%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUN059+1 : TPTP v9.3.1. Bugfixed v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 01:57:36 PM UTC 2026
% Result : Theorem 14.93s 2.61s
% Output : CNFRefutation 14.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 111 ( 34 unt; 0 def)
% Number of atoms : 319 ( 0 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 365 ( 157 ~; 142 |; 66 &)
% ( 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 : 15 ( 15 usr; 1 con; 0-2 aty)
% Number of variables : 249 ( 30 sgn 85 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_6,axiom,
! [X15,X16] :
( id(X16,X15)
| ~ id(X15,X16) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_6) ).
fof(axiom_8,axiom,
! [X20,X21] :
( ( r1(X21)
& r1(X20) )
| ( ~ r1(X21)
& ~ r1(X20) )
| ~ id(X20,X21) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_8) ).
fof(axiom_4a,axiom,
! [X54] :
? [X55] :
( ? [X56] :
( r3(X54,X56,X55)
& r1(X56) )
& id(X55,X54) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_4a) ).
fof(axiom_11,axiom,
! [X32,X33,X34,X35,X36,X37] :
( ( r4(X35,X36,X37)
& r4(X32,X33,X34) )
| ( ~ r4(X35,X36,X37)
& ~ r4(X32,X33,X34) )
| ~ id(X34,X37)
| ~ id(X33,X36)
| ~ id(X32,X35) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_11) ).
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_5a,axiom,
! [X57] :
? [X58] :
( ? [X60] :
( r1(X60)
& id(X58,X60) )
& ? [X59] :
( r4(X57,X59,X58)
& r1(X59) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_5a) ).
fof(axiom_7,axiom,
! [X17,X18,X19] :
( ~ id(X18,X19)
| id(X17,X19)
| ~ id(X17,X18) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_7) ).
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_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_7a,axiom,
! [X65,X66] :
( ~ r2(X65,X66)
| ! [X67] :
( ~ r1(X67)
| ~ id(X67,X66) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_7a) ).
fof(axiom_5,axiom,
! [X14] : id(X14,X14),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_5) ).
fof(fermattothepoweroftwoid,conjecture,
? [X63,X47,X46,X40] :
( ? [X49] :
( ? [X43] :
( r3(X43,X49,X40)
& r4(X63,X63,X43) )
& r4(X47,X47,X49) )
& ? [X41] :
( r4(X46,X46,X41)
& id(X40,X41) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fermattothepoweroftwoid) ).
fof(axiom_2a,axiom,
! [X44,X45] :
? [X46] :
( ? [X49] :
( r4(X44,X45,X49)
& r3(X49,X44,X46) )
& ? [X47] :
( ? [X48] :
( r4(X44,X48,X47)
& r2(X45,X48) )
& id(X47,X46) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_2a) ).
fof(axiom_6a,axiom,
! [X61] :
( ? [X63,X64] :
( r2(X63,X64)
& id(X61,X64) )
| ? [X62] :
( r1(X62)
& id(X61,X62) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_6a) ).
fof(c_0_14,plain,
! [X15,X16] :
( id(X16,X15)
| ~ id(X15,X16) ),
inference(fof_simplification,[status(thm)],[axiom_6]) ).
fof(c_0_15,plain,
! [X20,X21] :
( ( r1(X21)
& r1(X20) )
| ( ~ r1(X21)
& ~ r1(X20) )
| ~ id(X20,X21) ),
inference(fof_simplification,[status(thm)],[axiom_8]) ).
fof(c_0_16,plain,
! [X82,X83] :
( id(X83,X82)
| ~ id(X82,X83) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_14])]) ).
fof(c_0_17,plain,
! [X121] :
( r3(X121,esk14_1(X121),esk13_1(X121))
& r1(esk14_1(X121))
& id(esk13_1(X121),X121) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_4a])]) ).
fof(c_0_18,plain,
! [X32,X33,X34,X35,X36,X37] :
( ( r4(X35,X36,X37)
& r4(X32,X33,X34) )
| ( ~ r4(X35,X36,X37)
& ~ r4(X32,X33,X34) )
| ~ id(X34,X37)
| ~ id(X33,X36)
| ~ id(X32,X35) ),
inference(fof_simplification,[status(thm)],[axiom_11]) ).
fof(c_0_19,plain,
? [X1] :
! [X2] :
( ( ~ id(X2,X1)
& ~ r1(X2) )
| ( r1(X2)
& id(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[axiom_1]) ).
fof(c_0_20,plain,
! [X87,X88] :
( ( ~ id(X87,X88)
| ~ r1(X88)
| r1(X88) )
& ( ~ id(X87,X88)
| ~ r1(X88)
| r1(X87) )
& ( ~ id(X87,X88)
| ~ r1(X87)
| r1(X88) )
& ( ~ id(X87,X88)
| ~ r1(X87)
| r1(X87) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_15])])]) ).
fof(c_0_21,plain,
! [X124] :
( r1(esk17_1(X124))
& id(esk15_1(X124),esk17_1(X124))
& r4(X124,esk16_1(X124),esk15_1(X124))
& r1(esk16_1(X124)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_5a])]) ).
cnf(c_0_22,plain,
( ~ id(X1,X2)
| id(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
id(esk13_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_24,plain,
! [X99,X100,X101,X102,X103,X104] :
( ( ~ id(X101,X104)
| ~ id(X100,X103)
| ~ id(X99,X102)
| ~ r4(X102,X103,X104)
| r4(X102,X103,X104) )
& ( ~ id(X101,X104)
| ~ id(X100,X103)
| ~ id(X99,X102)
| ~ r4(X102,X103,X104)
| r4(X99,X100,X101) )
& ( ~ id(X101,X104)
| ~ id(X100,X103)
| ~ id(X99,X102)
| ~ r4(X99,X100,X101)
| r4(X102,X103,X104) )
& ( ~ id(X101,X104)
| ~ id(X100,X103)
| ~ id(X99,X102)
| ~ r4(X99,X100,X101)
| r4(X99,X100,X101) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_18])])]) ).
fof(c_0_25,plain,
! [X69] :
( ( r1(X69)
| ~ id(X69,esk1_0) )
& ( r1(X69)
| ~ r1(X69) )
& ( id(X69,esk1_0)
| ~ id(X69,esk1_0) )
& ( id(X69,esk1_0)
| ~ r1(X69) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_19])])])]) ).
cnf(c_0_26,plain,
( ~ id(X1,X2)
| ~ r1(X2)
| r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
id(esk15_1(X1),esk17_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,plain,
r1(esk17_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_29,plain,
! [X17,X18,X19] :
( ~ id(X18,X19)
| id(X17,X19)
| ~ id(X17,X18) ),
inference(fof_simplification,[status(thm)],[axiom_7]) ).
cnf(c_0_30,plain,
( ~ id(X2,X1)
| ~ r1(X2)
| r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_31,plain,
id(X1,esk13_1(X1)),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_32,plain,
( ~ id(X6,X3)
| ~ id(X5,X2)
| ~ id(X4,X1)
| ~ r4(X4,X5,X6)
| r4(X1,X2,X3) ),
inference(split_conjunct,[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_21]) ).
cnf(c_0_34,plain,
( ~ r1(X1)
| id(X1,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_35,plain,
r1(esk15_1(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).
fof(c_0_36,plain,
! [X84,X85,X86] :
( ~ id(X85,X86)
| id(X84,X86)
| ~ id(X84,X85) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_29])]) ).
cnf(c_0_37,plain,
( ~ r1(X1)
| r1(esk13_1(X1)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_38,plain,
r1(esk14_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_39,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_40,plain,
( ~ id(X4,X1)
| ~ id(esk16_1(X4),X2)
| ~ id(esk15_1(X4),X3)
| r4(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_41,plain,
id(esk15_1(X1),esk1_0),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_42,plain,
r1(esk16_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_43,plain,
( ~ id(X2,X3)
| ~ id(X1,X2)
| id(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_44,plain,
! [X3] :
? [X4] :
! [X5] :
( ( ~ id(X5,X4)
& ~ r2(X3,X5) )
| ( r2(X3,X5)
& id(X5,X4) ) ),
inference(fof_simplification,[status(thm)],[axiom_2]) ).
cnf(c_0_45,plain,
( ~ r1(X1)
| id(esk13_1(X1),esk1_0) ),
inference(spm,[status(thm)],[c_0_34,c_0_37]) ).
cnf(c_0_46,plain,
id(esk14_1(X1),esk1_0),
inference(spm,[status(thm)],[c_0_34,c_0_38]) ).
fof(c_0_47,plain,
! [X77,X78,X80] :
( ( r4(X77,X78,X80)
| ~ id(X80,esk4_2(X77,X78)) )
& ( r4(X77,X78,X80)
| ~ r4(X77,X78,X80) )
& ( id(X80,esk4_2(X77,X78))
| ~ id(X80,esk4_2(X77,X78)) )
& ( id(X80,esk4_2(X77,X78))
| ~ r4(X77,X78,X80) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_39])])])]) ).
cnf(c_0_48,plain,
( ~ id(X3,X1)
| ~ id(esk16_1(X3),X2)
| r4(X1,X2,esk1_0) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_49,plain,
id(esk16_1(X1),esk1_0),
inference(spm,[status(thm)],[c_0_34,c_0_42]) ).
cnf(c_0_50,plain,
( ~ id(X1,esk13_1(X2))
| id(X1,X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_23]) ).
fof(c_0_51,plain,
! [X65,X66] :
( ~ r2(X65,X66)
| ! [X67] :
( ~ r1(X67)
| ~ id(X67,X66) ) ),
inference(fof_simplification,[status(thm)],[axiom_7a]) ).
fof(c_0_52,plain,
! [X70,X72] :
( ( r2(X70,X72)
| ~ id(X72,esk2_1(X70)) )
& ( r2(X70,X72)
| ~ r2(X70,X72) )
& ( id(X72,esk2_1(X70))
| ~ id(X72,esk2_1(X70)) )
& ( id(X72,esk2_1(X70))
| ~ r2(X70,X72) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_44])])])]) ).
fof(c_0_53,plain,
! [X81] : id(X81,X81),
inference(variable_rename,[status(thm)],[axiom_5]) ).
cnf(c_0_54,plain,
( ~ r1(X1)
| id(esk1_0,esk13_1(X1)) ),
inference(spm,[status(thm)],[c_0_22,c_0_45]) ).
cnf(c_0_55,plain,
id(esk1_0,esk14_1(X1)),
inference(spm,[status(thm)],[c_0_22,c_0_46]) ).
cnf(c_0_56,plain,
( ~ r4(X1,X2,X3)
| id(X3,esk4_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_57,plain,
( ~ id(X2,X1)
| r4(X1,esk1_0,esk1_0) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_58,plain,
id(esk13_1(esk13_1(X1)),X1),
inference(spm,[status(thm)],[c_0_50,c_0_23]) ).
fof(c_0_59,plain,
! [X132,X133,X134] :
( ~ r2(X132,X133)
| ~ r1(X134)
| ~ id(X134,X133) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_51])])]) ).
cnf(c_0_60,plain,
( ~ id(X1,esk2_1(X2))
| r2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_61,plain,
id(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_62,plain,
( ~ id(X1,esk1_0)
| ~ r1(X2)
| id(X1,esk13_1(X2)) ),
inference(spm,[status(thm)],[c_0_43,c_0_54]) ).
cnf(c_0_63,plain,
( ~ id(X1,esk1_0)
| id(X1,esk14_1(X2)) ),
inference(spm,[status(thm)],[c_0_43,c_0_55]) ).
cnf(c_0_64,plain,
( ~ r1(X3)
| ~ r4(X1,X2,X3)
| r1(esk4_2(X1,X2)) ),
inference(spm,[status(thm)],[c_0_30,c_0_56]) ).
cnf(c_0_65,plain,
r4(X1,esk1_0,esk1_0),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_66,plain,
r1(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_46]),c_0_38])]) ).
cnf(c_0_67,plain,
( ~ r2(X3,X2)
| ~ r1(X1)
| ~ id(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_68,plain,
r2(X1,esk2_1(X1)),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
fof(c_0_69,negated_conjecture,
~ ? [X63,X47,X46,X40] :
( ? [X49] :
( ? [X43] :
( r3(X43,X49,X40)
& r4(X63,X63,X43) )
& r4(X47,X47,X49) )
& ? [X41] :
( r4(X46,X46,X41)
& id(X40,X41) ) ),
inference(assume_negation,[status(cth)],[fermattothepoweroftwoid]) ).
cnf(c_0_70,plain,
( ~ id(X1,esk1_0)
| ~ r1(X2)
| id(X1,X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_62]) ).
cnf(c_0_71,plain,
( ~ id(X2,esk1_0)
| id(esk14_1(X1),X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_63]) ).
cnf(c_0_72,plain,
( ~ r1(esk4_2(X2,X3))
| ~ r4(X2,X3,X1)
| r1(X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_56]) ).
cnf(c_0_73,plain,
r1(esk4_2(X1,esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66])]) ).
cnf(c_0_74,plain,
( ~ id(X1,esk4_2(X2,X3))
| r4(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
fof(c_0_75,plain,
! [X111,X112] :
( r4(X111,X112,esk12_2(X111,X112))
& r3(esk12_2(X111,X112),X111,esk9_2(X111,X112))
& r4(X111,esk11_2(X111,X112),esk10_2(X111,X112))
& r2(X112,esk11_2(X111,X112))
& id(esk10_2(X111,X112),esk9_2(X111,X112)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_2a])]) ).
fof(c_0_76,plain,
! [X128] :
( ( r1(esk18_1(X128))
| r2(esk19_1(X128),esk20_1(X128)) )
& ( r1(esk18_1(X128))
| id(X128,esk20_1(X128)) )
& ( id(X128,esk18_1(X128))
| r2(esk19_1(X128),esk20_1(X128)) )
& ( id(X128,esk18_1(X128))
| id(X128,esk20_1(X128)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_6a])])]) ).
cnf(c_0_77,plain,
( ~ id(X1,esk2_1(X2))
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_78,plain,
( ~ r2(X1,X2)
| id(X2,esk2_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
fof(c_0_79,negated_conjecture,
! [X135,X136,X137,X138,X139,X140,X141] :
( ~ r3(X141,X140,X138)
| ~ r4(X135,X135,X141)
| ~ r4(X136,X136,X140)
| ~ r4(X137,X137,X139)
| ~ id(X138,X139) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_69])])])]) ).
cnf(c_0_80,plain,
( ~ r1(X2)
| id(esk14_1(X1),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_61])]) ).
cnf(c_0_81,plain,
( ~ r4(X2,esk1_0,X1)
| r1(X1) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_82,plain,
r4(X1,X2,esk13_1(esk4_2(X1,X2))),
inference(spm,[status(thm)],[c_0_74,c_0_23]) ).
cnf(c_0_83,plain,
r4(X1,X2,esk12_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_84,plain,
( id(X1,esk18_1(X1))
| id(X1,esk20_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_85,plain,
( ~ r1(X2)
| ~ r2(X1,X2) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_86,plain,
( id(X1,esk18_1(X1))
| r2(esk19_1(X1),esk20_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_87,negated_conjecture,
( ~ r3(X7,X5,X1)
| ~ r4(X6,X6,X7)
| ~ r4(X4,X4,X5)
| ~ r4(X3,X3,X2)
| ~ id(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_88,plain,
( ~ r1(esk13_1(X2))
| id(esk14_1(X1),X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_80]) ).
cnf(c_0_89,plain,
r1(esk13_1(esk4_2(X1,esk1_0))),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_90,plain,
( ~ id(X1,X2)
| id(X1,esk13_1(X2)) ),
inference(spm,[status(thm)],[c_0_43,c_0_31]) ).
cnf(c_0_91,plain,
( ~ r1(X1)
| id(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_54]) ).
cnf(c_0_92,plain,
r1(esk12_2(X1,esk1_0)),
inference(spm,[status(thm)],[c_0_81,c_0_83]) ).
cnf(c_0_93,plain,
( ~ r1(X1)
| id(X1,esk18_1(X1))
| r1(esk20_1(X1)) ),
inference(spm,[status(thm)],[c_0_30,c_0_84]) ).
cnf(c_0_94,plain,
( ~ r1(esk20_1(X1))
| id(X1,esk18_1(X1)) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_95,negated_conjecture,
( ~ id(X6,X4)
| ~ r3(esk12_2(X5,X5),X2,X6)
| ~ r4(X3,X3,X4)
| ~ r4(X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_87,c_0_83]) ).
cnf(c_0_96,plain,
r3(X1,esk14_1(X1),esk13_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_97,plain,
id(esk14_1(X1),esk4_2(X2,esk1_0)),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_98,plain,
( ~ id(X2,X1)
| ~ r1(X2)
| r1(esk13_1(X1)) ),
inference(spm,[status(thm)],[c_0_30,c_0_90]) ).
cnf(c_0_99,plain,
id(esk1_0,esk12_2(X1,esk1_0)),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_100,plain,
id(esk1_0,esk18_1(esk1_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_66]),c_0_94]) ).
cnf(c_0_101,negated_conjecture,
( ~ id(esk13_1(esk12_2(X2,X2)),X4)
| ~ r4(X3,X3,X4)
| ~ r4(X1,X1,esk14_1(esk12_2(X2,X2))) ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_102,plain,
r4(X1,esk1_0,esk14_1(X2)),
inference(spm,[status(thm)],[c_0_74,c_0_97]) ).
cnf(c_0_103,plain,
r1(esk13_1(esk12_2(X1,esk1_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_66])]) ).
cnf(c_0_104,plain,
( ~ id(X1,esk1_0)
| id(X1,esk18_1(esk1_0)) ),
inference(spm,[status(thm)],[c_0_43,c_0_100]) ).
cnf(c_0_105,negated_conjecture,
( ~ id(esk13_1(esk12_2(X3,X3)),X2)
| ~ r4(X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_106,plain,
id(esk13_1(esk12_2(X1,esk1_0)),esk1_0),
inference(spm,[status(thm)],[c_0_34,c_0_103]) ).
cnf(c_0_107,plain,
( ~ id(X2,X1)
| r4(X1,esk18_1(esk1_0),esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_104]),c_0_49])]) ).
cnf(c_0_108,negated_conjecture,
~ r4(X1,X1,esk1_0),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_109,plain,
r4(X1,esk18_1(esk1_0),esk1_0),
inference(spm,[status(thm)],[c_0_107,c_0_58]) ).
cnf(c_0_110,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_108,c_0_109]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN059+1 : TPTP v9.3.1. Bugfixed v7.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n026.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 03:26:21 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.44 Running first-order theorem proving
% 0.15/0.44 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
% 14.93/2.61 % Version: 3.5.1
% 14.93/2.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 14.93/2.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.93/2.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 14.93/2.61 % Starting new_bool_3 with 300s (1) cores
% 14.93/2.61 % Starting new_bool_1 with 300s (1) cores
% 14.93/2.61 % Starting sh5l with 300s (1) cores
% 14.93/2.61 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1265497 completed with status 0
% 14.93/2.61 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 14.93/2.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 14.93/2.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.93/2.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 14.93/2.61 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 14.93/2.61 % No SInE strategy applied
% 14.93/2.61 % Search class: FGHNM-FFMF21-SFFFFFNN
% 14.93/2.61 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 14.93/2.61 % Starting SubtermCWHack with 136s (1) cores
% 14.93/2.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 14.93/2.61 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 231s (1) cores
% 14.93/2.61 % Starting new_bool_3 with 211s (1) cores
% 14.93/2.61 % Starting G-E--_107_C18_F1_PI_AE_Q4_CS_SP_PS_S4S with 136s (1) cores
% 14.93/2.61 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1265502 completed with status 0
% 14.93/2.61 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 14.93/2.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 14.93/2.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.93/2.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 14.93/2.61 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 14.93/2.61 % No SInE strategy applied
% 14.93/2.61 % Search class: FGHNM-FFMF21-SFFFFFNN
% 14.93/2.61 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 14.93/2.61 % Starting SubtermCWHack with 136s (1) cores
% 14.93/2.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 14.93/2.61 % Preprocessing time : 0.003 s
% 14.93/2.61 % Presaturation interreduction done
% 14.93/2.61
% 14.93/2.61 % Proof found!
% 14.93/2.61 % SZS status Theorem
% 14.93/2.61 % SZS output start CNFRefutation
% See solution above
% 14.93/2.61 % Parsed axioms : 19
% 14.93/2.61 % Removed by relevancy pruning/SinE : 0
% 14.93/2.61 % Initial clauses : 59
% 14.93/2.61 % Removed in clause preprocessing : 16
% 14.93/2.61 % Initial clauses in saturation : 43
% 14.93/2.61 % Processed clauses : 15522
% 14.93/2.61 % ...of these trivial : 806
% 14.93/2.61 % ...subsumed : 12093
% 14.93/2.61 % ...remaining for further processing : 2623
% 14.93/2.61 % Other redundant clauses eliminated : 0
% 14.93/2.61 % Clauses deleted for lack of memory : 0
% 14.93/2.61 % Backward-subsumed : 58
% 14.93/2.61 % Backward-rewritten : 36
% 14.93/2.61 % Generated clauses : 88224
% 14.93/2.61 % ...of the previous two non-redundant : 69063
% 14.93/2.61 % ...aggressively subsumed : 0
% 14.93/2.61 % Contextual simplify-reflections : 30
% 14.93/2.61 % Paramodulations : 88224
% 14.93/2.61 % Factorizations : 0
% 14.93/2.61 % NegExts : 0
% 14.93/2.61 % Equation resolutions : 0
% 14.93/2.61 % Disequality decompositions : 0
% 14.93/2.61 % Total rewrite steps : 39171
% 14.93/2.61 % ...of those cached : 38034
% 14.93/2.61 % Propositional unsat checks : 0
% 14.93/2.61 % Propositional check models : 0
% 14.93/2.61 % Propositional check unsatisfiable : 0
% 14.93/2.61 % Propositional clauses : 0
% 14.93/2.61 % Propositional clauses after purity: 0
% 14.93/2.61 % Propositional unsat core size : 0
% 14.93/2.61 % Propositional preprocessing time : 0.000
% 14.93/2.61 % Propositional encoding time : 0.000
% 14.93/2.61 % Propositional solver time : 0.000
% 14.93/2.61 % Success case prop preproc time : 0.000
% 14.93/2.61 % Success case prop encoding time : 0.000
% 14.93/2.61 % Success case prop solver time : 0.000
% 14.93/2.61 % Current number of processed clauses : 2486
% 14.93/2.61 % Positive orientable unit clauses : 498
% 14.93/2.61 % Positive unorientable unit clauses: 0
% 14.93/2.61 % Negative unit clauses : 437
% 14.93/2.61 % Non-unit-clauses : 1551
% 14.93/2.61 % Current number of unprocessed clauses: 52590
% 14.93/2.61 % ...number of literals in the above : 139375
% 14.93/2.61 % Current number of archived formulas : 0
% 14.93/2.61 % Current number of archived clauses : 137
% 14.93/2.61 % Clause-clause subsumption calls (NU) : 315821
% 14.93/2.61 % Rec. Clause-clause subsumption calls : 193474
% 14.93/2.61 % Non-unit clause-clause subsumptions : 3273
% 14.93/2.61 % Unit Clause-clause subsumption calls : 76741
% 14.93/2.61 % Rewrite failures with RHS unbound : 0
% 14.93/2.61 % BW rewrite match attempts : 1891
% 14.93/2.61 % BW rewrite match successes : 43
% 14.93/2.61 % Condensation attempts : 0
% 14.93/2.61 % Condensation successes : 0
% 14.93/2.61 % Termbank termtop insertions : 1078284
% 14.93/2.61 % Search garbage collected termcells : 418
% 14.93/2.61
% 14.93/2.61 % -------------------------------------------------
% 14.93/2.61 % User time : 2.010 s
% 14.93/2.61 % System time : 0.065 s
% 14.93/2.61 % Total time : 2.075 s
% 14.93/2.61 % Maximum resident set size: 3440 pages
% 14.93/2.61
% 14.93/2.61 % -------------------------------------------------
% 14.93/2.61 % User time : 9.997 s
% 14.93/2.61 % System time : 0.465 s
% 14.93/2.61 % Total time : 10.462 s
% 14.93/2.61 % Maximum resident set size: 4608 pages
% 14.93/2.61 % E exiting
%------------------------------------------------------------------------------