TSTP Solution File: NUN059+1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUN059+1 : TPTP v8.1.2. Bugfixed v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n020.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 : Thu Aug 31 12:45:46 EDT 2023
% Result : Theorem 0.19s 0.74s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 60
% Syntax : Number of formulae : 113 ( 21 unt; 48 typ; 0 def)
% Number of atoms : 236 ( 0 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 304 ( 133 ~; 115 |; 54 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 40 ( 24 >; 16 *; 0 +; 0 <<)
% Number of predicates : 29 ( 28 usr; 24 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 1 con; 0-2 aty)
% Number of variables : 174 ( 9 sgn; 75 !; 25 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
id: ( $i * $i ) > $o ).
tff(decl_23,type,
r1: $i > $o ).
tff(decl_24,type,
r2: ( $i * $i ) > $o ).
tff(decl_25,type,
r3: ( $i * $i * $i ) > $o ).
tff(decl_26,type,
r4: ( $i * $i * $i ) > $o ).
tff(decl_27,type,
esk1_0: $i ).
tff(decl_28,type,
esk2_1: $i > $i ).
tff(decl_29,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_30,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_31,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_32,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_33,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_34,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_35,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_36,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_37,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_39,type,
esk13_1: $i > $i ).
tff(decl_40,type,
esk14_1: $i > $i ).
tff(decl_41,type,
esk15_1: $i > $i ).
tff(decl_42,type,
esk16_1: $i > $i ).
tff(decl_43,type,
esk17_1: $i > $i ).
tff(decl_44,type,
esk18_1: $i > $i ).
tff(decl_45,type,
esk19_1: $i > $i ).
tff(decl_46,type,
esk20_1: $i > $i ).
tff(decl_47,type,
epred1_0: $o ).
tff(decl_48,type,
epred2_0: $o ).
tff(decl_49,type,
epred3_0: $o ).
tff(decl_50,type,
epred4_0: $o ).
tff(decl_51,type,
epred5_0: $o ).
tff(decl_52,type,
epred6_0: $o ).
tff(decl_53,type,
epred7_0: $o ).
tff(decl_54,type,
epred8_0: $o ).
tff(decl_55,type,
epred9_0: $o ).
tff(decl_56,type,
epred10_0: $o ).
tff(decl_57,type,
epred11_0: $o ).
tff(decl_58,type,
epred12_0: $o ).
tff(decl_59,type,
epred13_0: $o ).
tff(decl_60,type,
epred14_0: $o ).
tff(decl_61,type,
epred15_0: $o ).
tff(decl_62,type,
epred16_0: $o ).
tff(decl_63,type,
epred17_0: $o ).
tff(decl_64,type,
epred18_0: $o ).
tff(decl_65,type,
epred19_0: $o ).
tff(decl_66,type,
epred20_0: $o ).
tff(decl_67,type,
epred21_0: $o ).
tff(decl_68,type,
epred22_0: $o ).
tff(decl_69,type,
epred23_0: $o ).
fof(axiom_10,axiom,
! [X26,X27,X28,X29,X30,X31] :
( ~ id(X26,X29)
| ~ id(X27,X30)
| ~ id(X28,X31)
| ( ~ r3(X26,X27,X28)
& ~ r3(X29,X30,X31) )
| ( r3(X26,X27,X28)
& r3(X29,X30,X31) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_10) ).
fof(axiom_8,axiom,
! [X20,X21] :
( ~ id(X20,X21)
| ( ~ r1(X20)
& ~ r1(X21) )
| ( r1(X20)
& r1(X21) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_8) ).
fof(axiom_4a,axiom,
! [X54] :
? [X55] :
( id(X55,X54)
& ? [X56] :
( r1(X56)
& r3(X54,X56,X55) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_4a) ).
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_11,axiom,
! [X32,X33,X34,X35,X36,X37] :
( ~ id(X32,X35)
| ~ id(X33,X36)
| ~ id(X34,X37)
| ( ~ r4(X32,X33,X34)
& ~ r4(X35,X36,X37) )
| ( r4(X32,X33,X34)
& r4(X35,X36,X37) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_11) ).
fof(axiom_5a,axiom,
! [X57] :
? [X58] :
( ? [X59] :
( r1(X59)
& r4(X57,X59,X58) )
& ? [X60] :
( id(X58,X60)
& r1(X60) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_5a) ).
fof(axiom_7,axiom,
! [X17,X18,X19] :
( ~ id(X17,X18)
| id(X17,X19)
| ~ id(X18,X19) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_7) ).
fof(fermattothepoweroftwoid,conjecture,
? [X63,X47,X46,X40] :
( ? [X41] :
( id(X40,X41)
& r4(X46,X46,X41) )
& ? [X49] :
( r4(X47,X47,X49)
& ? [X43] :
( r4(X63,X63,X43)
& r3(X43,X49,X40) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fermattothepoweroftwoid) ).
fof(axiom_2a,axiom,
! [X44,X45] :
? [X46] :
( ? [X47] :
( id(X47,X46)
& ? [X48] :
( r2(X45,X48)
& r4(X44,X48,X47) ) )
& ? [X49] :
( r3(X49,X44,X46)
& r4(X44,X45,X49) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_2a) ).
fof(axiom_5,axiom,
! [X14] : id(X14,X14),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_5) ).
fof(c_0_10,plain,
! [X26,X27,X28,X29,X30,X31] :
( ~ id(X26,X29)
| ~ id(X27,X30)
| ~ id(X28,X31)
| ( ~ r3(X26,X27,X28)
& ~ r3(X29,X30,X31) )
| ( r3(X26,X27,X28)
& r3(X29,X30,X31) ) ),
inference(fof_simplification,[status(thm)],[axiom_10]) ).
fof(c_0_11,plain,
! [X20,X21] :
( ~ id(X20,X21)
| ( ~ r1(X20)
& ~ r1(X21) )
| ( r1(X20)
& r1(X21) ) ),
inference(fof_simplification,[status(thm)],[axiom_8]) ).
fof(c_0_12,plain,
! [X93,X94,X95,X96,X97,X98] :
( ( r3(X93,X94,X95)
| ~ r3(X93,X94,X95)
| ~ id(X93,X96)
| ~ id(X94,X97)
| ~ id(X95,X98) )
& ( r3(X96,X97,X98)
| ~ r3(X93,X94,X95)
| ~ id(X93,X96)
| ~ id(X94,X97)
| ~ id(X95,X98) )
& ( r3(X93,X94,X95)
| ~ r3(X96,X97,X98)
| ~ id(X93,X96)
| ~ id(X94,X97)
| ~ id(X95,X98) )
& ( r3(X96,X97,X98)
| ~ r3(X96,X97,X98)
| ~ id(X93,X96)
| ~ id(X94,X97)
| ~ id(X95,X98) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_10])]) ).
fof(c_0_13,plain,
! [X121] :
( id(esk13_1(X121),X121)
& r1(esk14_1(X121))
& r3(X121,esk14_1(X121),esk13_1(X121)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_4a])]) ).
fof(c_0_14,plain,
? [X1] :
! [X2] :
( ( id(X2,X1)
& r1(X2) )
| ( ~ r1(X2)
& ~ id(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[axiom_1]) ).
fof(c_0_15,plain,
! [X32,X33,X34,X35,X36,X37] :
( ~ id(X32,X35)
| ~ id(X33,X36)
| ~ id(X34,X37)
| ( ~ r4(X32,X33,X34)
& ~ r4(X35,X36,X37) )
| ( r4(X32,X33,X34)
& r4(X35,X36,X37) ) ),
inference(fof_simplification,[status(thm)],[axiom_11]) ).
fof(c_0_16,plain,
! [X87,X88] :
( ( r1(X87)
| ~ r1(X87)
| ~ id(X87,X88) )
& ( r1(X88)
| ~ r1(X87)
| ~ id(X87,X88) )
& ( r1(X87)
| ~ r1(X88)
| ~ id(X87,X88) )
& ( r1(X88)
| ~ r1(X88)
| ~ id(X87,X88) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_11])]) ).
fof(c_0_17,plain,
! [X124] :
( r1(esk16_1(X124))
& r4(X124,esk16_1(X124),esk15_1(X124))
& id(esk15_1(X124),esk17_1(X124))
& r1(esk17_1(X124)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_5a])]) ).
cnf(c_0_18,plain,
( r3(X1,X2,X3)
| ~ r3(X4,X5,X6)
| ~ id(X4,X1)
| ~ id(X5,X2)
| ~ id(X6,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
r3(X1,esk14_1(X1),esk13_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_20,plain,
! [X69] :
( ( ~ r1(X69)
| id(X69,esk1_0) )
& ( ~ id(X69,esk1_0)
| id(X69,esk1_0) )
& ( ~ r1(X69)
| r1(X69) )
& ( ~ id(X69,esk1_0)
| r1(X69) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_14])])]) ).
fof(c_0_21,plain,
! [X99,X100,X101,X102,X103,X104] :
( ( r4(X99,X100,X101)
| ~ r4(X99,X100,X101)
| ~ id(X99,X102)
| ~ id(X100,X103)
| ~ id(X101,X104) )
& ( r4(X102,X103,X104)
| ~ r4(X99,X100,X101)
| ~ id(X99,X102)
| ~ id(X100,X103)
| ~ id(X101,X104) )
& ( r4(X99,X100,X101)
| ~ r4(X102,X103,X104)
| ~ id(X99,X102)
| ~ id(X100,X103)
| ~ id(X101,X104) )
& ( r4(X102,X103,X104)
| ~ r4(X102,X103,X104)
| ~ id(X99,X102)
| ~ id(X100,X103)
| ~ id(X101,X104) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_15])]) ).
cnf(c_0_22,plain,
( r1(X1)
| ~ r1(X2)
| ~ id(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
id(esk15_1(X1),esk17_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
r1(esk17_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_25,plain,
! [X17,X18,X19] :
( ~ id(X17,X18)
| id(X17,X19)
| ~ id(X18,X19) ),
inference(fof_simplification,[status(thm)],[axiom_7]) ).
fof(c_0_26,negated_conjecture,
~ ? [X63,X47,X46,X40] :
( ? [X41] :
( id(X40,X41)
& r4(X46,X46,X41) )
& ? [X49] :
( r4(X47,X47,X49)
& ? [X43] :
( r4(X63,X63,X43)
& r3(X43,X49,X40) ) ) ),
inference(assume_negation,[status(cth)],[fermattothepoweroftwoid]) ).
cnf(c_0_27,plain,
( r3(X1,X2,X3)
| ~ id(esk13_1(X4),X3)
| ~ id(esk14_1(X4),X2)
| ~ id(X4,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_28,plain,
id(esk13_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_29,plain,
( id(X1,esk1_0)
| ~ r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,plain,
r1(esk14_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_31,plain,
( r4(X1,X2,X3)
| ~ r4(X4,X5,X6)
| ~ id(X4,X1)
| ~ id(X5,X2)
| ~ id(X6,X3) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_32,plain,
r4(X1,esk16_1(X1),esk15_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_33,plain,
r1(esk15_1(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
fof(c_0_34,plain,
! [X84,X85,X86] :
( ~ id(X84,X85)
| id(X84,X86)
| ~ id(X85,X86) ),
inference(variable_rename,[status(thm)],[c_0_25]) ).
fof(c_0_35,negated_conjecture,
! [X135,X136,X137,X138,X139,X140,X141] :
( ~ id(X138,X139)
| ~ r4(X137,X137,X139)
| ~ r4(X136,X136,X140)
| ~ r4(X135,X135,X141)
| ~ r3(X141,X140,X138) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])]) ).
fof(c_0_36,plain,
! [X111,X112] :
( id(esk10_2(X111,X112),esk9_2(X111,X112))
& r2(X112,esk11_2(X111,X112))
& r4(X111,esk11_2(X111,X112),esk10_2(X111,X112))
& r3(esk12_2(X111,X112),X111,esk9_2(X111,X112))
& r4(X111,X112,esk12_2(X111,X112)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_2a])]) ).
cnf(c_0_37,plain,
( r3(X1,X2,X3)
| ~ id(esk14_1(X3),X2)
| ~ id(X3,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_38,plain,
id(esk14_1(X1),esk1_0),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
fof(c_0_39,plain,
! [X81] : id(X81,X81),
inference(variable_rename,[status(thm)],[axiom_5]) ).
fof(c_0_40,plain,
( ~ epred2_0
<=> ! [X2,X4,X3] :
( ~ id(esk12_2(X4,X4),X3)
| ~ r4(X2,X2,X3) ) ),
introduced(definition) ).
cnf(c_0_41,plain,
( r4(X1,X2,X3)
| ~ id(esk15_1(X4),X3)
| ~ id(esk16_1(X4),X2)
| ~ id(X4,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_42,plain,
id(esk15_1(X1),esk1_0),
inference(spm,[status(thm)],[c_0_29,c_0_33]) ).
cnf(c_0_43,plain,
r1(esk16_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_44,plain,
( id(X1,X3)
| ~ id(X1,X2)
| ~ id(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_45,negated_conjecture,
( ~ id(X1,X2)
| ~ r4(X3,X3,X2)
| ~ r4(X4,X4,X5)
| ~ r4(X6,X6,X7)
| ~ r3(X7,X5,X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_46,plain,
r4(X1,X2,esk12_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_47,plain,
( r3(X1,esk1_0,X2)
| ~ id(X2,X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_48,plain,
id(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_49,negated_conjecture,
( epred2_0
| ~ r4(X1,X1,X2)
| ~ id(esk12_2(X3,X3),X2) ),
inference(split_equiv,[status(thm)],[c_0_40]) ).
cnf(c_0_50,plain,
( r4(X1,X2,esk1_0)
| ~ id(esk16_1(X3),X2)
| ~ id(X3,X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_51,plain,
id(esk16_1(X1),esk1_0),
inference(spm,[status(thm)],[c_0_29,c_0_43]) ).
cnf(c_0_52,plain,
( id(X1,X2)
| ~ id(X1,esk13_1(X2)) ),
inference(spm,[status(thm)],[c_0_44,c_0_28]) ).
fof(c_0_53,plain,
( ~ epred1_0
<=> ! [X1] : ~ r4(X1,X1,esk1_0) ),
introduced(definition) ).
cnf(c_0_54,negated_conjecture,
( ~ r4(X1,X1,X2)
| ~ r4(X3,X3,X4)
| ~ r3(esk12_2(X5,X5),X2,X6)
| ~ id(X6,X4) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_55,plain,
r3(X1,esk1_0,X1),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_56,negated_conjecture,
( epred2_0
| ~ r4(X1,X1,esk12_2(X2,X2)) ),
inference(spm,[status(thm)],[c_0_49,c_0_48]) ).
cnf(c_0_57,plain,
( r4(X1,esk1_0,esk1_0)
| ~ id(X2,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_58,plain,
id(esk13_1(esk13_1(X1)),X1),
inference(spm,[status(thm)],[c_0_52,c_0_28]) ).
cnf(c_0_59,negated_conjecture,
( ~ epred2_0
| ~ epred1_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_53]),c_0_40]) ).
cnf(c_0_60,negated_conjecture,
epred2_0,
inference(spm,[status(thm)],[c_0_56,c_0_46]) ).
cnf(c_0_61,negated_conjecture,
( epred1_0
| ~ r4(X1,X1,esk1_0) ),
inference(split_equiv,[status(thm)],[c_0_53]) ).
cnf(c_0_62,plain,
r4(X1,esk1_0,esk1_0),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_63,negated_conjecture,
~ epred1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60])]) ).
cnf(c_0_64,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN059+1 : TPTP v8.1.2. Bugfixed v7.4.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.17/0.33 % Computer : n020.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Sun Aug 27 09:35:14 EDT 2023
% 0.17/0.33 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 0.19/0.74 % Version : CSE_E---1.5
% 0.19/0.74 % Problem : theBenchmark.p
% 0.19/0.74 % Proof found
% 0.19/0.74 % SZS status Theorem for theBenchmark.p
% 0.19/0.74 % SZS output start Proof
% See solution above
% 0.19/0.75 % Total time : 0.173000 s
% 0.19/0.75 % SZS output end Proof
% 0.19/0.75 % Total time : 0.177000 s
%------------------------------------------------------------------------------