TSTP Solution File: NUM696^1 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM696^1 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n015.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 : 600s
% DateTime : Mon Jul 18 13:55:22 EDT 2022
% Result : Theorem 44.68s 44.14s
% Output : Proof 44.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 28
% Syntax : Number of formulae : 101 ( 39 unt; 0 typ; 0 def)
% Number of atoms : 388 ( 60 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 335 ( 92 ~; 68 |; 1 &; 157 @)
% ( 0 <=>; 14 =>; 3 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 32 usr; 33 con; 0-2 aty)
% Number of variables : 43 ( 0 ^ 43 !; 0 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
thf(satz25,conjecture,
( ! [X1: nat] :
( y
!= ( pl @ ( pl @ x @ n_1 ) @ X1 ) )
=> ( y
= ( pl @ x @ n_1 ) ) ) ).
thf(h0,negated_conjecture,
~ ( ! [X1: nat] :
( y
!= ( pl @ ( pl @ x @ n_1 ) @ X1 ) )
=> ( y
= ( pl @ x @ n_1 ) ) ),
inference(assume_negation,[status(cth)],[satz25]) ).
thf(ax118,axiom,
( ~ p10
| p11 ),
file('<stdin>',ax118) ).
thf(ax109,axiom,
( ~ p11
| p19 ),
file('<stdin>',ax109) ).
thf(ax119,axiom,
p10,
file('<stdin>',ax119) ).
thf(ax108,axiom,
( ~ p19
| ~ p17
| p18 ),
file('<stdin>',ax108) ).
thf(ax126,axiom,
~ p2,
file('<stdin>',ax126) ).
thf(ax110,axiom,
( p2
| p17 ),
file('<stdin>',ax110) ).
thf(ax120,axiom,
( p1
| ~ p8 ),
file('<stdin>',ax120) ).
thf(ax127,axiom,
~ p1,
file('<stdin>',ax127) ).
thf(ax94,axiom,
( p23
| ~ p28
| ~ p29 ),
file('<stdin>',ax94) ).
thf(ax101,axiom,
( ~ p17
| p8
| ~ p18
| ~ p23 ),
file('<stdin>',ax101) ).
thf(ax53,axiom,
( ~ p4
| p57 ),
file('<stdin>',ax53) ).
thf(ax89,axiom,
p28,
file('<stdin>',ax89) ).
thf(pax57,axiom,
( p57
=> ( ! [X1: nat] :
( f__0
!= ( fpl @ fn_1 @ X1 ) )
=> ( f__0 = fn_1 ) ) ),
file('<stdin>',pax57) ).
thf(ax124,axiom,
p4,
file('<stdin>',ax124) ).
thf(nax29,axiom,
( p29
<= ( f__0 = fn_1 ) ),
file('<stdin>',nax29) ).
thf(pax62,axiom,
( p62
=> ! [X1: nat] :
( ( ( fpl @ fx @ f__0 )
= X1 )
=> ( X1
!= ( fpl @ fx @ f__0 ) ) ) ),
file('<stdin>',pax62) ).
thf(pax7,axiom,
( p7
=> ! [X1: nat] :
( fy
!= ( fpl @ ( fpl @ fx @ fn_1 ) @ X1 ) ) ),
file('<stdin>',pax7) ).
thf(ax121,axiom,
( p1
| p7 ),
file('<stdin>',ax121) ).
thf(pax6,axiom,
( p6
=> ! [X1: nat,X2: nat] :
( ( fpl @ X1 @ X2 )
= ( fpl @ X2 @ X1 ) ) ),
file('<stdin>',pax6) ).
thf(ax122,axiom,
p6,
file('<stdin>',ax122) ).
thf(pax5,axiom,
( p5
=> ! [X1: nat,X2: nat,X3: nat] :
( ~ ! [X4: nat] :
( X1
!= ( fpl @ X2 @ X4 ) )
=> ~ ! [X4: nat] :
( ( fpl @ X1 @ X3 )
!= ( fpl @ ( fpl @ X2 @ X3 ) @ X4 ) ) ) ),
file('<stdin>',pax5) ).
thf(pax52,axiom,
( p52
=> ! [X1: nat] :
( f__0
!= ( fpl @ fn_1 @ X1 ) ) ),
file('<stdin>',pax52) ).
thf(nax62,axiom,
( p62
<= ! [X1: nat] :
( ( ( fpl @ fx @ f__0 )
= X1 )
=> ( X1
!= ( fpl @ fx @ f__0 ) ) ) ),
file('<stdin>',nax62) ).
thf(ax123,axiom,
p5,
file('<stdin>',ax123) ).
thf(nax52,axiom,
( p52
<= ! [X1: nat] :
( f__0
!= ( fpl @ fn_1 @ X1 ) ) ),
file('<stdin>',nax52) ).
thf(pax17,axiom,
( p17
=> ( fy
= ( fpl @ fx @ f__0 ) ) ),
file('<stdin>',pax17) ).
thf(c_0_26,plain,
( ~ p10
| p11 ),
inference(fof_simplification,[status(thm)],[ax118]) ).
thf(c_0_27,plain,
( ~ p11
| p19 ),
inference(fof_simplification,[status(thm)],[ax109]) ).
thf(c_0_28,plain,
( p11
| ~ p10 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_29,plain,
p10,
inference(split_conjunct,[status(thm)],[ax119]) ).
thf(c_0_30,plain,
( ~ p19
| ~ p17
| p18 ),
inference(fof_simplification,[status(thm)],[ax108]) ).
thf(c_0_31,plain,
( p19
| ~ p11 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_32,plain,
p11,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]) ).
thf(c_0_33,plain,
~ p2,
inference(fof_simplification,[status(thm)],[ax126]) ).
thf(c_0_34,plain,
( p18
| ~ p19
| ~ p17 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_35,plain,
p19,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]) ).
thf(c_0_36,plain,
( p2
| p17 ),
inference(split_conjunct,[status(thm)],[ax110]) ).
thf(c_0_37,plain,
~ p2,
inference(split_conjunct,[status(thm)],[c_0_33]) ).
thf(c_0_38,plain,
( p1
| ~ p8 ),
inference(fof_simplification,[status(thm)],[ax120]) ).
thf(c_0_39,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax127]) ).
thf(c_0_40,plain,
( p23
| ~ p28
| ~ p29 ),
inference(fof_simplification,[status(thm)],[ax94]) ).
thf(c_0_41,plain,
( ~ p17
| p8
| ~ p18
| ~ p23 ),
inference(fof_simplification,[status(thm)],[ax101]) ).
thf(c_0_42,plain,
( p18
| ~ p17 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]) ).
thf(c_0_43,plain,
p17,
inference(sr,[status(thm)],[c_0_36,c_0_37]) ).
thf(c_0_44,plain,
( p1
| ~ p8 ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
thf(c_0_45,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_46,plain,
( ~ p4
| p57 ),
inference(fof_simplification,[status(thm)],[ax53]) ).
thf(c_0_47,plain,
( p23
| ~ p28
| ~ p29 ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_48,plain,
p28,
inference(split_conjunct,[status(thm)],[ax89]) ).
thf(c_0_49,plain,
( p8
| ~ p17
| ~ p18
| ~ p23 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_50,plain,
p18,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]) ).
thf(c_0_51,plain,
~ p8,
inference(sr,[status(thm)],[c_0_44,c_0_45]) ).
thf(c_0_52,plain,
( ~ p57
| ( f__0
= ( fpl @ fn_1 @ esk29_0 ) )
| ( f__0 = fn_1 ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax57])])])]) ).
thf(c_0_53,plain,
( p57
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
thf(c_0_54,plain,
p4,
inference(split_conjunct,[status(thm)],[ax124]) ).
thf(c_0_55,plain,
( p23
| ~ p29 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]) ).
thf(c_0_56,plain,
~ p23,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_43]),c_0_50])]),c_0_51]) ).
thf(c_0_57,plain,
( ( f__0 != fn_1 )
| p29 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax29])]) ).
thf(c_0_58,plain,
! [X57: nat] :
( ~ p62
| ( ( fpl @ fx @ f__0 )
!= X57 )
| ( X57
!= ( fpl @ fx @ f__0 ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax62])])])]) ).
thf(c_0_59,plain,
! [X123: nat] :
( ~ p7
| ( fy
!= ( fpl @ ( fpl @ fx @ fn_1 ) @ X123 ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax7])])])]) ).
thf(c_0_60,plain,
( p1
| p7 ),
inference(split_conjunct,[status(thm)],[ax121]) ).
thf(c_0_61,plain,
! [X125: nat,X126: nat] :
( ~ p6
| ( ( fpl @ X125 @ X126 )
= ( fpl @ X126 @ X125 ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax6])])]) ).
thf(c_0_62,plain,
( ( f__0
= ( fpl @ fn_1 @ esk29_0 ) )
| ( f__0 = fn_1 )
| ~ p57 ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
thf(c_0_63,plain,
p57,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_54])]) ).
thf(c_0_64,plain,
~ p29,
inference(sr,[status(thm)],[c_0_55,c_0_56]) ).
thf(c_0_65,plain,
( p29
| ( f__0 != fn_1 ) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
thf(c_0_66,plain,
! [X1: nat] :
( ~ p62
| ( ( fpl @ fx @ f__0 )
!= X1 )
| ( X1
!= ( fpl @ fx @ f__0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
thf(c_0_67,plain,
! [X1: nat] :
( ~ p7
| ( fy
!= ( fpl @ ( fpl @ fx @ fn_1 ) @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
thf(c_0_68,plain,
p7,
inference(sr,[status(thm)],[c_0_60,c_0_45]) ).
thf(c_0_69,plain,
! [X2: nat,X1: nat] :
( ( ( fpl @ X1 @ X2 )
= ( fpl @ X2 @ X1 ) )
| ~ p6 ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
thf(c_0_70,plain,
p6,
inference(split_conjunct,[status(thm)],[ax122]) ).
thf(c_0_71,plain,
! [X129: nat,X130: nat,X131: nat,X132: nat] :
( ~ p5
| ( X129
!= ( fpl @ X130 @ X131 ) )
| ( ( fpl @ X129 @ X132 )
= ( fpl @ ( fpl @ X130 @ X132 ) @ ( esk63_3 @ X129 @ X130 @ X132 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax5])])])])])]) ).
thf(c_0_72,plain,
! [X67: nat] :
( ~ p52
| ( f__0
!= ( fpl @ fn_1 @ X67 ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax52])])])]) ).
thf(c_0_73,plain,
( ( ( fpl @ fn_1 @ esk29_0 )
= f__0 )
| ( f__0 = fn_1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_63])]) ).
thf(c_0_74,plain,
f__0 != fn_1,
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
thf(c_0_75,plain,
( ( ( ( fpl @ fx @ f__0 )
= esk27_0 )
| p62 )
& ( ( esk27_0
= ( fpl @ fx @ f__0 ) )
| p62 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax62])])])])]) ).
thf(c_0_76,plain,
! [X1: nat] :
( ( ( fpl @ fx @ f__0 )
!= X1 )
| ~ p62 ),
inference(cn,[status(thm)],[c_0_66]) ).
thf(c_0_77,plain,
! [X1: nat] :
( ( fpl @ ( fpl @ fx @ fn_1 ) @ X1 )
!= fy ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68])]) ).
thf(c_0_78,plain,
! [X2: nat,X1: nat] :
( ( fpl @ X1 @ X2 )
= ( fpl @ X2 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70])]) ).
thf(c_0_79,plain,
! [X1: nat,X2: nat,X4: nat,X3: nat] :
( ( ( fpl @ X1 @ X4 )
= ( fpl @ ( fpl @ X2 @ X4 ) @ ( esk63_3 @ X1 @ X2 @ X4 ) ) )
| ~ p5
| ( X1
!= ( fpl @ X2 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
thf(c_0_80,plain,
p5,
inference(split_conjunct,[status(thm)],[ax123]) ).
thf(c_0_81,plain,
( ( f__0
= ( fpl @ fn_1 @ esk32_0 ) )
| p52 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax52])])])]) ).
thf(c_0_82,plain,
! [X1: nat] :
( ~ p52
| ( f__0
!= ( fpl @ fn_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
thf(c_0_83,plain,
( ( fpl @ fn_1 @ esk29_0 )
= f__0 ),
inference(sr,[status(thm)],[c_0_73,c_0_74]) ).
thf(c_0_84,plain,
( ~ p17
| ( fy
= ( fpl @ fx @ f__0 ) ) ),
inference(fof_nnf,[status(thm)],[pax17]) ).
thf(c_0_85,plain,
( ( esk27_0
= ( fpl @ fx @ f__0 ) )
| p62 ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_86,plain,
~ p62,
inference(er,[status(thm)],[c_0_76]) ).
thf(c_0_87,plain,
! [X1: nat] :
( ( fpl @ ( fpl @ fn_1 @ fx ) @ X1 )
!= fy ),
inference(rw,[status(thm)],[c_0_77,c_0_78]) ).
thf(c_0_88,plain,
! [X1: nat,X3: nat,X2: nat] :
( ( fpl @ ( fpl @ X1 @ X2 ) @ ( esk63_3 @ ( fpl @ X1 @ X3 ) @ X1 @ X2 ) )
= ( fpl @ ( fpl @ X1 @ X3 ) @ X2 ) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80])])]) ).
thf(c_0_89,plain,
( ( f__0
= ( fpl @ fn_1 @ esk32_0 ) )
| p52 ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
thf(c_0_90,plain,
~ p52,
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
thf(c_0_91,plain,
( ( fy
= ( fpl @ fx @ f__0 ) )
| ~ p17 ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
thf(c_0_92,plain,
( ( fpl @ fx @ f__0 )
= esk27_0 ),
inference(sr,[status(thm)],[c_0_85,c_0_86]) ).
thf(c_0_93,plain,
! [X1: nat] :
( ( fpl @ fx @ ( fpl @ fn_1 @ X1 ) )
!= fy ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_78]) ).
thf(c_0_94,plain,
( ( fpl @ fn_1 @ esk32_0 )
= f__0 ),
inference(sr,[status(thm)],[c_0_89,c_0_90]) ).
thf(c_0_95,plain,
esk27_0 = fy,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_92]),c_0_43])]) ).
thf(c_0_96,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_92]),c_0_95])]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],]) ).
thf(0,theorem,
( ! [X1: nat] :
( y
!= ( pl @ ( pl @ x @ n_1 ) @ X1 ) )
=> ( y
= ( pl @ x @ n_1 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM696^1 : TPTP v8.1.0. Released v3.7.0.
% 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jul 7 02:40:19 EDT 2022
% 0.13/0.35 % CPUTime :
% 44.68/44.14 % SZS status Theorem
% 44.68/44.14 % Mode: mode459
% 44.68/44.14 % Inferences: 29
% 44.68/44.14 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------