%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUN082+1 : 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 : n015.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 01:57:41 PM UTC 2026
% Result : Theorem 17.87s 3.07s
% Output : CNFRefutation 17.87s
% 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/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_1) ).
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_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_6,axiom,
! [X15,X16] :
( id(X16,X15)
| ~ id(X15,X16) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_6) ).
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_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_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(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_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_10,axiom,
! [X26,X27,X28,X29,X30,X31] :
( ( r3(X29,X30,X31)
& r3(X26,X27,X28) )
| ( ~ r3(X29,X30,X31)
& ~ r3(X26,X27,X28) )
| ~ id(X28,X31)
| ~ id(X27,X30)
| ~ id(X26,X29) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_10) ).
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_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_9,axiom,
! [X22,X23,X24,X25] :
( ( r2(X24,X25)
& r2(X22,X23) )
| ( ~ r2(X24,X25)
& ~ r2(X22,X23) )
| ~ id(X23,X25)
| ~ id(X22,X24) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_9) ).
fof(axiom_5,axiom,
! [X14] : id(X14,X14),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_5) ).
fof(xtimesoneidzero,conjecture,
? [X63,X46] :
( ? [X41] :
( r1(X41)
& id(X46,X41) )
& ? [X47] :
( ? [X40] :
( r2(X40,X47)
& r1(X40) )
& r4(X63,X47,X46) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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] :
( ( r1(X21)
& r1(X20) )
| ( ~ r1(X21)
& ~ r1(X20) )
| ~ id(X20,X21) ),
inference(fof_simplification,[status(thm)],[axiom_8]) ).
fof(c_0_19,plain,
! [X65,X66] :
( ~ r2(X65,X66)
| ! [X67] :
( ~ r1(X67)
| ~ id(X67,X66) ) ),
inference(fof_simplification,[status(thm)],[axiom_7a]) ).
fof(c_0_20,plain,
! [X15,X16] :
( id(X16,X15)
| ~ id(X15,X16) ),
inference(fof_simplification,[status(thm)],[axiom_6]) ).
fof(c_0_21,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_17])])])]) ).
fof(c_0_22,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])]) ).
fof(c_0_23,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_18])])]) ).
fof(c_0_24,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_25,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_19])])]) ).
fof(c_0_26,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])])]) ).
fof(c_0_27,plain,
! [X17,X18,X19] :
( ~ id(X18,X19)
| id(X17,X19)
| ~ id(X17,X18) ),
inference(fof_simplification,[status(thm)],[axiom_7]) ).
fof(c_0_28,plain,
! [X82,X83] :
( id(X83,X82)
| ~ id(X82,X83) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_20])]) ).
cnf(c_0_29,plain,
( ~ r1(X1)
| id(X1,esk1_0) ),
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] :
( ( 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]) ).
cnf(c_0_32,plain,
( ~ id(X1,X2)
| ~ r1(X2)
| r1(X1) ),
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,
( ~ r2(X3,X2)
| ~ r1(X1)
| ~ id(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_35,plain,
( id(X1,esk18_1(X1))
| r2(esk19_1(X1),esk20_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_36,plain,
! [X26,X27,X28,X29,X30,X31] :
( ( r3(X29,X30,X31)
& r3(X26,X27,X28) )
| ( ~ r3(X29,X30,X31)
& ~ r3(X26,X27,X28) )
| ~ id(X28,X31)
| ~ id(X27,X30)
| ~ id(X26,X29) ),
inference(fof_simplification,[status(thm)],[axiom_10]) ).
fof(c_0_37,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_27])]) ).
cnf(c_0_38,plain,
( ~ id(X1,X2)
| id(X2,X1) ),
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,
! [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_31])])]) ).
fof(c_0_42,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_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] :
( ( r2(X24,X25)
& r2(X22,X23) )
| ( ~ r2(X24,X25)
& ~ r2(X22,X23) )
| ~ id(X23,X25)
| ~ id(X22,X24) ),
inference(fof_simplification,[status(thm)],[axiom_9]) ).
cnf(c_0_45,plain,
( ~ r1(X1)
| r1(esk13_1(X1)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_46,plain,
( ~ id(X2,esk20_1(X1))
| ~ r1(X2)
| id(X1,esk18_1(X1)) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_47,plain,
( id(X1,esk18_1(X1))
| id(X1,esk20_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_48,plain,
! [X81] : id(X81,X81),
inference(variable_rename,[status(thm)],[axiom_5]) ).
fof(c_0_49,plain,
! [X93,X94,X95,X96,X97,X98] :
( ( ~ id(X95,X98)
| ~ id(X94,X97)
| ~ id(X93,X96)
| ~ r3(X96,X97,X98)
| r3(X96,X97,X98) )
& ( ~ id(X95,X98)
| ~ id(X94,X97)
| ~ id(X93,X96)
| ~ r3(X96,X97,X98)
| r3(X93,X94,X95) )
& ( ~ id(X95,X98)
| ~ id(X94,X97)
| ~ id(X93,X96)
| ~ r3(X93,X94,X95)
| r3(X96,X97,X98) )
& ( ~ id(X95,X98)
| ~ id(X94,X97)
| ~ id(X93,X96)
| ~ r3(X93,X94,X95)
| r3(X93,X94,X95) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_36])])]) ).
cnf(c_0_50,plain,
( ~ id(X2,X3)
| ~ id(X1,X2)
| id(X1,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,
( ~ id(X6,X3)
| ~ id(X5,X2)
| ~ id(X4,X1)
| ~ r4(X4,X5,X6)
| r4(X1,X2,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,
! [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_43])])])]) ).
fof(c_0_56,plain,
! [X89,X90,X91,X92] :
( ( ~ id(X90,X92)
| ~ id(X89,X91)
| ~ r2(X91,X92)
| r2(X91,X92) )
& ( ~ id(X90,X92)
| ~ id(X89,X91)
| ~ r2(X91,X92)
| r2(X89,X90) )
& ( ~ id(X90,X92)
| ~ id(X89,X91)
| ~ r2(X89,X90)
| r2(X91,X92) )
& ( ~ id(X90,X92)
| ~ id(X89,X91)
| ~ r2(X89,X90)
| r2(X89,X90) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_44])])]) ).
cnf(c_0_57,plain,
( ~ r1(X1)
| id(esk13_1(X1),esk1_0) ),
inference(spm,[status(thm)],[c_0_29,c_0_45]) ).
cnf(c_0_58,plain,
( ~ r1(X1)
| id(X1,esk18_1(X1)) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_59,plain,
( ~ id(X1,esk1_0)
| r1(X1) ),
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,
( ~ id(X6,X3)
| ~ id(X5,X2)
| ~ id(X4,X1)
| ~ r3(X4,X5,X6)
| r3(X1,X2,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,esk1_0)
| id(X1,esk17_1(X2)) ),
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,
( ~ id(X4,X1)
| ~ id(esk11_2(X4,X5),X2)
| ~ id(esk10_2(X4,X5),X3)
| r4(X1,X2,X3) ),
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,
( ~ r2(X1,X2)
| id(X2,esk2_1(X1)) ),
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,
( ~ id(X4,X2)
| ~ id(X3,X1)
| ~ r2(X3,X4)
| r2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_72,plain,
( ~ id(X1,esk2_1(X2))
| r2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_73,plain,
( ~ id(X1,esk13_1(X2))
| id(X1,X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_33]) ).
cnf(c_0_74,plain,
( ~ r1(X1)
| id(esk1_0,esk13_1(X1)) ),
inference(spm,[status(thm)],[c_0_38,c_0_57]) ).
cnf(c_0_75,plain,
( ~ r1(X1)
| id(esk18_1(X1),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,
( ~ id(X4,X1)
| ~ id(esk14_1(X4),X2)
| ~ id(esk13_1(X4),X3)
| r3(X1,X2,X3) ),
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,
( ~ id(X4,X1)
| ~ id(esk16_1(X4),X2)
| ~ id(esk15_1(X4),X3)
| r4(X1,X2,X3) ),
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,X2)
| id(X1,esk13_1(X2)) ),
inference(spm,[status(thm)],[c_0_50,c_0_66]) ).
fof(c_0_83,negated_conjecture,
~ ? [X63,X46] :
( ? [X41] :
( r1(X41)
& id(X46,X41) )
& ? [X47] :
( ? [X40] :
( r2(X40,X47)
& r1(X40) )
& r4(X63,X47,X46) ) ),
inference(assume_negation,[status(cth)],[xtimesoneidzero]) ).
cnf(c_0_84,plain,
( ~ id(X3,X1)
| ~ id(esk11_2(X3,X4),X2)
| r4(X1,X2,esk9_2(X3,X4)) ),
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,
( ~ id(X3,X1)
| ~ r2(X3,esk13_1(X2))
| r2(X1,X2) ),
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,
( ~ r1(X1)
| id(esk1_0,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,
( ~ id(X3,X1)
| ~ id(esk14_1(X3),X2)
| r3(X1,X2,esk13_1(X3)) ),
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,
( ~ id(X4,X1)
| ~ id(esk16_1(X4),X2)
| r4(X1,X2,esk17_1(X3)) ),
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,
! [X135,X136,X137,X138,X139] :
( ~ r1(X139)
| ~ id(X136,X139)
| ~ r2(X138,X137)
| ~ r1(X138)
| ~ r4(X135,X137,X136) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_83])])])]) ).
cnf(c_0_98,plain,
( ~ id(X3,X1)
| r4(X1,esk2_1(X2),esk9_2(X3,X2)) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_99,plain,
( ~ id(X3,X1)
| ~ r2(X3,X2)
| r2(X1,X2) ),
inference(spm,[status(thm)],[c_0_71,c_0_60]) ).
cnf(c_0_100,plain,
( ~ id(X2,X1)
| r2(X1,esk2_1(X2)) ),
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,X2)
| ~ r1(X2)
| id(X1,esk18_1(X2)) ),
inference(spm,[status(thm)],[c_0_50,c_0_58]) ).
fof(c_0_103,plain,
! [X73,X74,X76] :
( ( r3(X73,X74,X76)
| ~ id(X76,esk3_2(X73,X74)) )
& ( r3(X73,X74,X76)
| ~ r3(X73,X74,X76) )
& ( id(X76,esk3_2(X73,X74))
| ~ id(X76,esk3_2(X73,X74)) )
& ( id(X76,esk3_2(X73,X74))
| ~ r3(X73,X74,X76) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_90])])])]) ).
cnf(c_0_104,plain,
( ~ id(X2,X1)
| r3(X1,esk1_0,esk13_1(X2)) ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
fof(c_0_105,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_93])])])]) ).
cnf(c_0_106,plain,
( ~ id(X3,X1)
| r4(X1,esk1_0,esk17_1(X2)) ),
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,
( ~ r1(X5)
| ~ id(X3,X5)
| ~ r2(X4,X2)
| ~ r1(X4)
| ~ r4(X1,X2,X3) ),
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,
( ~ r1(X1)
| ~ r2(X1,X2)
| r2(esk18_1(X1),X2) ),
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,
( ~ id(X2,X1)
| ~ r1(X2)
| r1(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,
( ~ r3(X1,X2,X3)
| id(X3,esk3_2(X1,X2)) ),
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,
( ~ r4(X1,X2,X3)
| id(X3,esk4_2(X1,X2)) ),
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,
( ~ id(esk9_2(X4,X2),X3)
| ~ r1(X1)
| ~ r1(X3)
| ~ r2(X1,esk2_1(X2)) ),
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,
( ~ id(esk9_2(X2,esk1_0),X1)
| ~ r1(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(esk13_1(X1))
| r1(esk3_2(X1,esk1_0)) ),
inference(spm,[status(thm)],[c_0_112,c_0_123]) ).
cnf(c_0_129,plain,
( ~ r1(esk4_2(X1,X2))
| r1(esk12_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(X1)
| r1(esk3_2(X1,esk1_0)) ),
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
% 0.00/0.03 % Problem : NUN082+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 03:28:35 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 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
% 17.87/3.07 % Version: 3.5.1
% 17.87/3.07 % Preprocessing class: FSMSSMSSSSSNFFN.
% 17.87/3.07 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 17.87/3.07 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 17.87/3.07 % Starting new_bool_3 with 300s (1) cores
% 17.87/3.07 % Starting new_bool_1 with 300s (1) cores
% 17.87/3.07 % Starting sh5l with 300s (1) cores
% 17.87/3.07 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 461263 completed with status 0
% 17.87/3.07 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 17.87/3.07 % Preprocessing class: FSMSSMSSSSSNFFN.
% 17.87/3.07 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 17.87/3.07 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 17.87/3.07 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 17.87/3.07 % No SInE strategy applied
% 17.87/3.07 % Search class: FGHNM-FFMF21-SFFFFFNN
% 17.87/3.07 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 17.87/3.07 % Starting SubtermCWHack with 136s (1) cores
% 17.87/3.07 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 17.87/3.07 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 231s (1) cores
% 17.87/3.07 % Starting new_bool_3 with 211s (1) cores
% 17.87/3.07 % Starting G-E--_107_C18_F1_PI_AE_Q4_CS_SP_PS_S4S with 136s (1) cores
% 17.87/3.07 % G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with pid 461272 completed with status 0
% 17.87/3.07 % Result found by G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S
% 17.87/3.07 % Preprocessing class: FSMSSMSSSSSNFFN.
% 17.87/3.07 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 17.87/3.07 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 17.87/3.07 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 17.87/3.07 % No SInE strategy applied
% 17.87/3.07 % Search class: FGHNM-FFMF21-SFFFFFNN
% 17.87/3.07 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 17.87/3.07 % Starting SubtermCWHack with 136s (1) cores
% 17.87/3.07 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 17.87/3.07 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 231s (1) cores
% 17.87/3.07 % Preprocessing time : 0.002 s
% 17.87/3.07 % Presaturation interreduction done
% 17.87/3.07
% 17.87/3.07 % Proof found!
% 17.87/3.07 % SZS status Theorem
% 17.87/3.07 % SZS output start CNFRefutation
% See solution above
% 17.87/3.07 % Parsed axioms : 19
% 17.87/3.07 % Removed by relevancy pruning/SinE : 0
% 17.87/3.07 % Initial clauses : 59
% 17.87/3.07 % Removed in clause preprocessing : 16
% 17.87/3.07 % Initial clauses in saturation : 43
% 17.87/3.07 % Processed clauses : 14972
% 17.87/3.07 % ...of these trivial : 1933
% 17.87/3.07 % ...subsumed : 9564
% 17.87/3.07 % ...remaining for further processing : 3475
% 17.87/3.07 % Other redundant clauses eliminated : 0
% 17.87/3.07 % Clauses deleted for lack of memory : 0
% 17.87/3.07 % Backward-subsumed : 32
% 17.87/3.07 % Backward-rewritten : 73
% 17.87/3.07 % Generated clauses : 243729
% 17.87/3.07 % ...of the previous two non-redundant : 213466
% 17.87/3.07 % ...aggressively subsumed : 0
% 17.87/3.07 % Contextual simplify-reflections : 17
% 17.87/3.07 % Paramodulations : 243729
% 17.87/3.07 % Factorizations : 0
% 17.87/3.07 % NegExts : 0
% 17.87/3.07 % Equation resolutions : 0
% 17.87/3.07 % Disequality decompositions : 0
% 17.87/3.07 % Total rewrite steps : 77705
% 17.87/3.07 % ...of those cached : 76135
% 17.87/3.07 % Propositional unsat checks : 0
% 17.87/3.07 % Propositional check models : 0
% 17.87/3.07 % Propositional check unsatisfiable : 0
% 17.87/3.07 % Propositional clauses : 0
% 17.87/3.07 % Propositional clauses after purity: 0
% 17.87/3.07 % Propositional unsat core size : 0
% 17.87/3.07 % Propositional preprocessing time : 0.000
% 17.87/3.07 % Propositional encoding time : 0.000
% 17.87/3.07 % Propositional solver time : 0.000
% 17.87/3.07 % Success case prop preproc time : 0.000
% 17.87/3.07 % Success case prop encoding time : 0.000
% 17.87/3.07 % Success case prop solver time : 0.000
% 17.87/3.07 % Current number of processed clauses : 3327
% 17.87/3.07 % Positive orientable unit clauses : 1157
% 17.87/3.07 % Positive unorientable unit clauses: 0
% 17.87/3.07 % Negative unit clauses : 449
% 17.87/3.07 % Non-unit-clauses : 1721
% 17.87/3.07 % Current number of unprocessed clauses: 194183
% 17.87/3.07 % ...number of literals in the above : 363457
% 17.87/3.07 % Current number of archived formulas : 0
% 17.87/3.07 % Current number of archived clauses : 148
% 17.87/3.07 % Clause-clause subsumption calls (NU) : 203031
% 17.87/3.07 % Rec. Clause-clause subsumption calls : 139471
% 17.87/3.07 % Non-unit clause-clause subsumptions : 6533
% 17.87/3.07 % Unit Clause-clause subsumption calls : 66121
% 17.87/3.07 % Rewrite failures with RHS unbound : 0
% 17.87/3.07 % BW rewrite match attempts : 5626
% 17.87/3.07 % BW rewrite match successes : 74
% 17.87/3.07 % Condensation attempts : 0
% 17.87/3.07 % Condensation successes : 0
% 17.87/3.07 % Termbank termtop insertions : 2883275
% 17.87/3.07 % Search garbage collected termcells : 408
% 17.87/3.07
% 17.87/3.07 % -------------------------------------------------
% 17.87/3.07 % User time : 2.434 s
% 17.87/3.07 % System time : 0.107 s
% 17.87/3.07 % Total time : 2.541 s
% 17.87/3.07 % Maximum resident set size: 3696 pages
% 17.87/3.07
% 17.87/3.07 % -------------------------------------------------
% 17.87/3.07 % User time : 12.028 s
% 17.87/3.07 % System time : 0.544 s
% 17.87/3.07 % Total time : 12.572 s
% 17.87/3.07 % Maximum resident set size: 4608 pages
% 17.87/3.07 % E exiting
%------------------------------------------------------------------------------