TSTP Solution File: ALG273^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ALG273^5 : TPTP v8.1.0. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n025.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 : Thu Jul 14 17:57:53 EDT 2022
% Result : Theorem 152.21s 151.82s
% Output : Proof 152.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 59
% Syntax : Number of formulae : 282 ( 49 unt; 0 typ; 7 def)
% Number of atoms : 1364 ( 217 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 1348 ( 264 ~; 255 |; 6 &; 775 @)
% ( 0 <=>; 35 =>; 13 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 66 ( 64 usr; 65 con; 0-2 aty)
% Number of variables : 232 ( 13 ^ 219 !; 0 ?; 232 :)
% Comments :
%------------------------------------------------------------------------------
thf(def_cGRP_ASSOC,definition,
( cGRP_ASSOC
= ( ^ [X1: g > g > g] :
! [X2: g,X3: g,X4: g] :
( ( X1 @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ X2 @ ( X1 @ X3 @ X4 ) ) ) ) ) ).
thf(def_cGRP_LEFT_INVERSE,definition,
( cGRP_LEFT_INVERSE
= ( ^ [X1: g > g > g,X2: g] :
! [X3: g] :
~ ! [X4: g] :
( ( X1 @ X4 @ X3 )
!= X2 ) ) ) ).
thf(def_cGRP_LEFT_UNIT,definition,
( cGRP_LEFT_UNIT
= ( ^ [X1: g > g > g,X2: g] :
! [X3: g] :
( ( X1 @ X2 @ X3 )
= X3 ) ) ) ).
thf(def_cGRP_RIGHT_INVERSE,definition,
( cGRP_RIGHT_INVERSE
= ( ^ [X1: g > g > g,X2: g] :
! [X3: g] :
~ ! [X4: g] :
( ( X1 @ X3 @ X4 )
!= X2 ) ) ) ).
thf(def_cGRP_RIGHT_UNIT,definition,
( cGRP_RIGHT_UNIT
= ( ^ [X1: g > g > g,X2: g] :
! [X3: g] :
( ( X1 @ X3 @ X2 )
= X3 ) ) ) ).
thf(def_cGROUP2,definition,
( cGROUP2
= ( ^ [X1: g > g > g,X2: g] :
~ ( ~ ( ( cGRP_ASSOC @ X1 )
=> ~ ( cGRP_LEFT_UNIT @ X1 @ X2 ) )
=> ~ ( cGRP_LEFT_INVERSE @ X1 @ X2 ) ) ) ) ).
thf(def_cGROUP3,definition,
( cGROUP3
= ( ^ [X1: g > g > g,X2: g] :
~ ( ~ ( ( cGRP_ASSOC @ X1 )
=> ~ ( cGRP_RIGHT_UNIT @ X1 @ X2 ) )
=> ~ ( cGRP_RIGHT_INVERSE @ X1 @ X2 ) ) ) ) ).
thf(cEQUIV_02_03,conjecture,
! [X1: g > g > g,X2: g] :
( ( ~ ( ~ ( ! [X3: g,X4: g,X5: g] :
( ( X1 @ ( X1 @ X3 @ X4 ) @ X5 )
= ( X1 @ X3 @ ( X1 @ X4 @ X5 ) ) )
=> ~ ! [X3: g] :
( ( X1 @ X2 @ X3 )
= X3 ) )
=> ~ ! [X3: g] :
~ ! [X4: g] :
( ( X1 @ X4 @ X3 )
!= X2 ) ) )
= ( ~ ( ~ ( ! [X3: g,X4: g,X5: g] :
( ( X1 @ ( X1 @ X3 @ X4 ) @ X5 )
= ( X1 @ X3 @ ( X1 @ X4 @ X5 ) ) )
=> ~ ! [X3: g] :
( ( X1 @ X3 @ X2 )
= X3 ) )
=> ~ ! [X3: g] :
~ ! [X4: g] :
( ( X1 @ X3 @ X4 )
!= X2 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: g > g > g,X2: g] :
( ( ~ ( ~ ( ! [X3: g,X4: g,X5: g] :
( ( X1 @ ( X1 @ X3 @ X4 ) @ X5 )
= ( X1 @ X3 @ ( X1 @ X4 @ X5 ) ) )
=> ~ ! [X3: g] :
( ( X1 @ X2 @ X3 )
= X3 ) )
=> ~ ! [X3: g] :
~ ! [X4: g] :
( ( X1 @ X4 @ X3 )
!= X2 ) ) )
= ( ~ ( ~ ( ! [X3: g,X4: g,X5: g] :
( ( X1 @ ( X1 @ X3 @ X4 ) @ X5 )
= ( X1 @ X3 @ ( X1 @ X4 @ X5 ) ) )
=> ~ ! [X3: g] :
( ( X1 @ X3 @ X2 )
= X3 ) )
=> ~ ! [X3: g] :
~ ! [X4: g] :
( ( X1 @ X3 @ X4 )
!= X2 ) ) ) ),
inference(assume_negation,[status(cth)],[cEQUIV_02_03]) ).
thf(ax1480,axiom,
( p1
| ~ p2 ),
file('<stdin>',ax1480) ).
thf(ax1481,axiom,
~ p1,
file('<stdin>',ax1481) ).
thf(ax1479,axiom,
( p2
| ~ p3 ),
file('<stdin>',ax1479) ).
thf(ax1471,axiom,
( p3
| ~ p10
| ~ p11 ),
file('<stdin>',ax1471) ).
thf(nax11,axiom,
( p11
<= ( ~ ( ! [X1: g,X2: g,X3: g] :
( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
= ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) )
=> ~ ! [X1: g] :
( ( f__0 @ X1 @ f__1 )
= X1 ) )
=> ~ ! [X1: g] :
~ ! [X2: g] :
( ( f__0 @ X1 @ X2 )
!= f__1 ) ) ),
file('<stdin>',nax11) ).
thf(nax10,axiom,
( p10
<= ( ~ ( ! [X1: g,X2: g,X3: g] :
( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
= ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) )
=> ~ ! [X1: g] :
( ( f__0 @ f__1 @ X1 )
= X1 ) )
=> ~ ! [X1: g] :
~ ! [X2: g] :
( ( f__0 @ X2 @ X1 )
!= f__1 ) ) ),
file('<stdin>',nax10) ).
thf(pax32,axiom,
( p32
=> ! [X1: g] :
( ( f__0 @ X1 @ f__3 )
!= f__1 ) ),
file('<stdin>',pax32) ).
thf(ax979,axiom,
( p32
| p341 ),
file('<stdin>',ax979) ).
thf(ax1445,axiom,
( ~ p13
| ~ p32 ),
file('<stdin>',ax1445) ).
thf(ax1458,axiom,
( p10
| p13 ),
file('<stdin>',ax1458) ).
thf(pax341,axiom,
( p341
=> ( ( f__0 @ f__8 @ f__3 )
= f__1 ) ),
file('<stdin>',pax341) ).
thf(ax1442,axiom,
( ~ p18
| ~ p35 ),
file('<stdin>',ax1442) ).
thf(ax1247,axiom,
( p35
| p165 ),
file('<stdin>',ax1247) ).
thf(nax35,axiom,
( p35
<= ! [X1: g] :
( ( f__0 @ f__3 @ X1 )
!= f__1 ) ),
file('<stdin>',nax35) ).
thf(ax1465,axiom,
( p11
| p18 ),
file('<stdin>',ax1465) ).
thf(ax1438,axiom,
( ~ p15
| p20 ),
file('<stdin>',ax1438) ).
thf(ax1459,axiom,
( p10
| ~ p12 ),
file('<stdin>',ax1459) ).
thf(ax1440,axiom,
( p12
| p15 ),
file('<stdin>',ax1440) ).
thf(nax15,axiom,
( p15
<= ! [X1: g] :
( ( f__0 @ f__1 @ X1 )
= X1 ) ),
file('<stdin>',nax15) ).
thf(pax15,axiom,
( p15
=> ! [X1: g] :
( ( f__0 @ f__1 @ X1 )
= X1 ) ),
file('<stdin>',pax15) ).
thf(ax1462,axiom,
( p15
| ~ p20 ),
file('<stdin>',ax1462) ).
thf(nax28,axiom,
( p28
<= ! [X1: g] :
( ( f__0 @ X1 @ ( f__0 @ f__1 @ f__3 ) )
!= f__1 ) ),
file('<stdin>',nax28) ).
thf(pax165,axiom,
( p165
=> ( ( f__0 @ f__3 @ f__7 )
= f__1 ) ),
file('<stdin>',pax165) ).
thf(pax10,axiom,
( p10
=> ( ~ ( ! [X1: g,X2: g,X3: g] :
( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
= ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) )
=> ~ ! [X1: g] :
( ( f__0 @ f__1 @ X1 )
= X1 ) )
=> ~ ! [X1: g] :
~ ! [X2: g] :
( ( f__0 @ X2 @ X1 )
!= f__1 ) ) ),
file('<stdin>',pax10) ).
thf(ax1468,axiom,
( ~ p12
| ~ p14
| ~ p15 ),
file('<stdin>',ax1468) ).
thf(nax14,axiom,
( p14
<= ! [X1: g,X2: g,X3: g] :
( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
= ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) ) ),
file('<stdin>',nax14) ).
thf(nax12,axiom,
( p12
<= ( ! [X1: g,X2: g,X3: g] :
( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
= ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) )
=> ~ ! [X1: g] :
( ( f__0 @ f__1 @ X1 )
= X1 ) ) ),
file('<stdin>',nax12) ).
thf(ax1470,axiom,
( p3
| p10
| p11 ),
file('<stdin>',ax1470) ).
thf(ax1449,axiom,
( ~ p13
| ~ p28 ),
file('<stdin>',ax1449) ).
thf(nax13,axiom,
( p13
<= ! [X1: g] :
~ ! [X2: g] :
( ( f__0 @ X2 @ X1 )
!= f__1 ) ),
file('<stdin>',nax13) ).
thf(nax17,axiom,
( p17
<= ( ! [X1: g,X2: g,X3: g] :
( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
= ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) )
=> ~ ! [X1: g] :
( ( f__0 @ X1 @ f__1 )
= X1 ) ) ),
file('<stdin>',nax17) ).
thf(ax1466,axiom,
( p11
| ~ p17 ),
file('<stdin>',ax1466) ).
thf(nax32,axiom,
( p32
<= ! [X1: g] :
( ( f__0 @ X1 @ f__3 )
!= f__1 ) ),
file('<stdin>',nax32) ).
thf(ax1404,axiom,
( ~ p43
| p63 ),
file('<stdin>',ax1404) ).
thf(ax1443,axiom,
( ~ p19
| p34 ),
file('<stdin>',ax1443) ).
thf(ax1204,axiom,
( ~ p63
| p201 ),
file('<stdin>',ax1204) ).
thf(ax1431,axiom,
p43,
file('<stdin>',ax1431) ).
thf(ax1463,axiom,
( p17
| p19 ),
file('<stdin>',ax1463) ).
thf(ax1205,axiom,
( ~ p201
| p200 ),
file('<stdin>',ax1205) ).
thf(ax1206,axiom,
( ~ p200
| ~ p186
| p194 ),
file('<stdin>',ax1206) ).
thf(ax1213,axiom,
( ~ p194
| ~ p34
| p20 ),
file('<stdin>',ax1213) ).
thf(nax186,axiom,
( p186
<= ( ( f__0 @ f__1 @ f__3 )
= ( f__0 @ f__3 @ f__1 ) ) ),
file('<stdin>',nax186) ).
thf(pax18,axiom,
( p18
=> ! [X1: g] :
~ ! [X2: g] :
( ( f__0 @ X1 @ X2 )
!= f__1 ) ),
file('<stdin>',pax18) ).
thf(pax11,axiom,
( p11
=> ( ~ ( ! [X1: g,X2: g,X3: g] :
( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
= ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) )
=> ~ ! [X1: g] :
( ( f__0 @ X1 @ f__1 )
= X1 ) )
=> ~ ! [X1: g] :
~ ! [X2: g] :
( ( f__0 @ X1 @ X2 )
!= f__1 ) ) ),
file('<stdin>',pax11) ).
thf(pax13,axiom,
( p13
=> ! [X1: g] :
~ ! [X2: g] :
( ( f__0 @ X2 @ X1 )
!= f__1 ) ),
file('<stdin>',pax13) ).
thf(nax37,axiom,
( p37
<= ! [X1: g] :
( ( f__0 @ f__5 @ X1 )
!= f__1 ) ),
file('<stdin>',nax37) ).
thf(ax1437,axiom,
( p18
| p37 ),
file('<stdin>',ax1437) ).
thf(ax1460,axiom,
( ~ p17
| ~ p14
| ~ p19 ),
file('<stdin>',ax1460) ).
thf(pax37,axiom,
( p37
=> ! [X1: g] :
( ( f__0 @ f__5 @ X1 )
!= f__1 ) ),
file('<stdin>',pax37) ).
thf(nax19,axiom,
( p19
<= ! [X1: g] :
( ( f__0 @ X1 @ f__1 )
= X1 ) ),
file('<stdin>',nax19) ).
thf(c_0_50,plain,
( p1
| ~ p2 ),
inference(fof_simplification,[status(thm)],[ax1480]) ).
thf(c_0_51,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax1481]) ).
thf(c_0_52,plain,
( p2
| ~ p3 ),
inference(fof_simplification,[status(thm)],[ax1479]) ).
thf(c_0_53,plain,
( p1
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
thf(c_0_54,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_51]) ).
thf(c_0_55,plain,
( p3
| ~ p10
| ~ p11 ),
inference(fof_simplification,[status(thm)],[ax1471]) ).
thf(c_0_56,plain,
( p2
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
thf(c_0_57,plain,
~ p2,
inference(sr,[status(thm)],[c_0_53,c_0_54]) ).
thf(c_0_58,plain,
( p3
| ~ p10
| ~ p11 ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
thf(c_0_59,plain,
~ p3,
inference(sr,[status(thm)],[c_0_56,c_0_57]) ).
thf(c_0_60,plain,
! [X460: g,X461: g,X462: g,X463: g,X464: g] :
( ( ( ( f__0 @ ( f__0 @ X460 @ X461 ) @ X462 )
= ( f__0 @ X460 @ ( f__0 @ X461 @ X462 ) ) )
| p11 )
& ( ( ( f__0 @ X463 @ f__1 )
= X463 )
| p11 )
& ( ( ( f__0 @ X464 @ ( esk231_1 @ X464 ) )
= f__1 )
| p11 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax11])])])])])]) ).
thf(c_0_61,plain,
! [X472: g,X473: g,X474: g,X475: g,X476: g] :
( ( ( ( f__0 @ ( f__0 @ X472 @ X473 ) @ X474 )
= ( f__0 @ X472 @ ( f__0 @ X473 @ X474 ) ) )
| p10 )
& ( ( ( f__0 @ f__1 @ X475 )
= X475 )
| p10 )
& ( ( ( f__0 @ ( esk237_1 @ X476 ) @ X476 )
= f__1 )
| p10 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax10])])])])])]) ).
thf(c_0_62,plain,
! [X396: g] :
( ~ p32
| ( ( f__0 @ X396 @ f__3 )
!= f__1 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax32])])])]) ).
thf(c_0_63,plain,
( ~ p10
| ~ p11 ),
inference(sr,[status(thm)],[c_0_58,c_0_59]) ).
thf(c_0_64,plain,
! [X1: g,X2: g,X3: g] :
( ( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
= ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) )
| p11 ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
thf(c_0_65,plain,
! [X1: g,X2: g,X3: g] :
( ( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
= ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) )
| p10 ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
thf(c_0_66,plain,
! [X1: g] :
( ~ p32
| ( ( f__0 @ X1 @ f__3 )
!= f__1 ) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
thf(c_0_67,plain,
( p32
| p341 ),
inference(split_conjunct,[status(thm)],[ax979]) ).
thf(c_0_68,plain,
! [X1: g] :
( ( ( f__0 @ X1 @ ( esk231_1 @ X1 ) )
= f__1 )
| p11 ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
thf(c_0_69,plain,
! [X1: g,X2: g,X3: g] :
( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
= ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]) ).
thf(c_0_70,plain,
! [X1: g] :
( p341
| ( ( f__0 @ X1 @ f__3 )
!= f__1 ) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
thf(c_0_71,plain,
! [X1: g,X2: g] :
( ( ( f__0 @ X1 @ ( f__0 @ X2 @ ( esk231_1 @ ( f__0 @ X1 @ X2 ) ) ) )
= f__1 )
| p11 ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
thf(c_0_72,plain,
! [X1: g] :
( ( ( f__0 @ X1 @ f__1 )
= X1 )
| p11 ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
thf(c_0_73,plain,
! [X1: g,X2: g] :
( ( ( f__0 @ X1 @ ( f__0 @ ( esk231_1 @ X1 ) @ X2 ) )
= ( f__0 @ f__1 @ X2 ) )
| p11 ),
inference(spm,[status(thm)],[c_0_69,c_0_68]) ).
thf(c_0_74,plain,
! [X1: g,X2: g] :
( p341
| ( ( f__0 @ X1 @ ( f__0 @ X2 @ f__3 ) )
!= f__1 ) ),
inference(spm,[status(thm)],[c_0_70,c_0_69]) ).
thf(c_0_75,plain,
! [X1: g] :
( ( ( f__0 @ X1 @ ( f__0 @ f__1 @ ( esk231_1 @ X1 ) ) )
= f__1 )
| p11 ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
thf(c_0_76,plain,
! [X1: g] :
( ( ( f__0 @ f__1 @ ( esk231_1 @ ( esk231_1 @ X1 ) ) )
= ( f__0 @ X1 @ f__1 ) )
| p11 ),
inference(spm,[status(thm)],[c_0_73,c_0_68]) ).
thf(c_0_77,plain,
( ~ p13
| ~ p32 ),
inference(fof_simplification,[status(thm)],[ax1445]) ).
thf(c_0_78,plain,
! [X1: g,X2: g,X3: g] :
( p341
| ( ( f__0 @ X1 @ ( f__0 @ X2 @ ( f__0 @ X3 @ f__3 ) ) )
!= f__1 ) ),
inference(spm,[status(thm)],[c_0_74,c_0_69]) ).
thf(c_0_79,plain,
! [X1: g,X2: g] :
( ( ( f__0 @ X1 @ ( f__0 @ X2 @ f__1 ) )
= ( f__0 @ X1 @ X2 ) )
| p11 ),
inference(spm,[status(thm)],[c_0_72,c_0_69]) ).
thf(c_0_80,plain,
! [X1: g] :
( ( ( f__0 @ ( esk231_1 @ X1 ) @ ( f__0 @ X1 @ f__1 ) )
= f__1 )
| p11 ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
thf(c_0_81,plain,
( ~ p13
| ~ p32 ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
thf(c_0_82,plain,
! [X1: g,X2: g,X3: g,X4: g] :
( p341
| ( ( f__0 @ X1 @ ( f__0 @ X2 @ ( f__0 @ X3 @ ( f__0 @ X4 @ f__3 ) ) ) )
!= f__1 ) ),
inference(spm,[status(thm)],[c_0_78,c_0_69]) ).
thf(c_0_83,plain,
! [X1: g] :
( ( ( f__0 @ ( esk231_1 @ X1 ) @ X1 )
= f__1 )
| p11 ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
thf(c_0_84,plain,
( p341
| ~ p13 ),
inference(spm,[status(thm)],[c_0_81,c_0_67]) ).
thf(c_0_85,plain,
( p10
| p13 ),
inference(split_conjunct,[status(thm)],[ax1458]) ).
thf(c_0_86,plain,
( ~ p341
| ( ( f__0 @ f__8 @ f__3 )
= f__1 ) ),
inference(fof_nnf,[status(thm)],[pax341]) ).
thf(c_0_87,plain,
( p11
| p341 ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
thf(c_0_88,plain,
( p10
| p341 ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
thf(c_0_89,plain,
( ~ p18
| ~ p35 ),
inference(fof_simplification,[status(thm)],[ax1442]) ).
thf(c_0_90,plain,
! [X1: g] :
( ( ( f__0 @ X1 @ f__1 )
= X1 )
| ~ p10 ),
inference(spm,[status(thm)],[c_0_63,c_0_72]) ).
thf(c_0_91,plain,
! [X1: g] :
( ( ( f__0 @ f__1 @ X1 )
= X1 )
| p10 ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
thf(c_0_92,plain,
( ( ( f__0 @ f__8 @ f__3 )
= f__1 )
| ~ p341 ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
thf(c_0_93,plain,
p341,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_87]),c_0_88]) ).
thf(c_0_94,plain,
( ~ p18
| ~ p35 ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
thf(c_0_95,plain,
( p35
| p165 ),
inference(split_conjunct,[status(thm)],[ax1247]) ).
thf(c_0_96,plain,
! [X1: g,X2: g] :
( ( ( f__0 @ f__1 @ X1 )
= X1 )
| ( ( f__0 @ X2 @ f__1 )
= X2 ) ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
thf(c_0_97,plain,
( ( f__0 @ f__8 @ f__3 )
= f__1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_93])]) ).
thf(c_0_98,plain,
( ( ( f__0 @ f__3 @ esk194_0 )
= f__1 )
| p35 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax35])])])]) ).
thf(c_0_99,plain,
( p165
| ~ p18 ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
thf(c_0_100,plain,
( p11
| p18 ),
inference(split_conjunct,[status(thm)],[ax1465]) ).
thf(c_0_101,plain,
( ~ p15
| p20 ),
inference(fof_simplification,[status(thm)],[ax1438]) ).
thf(c_0_102,plain,
( ( f__0 @ f__1 @ f__1 )
= f__1 ),
inference(ef,[status(thm)],[c_0_96]) ).
thf(c_0_103,plain,
! [X1: g] :
( ( f__0 @ f__8 @ ( f__0 @ f__3 @ X1 ) )
= ( f__0 @ f__1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_69,c_0_97]) ).
thf(c_0_104,plain,
( ( ( f__0 @ f__3 @ esk194_0 )
= f__1 )
| p35 ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
thf(c_0_105,plain,
( p11
| p165 ),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
thf(c_0_106,plain,
( p10
| ~ p12 ),
inference(fof_simplification,[status(thm)],[ax1459]) ).
thf(c_0_107,plain,
( p20
| ~ p15 ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
thf(c_0_108,plain,
( p12
| p15 ),
inference(split_conjunct,[status(thm)],[ax1440]) ).
thf(c_0_109,plain,
! [X1: g] :
( ( f__0 @ f__1 @ ( f__0 @ f__1 @ X1 ) )
= ( f__0 @ f__1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_69,c_0_102]) ).
thf(c_0_110,plain,
( ( ( f__0 @ f__1 @ esk194_0 )
= ( f__0 @ f__8 @ f__1 ) )
| p35 ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
thf(c_0_111,plain,
( ( ( f__0 @ f__1 @ esk216_0 )
!= esk216_0 )
| p15 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax15])])])]) ).
thf(c_0_112,plain,
( p165
| ~ p10 ),
inference(spm,[status(thm)],[c_0_63,c_0_105]) ).
thf(c_0_113,plain,
( p10
| ~ p12 ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
thf(c_0_114,plain,
( p12
| p20 ),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
thf(c_0_115,plain,
( ( ( f__0 @ f__1 @ ( esk231_1 @ f__3 ) )
= ( f__0 @ f__8 @ f__1 ) )
| p11 ),
inference(spm,[status(thm)],[c_0_103,c_0_68]) ).
thf(c_0_116,plain,
( ( ( f__0 @ f__1 @ ( f__0 @ f__8 @ f__1 ) )
= ( f__0 @ f__8 @ f__1 ) )
| p35 ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
thf(c_0_117,plain,
( p15
| ( ( f__0 @ f__1 @ esk216_0 )
!= esk216_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
thf(c_0_118,plain,
! [X1: g] :
( ( ( f__0 @ f__1 @ X1 )
= X1 )
| p165 ),
inference(spm,[status(thm)],[c_0_112,c_0_91]) ).
thf(c_0_119,plain,
( p20
| p10 ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
thf(c_0_120,plain,
( ( ( f__0 @ f__3 @ ( f__0 @ f__8 @ f__1 ) )
= f__1 )
| p11 ),
inference(spm,[status(thm)],[c_0_75,c_0_115]) ).
thf(c_0_121,plain,
( ( ( f__0 @ f__1 @ ( f__0 @ f__8 @ f__1 ) )
= ( f__0 @ f__8 @ f__1 ) )
| ~ p18 ),
inference(spm,[status(thm)],[c_0_94,c_0_116]) ).
thf(c_0_122,plain,
! [X434: g] :
( ~ p15
| ( ( f__0 @ f__1 @ X434 )
= X434 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax15])])]) ).
thf(c_0_123,plain,
( p15
| ~ p20 ),
inference(fof_simplification,[status(thm)],[ax1462]) ).
thf(c_0_124,plain,
( ( ( f__0 @ esk201_0 @ ( f__0 @ f__1 @ f__3 ) )
= f__1 )
| p28 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax28])])])]) ).
thf(c_0_125,plain,
( ~ p165
| ( ( f__0 @ f__3 @ f__7 )
= f__1 ) ),
inference(fof_nnf,[status(thm)],[pax165]) ).
thf(c_0_126,plain,
( p165
| p15 ),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
thf(c_0_127,plain,
! [X1: g] :
( ( ( f__0 @ X1 @ f__1 )
= X1 )
| p20 ),
inference(spm,[status(thm)],[c_0_90,c_0_119]) ).
thf(c_0_128,plain,
( ( ( f__0 @ f__3 @ ( f__0 @ f__8 @ f__1 ) )
= f__1 )
| ~ p10 ),
inference(spm,[status(thm)],[c_0_63,c_0_120]) ).
thf(c_0_129,plain,
( ( ( f__0 @ f__1 @ ( f__0 @ f__8 @ f__1 ) )
= ( f__0 @ f__8 @ f__1 ) )
| p11 ),
inference(spm,[status(thm)],[c_0_121,c_0_100]) ).
thf(c_0_130,plain,
! [X1: g] :
( ( ( f__0 @ f__1 @ X1 )
= X1 )
| ~ p15 ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
thf(c_0_131,plain,
( p15
| ~ p20 ),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
thf(c_0_132,plain,
! [X471: g] :
( ~ p10
| ( ( f__0 @ ( f__0 @ esk232_0 @ esk233_0 ) @ esk234_0 )
!= ( f__0 @ esk232_0 @ ( f__0 @ esk233_0 @ esk234_0 ) ) )
| ( ( f__0 @ f__1 @ esk235_0 )
!= esk235_0 )
| ( ( f__0 @ X471 @ esk236_0 )
!= f__1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax10])])])])]) ).
thf(c_0_133,plain,
( ( ( f__0 @ esk201_0 @ ( f__0 @ f__1 @ f__3 ) )
= f__1 )
| p28 ),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
thf(c_0_134,plain,
( ( ( f__0 @ f__3 @ f__7 )
= f__1 )
| ~ p165 ),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
thf(c_0_135,plain,
( p165
| p20 ),
inference(spm,[status(thm)],[c_0_107,c_0_126]) ).
thf(c_0_136,plain,
! [X1: g,X2: g] :
( ( ( f__0 @ X1 @ ( f__0 @ X2 @ f__1 ) )
= ( f__0 @ X1 @ X2 ) )
| p20 ),
inference(spm,[status(thm)],[c_0_127,c_0_69]) ).
thf(c_0_137,plain,
( ( ( f__0 @ f__3 @ ( f__0 @ f__8 @ f__1 ) )
= f__1 )
| p20 ),
inference(spm,[status(thm)],[c_0_128,c_0_119]) ).
thf(c_0_138,plain,
( ( f__0 @ f__1 @ ( f__0 @ f__8 @ f__1 ) )
= ( f__0 @ f__8 @ f__1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_129]),c_0_91]) ).
thf(c_0_139,plain,
! [X1: g] :
( ( ( f__0 @ f__1 @ X1 )
= X1 )
| ~ p20 ),
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
thf(c_0_140,plain,
( ~ p12
| ~ p14
| ~ p15 ),
inference(fof_simplification,[status(thm)],[ax1468]) ).
thf(c_0_141,plain,
( ( ( f__0 @ ( f__0 @ esk217_0 @ esk218_0 ) @ esk219_0 )
!= ( f__0 @ esk217_0 @ ( f__0 @ esk218_0 @ esk219_0 ) ) )
| p14 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax14])])])]) ).
thf(c_0_142,plain,
! [X1: g] :
( ~ p10
| ( ( f__0 @ ( f__0 @ esk232_0 @ esk233_0 ) @ esk234_0 )
!= ( f__0 @ esk232_0 @ ( f__0 @ esk233_0 @ esk234_0 ) ) )
| ( ( f__0 @ f__1 @ esk235_0 )
!= esk235_0 )
| ( ( f__0 @ X1 @ esk236_0 )
!= f__1 ) ),
inference(split_conjunct,[status(thm)],[c_0_132]) ).
thf(c_0_143,plain,
! [X450: g,X451: g,X452: g,X453: g] :
( ( ( ( f__0 @ ( f__0 @ X450 @ X451 ) @ X452 )
= ( f__0 @ X450 @ ( f__0 @ X451 @ X452 ) ) )
| p12 )
& ( ( ( f__0 @ f__1 @ X453 )
= X453 )
| p12 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax12])])])])]) ).
thf(c_0_144,plain,
! [X1: g] :
( ( ( f__0 @ esk201_0 @ ( f__0 @ f__1 @ ( f__0 @ f__3 @ X1 ) ) )
= ( f__0 @ f__1 @ X1 ) )
| p28 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_133]),c_0_69]) ).
thf(c_0_145,plain,
( ( ( f__0 @ f__3 @ f__7 )
= f__1 )
| p20 ),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
thf(c_0_146,plain,
( ( ( f__0 @ f__3 @ f__8 )
= f__1 )
| p20 ),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
thf(c_0_147,plain,
( ( f__0 @ f__1 @ f__8 )
= f__8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_127]),c_0_139]) ).
thf(c_0_148,plain,
( ~ p12
| ~ p14
| ~ p15 ),
inference(split_conjunct,[status(thm)],[c_0_140]) ).
thf(c_0_149,plain,
( p14
| ( ( f__0 @ ( f__0 @ esk217_0 @ esk218_0 ) @ esk219_0 )
!= ( f__0 @ esk217_0 @ ( f__0 @ esk218_0 @ esk219_0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_141]) ).
thf(c_0_150,plain,
! [X1: g] :
( ( ( f__0 @ f__1 @ esk235_0 )
!= esk235_0 )
| ( ( f__0 @ X1 @ esk236_0 )
!= f__1 )
| ~ p10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_142,c_0_69])]) ).
thf(c_0_151,plain,
! [X1: g] :
( ( ( f__0 @ f__1 @ X1 )
= X1 )
| p12 ),
inference(split_conjunct,[status(thm)],[c_0_143]) ).
thf(c_0_152,plain,
( p3
| p10
| p11 ),
inference(split_conjunct,[status(thm)],[ax1470]) ).
thf(c_0_153,plain,
( ~ p13
| ~ p28 ),
inference(fof_simplification,[status(thm)],[ax1449]) ).
thf(c_0_154,plain,
( ( ( f__0 @ esk201_0 @ f__1 )
= ( f__0 @ f__1 @ f__7 ) )
| p20
| p28 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_102]) ).
thf(c_0_155,plain,
( ( ( f__0 @ esk201_0 @ f__1 )
= f__8 )
| p20
| p28 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_146]),c_0_102]),c_0_147]) ).
thf(c_0_156,plain,
! [X445: g] :
( ( ( f__0 @ X445 @ esk221_0 )
!= f__1 )
| p13 ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax13])])])])]) ).
thf(c_0_157,plain,
( ~ p12
| ~ p14
| ~ p20 ),
inference(spm,[status(thm)],[c_0_148,c_0_131]) ).
thf(c_0_158,plain,
p14,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_149,c_0_69])]) ).
thf(c_0_159,plain,
! [X1: g] :
( p12
| ( ( f__0 @ X1 @ esk236_0 )
!= f__1 )
| ~ p10 ),
inference(spm,[status(thm)],[c_0_150,c_0_151]) ).
thf(c_0_160,plain,
( p11
| p10 ),
inference(sr,[status(thm)],[c_0_152,c_0_59]) ).
thf(c_0_161,plain,
( ~ p13
| ~ p28 ),
inference(split_conjunct,[status(thm)],[c_0_153]) ).
thf(c_0_162,plain,
( ( ( f__0 @ f__1 @ f__7 )
= f__8 )
| p28
| p20 ),
inference(spm,[status(thm)],[c_0_154,c_0_155]) ).
thf(c_0_163,plain,
! [X1: g] :
( p13
| ( ( f__0 @ X1 @ esk221_0 )
!= f__1 ) ),
inference(split_conjunct,[status(thm)],[c_0_156]) ).
thf(c_0_164,plain,
( ~ p12
| ~ p20 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_157,c_0_158])]) ).
thf(c_0_165,plain,
( p11
| p12 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_83]),c_0_160]) ).
thf(c_0_166,plain,
( ( ( f__0 @ f__1 @ f__7 )
= f__8 )
| p20
| ~ p13 ),
inference(spm,[status(thm)],[c_0_161,c_0_162]) ).
thf(c_0_167,plain,
( p11
| p13 ),
inference(spm,[status(thm)],[c_0_163,c_0_83]) ).
thf(c_0_168,plain,
( p11
| ~ p20 ),
inference(spm,[status(thm)],[c_0_164,c_0_165]) ).
thf(c_0_169,plain,
( ( ( f__0 @ f__1 @ f__7 )
= f__8 )
| p11 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_167]),c_0_168]) ).
thf(c_0_170,plain,
! [X426: g,X427: g,X428: g,X429: g] :
( ( ( ( f__0 @ ( f__0 @ X426 @ X427 ) @ X428 )
= ( f__0 @ X426 @ ( f__0 @ X427 @ X428 ) ) )
| p17 )
& ( ( ( f__0 @ X429 @ f__1 )
= X429 )
| p17 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax17])])])])]) ).
thf(c_0_171,plain,
( ( ( f__0 @ f__1 @ f__7 )
= f__8 )
| ~ p10 ),
inference(spm,[status(thm)],[c_0_63,c_0_169]) ).
thf(c_0_172,plain,
! [X1: g] :
( ( ( f__0 @ X1 @ f__1 )
= X1 )
| p17 ),
inference(split_conjunct,[status(thm)],[c_0_170]) ).
thf(c_0_173,plain,
( p11
| ~ p17 ),
inference(fof_simplification,[status(thm)],[ax1466]) ).
thf(c_0_174,plain,
! [X1: g,X2: g] :
( ( ( f__0 @ X1 @ ( f__0 @ f__1 @ X2 ) )
= ( f__0 @ X1 @ X2 ) )
| p20 ),
inference(spm,[status(thm)],[c_0_69,c_0_127]) ).
thf(c_0_175,plain,
( ( ( f__0 @ f__1 @ f__7 )
= f__8 )
| p20 ),
inference(spm,[status(thm)],[c_0_171,c_0_119]) ).
thf(c_0_176,plain,
! [X1: g,X2: g] :
( ( ( f__0 @ X1 @ ( f__0 @ X2 @ f__1 ) )
= ( f__0 @ X1 @ X2 ) )
| p17 ),
inference(spm,[status(thm)],[c_0_172,c_0_69]) ).
thf(c_0_177,plain,
( p11
| ~ p17 ),
inference(split_conjunct,[status(thm)],[c_0_173]) ).
thf(c_0_178,plain,
! [X1: g] :
( ( ( f__0 @ X1 @ f__7 )
= ( f__0 @ X1 @ f__8 ) )
| p20 ),
inference(spm,[status(thm)],[c_0_174,c_0_175]) ).
thf(c_0_179,plain,
! [X1: g,X2: g] :
( ( ( f__0 @ X1 @ ( f__0 @ ( esk231_1 @ X1 ) @ X2 ) )
= ( f__0 @ f__1 @ ( f__0 @ X2 @ f__1 ) ) )
| p11 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_176]),c_0_177]) ).
thf(c_0_180,plain,
( ( ( f__0 @ ( esk231_1 @ f__7 ) @ f__8 )
= f__1 )
| p11 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_178]),c_0_168]) ).
thf(c_0_181,plain,
! [X1: g] :
( ( f__0 @ f__1 @ ( f__0 @ f__8 @ X1 ) )
= ( f__0 @ f__8 @ X1 ) ),
inference(spm,[status(thm)],[c_0_69,c_0_147]) ).
thf(c_0_182,plain,
( ( ( f__0 @ esk197_0 @ f__3 )
= f__1 )
| p32 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax32])])])]) ).
thf(c_0_183,plain,
( ( ( f__0 @ f__7 @ f__1 )
= ( f__0 @ f__8 @ f__1 ) )
| p11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_180]),c_0_181]) ).
thf(c_0_184,plain,
( ( ( f__0 @ esk197_0 @ f__3 )
= f__1 )
| p32 ),
inference(split_conjunct,[status(thm)],[c_0_182]) ).
thf(c_0_185,plain,
( ( ( f__0 @ f__7 @ f__1 )
= ( f__0 @ f__8 @ f__1 ) )
| ~ p10 ),
inference(spm,[status(thm)],[c_0_63,c_0_183]) ).
thf(c_0_186,plain,
! [X1: g] :
( ( ( f__0 @ esk197_0 @ ( f__0 @ f__3 @ X1 ) )
= ( f__0 @ f__1 @ X1 ) )
| p32 ),
inference(spm,[status(thm)],[c_0_69,c_0_184]) ).
thf(c_0_187,plain,
( ( ( f__0 @ f__7 @ f__1 )
= ( f__0 @ f__8 @ f__1 ) )
| p20 ),
inference(spm,[status(thm)],[c_0_185,c_0_119]) ).
thf(c_0_188,plain,
( ( ( f__0 @ esk197_0 @ f__1 )
= ( f__0 @ f__1 @ f__7 ) )
| p20
| p32 ),
inference(spm,[status(thm)],[c_0_186,c_0_145]) ).
thf(c_0_189,plain,
( ( ( f__0 @ f__8 @ f__1 )
= f__7 )
| p20 ),
inference(spm,[status(thm)],[c_0_127,c_0_187]) ).
thf(c_0_190,plain,
( ~ p43
| p63 ),
inference(fof_simplification,[status(thm)],[ax1404]) ).
thf(c_0_191,plain,
( ~ p19
| p34 ),
inference(fof_simplification,[status(thm)],[ax1443]) ).
thf(c_0_192,plain,
( ( esk197_0
= ( f__0 @ f__1 @ f__7 ) )
| p32
| p20 ),
inference(spm,[status(thm)],[c_0_127,c_0_188]) ).
thf(c_0_193,plain,
( ( f__0 @ f__1 @ f__7 )
= f__7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_189]),c_0_139]) ).
thf(c_0_194,plain,
( ~ p63
| p201 ),
inference(fof_simplification,[status(thm)],[ax1204]) ).
thf(c_0_195,plain,
( p63
| ~ p43 ),
inference(split_conjunct,[status(thm)],[c_0_190]) ).
thf(c_0_196,plain,
p43,
inference(split_conjunct,[status(thm)],[ax1431]) ).
thf(c_0_197,plain,
( p34
| ~ p19 ),
inference(split_conjunct,[status(thm)],[c_0_191]) ).
thf(c_0_198,plain,
( p17
| p19 ),
inference(split_conjunct,[status(thm)],[ax1463]) ).
thf(c_0_199,plain,
( ( esk197_0 = f__7 )
| p20
| p32 ),
inference(rw,[status(thm)],[c_0_192,c_0_193]) ).
thf(c_0_200,plain,
( ~ p201
| p200 ),
inference(fof_simplification,[status(thm)],[ax1205]) ).
thf(c_0_201,plain,
( p201
| ~ p63 ),
inference(split_conjunct,[status(thm)],[c_0_194]) ).
thf(c_0_202,plain,
p63,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_195,c_0_196])]) ).
thf(c_0_203,plain,
( p17
| p34 ),
inference(spm,[status(thm)],[c_0_197,c_0_198]) ).
thf(c_0_204,plain,
( ( ( f__0 @ f__7 @ f__3 )
= f__1 )
| p20
| p32 ),
inference(spm,[status(thm)],[c_0_184,c_0_199]) ).
thf(c_0_205,plain,
( ~ p200
| ~ p186
| p194 ),
inference(fof_simplification,[status(thm)],[ax1206]) ).
thf(c_0_206,plain,
( p200
| ~ p201 ),
inference(split_conjunct,[status(thm)],[c_0_200]) ).
thf(c_0_207,plain,
p201,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_201,c_0_202])]) ).
thf(c_0_208,plain,
( p34
| p11 ),
inference(spm,[status(thm)],[c_0_177,c_0_203]) ).
thf(c_0_209,plain,
( ( ( f__0 @ f__7 @ f__3 )
= f__1 )
| p20
| ~ p13 ),
inference(spm,[status(thm)],[c_0_81,c_0_204]) ).
thf(c_0_210,plain,
( ~ p194
| ~ p34
| p20 ),
inference(fof_simplification,[status(thm)],[ax1213]) ).
thf(c_0_211,plain,
( p194
| ~ p200
| ~ p186 ),
inference(split_conjunct,[status(thm)],[c_0_205]) ).
thf(c_0_212,plain,
p200,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_206,c_0_207])]) ).
thf(c_0_213,plain,
( p34
| ~ p10 ),
inference(spm,[status(thm)],[c_0_63,c_0_208]) ).
thf(c_0_214,plain,
( ( ( f__0 @ f__7 @ f__3 )
= f__1 )
| p11 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_167]),c_0_168]) ).
thf(c_0_215,plain,
( p20
| ~ p194
| ~ p34 ),
inference(split_conjunct,[status(thm)],[c_0_210]) ).
thf(c_0_216,plain,
( p194
| ~ p186 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_211,c_0_212])]) ).
thf(c_0_217,plain,
( p20
| p34 ),
inference(spm,[status(thm)],[c_0_213,c_0_119]) ).
thf(c_0_218,plain,
( ( ( f__0 @ f__1 @ f__3 )
!= ( f__0 @ f__3 @ f__1 ) )
| p186 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax186])]) ).
thf(c_0_219,plain,
( ( ( f__0 @ f__7 @ f__3 )
= f__1 )
| ~ p10 ),
inference(spm,[status(thm)],[c_0_63,c_0_214]) ).
thf(c_0_220,plain,
( p20
| ~ p186 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_216]),c_0_217]) ).
thf(c_0_221,plain,
( p186
| ( ( f__0 @ f__1 @ f__3 )
!= ( f__0 @ f__3 @ f__1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_218]) ).
thf(c_0_222,plain,
! [X1: g] :
( ( ( f__0 @ f__3 @ ( f__0 @ f__7 @ X1 ) )
= ( f__0 @ f__1 @ X1 ) )
| p20 ),
inference(spm,[status(thm)],[c_0_69,c_0_145]) ).
thf(c_0_223,plain,
( ( ( f__0 @ f__7 @ f__3 )
= f__1 )
| p20 ),
inference(spm,[status(thm)],[c_0_219,c_0_119]) ).
thf(c_0_224,plain,
( p20
| ( ( f__0 @ f__3 @ f__1 )
!= ( f__0 @ f__1 @ f__3 ) ) ),
inference(spm,[status(thm)],[c_0_220,c_0_221]) ).
thf(c_0_225,plain,
! [X418: g] :
( ~ p18
| ( ( f__0 @ X418 @ ( esk208_1 @ X418 ) )
= f__1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax18])])])])]) ).
thf(c_0_226,plain,
! [X1: g] :
( ( ( f__0 @ ( esk237_1 @ X1 ) @ X1 )
= f__1 )
| p10 ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
thf(c_0_227,plain,
( ~ p10
| ~ p20 ),
inference(spm,[status(thm)],[c_0_63,c_0_168]) ).
thf(c_0_228,plain,
p20,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_222,c_0_223]),c_0_224]) ).
thf(c_0_229,plain,
! [X459: g] :
( ~ p11
| ( ( f__0 @ ( f__0 @ esk226_0 @ esk227_0 ) @ esk228_0 )
!= ( f__0 @ esk226_0 @ ( f__0 @ esk227_0 @ esk228_0 ) ) )
| ( ( f__0 @ esk229_0 @ f__1 )
!= esk229_0 )
| ( ( f__0 @ esk230_0 @ X459 )
!= f__1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax11])])])])]) ).
thf(c_0_230,plain,
! [X1: g] :
( ( ( f__0 @ X1 @ ( esk208_1 @ X1 ) )
= f__1 )
| ~ p18 ),
inference(split_conjunct,[status(thm)],[c_0_225]) ).
thf(c_0_231,plain,
! [X442: g] :
( ~ p13
| ( ( f__0 @ ( esk220_1 @ X442 ) @ X442 )
= f__1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax13])])])])]) ).
thf(c_0_232,plain,
! [X1: g,X2: g] :
( ( ( f__0 @ ( esk237_1 @ X1 ) @ ( f__0 @ X1 @ X2 ) )
= ( f__0 @ f__1 @ X2 ) )
| p10 ),
inference(spm,[status(thm)],[c_0_69,c_0_226]) ).
thf(c_0_233,plain,
~ p10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_227,c_0_228])]) ).
thf(c_0_234,plain,
! [X1: g] :
( ( f__0 @ f__1 @ X1 )
= X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_139,c_0_228])]) ).
thf(c_0_235,plain,
! [X1: g] :
( ~ p11
| ( ( f__0 @ ( f__0 @ esk226_0 @ esk227_0 ) @ esk228_0 )
!= ( f__0 @ esk226_0 @ ( f__0 @ esk227_0 @ esk228_0 ) ) )
| ( ( f__0 @ esk229_0 @ f__1 )
!= esk229_0 )
| ( ( f__0 @ esk230_0 @ X1 )
!= f__1 ) ),
inference(split_conjunct,[status(thm)],[c_0_229]) ).
thf(c_0_236,plain,
! [X1: g,X2: g] :
( ( ( f__0 @ X1 @ ( f__0 @ X2 @ ( esk208_1 @ ( f__0 @ X1 @ X2 ) ) ) )
= f__1 )
| ~ p18 ),
inference(spm,[status(thm)],[c_0_230,c_0_69]) ).
thf(c_0_237,plain,
( ( ( f__0 @ f__5 @ esk193_0 )
= f__1 )
| p37 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax37])])])]) ).
thf(c_0_238,plain,
! [X1: g] :
( ( ( f__0 @ ( esk220_1 @ X1 ) @ X1 )
= f__1 )
| ~ p13 ),
inference(split_conjunct,[status(thm)],[c_0_231]) ).
thf(c_0_239,plain,
! [X1: g,X2: g] :
( ( f__0 @ ( esk237_1 @ X1 ) @ ( f__0 @ X1 @ X2 ) )
= X2 ),
inference(rw,[status(thm)],[inference(sr,[status(thm)],[c_0_232,c_0_233]),c_0_234]) ).
thf(c_0_240,plain,
! [X1: g] :
( ( f__0 @ ( esk237_1 @ X1 ) @ X1 )
= f__1 ),
inference(sr,[status(thm)],[c_0_226,c_0_233]) ).
thf(c_0_241,plain,
! [X1: g] :
( ( ( f__0 @ esk229_0 @ f__1 )
!= esk229_0 )
| ( ( f__0 @ esk230_0 @ X1 )
!= f__1 )
| ~ p11 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_235,c_0_69])]) ).
thf(c_0_242,plain,
p11,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_168,c_0_228])]) ).
thf(c_0_243,plain,
! [X1: g,X2: g,X3: g] :
( ( ( f__0 @ X1 @ ( f__0 @ X2 @ ( f__0 @ X3 @ ( esk208_1 @ ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) ) ) ) )
= f__1 )
| ~ p18 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_236]),c_0_69]) ).
thf(c_0_244,plain,
( ( ( f__0 @ f__5 @ esk193_0 )
= f__1 )
| p37 ),
inference(split_conjunct,[status(thm)],[c_0_237]) ).
thf(c_0_245,plain,
( p18
| p37 ),
inference(split_conjunct,[status(thm)],[ax1437]) ).
thf(c_0_246,plain,
! [X1: g,X2: g] :
( ( ( f__0 @ ( esk220_1 @ X1 ) @ ( f__0 @ X1 @ X2 ) )
= ( f__0 @ f__1 @ X2 ) )
| ~ p13 ),
inference(spm,[status(thm)],[c_0_69,c_0_238]) ).
thf(c_0_247,plain,
p13,
inference(sr,[status(thm)],[c_0_85,c_0_233]) ).
thf(c_0_248,plain,
! [X1: g] :
( ( f__0 @ ( esk237_1 @ ( esk237_1 @ X1 ) ) @ f__1 )
= X1 ),
inference(spm,[status(thm)],[c_0_239,c_0_240]) ).
thf(c_0_249,plain,
! [X1: g] :
( ( ( f__0 @ esk229_0 @ f__1 )
!= esk229_0 )
| ( ( f__0 @ esk230_0 @ X1 )
!= f__1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_241,c_0_242])]) ).
thf(c_0_250,plain,
! [X1: g] :
( ( ( f__0 @ X1 @ ( f__0 @ f__5 @ ( f__0 @ esk193_0 @ ( esk208_1 @ ( f__0 @ X1 @ f__1 ) ) ) ) )
= f__1 )
| p37 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_243,c_0_244]),c_0_245]) ).
thf(c_0_251,plain,
! [X1: g,X2: g] :
( ( f__0 @ ( esk220_1 @ X1 ) @ ( f__0 @ X1 @ X2 ) )
= X2 ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_246,c_0_247])]),c_0_234]) ).
thf(c_0_252,plain,
! [X1: g] :
( ( f__0 @ ( esk220_1 @ X1 ) @ X1 )
= f__1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_238,c_0_247])]) ).
thf(c_0_253,plain,
( ~ p17
| ~ p14
| ~ p19 ),
inference(fof_simplification,[status(thm)],[ax1460]) ).
thf(c_0_254,plain,
! [X388: g] :
( ~ p37
| ( ( f__0 @ f__5 @ X388 )
!= f__1 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax37])])])]) ).
thf(c_0_255,plain,
! [X1: g] :
( ( ( esk237_1 @ ( esk237_1 @ X1 ) )
= X1 )
| p17 ),
inference(spm,[status(thm)],[c_0_172,c_0_248]) ).
thf(c_0_256,plain,
( p37
| ( ( f__0 @ esk229_0 @ f__1 )
!= esk229_0 ) ),
inference(spm,[status(thm)],[c_0_249,c_0_250]) ).
thf(c_0_257,plain,
! [X1: g] :
( ( f__0 @ ( esk220_1 @ ( esk237_1 @ ( esk237_1 @ X1 ) ) ) @ X1 )
= f__1 ),
inference(spm,[status(thm)],[c_0_251,c_0_248]) ).
thf(c_0_258,plain,
! [X1: g] :
( ( f__0 @ ( esk220_1 @ ( esk220_1 @ X1 ) ) @ f__1 )
= X1 ),
inference(spm,[status(thm)],[c_0_251,c_0_252]) ).
thf(c_0_259,plain,
( ~ p17
| ~ p14
| ~ p19 ),
inference(split_conjunct,[status(thm)],[c_0_253]) ).
thf(c_0_260,plain,
! [X1: g] :
( ~ p37
| ( ( f__0 @ f__5 @ X1 )
!= f__1 ) ),
inference(split_conjunct,[status(thm)],[c_0_254]) ).
thf(c_0_261,plain,
! [X1: g] :
( ( ( f__0 @ X1 @ ( esk237_1 @ X1 ) )
= f__1 )
| p17 ),
inference(spm,[status(thm)],[c_0_240,c_0_255]) ).
thf(c_0_262,plain,
( p17
| p37 ),
inference(spm,[status(thm)],[c_0_256,c_0_172]) ).
thf(c_0_263,plain,
( ( ( f__0 @ esk207_0 @ f__1 )
!= esk207_0 )
| p19 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax19])])])]) ).
thf(c_0_264,plain,
! [X1: g] :
( ( esk237_1 @ ( esk237_1 @ X1 ) )
= X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_251,c_0_257]),c_0_258]) ).
thf(c_0_265,plain,
( ~ p17
| ~ p19 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_259,c_0_158])]) ).
thf(c_0_266,plain,
p17,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_260,c_0_261]),c_0_262]) ).
thf(c_0_267,plain,
( p19
| ( ( f__0 @ esk207_0 @ f__1 )
!= esk207_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_263]) ).
thf(c_0_268,plain,
! [X1: g] :
( ( f__0 @ X1 @ f__1 )
= X1 ),
inference(rw,[status(thm)],[c_0_248,c_0_264]) ).
thf(c_0_269,plain,
~ p19,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_265,c_0_266])]) ).
thf(c_0_270,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_267,c_0_268])]),c_0_269]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],]) ).
thf(0,theorem,
! [X1: g > g > g,X2: g] :
( ( ~ ( ~ ( ! [X3: g,X4: g,X5: g] :
( ( X1 @ ( X1 @ X3 @ X4 ) @ X5 )
= ( X1 @ X3 @ ( X1 @ X4 @ X5 ) ) )
=> ~ ! [X3: g] :
( ( X1 @ X2 @ X3 )
= X3 ) )
=> ~ ! [X3: g] :
~ ! [X4: g] :
( ( X1 @ X4 @ X3 )
!= X2 ) ) )
= ( ~ ( ~ ( ! [X3: g,X4: g,X5: g] :
( ( X1 @ ( X1 @ X3 @ X4 ) @ X5 )
= ( X1 @ X3 @ ( X1 @ X4 @ X5 ) ) )
=> ~ ! [X3: g] :
( ( X1 @ X3 @ X2 )
= X3 ) )
=> ~ ! [X3: g] :
~ ! [X4: g] :
( ( X1 @ X3 @ X4 )
!= X2 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : ALG273^5 : TPTP v8.1.0. Bugfixed v5.3.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.33 % Computer : n025.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Wed Jun 8 02:58:04 EDT 2022
% 0.11/0.33 % CPUTime :
% 152.21/151.82 % SZS status Theorem
% 152.21/151.82 % Mode: mode446
% 152.21/151.82 % Inferences: 15598
% 152.21/151.82 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------