%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUN072+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:57:39 PM UTC 2026
% Result : Theorem 1.73s 0.78s
% Output : CNFRefutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 99 ( 53 unt; 0 def)
% Number of atoms : 271 ( 79 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 297 ( 125 ~; 100 |; 72 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 4 ( 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 : 242 ( 14 sgn 48 !; 39 ?)
% Comments :
%------------------------------------------------------------------------------
fof(onetimestwoeqtwo,conjecture,
? [X39] :
( ? [X23] :
( ? [X25] :
( ? [X31] :
( r2(X31,X25)
& r1(X31) )
& r2(X25,X23) )
& X39 = X23 )
& ? [X22] :
( ? [X17] :
( ? [X34] :
( r2(X34,X17)
& r1(X34) )
& r4(X17,X22,X39) )
& ? [X16] :
( ? [X19] :
( r2(X19,X16)
& r1(X19) )
& r2(X16,X22) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',onetimestwoeqtwo) ).
fof(axiom_2,axiom,
! [X3] :
? [X4] :
! [X5] :
( ( X5 = X4
& r2(X3,X5) )
| ( X5 != X4
& ~ r2(X3,X5) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_2) ).
fof(axiom_1,axiom,
? [X1] :
! [X2] :
( ( X2 = X1
& r1(X2) )
| ( X2 != X1
& ~ r1(X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_1) ).
fof(axiom_5a,axiom,
! [X33] :
? [X34] :
( ? [X36] :
( X34 = X36
& r1(X36) )
& ? [X35] :
( r4(X33,X35,X34)
& r1(X35) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_5a) ).
fof(axiom_2a,axiom,
! [X20,X21] :
? [X22] :
( ? [X25] :
( r4(X20,X21,X25)
& r3(X25,X20,X22) )
& ? [X23] :
( X23 = X22
& ? [X24] :
( r4(X20,X24,X23)
& r2(X21,X24) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_2a) ).
fof(axiom_3,axiom,
! [X6,X7] :
? [X8] :
! [X9] :
( ( X9 = X8
& r3(X6,X7,X9) )
| ( X9 != X8
& ~ r3(X6,X7,X9) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_3) ).
fof(axiom_4,axiom,
! [X10,X11] :
? [X12] :
! [X13] :
( ( X13 = X12
& r4(X10,X11,X13) )
| ( X13 != X12
& ~ r4(X10,X11,X13) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_4) ).
fof(axiom_1a,axiom,
! [X14,X15] :
? [X16] :
( ? [X19] :
( r3(X14,X15,X19)
& r2(X19,X16) )
& ? [X17] :
( X17 = X16
& ? [X18] :
( r3(X14,X18,X17)
& r2(X15,X18) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_1a) ).
fof(axiom_4a,axiom,
! [X30] :
? [X31] :
( X31 = X30
& ? [X32] :
( r3(X30,X32,X31)
& r1(X32) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_4a) ).
fof(c_0_9,negated_conjecture,
~ ? [X39] :
( ? [X23] :
( ? [X25] :
( ? [X31] :
( r2(X31,X25)
& r1(X31) )
& r2(X25,X23) )
& X39 = X23 )
& ? [X22] :
( ? [X17] :
( ? [X34] :
( r2(X34,X17)
& r1(X34) )
& r4(X17,X22,X39) )
& ? [X16] :
( ? [X19] :
( r2(X19,X16)
& r1(X19) )
& r2(X16,X22) ) ) ),
inference(assume_negation,[status(cth)],[onetimestwoeqtwo]) ).
fof(c_0_10,negated_conjecture,
! [X87,X88,X89,X90,X91,X92,X93,X94,X95] :
( ~ r2(X95,X94)
| ~ r1(X95)
| ~ r2(X94,X93)
| X87 != X93
| ~ r2(X92,X91)
| ~ r1(X92)
| ~ r4(X91,X88,X87)
| ~ r2(X90,X89)
| ~ r1(X90)
| ~ r2(X89,X88) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
fof(c_0_11,plain,
! [X3] :
? [X4] :
! [X5] :
( ( X5 = X4
& r2(X3,X5) )
| ( X5 != X4
& ~ r2(X3,X5) ) ),
inference(fof_simplification,[status(thm)],[axiom_2]) ).
fof(c_0_12,plain,
? [X1] :
! [X2] :
( ( X2 = X1
& r1(X2) )
| ( X2 != X1
& ~ r1(X2) ) ),
inference(fof_simplification,[status(thm)],[axiom_1]) ).
fof(c_0_13,plain,
! [X76] :
( esk15_1(X76) = esk17_1(X76)
& r1(esk17_1(X76))
& r4(X76,esk16_1(X76),esk15_1(X76))
& r1(esk16_1(X76)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_5a])]) ).
cnf(c_0_14,negated_conjecture,
( ~ r2(X9,X8)
| ~ r1(X9)
| ~ r2(X8,X7)
| X5 != X7
| ~ r2(X6,X4)
| ~ r1(X6)
| ~ r4(X4,X2,X5)
| ~ r2(X3,X1)
| ~ r1(X3)
| ~ r2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,plain,
! [X63,X64] :
( r4(X63,X64,esk12_2(X63,X64))
& r3(esk12_2(X63,X64),X63,esk9_2(X63,X64))
& esk10_2(X63,X64) = esk9_2(X63,X64)
& r4(X63,esk11_2(X63,X64),esk10_2(X63,X64))
& r2(X64,esk11_2(X63,X64)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_2a])]) ).
fof(c_0_16,plain,
! [X46,X48] :
( ( X48 != esk2_1(X46)
| X48 = esk2_1(X46) )
& ( X48 != esk2_1(X46)
| r2(X46,X48) )
& ( ~ r2(X46,X48)
| X48 = esk2_1(X46) )
& ( ~ r2(X46,X48)
| r2(X46,X48) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_11])])])]) ).
fof(c_0_17,plain,
! [X45] :
( ( X45 != esk1_0
| X45 = esk1_0 )
& ( X45 != esk1_0
| r1(X45) )
& ( ~ r1(X45)
| X45 = esk1_0 )
& ( ~ r1(X45)
| r1(X45) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_12])])])]) ).
cnf(c_0_18,plain,
r1(esk17_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
esk15_1(X1) = esk17_1(X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
( ~ r1(X7)
| ~ r1(X6)
| ~ r1(X4)
| ~ r2(X8,X2)
| ~ r2(X7,X8)
| ~ r2(X6,X1)
| ~ r2(X5,X3)
| ~ r2(X4,X5)
| ~ r4(X1,X2,X3) ),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
r4(X1,X2,esk12_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
( X2 != esk2_1(X1)
| r2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_23,plain,
! [X6,X7] :
? [X8] :
! [X9] :
( ( X9 = X8
& r3(X6,X7,X9) )
| ( X9 != X8
& ~ r3(X6,X7,X9) ) ),
inference(fof_simplification,[status(thm)],[axiom_3]) ).
fof(c_0_24,plain,
! [X10,X11] :
? [X12] :
! [X13] :
( ( X13 = X12
& r4(X10,X11,X13) )
| ( X13 != X12
& ~ r4(X10,X11,X13) ) ),
inference(fof_simplification,[status(thm)],[axiom_4]) ).
cnf(c_0_25,plain,
( ~ r1(X1)
| X1 = esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,plain,
r1(esk16_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_27,plain,
r1(esk15_1(X1)),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_28,negated_conjecture,
( ~ r1(X6)
| ~ r1(X5)
| ~ r1(X4)
| ~ r2(X7,X3)
| ~ r2(X6,X7)
| ~ r2(X5,X2)
| ~ r2(X4,X1)
| ~ r2(X1,esk12_2(X2,X3)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_29,plain,
r2(X1,esk2_1(X1)),
inference(er,[status(thm)],[c_0_22]) ).
fof(c_0_30,plain,
! [X49,X50,X52] :
( ( X52 != esk3_2(X49,X50)
| X52 = esk3_2(X49,X50) )
& ( X52 != esk3_2(X49,X50)
| r3(X49,X50,X52) )
& ( ~ r3(X49,X50,X52)
| X52 = esk3_2(X49,X50) )
& ( ~ r3(X49,X50,X52)
| r3(X49,X50,X52) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_23])])])]) ).
fof(c_0_31,plain,
! [X57,X58] :
( r3(X57,X58,esk8_2(X57,X58))
& r2(esk8_2(X57,X58),esk5_2(X57,X58))
& esk6_2(X57,X58) = esk5_2(X57,X58)
& r3(X57,esk7_2(X57,X58),esk6_2(X57,X58))
& r2(X58,esk7_2(X57,X58)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_1a])]) ).
fof(c_0_32,plain,
! [X53,X54,X56] :
( ( X56 != esk4_2(X53,X54)
| X56 = esk4_2(X53,X54) )
& ( X56 != esk4_2(X53,X54)
| r4(X53,X54,X56) )
& ( ~ r4(X53,X54,X56)
| X56 = esk4_2(X53,X54) )
& ( ~ r4(X53,X54,X56)
| r4(X53,X54,X56) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_24])])])]) ).
cnf(c_0_33,plain,
r4(X1,esk16_1(X1),esk15_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_34,plain,
esk16_1(X1) = esk1_0,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_35,plain,
esk15_1(X1) = esk1_0,
inference(spm,[status(thm)],[c_0_25,c_0_27]) ).
fof(c_0_36,plain,
! [X73] :
( esk13_1(X73) = X73
& r3(X73,esk14_1(X73),esk13_1(X73))
& r1(esk14_1(X73)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_4a])]) ).
cnf(c_0_37,negated_conjecture,
( ~ r1(X5)
| ~ r1(X4)
| ~ r1(X1)
| ~ r2(X6,X3)
| ~ r2(X5,X6)
| ~ r2(X4,X2)
| ~ r2(esk2_1(X1),esk12_2(X2,X3)) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_38,plain,
( ~ r3(X2,X3,X1)
| X1 = esk3_2(X2,X3) ),
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]) ).
cnf(c_0_40,plain,
( ~ r4(X2,X3,X1)
| X1 = esk4_2(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_41,plain,
r4(X1,esk11_2(X1,X2),esk10_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_42,plain,
esk10_2(X1,X2) = esk9_2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_43,plain,
( ~ r2(X2,X1)
| X1 = esk2_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_44,plain,
r2(X1,esk11_2(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_45,plain,
r4(X1,esk1_0,esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_46,plain,
r3(X1,esk14_1(X1),esk13_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_47,plain,
esk13_1(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_48,plain,
r1(esk14_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_49,negated_conjecture,
( ~ r1(X4)
| ~ r1(X2)
| ~ r1(X1)
| ~ r2(X5,X3)
| ~ r2(X4,X5)
| ~ r2(esk2_1(X1),esk12_2(esk2_1(X2),X3)) ),
inference(spm,[status(thm)],[c_0_37,c_0_29]) ).
cnf(c_0_50,plain,
esk3_2(X1,X2) = esk8_2(X1,X2),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_51,plain,
esk4_2(X1,X2) = esk12_2(X1,X2),
inference(spm,[status(thm)],[c_0_40,c_0_21]) ).
cnf(c_0_52,plain,
r4(X1,esk11_2(X1,X2),esk9_2(X1,X2)),
inference(rw,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_53,plain,
esk11_2(X1,X2) = esk2_1(X2),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_54,plain,
esk4_2(X1,esk1_0) = esk1_0,
inference(spm,[status(thm)],[c_0_40,c_0_45]) ).
cnf(c_0_55,plain,
r3(X1,esk14_1(X1),X1),
inference(rw,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_56,plain,
esk14_1(X1) = esk1_0,
inference(spm,[status(thm)],[c_0_25,c_0_48]) ).
cnf(c_0_57,negated_conjecture,
( ~ r1(X4)
| ~ r1(X2)
| ~ r1(X1)
| ~ r2(esk2_1(X4),X3)
| ~ r2(esk2_1(X1),esk12_2(esk2_1(X2),X3)) ),
inference(spm,[status(thm)],[c_0_49,c_0_29]) ).
cnf(c_0_58,plain,
r2(esk8_2(X1,X2),esk5_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_59,plain,
( ~ r3(X2,X3,X1)
| X1 = esk8_2(X2,X3) ),
inference(rw,[status(thm)],[c_0_38,c_0_50]) ).
cnf(c_0_60,plain,
r3(esk12_2(X1,X2),X1,esk9_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_61,plain,
( ~ r4(X2,X3,X1)
| X1 = esk12_2(X2,X3) ),
inference(rw,[status(thm)],[c_0_40,c_0_51]) ).
cnf(c_0_62,plain,
r4(X1,esk2_1(X2),esk9_2(X1,X2)),
inference(rw,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_63,plain,
esk12_2(X1,esk1_0) = esk1_0,
inference(rw,[status(thm)],[c_0_54,c_0_51]) ).
cnf(c_0_64,plain,
r3(X1,esk1_0,X1),
inference(rw,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_65,negated_conjecture,
( ~ r1(X3)
| ~ r1(X2)
| ~ r1(X1)
| ~ r2(esk2_1(X1),esk12_2(esk2_1(X2),esk2_1(esk2_1(X3)))) ),
inference(spm,[status(thm)],[c_0_57,c_0_29]) ).
cnf(c_0_66,plain,
esk2_1(esk8_2(X1,X2)) = esk5_2(X1,X2),
inference(spm,[status(thm)],[c_0_43,c_0_58]) ).
cnf(c_0_67,plain,
esk8_2(esk12_2(X1,X2),X1) = esk9_2(X1,X2),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_68,plain,
esk12_2(X1,esk2_1(X2)) = esk9_2(X1,X2),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_69,plain,
r3(esk1_0,X1,esk9_2(X1,esk1_0)),
inference(spm,[status(thm)],[c_0_60,c_0_63]) ).
cnf(c_0_70,plain,
esk3_2(X1,esk1_0) = X1,
inference(spm,[status(thm)],[c_0_38,c_0_64]) ).
cnf(c_0_71,negated_conjecture,
( ~ r1(X2)
| ~ r1(X1)
| ~ r1(esk8_2(X3,X4))
| ~ r2(esk2_1(X1),esk12_2(esk2_1(X2),esk2_1(esk5_2(X3,X4)))) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_72,plain,
esk8_2(esk9_2(X1,X2),X1) = esk9_2(X1,esk2_1(X2)),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_73,plain,
esk9_2(X1,esk1_0) = esk8_2(esk1_0,X1),
inference(spm,[status(thm)],[c_0_59,c_0_69]) ).
cnf(c_0_74,plain,
esk8_2(X1,esk1_0) = X1,
inference(rw,[status(thm)],[c_0_70,c_0_50]) ).
cnf(c_0_75,plain,
r3(X1,esk7_2(X1,X2),esk6_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_76,plain,
esk6_2(X1,X2) = esk5_2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_77,plain,
r2(X1,esk7_2(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_78,negated_conjecture,
( ~ r1(X2)
| ~ r1(X1)
| ~ r1(esk8_2(X3,X4))
| ~ r2(esk2_1(X1),esk9_2(esk2_1(X2),esk5_2(X3,X4))) ),
inference(rw,[status(thm)],[c_0_71,c_0_68]) ).
cnf(c_0_79,plain,
esk8_2(esk8_2(esk1_0,X1),X1) = esk9_2(X1,esk2_1(esk1_0)),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_80,plain,
r2(X1,esk5_2(X1,esk1_0)),
inference(spm,[status(thm)],[c_0_58,c_0_74]) ).
cnf(c_0_81,plain,
( X1 != esk1_0
| r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_82,plain,
r3(X1,esk7_2(X1,X2),esk5_2(X1,X2)),
inference(rw,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_83,plain,
esk7_2(X1,X2) = esk2_1(X2),
inference(spm,[status(thm)],[c_0_43,c_0_77]) ).
cnf(c_0_84,negated_conjecture,
( ~ r1(X2)
| ~ r1(X1)
| ~ r1(esk9_2(X3,esk2_1(esk1_0)))
| ~ r2(esk2_1(X1),esk9_2(esk2_1(X2),esk5_2(esk8_2(esk1_0,X3),X3))) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_85,plain,
esk9_2(esk1_0,X1) = esk12_2(esk1_0,X1),
inference(spm,[status(thm)],[c_0_74,c_0_67]) ).
cnf(c_0_86,plain,
esk5_2(X1,esk1_0) = esk2_1(X1),
inference(spm,[status(thm)],[c_0_43,c_0_80]) ).
cnf(c_0_87,plain,
r1(esk1_0),
inference(er,[status(thm)],[c_0_81]) ).
cnf(c_0_88,plain,
r3(X1,esk2_1(X2),esk5_2(X1,X2)),
inference(rw,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_89,negated_conjecture,
( ~ r1(X2)
| ~ r1(X1)
| ~ r2(esk2_1(X1),esk9_2(esk2_1(X2),esk2_1(esk1_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_74]),c_0_86]),c_0_68]),c_0_73]),c_0_74]),c_0_87])]) ).
cnf(c_0_90,plain,
esk8_2(X1,esk2_1(X2)) = esk5_2(X1,X2),
inference(spm,[status(thm)],[c_0_59,c_0_88]) ).
cnf(c_0_91,negated_conjecture,
( ~ r1(X1)
| ~ r1(esk8_2(X2,X3))
| ~ r2(esk2_1(X1),esk9_2(esk5_2(X2,X3),esk2_1(esk1_0))) ),
inference(spm,[status(thm)],[c_0_89,c_0_66]) ).
cnf(c_0_92,plain,
esk5_2(esk12_2(esk2_1(X1),X2),X1) = esk9_2(esk2_1(X1),X2),
inference(spm,[status(thm)],[c_0_90,c_0_67]) ).
cnf(c_0_93,negated_conjecture,
( ~ r1(X1)
| ~ r1(esk9_2(X2,esk2_1(esk1_0)))
| ~ r2(esk2_1(X1),esk9_2(esk5_2(esk8_2(esk1_0,X2),X2),esk2_1(esk1_0))) ),
inference(spm,[status(thm)],[c_0_91,c_0_79]) ).
cnf(c_0_94,plain,
esk2_1(esk12_2(esk2_1(esk1_0),X1)) = esk9_2(esk2_1(esk1_0),X1),
inference(spm,[status(thm)],[c_0_86,c_0_92]) ).
cnf(c_0_95,negated_conjecture,
( ~ r1(X1)
| ~ r2(esk2_1(X1),esk9_2(esk2_1(esk1_0),esk2_1(esk1_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_85]),c_0_74]),c_0_86]),c_0_68]),c_0_73]),c_0_74]),c_0_87])]) ).
cnf(c_0_96,plain,
esk9_2(esk2_1(esk1_0),esk2_1(X1)) = esk2_1(esk9_2(esk2_1(esk1_0),X1)),
inference(spm,[status(thm)],[c_0_94,c_0_68]) ).
cnf(c_0_97,negated_conjecture,
( ~ r1(X1)
| ~ r2(esk2_1(X1),esk2_1(esk2_1(esk1_0))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_96]),c_0_73]),c_0_90]),c_0_86]) ).
cnf(c_0_98,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_29]),c_0_87])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUN072+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.43 % Computer : n019.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 21 03:25:04 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.50 Running first-order theorem proving
% 0.16/0.50 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.73/0.78 % Version: 3.5.1
% 1.73/0.78 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.73/0.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.73/0.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.73/0.78 % Starting new_bool_3 with 300s (1) cores
% 1.73/0.78 % Starting new_bool_1 with 300s (1) cores
% 1.73/0.78 % Starting sh5l with 300s (1) cores
% 1.73/0.78 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1592207 completed with status 0
% 1.73/0.78 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1.73/0.78 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.73/0.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.73/0.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.73/0.78 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.73/0.78 % No SInE strategy applied
% 1.73/0.78 % Search class: FGHSM-FFMF21-SFFFFFNN
% 1.73/0.78 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.73/0.78 % Starting SubtermCWHack with 136s (1) cores
% 1.73/0.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.73/0.78 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.73/0.78 % Starting new_bool_3 with 136s (1) cores
% 1.73/0.78 % Starting new_bool_1 with 136s (1) cores
% 1.73/0.78 % new_bool_3 with pid 1592217 completed with status 0
% 1.73/0.78 % Result found by new_bool_3
% 1.73/0.78 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.73/0.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.73/0.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.73/0.78 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.73/0.78 % No SInE strategy applied
% 1.73/0.78 % Search class: FGHSM-FFMF21-SFFFFFNN
% 1.73/0.78 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.73/0.78 % Starting SubtermCWHack with 136s (1) cores
% 1.73/0.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.73/0.78 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.73/0.78 % Starting new_bool_3 with 136s (1) cores
% 1.73/0.78 % Preprocessing time : 0.002 s
% 1.73/0.78 % Presaturation interreduction done
% 1.73/0.78
% 1.73/0.78 % Proof found!
% 1.73/0.78 % SZS status Theorem
% 1.73/0.78 % SZS output start CNFRefutation
% See solution above
% 1.73/0.78 % Parsed axioms : 12
% 1.73/0.78 % Removed by relevancy pruning/SinE : 0
% 1.73/0.78 % Initial clauses : 40
% 1.73/0.78 % Removed in clause preprocessing : 12
% 1.73/0.78 % Initial clauses in saturation : 28
% 1.73/0.78 % Processed clauses : 1462
% 1.73/0.78 % ...of these trivial : 7
% 1.73/0.78 % ...subsumed : 933
% 1.73/0.78 % ...remaining for further processing : 522
% 1.73/0.78 % Other redundant clauses eliminated : 7
% 1.73/0.78 % Clauses deleted for lack of memory : 0
% 1.73/0.78 % Backward-subsumed : 17
% 1.73/0.78 % Backward-rewritten : 30
% 1.73/0.78 % Generated clauses : 6843
% 1.73/0.78 % ...of the previous two non-redundant : 6579
% 1.73/0.78 % ...aggressively subsumed : 0
% 1.73/0.78 % Contextual simplify-reflections : 5
% 1.73/0.78 % Paramodulations : 6834
% 1.73/0.78 % Factorizations : 2
% 1.73/0.78 % NegExts : 0
% 1.73/0.78 % Equation resolutions : 7
% 1.73/0.78 % Disequality decompositions : 0
% 1.73/0.78 % Total rewrite steps : 1009
% 1.73/0.78 % ...of those cached : 770
% 1.73/0.78 % Propositional unsat checks : 0
% 1.73/0.78 % Propositional check models : 0
% 1.73/0.78 % Propositional check unsatisfiable : 0
% 1.73/0.78 % Propositional clauses : 0
% 1.73/0.78 % Propositional clauses after purity: 0
% 1.73/0.78 % Propositional unsat core size : 0
% 1.73/0.78 % Propositional preprocessing time : 0.000
% 1.73/0.78 % Propositional encoding time : 0.000
% 1.73/0.78 % Propositional solver time : 0.000
% 1.73/0.78 % Success case prop preproc time : 0.000
% 1.73/0.78 % Success case prop encoding time : 0.000
% 1.73/0.78 % Success case prop solver time : 0.000
% 1.73/0.78 % Current number of processed clauses : 440
% 1.73/0.78 % Positive orientable unit clauses : 49
% 1.73/0.78 % Positive unorientable unit clauses: 0
% 1.73/0.78 % Negative unit clauses : 71
% 1.73/0.78 % Non-unit-clauses : 320
% 1.73/0.78 % Current number of unprocessed clauses: 5120
% 1.73/0.78 % ...number of literals in the above : 15837
% 1.73/0.78 % Current number of archived formulas : 0
% 1.73/0.78 % Current number of archived clauses : 79
% 1.73/0.78 % Clause-clause subsumption calls (NU) : 49567
% 1.73/0.78 % Rec. Clause-clause subsumption calls : 16546
% 1.73/0.78 % Non-unit clause-clause subsumptions : 536
% 1.73/0.78 % Unit Clause-clause subsumption calls : 9273
% 1.73/0.78 % Rewrite failures with RHS unbound : 0
% 1.73/0.78 % BW rewrite match attempts : 36
% 1.73/0.78 % BW rewrite match successes : 21
% 1.73/0.78 % Condensation attempts : 0
% 1.73/0.78 % Condensation successes : 0
% 1.73/0.78 % Termbank termtop insertions : 78448
% 1.73/0.78 % Search garbage collected termcells : 374
% 1.73/0.78
% 1.73/0.78 % -------------------------------------------------
% 1.73/0.78 % User time : 0.228 s
% 1.73/0.78 % System time : 0.017 s
% 1.73/0.78 % Total time : 0.245 s
% 1.73/0.78 % Maximum resident set size: 3616 pages
% 1.73/0.78
% 1.73/0.78 % -------------------------------------------------
% 1.73/0.78 % User time : 1.142 s
% 1.73/0.78 % System time : 0.069 s
% 1.73/0.78 % Total time : 1.211 s
% 1.73/0.78 % Maximum resident set size: 4608 pages
% 1.73/0.78 % E exiting
%------------------------------------------------------------------------------