8)
| ~ r2(X8,X9)
| ~ r2(X9,X10)
| ~ r2(X10,X11)
| ~ r2(X11,X1)
| ~ r1(X7) ),
inference(spm,[status(thm)],[c_0_23,c_0_20]) ).
cnf(c_0_29,plain,
( r2(X1,X2)
| X2 != esk2_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_30,plain,
! [X107,X108,X110] :
( ( r3(X107,X108,X110)
| ~ r3(X107,X108,X110) )
& ( X110 = esk3_2(X107,X108)
| ~ r3(X107,X108,X110) )
& ( r3(X107,X108,X110)
| X110 != esk3_2(X107,X108) )
& ( X110 = esk3_2(X107,X108)
| X110 != esk3_2(X107,X108) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_25])])]) ).
fof(c_0_31,plain,
! [X115,X116] :
( r2(X116,esk7_2(X115,X116))
& r3(X115,esk7_2(X115,X116),esk6_2(X115,X116))
& esk6_2(X115,X116) = esk5_2(X115,X116)
& r2(esk8_2(X115,X116),esk5_2(X115,X116))
& r3(X115,X116,esk8_2(X115,X116)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_1a])]) ).
fof(c_0_32,plain,
! [X10,X11] :
? [X12] :
! [X13] :
( ( ~ r4(X10,X11,X13)
& X13 != X12 )
| ( r4(X10,X11,X13)
& X13 = X12 ) ),
inference(fof_simplification,[status(thm)],[axiom_4]) ).
cnf(c_0_33,plain,
( X1 = esk1_0
| ~ r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_34,plain,
r1(esk16_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_35,plain,
r1(esk15_1(X1)),
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_36,negated_conjecture,
( ~ r2(X1,esk12_2(X2,X3))
| ~ r2(esk1_0,X4)
| ~ r2(esk1_0,X5)
| ~ r2(esk1_0,X6)
| ~ r2(X4,X2)
| ~ r2(X5,X7)
| ~ r2(X7,X3)
| ~ r2(X6,X8)
| ~ r2(X8,X9)
| ~ r2(X9,X10)
| ~ r2(X10,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_20]) ).
cnf(c_0_37,plain,
r2(X1,esk2_1(X1)),
inference(er,[status(thm)],[c_0_29]) ).
cnf(c_0_38,plain,
( X1 = esk3_2(X2,X3)
| ~ r3(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_39,plain,
r3(X1,X2,esk8_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_40,plain,
! [X111,X112,X114] :
( ( r4(X111,X112,X114)
| ~ r4(X111,X112,X114) )
& ( X114 = esk4_2(X111,X112)
| ~ r4(X111,X112,X114) )
& ( r4(X111,X112,X114)
| X114 != esk4_2(X111,X112) )
& ( X114 = esk4_2(X111,X112)
| X114 != esk4_2(X111,X112) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_32])])]) ).
cnf(c_0_41,plain,
r4(X1,esk16_1(X1),esk15_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_42,plain,
esk16_1(X1) = esk1_0,
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_43,plain,
esk15_1(X1) = esk1_0,
inference(spm,[status(thm)],[c_0_33,c_0_35]) ).
cnf(c_0_44,negated_conjecture,
( ~ r2(X1,esk12_2(esk2_1(X2),X3))
| ~ r2(esk1_0,X2)
| ~ r2(esk1_0,X4)
| ~ r2(esk1_0,X5)
| ~ r2(X4,X6)
| ~ r2(X6,X3)
| ~ r2(X5,X7)
| ~ r2(X7,X8)
| ~ r2(X8,X9)
| ~ r2(X9,X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
fof(c_0_45,plain,
! [X26,X27] :
( ! [X28] :
( ! [X29] :
( ~ r2(X26,X29)
| X29 != X28 )
| ~ r2(X27,X28) )
| X26 = X27 ),
inference(fof_simplification,[status(thm)],[axiom_3a]) ).
cnf(c_0_46,plain,
esk3_2(X1,X2) = esk8_2(X1,X2),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_47,plain,
( X1 = esk4_2(X2,X3)
| ~ r4(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_48,plain,
r4(X1,esk11_2(X1,X2),esk10_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_49,plain,
esk10_2(X1,X2) = esk9_2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_50,plain,
( X1 = esk2_1(X2)
| ~ r2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_51,plain,
r2(X1,esk11_2(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_52,plain,
r4(X1,esk1_0,esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
fof(c_0_53,plain,
! [X131] :
( r1(esk14_1(X131))
& r3(X131,esk14_1(X131),esk13_1(X131))
& esk13_1(X131) = X131 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_4a])]) ).
cnf(c_0_54,negated_conjecture,
( ~ r2(X1,esk12_2(esk2_1(X2),X3))
| ~ r2(esk2_1(X4),X3)
| ~ r2(esk1_0,X2)
| ~ r2(esk1_0,X4)
| ~ r2(esk1_0,X5)
| ~ r2(X5,X6)
| ~ r2(X6,X7)
| ~ r2(X7,X8)
| ~ r2(X8,X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_37]) ).
fof(c_0_55,plain,
! [X127,X128,X129,X130] :
( ~ r2(X127,X130)
| X130 != X129
| ~ r2(X128,X129)
| X127 = X128 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_45])]) ).
cnf(c_0_56,plain,
r2(esk8_2(X1,X2),esk5_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_57,plain,
( X1 = esk8_2(X2,X3)
| ~ r3(X2,X3,X1) ),
inference(rw,[status(thm)],[c_0_38,c_0_46]) ).
cnf(c_0_58,plain,
r3(esk12_2(X1,X2),X1,esk9_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_59,plain,
esk4_2(X1,X2) = esk12_2(X1,X2),
inference(spm,[status(thm)],[c_0_47,c_0_17]) ).
cnf(c_0_60,plain,
r4(X1,esk11_2(X1,X2),esk9_2(X1,X2)),
inference(rw,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_61,plain,
esk11_2(X1,X2) = esk2_1(X2),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_62,plain,
r3(X1,esk7_2(X1,X2),esk6_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_63,plain,
esk6_2(X1,X2) = esk5_2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_64,plain,
r2(X1,esk7_2(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_65,plain,
esk4_2(X1,esk1_0) = esk1_0,
inference(spm,[status(thm)],[c_0_47,c_0_52]) ).
cnf(c_0_66,plain,
r3(X1,esk14_1(X1),esk13_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_67,plain,
esk13_1(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_68,plain,
r1(esk14_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_69,negated_conjecture,
( ~ r2(X1,esk12_2(esk2_1(X2),X3))
| ~ r2(esk2_1(X4),X3)
| ~ r2(esk2_1(X5),X6)
| ~ r2(esk1_0,X2)
| ~ r2(esk1_0,X4)
| ~ r2(esk1_0,X5)
| ~ r2(X6,X7)
| ~ r2(X7,X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_37]) ).
cnf(c_0_70,plain,
( X1 = X4
| ~ r2(X1,X2)
| X2 != X3
| ~ r2(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_71,plain,
esk2_1(esk8_2(X1,X2)) = esk5_2(X1,X2),
inference(spm,[status(thm)],[c_0_50,c_0_56]) ).
cnf(c_0_72,plain,
esk8_2(esk12_2(X1,X2),X1) = esk9_2(X1,X2),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_73,plain,
( X1 = esk12_2(X2,X3)
| ~ r4(X2,X3,X1) ),
inference(rw,[status(thm)],[c_0_47,c_0_59]) ).
cnf(c_0_74,plain,
r4(X1,esk2_1(X2),esk9_2(X1,X2)),
inference(rw,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_75,plain,
r3(X1,esk7_2(X1,X2),esk5_2(X1,X2)),
inference(rw,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_76,plain,
esk7_2(X1,X2) = esk2_1(X2),
inference(spm,[status(thm)],[c_0_50,c_0_64]) ).
cnf(c_0_77,plain,
esk12_2(X1,esk1_0) = esk1_0,
inference(rw,[status(thm)],[c_0_65,c_0_59]) ).
cnf(c_0_78,plain,
r3(X1,esk14_1(X1),X1),
inference(rw,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_79,plain,
esk14_1(X1) = esk1_0,
inference(spm,[status(thm)],[c_0_33,c_0_68]) ).
cnf(c_0_80,negated_conjecture,
( ~ r2(X1,esk12_2(esk2_1(X2),X3))
| ~ r2(esk2_1(X4),X3)
| ~ r2(esk2_1(X5),X6)
| ~ r2(esk2_1(X6),X1)
| ~ r2(esk1_0,X2)
| ~ r2(esk1_0,X4)
| ~ r2(esk1_0,X5) ),
inference(spm,[status(thm)],[c_0_69,c_0_37]) ).
cnf(c_0_81,plain,
( X1 = X2
| ~ r2(X2,X3)
| ~ r2(X1,X3) ),
inference(er,[status(thm)],[c_0_70]) ).
cnf(c_0_82,plain,
esk5_2(esk12_2(X1,X2),X1) = esk2_1(esk9_2(X1,X2)),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_83,plain,
esk12_2(X1,esk2_1(X2)) = esk9_2(X1,X2),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_84,plain,
r3(X1,esk2_1(X2),esk5_2(X1,X2)),
inference(rw,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_85,plain,
r3(esk1_0,X1,esk9_2(X1,esk1_0)),
inference(spm,[status(thm)],[c_0_58,c_0_77]) ).
cnf(c_0_86,plain,
r3(X1,esk1_0,X1),
inference(rw,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_87,negated_conjecture,
( ~ r2(X1,esk12_2(esk2_1(esk2_1(esk1_0)),X2))
| ~ r2(esk2_1(X3),X2)
| ~ r2(esk2_1(X4),X5)
| ~ r2(esk2_1(X5),X1)
| ~ r2(esk1_0,X3)
| ~ r2(esk1_0,X4) ),
inference(spm,[status(thm)],[c_0_80,c_0_37]) ).
cnf(c_0_88,plain,
( X1 = X2
| ~ r2(X1,esk2_1(X2)) ),
inference(spm,[status(thm)],[c_0_81,c_0_37]) ).
cnf(c_0_89,plain,
esk5_2(esk9_2(X1,X2),X1) = esk2_1(esk9_2(X1,esk2_1(X2))),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_90,plain,
esk8_2(X1,esk2_1(X2)) = esk5_2(X1,X2),
inference(spm,[status(thm)],[c_0_57,c_0_84]) ).
cnf(c_0_91,plain,
esk8_2(esk1_0,X1) = esk9_2(X1,esk1_0),
inference(spm,[status(thm)],[c_0_57,c_0_85]) ).
cnf(c_0_92,plain,
esk3_2(X1,esk1_0) = X1,
inference(spm,[status(thm)],[c_0_38,c_0_86]) ).
cnf(c_0_93,negated_conjecture,
( ~ r2(X1,esk12_2(esk2_1(esk2_1(esk1_0)),X2))
| ~ r2(esk2_1(esk2_1(esk1_0)),X2)
| ~ r2(esk2_1(X3),X4)
| ~ r2(esk2_1(X4),X1)
| ~ r2(esk1_0,X3) ),
inference(spm,[status(thm)],[c_0_87,c_0_37]) ).
cnf(c_0_94,plain,
( X1 = esk9_2(X2,esk2_1(X3))
| ~ r2(X1,esk5_2(esk9_2(X2,X3),X2)) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_95,plain,
esk9_2(esk2_1(X1),esk1_0) = esk5_2(esk1_0,X1),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_96,plain,
esk5_2(X1,esk2_1(X2)) = esk2_1(esk5_2(X1,X2)),
inference(spm,[status(thm)],[c_0_71,c_0_90]) ).
cnf(c_0_97,plain,
esk8_2(X1,esk1_0) = X1,
inference(rw,[status(thm)],[c_0_92,c_0_46]) ).
cnf(c_0_98,negated_conjecture,
( ~ r2(X1,esk12_2(esk2_1(esk2_1(esk1_0)),X2))
| ~ r2(esk2_1(esk2_1(esk1_0)),X2)
| ~ r2(esk2_1(esk2_1(esk1_0)),X3)
| ~ r2(esk2_1(X3),X1) ),
inference(spm,[status(thm)],[c_0_93,c_0_37]) ).
cnf(c_0_99,plain,
( X1 = esk9_2(esk2_1(X2),esk2_1(esk1_0))
| ~ r2(X1,esk2_1(esk5_2(esk5_2(esk1_0,X2),X2))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_96]) ).
cnf(c_0_100,plain,
r2(X1,esk5_2(X1,esk1_0)),
inference(spm,[status(thm)],[c_0_56,c_0_97]) ).
cnf(c_0_101,negated_conjecture,
( ~ r2(esk2_1(esk2_1(X1)),esk12_2(esk2_1(esk2_1(esk1_0)),X2))
| ~ r2(esk2_1(esk2_1(esk1_0)),X2)
| ~ r2(esk2_1(esk2_1(esk1_0)),X1) ),
inference(spm,[status(thm)],[c_0_98,c_0_37]) ).
cnf(c_0_102,plain,
esk8_2(esk9_2(X1,X2),X1) = esk9_2(X1,esk2_1(X2)),
inference(spm,[status(thm)],[c_0_72,c_0_83]) ).
cnf(c_0_103,plain,
( X1 = esk9_2(esk2_1(esk2_1(X2)),esk2_1(esk1_0))
| ~ r2(X1,esk2_1(esk2_1(esk5_2(esk2_1(esk5_2(esk1_0,X2)),X2)))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_96]),c_0_96]) ).
cnf(c_0_104,plain,
esk5_2(X1,esk1_0) = esk2_1(X1),
inference(spm,[status(thm)],[c_0_50,c_0_100]) ).
cnf(c_0_105,negated_conjecture,
( ~ r2(esk2_1(esk2_1(X1)),esk12_2(esk2_1(esk2_1(esk1_0)),esk2_1(esk2_1(esk2_1(esk1_0)))))
| ~ r2(esk2_1(esk2_1(esk1_0)),X1) ),
inference(spm,[status(thm)],[c_0_101,c_0_37]) ).
cnf(c_0_106,plain,
esk5_2(esk9_2(esk2_1(X1),X2),X1) = esk9_2(esk2_1(X1),esk2_1(X2)),
inference(spm,[status(thm)],[c_0_90,c_0_102]) ).
cnf(c_0_107,plain,
( X1 = esk9_2(esk2_1(esk2_1(esk1_0)),esk2_1(esk1_0))
| ~ r2(X1,esk2_1(esk2_1(esk2_1(esk2_1(esk2_1(esk1_0)))))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_104]) ).
cnf(c_0_108,negated_conjecture,
~ r2(esk2_1(esk2_1(esk2_1(esk2_1(esk2_1(esk1_0))))),esk12_2(esk2_1(esk2_1(esk1_0)),esk2_1(esk2_1(esk2_1(esk1_0))))),
inference(spm,[status(thm)],[c_0_105,c_0_37]) ).
cnf(c_0_109,plain,
r2(esk8_2(esk9_2(esk2_1(X1),X2),X1),esk9_2(esk2_1(X1),esk2_1(X2))),
inference(spm,[status(thm)],[c_0_56,c_0_106]) ).
cnf(c_0_110,plain,
esk9_2(esk2_1(esk2_1(esk1_0)),esk2_1(esk1_0)) = esk2_1(esk2_1(esk2_1(esk2_1(esk1_0)))),
inference(spm,[status(thm)],[c_0_107,c_0_37]) ).
cnf(c_0_111,negated_conjecture,
~ r2(esk2_1(esk2_1(esk2_1(esk2_1(esk2_1(esk1_0))))),esk9_2(esk2_1(esk2_1(esk1_0)),esk2_1(esk2_1(esk1_0)))),
inference(rw,[status(thm)],[c_0_108,c_0_83]) ).
cnf(c_0_112,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_90]),c_0_104]),c_0_111]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUN077+2 : TPTP v9.2.1. Released v7.3.0.
% 0.00/0.11 % 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
% 0.13/0.32 % Computer : n026.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 01:27:38 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 125.38/80.11 % Version : CSE_E---1.7
% 125.38/80.11 % Problem : theBenchmark.p
% 125.38/80.11 % SZS status Theorem for theBenchmark.p
% 125.38/80.11 % SZS output start CNFRefutation
% See solution above
% 125.76/80.49 % Total time : 65.613s
%------------------------------------------------------------------------------