TSTP Solution File: ALG272^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ALG272^5 : 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 : 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 : 600s
% DateTime : Thu Jul 14 17:57:53 EDT 2022
% Result : Theorem 152.58s 152.00s
% Output : Proof 152.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 37
% Syntax : Number of formulae : 132 ( 34 unt; 0 typ; 7 def)
% Number of atoms : 581 ( 116 equ; 0 cnn)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 753 ( 200 ~; 131 |; 8 &; 369 @)
% ( 0 <=>; 41 =>; 4 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 33 usr; 34 con; 0-2 aty)
% Number of variables : 141 ( 13 ^ 128 !; 0 ?; 141 :)
% 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_INVERSE,definition,
( cGRP_INVERSE
= ( ^ [X1: g > g > g,X2: g] :
! [X3: g] :
~ ! [X4: g] :
( ( ( X1 @ X3 @ X4 )
= X2 )
=> ( ( X1 @ X4 @ X3 )
!= X2 ) ) ) ) ).
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_UNIT,definition,
( cGRP_UNIT
= ( ^ [X1: g > g > g,X2: g] :
! [X3: g] :
~ ( ( ( X1 @ X2 @ X3 )
= X3 )
=> ( ( X1 @ X3 @ X2 )
!= X3 ) ) ) ) ).
thf(def_cGROUP1,definition,
( cGROUP1
= ( ^ [X1: g > g > g,X2: g] :
~ ( ~ ( ( cGRP_ASSOC @ X1 )
=> ~ ( cGRP_UNIT @ X1 @ X2 ) )
=> ~ ( cGRP_INVERSE @ X1 @ X2 ) ) ) ) ).
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(cEQUIV_01_02,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 )
=> ( ( X1 @ X3 @ X2 )
!= X3 ) ) )
=> ~ ! [X3: g] :
~ ! [X4: g] :
( ( ( X1 @ X3 @ X4 )
= X2 )
=> ( ( X1 @ X4 @ X3 )
!= X2 ) ) ) )
= ( ~ ( ~ ( ! [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 ) ) ) ) ).
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 )
=> ( ( X1 @ X3 @ X2 )
!= X3 ) ) )
=> ~ ! [X3: g] :
~ ! [X4: g] :
( ( ( X1 @ X3 @ X4 )
= X2 )
=> ( ( X1 @ X4 @ X3 )
!= X2 ) ) ) )
= ( ~ ( ~ ( ! [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 ) ) ) ),
inference(assume_negation,[status(cth)],[cEQUIV_01_02]) ).
thf(ax1820,axiom,
( p1
| ~ p2 ),
file('<stdin>',ax1820) ).
thf(ax1821,axiom,
~ p1,
file('<stdin>',ax1821) ).
thf(ax1819,axiom,
( p2
| ~ p3 ),
file('<stdin>',ax1819) ).
thf(ax1811,axiom,
( p3
| ~ p10
| ~ p11 ),
file('<stdin>',ax1811) ).
thf(ax1806,axiom,
( p11
| ~ p17 ),
file('<stdin>',ax1806) ).
thf(ax1803,axiom,
( p17
| p19 ),
file('<stdin>',ax1803) ).
thf(ax1800,axiom,
( p10
| ~ p12 ),
file('<stdin>',ax1800) ).
thf(ax1797,axiom,
( p12
| p15 ),
file('<stdin>',ax1797) ).
thf(ax1779,axiom,
( ~ p15
| ~ p37 ),
file('<stdin>',ax1779) ).
thf(ax1795,axiom,
( ~ p17
| ~ p14
| ~ p19 ),
file('<stdin>',ax1795) ).
thf(ax1796,axiom,
( ~ p11
| p17
| ~ p18 ),
file('<stdin>',ax1796) ).
thf(ax1804,axiom,
( p17
| p14 ),
file('<stdin>',ax1804) ).
thf(ax1798,axiom,
( p12
| p14 ),
file('<stdin>',ax1798) ).
thf(ax1776,axiom,
( ~ p19
| p23 ),
file('<stdin>',ax1776) ).
thf(ax1712,axiom,
( p37
| p23 ),
file('<stdin>',ax1712) ).
thf(ax1810,axiom,
( p3
| p10
| p11 ),
file('<stdin>',ax1810) ).
thf(ax1794,axiom,
( p19
| ~ p23 ),
file('<stdin>',ax1794) ).
thf(nax18,axiom,
( p18
<= ! [X1: g] :
~ ! [X2: g] :
( ( f__0 @ X2 @ X1 )
!= f__1 ) ),
file('<stdin>',nax18) ).
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 )
=> ( ( f__0 @ X1 @ f__1 )
!= X1 ) ) )
=> ~ ! [X1: g] :
~ ! [X2: g] :
( ( ( f__0 @ X1 @ X2 )
= f__1 )
=> ( ( f__0 @ X2 @ X1 )
!= f__1 ) ) ) ),
file('<stdin>',nax10) ).
thf(ax1805,axiom,
( p11
| p18 ),
file('<stdin>',ax1805) ).
thf(pax14,axiom,
( p14
=> ! [X1: g,X2: g,X3: g] :
( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
= ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) ) ),
file('<stdin>',pax14) ).
thf(pax19,axiom,
( p19
=> ! [X1: g] :
( ( f__0 @ f__1 @ X1 )
= X1 ) ),
file('<stdin>',pax19) ).
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 @ f__1 @ X1 )
= X1 ) )
=> ~ ! [X1: g] :
~ ! [X2: g] :
( ( f__0 @ X2 @ X1 )
!= f__1 ) ) ),
file('<stdin>',nax11) ).
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 )
=> ( ( f__0 @ X1 @ f__1 )
!= X1 ) ) )
=> ~ ! [X1: g] :
~ ! [X2: g] :
( ( ( f__0 @ X1 @ X2 )
= f__1 )
=> ( ( f__0 @ X2 @ X1 )
!= f__1 ) ) ) ),
file('<stdin>',pax10) ).
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 )
=> ( ( f__0 @ X1 @ f__1 )
!= X1 ) ) ) ),
file('<stdin>',nax12) ).
thf(ax1808,axiom,
( ~ p12
| ~ p14
| ~ p15 ),
file('<stdin>',ax1808) ).
thf(pax20,axiom,
( p20
=> ( ( ( f__0 @ f__1 @ f__3 )
= f__3 )
=> ( ( f__0 @ f__3 @ f__1 )
!= f__3 ) ) ),
file('<stdin>',pax20) ).
thf(ax1802,axiom,
( p15
| p20 ),
file('<stdin>',ax1802) ).
thf(c_0_28,plain,
( p1
| ~ p2 ),
inference(fof_simplification,[status(thm)],[ax1820]) ).
thf(c_0_29,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax1821]) ).
thf(c_0_30,plain,
( p2
| ~ p3 ),
inference(fof_simplification,[status(thm)],[ax1819]) ).
thf(c_0_31,plain,
( p1
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_32,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_33,plain,
( p3
| ~ p10
| ~ p11 ),
inference(fof_simplification,[status(thm)],[ax1811]) ).
thf(c_0_34,plain,
( p2
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_35,plain,
~ p2,
inference(sr,[status(thm)],[c_0_31,c_0_32]) ).
thf(c_0_36,plain,
( p11
| ~ p17 ),
inference(fof_simplification,[status(thm)],[ax1806]) ).
thf(c_0_37,plain,
( p3
| ~ p10
| ~ p11 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
thf(c_0_38,plain,
~ p3,
inference(sr,[status(thm)],[c_0_34,c_0_35]) ).
thf(c_0_39,plain,
( p11
| ~ p17 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_40,plain,
( p17
| p19 ),
inference(split_conjunct,[status(thm)],[ax1803]) ).
thf(c_0_41,plain,
( p10
| ~ p12 ),
inference(fof_simplification,[status(thm)],[ax1800]) ).
thf(c_0_42,plain,
( ~ p10
| ~ p11 ),
inference(sr,[status(thm)],[c_0_37,c_0_38]) ).
thf(c_0_43,plain,
( p19
| p11 ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
thf(c_0_44,plain,
( p10
| ~ p12 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_45,plain,
( p12
| p15 ),
inference(split_conjunct,[status(thm)],[ax1797]) ).
thf(c_0_46,plain,
( ~ p15
| ~ p37 ),
inference(fof_simplification,[status(thm)],[ax1779]) ).
thf(c_0_47,plain,
( ~ p17
| ~ p14
| ~ p19 ),
inference(fof_simplification,[status(thm)],[ax1795]) ).
thf(c_0_48,plain,
( ~ p11
| p17
| ~ p18 ),
inference(fof_simplification,[status(thm)],[ax1796]) ).
thf(c_0_49,plain,
( p17
| p14 ),
inference(split_conjunct,[status(thm)],[ax1804]) ).
thf(c_0_50,plain,
( p12
| p14 ),
inference(split_conjunct,[status(thm)],[ax1798]) ).
thf(c_0_51,plain,
( ~ p19
| p23 ),
inference(fof_simplification,[status(thm)],[ax1776]) ).
thf(c_0_52,plain,
( p19
| ~ p10 ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
thf(c_0_53,plain,
( p15
| p10 ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
thf(c_0_54,plain,
( ~ p15
| ~ p37 ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
thf(c_0_55,plain,
( p37
| p23 ),
inference(split_conjunct,[status(thm)],[ax1712]) ).
thf(c_0_56,plain,
( ~ p17
| ~ p14
| ~ p19 ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
thf(c_0_57,plain,
( p17
| ~ p11
| ~ p18 ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
thf(c_0_58,plain,
( p3
| p10
| p11 ),
inference(split_conjunct,[status(thm)],[ax1810]) ).
thf(c_0_59,plain,
( p14
| p11 ),
inference(spm,[status(thm)],[c_0_39,c_0_49]) ).
thf(c_0_60,plain,
( p14
| p10 ),
inference(spm,[status(thm)],[c_0_44,c_0_50]) ).
thf(c_0_61,plain,
( p19
| ~ p23 ),
inference(fof_simplification,[status(thm)],[ax1794]) ).
thf(c_0_62,plain,
( p23
| ~ p19 ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
thf(c_0_63,plain,
( p15
| p19 ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
thf(c_0_64,plain,
( p23
| ~ p15 ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
thf(c_0_65,plain,
( ~ p14
| ~ p19
| ~ p11
| ~ p18 ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
thf(c_0_66,plain,
( p11
| p10 ),
inference(sr,[status(thm)],[c_0_58,c_0_38]) ).
thf(c_0_67,plain,
p14,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_59]),c_0_60]) ).
thf(c_0_68,plain,
( p19
| ~ p23 ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
thf(c_0_69,plain,
p23,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]) ).
thf(c_0_70,plain,
! [X433: g] :
( ( ( f__0 @ X433 @ esk215_0 )
!= f__1 )
| p18 ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax18])])])])]) ).
thf(c_0_71,plain,
! [X484: g,X485: g,X486: g,X487: g,X488: g] :
( ( ( ( f__0 @ ( f__0 @ X484 @ X485 ) @ X486 )
= ( f__0 @ X484 @ ( f__0 @ X485 @ X486 ) ) )
| p10 )
& ( ( ( f__0 @ f__1 @ X487 )
= X487 )
| p10 )
& ( ( ( f__0 @ X487 @ f__1 )
= X487 )
| p10 )
& ( ( ( f__0 @ X488 @ ( esk243_1 @ X488 ) )
= f__1 )
| p10 )
& ( ( ( f__0 @ ( esk243_1 @ X488 ) @ X488 )
= 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_72,plain,
( p11
| p18 ),
inference(split_conjunct,[status(thm)],[ax1805]) ).
thf(c_0_73,plain,
( p10
| ~ p14
| ~ p19
| ~ p18 ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
thf(c_0_74,plain,
( ~ p19
| ~ p11
| ~ p18 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_67])]) ).
thf(c_0_75,plain,
p19,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_69])]) ).
thf(c_0_76,plain,
! [X1: g] :
( p18
| ( ( f__0 @ X1 @ esk215_0 )
!= f__1 ) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
thf(c_0_77,plain,
! [X1: g] :
( ( ( f__0 @ ( esk243_1 @ X1 ) @ X1 )
= f__1 )
| p10 ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
thf(c_0_78,plain,
( p18
| ~ p10 ),
inference(spm,[status(thm)],[c_0_42,c_0_72]) ).
thf(c_0_79,plain,
! [X448: g,X449: g,X450: g] :
( ~ p14
| ( ( f__0 @ ( f__0 @ X448 @ X449 ) @ X450 )
= ( f__0 @ X448 @ ( f__0 @ X449 @ X450 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax14])])]) ).
thf(c_0_80,plain,
! [X428: g] :
( ~ p19
| ( ( f__0 @ f__1 @ X428 )
= X428 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax19])])]) ).
thf(c_0_81,plain,
( p10
| ~ p19
| ~ p18 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_67])]) ).
thf(c_0_82,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 ) ) )
| p11 )
& ( ( ( f__0 @ f__1 @ X475 )
= X475 )
| p11 )
& ( ( ( f__0 @ ( esk237_1 @ X476 ) @ X476 )
= 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_83,plain,
( ~ p11
| ~ p18 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_75])]) ).
thf(c_0_84,plain,
p18,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]) ).
thf(c_0_85,plain,
! [X483: g] :
( ~ p10
| ( ( f__0 @ ( f__0 @ esk238_0 @ esk239_0 ) @ esk240_0 )
!= ( f__0 @ esk238_0 @ ( f__0 @ esk239_0 @ esk240_0 ) ) )
| ( ( f__0 @ f__1 @ esk241_0 )
!= esk241_0 )
| ( ( f__0 @ esk241_0 @ f__1 )
!= esk241_0 )
| ( ( f__0 @ esk242_0 @ X483 )
!= f__1 )
| ( ( f__0 @ X483 @ esk242_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_86,plain,
! [X1: g,X2: g,X3: g] :
( ( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
= ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) )
| ~ p14 ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
thf(c_0_87,plain,
! [X1: g] :
( ( ( f__0 @ f__1 @ X1 )
= X1 )
| ~ p19 ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
thf(c_0_88,plain,
( p10
| ~ p18 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_75])]) ).
thf(c_0_89,plain,
! [X1: g] :
( ( ( f__0 @ ( esk237_1 @ X1 ) @ X1 )
= f__1 )
| p11 ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
thf(c_0_90,plain,
~ p11,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_84])]) ).
thf(c_0_91,plain,
! [X1: g] :
( ~ p10
| ( ( f__0 @ ( f__0 @ esk238_0 @ esk239_0 ) @ esk240_0 )
!= ( f__0 @ esk238_0 @ ( f__0 @ esk239_0 @ esk240_0 ) ) )
| ( ( f__0 @ f__1 @ esk241_0 )
!= esk241_0 )
| ( ( f__0 @ esk241_0 @ f__1 )
!= esk241_0 )
| ( ( f__0 @ esk242_0 @ X1 )
!= f__1 )
| ( ( f__0 @ X1 @ esk242_0 )
!= f__1 ) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
thf(c_0_92,plain,
! [X1: g,X2: g,X3: g] :
( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
= ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_67])]) ).
thf(c_0_93,plain,
! [X1: g] :
( ( f__0 @ f__1 @ X1 )
= X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_75])]) ).
thf(c_0_94,plain,
p10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_84])]) ).
thf(c_0_95,plain,
! [X462: g,X463: g,X464: g,X465: g] :
( ( ( ( f__0 @ ( f__0 @ X462 @ X463 ) @ X464 )
= ( f__0 @ X462 @ ( f__0 @ X463 @ X464 ) ) )
| p12 )
& ( ( ( f__0 @ f__1 @ X465 )
= X465 )
| p12 )
& ( ( ( f__0 @ X465 @ f__1 )
= X465 )
| 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_96,plain,
! [X1: g] :
( ( f__0 @ ( esk237_1 @ X1 ) @ X1 )
= f__1 ),
inference(sr,[status(thm)],[c_0_89,c_0_90]) ).
thf(c_0_97,plain,
! [X1: g] :
( ( ( f__0 @ esk241_0 @ f__1 )
!= esk241_0 )
| ( ( f__0 @ X1 @ esk242_0 )
!= f__1 )
| ( ( f__0 @ esk242_0 @ X1 )
!= f__1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_92]),c_0_93]),c_0_94])]) ).
thf(c_0_98,plain,
! [X1: g,X2: g,X3: g] :
( ( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
= ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) )
| p12 ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
thf(c_0_99,plain,
! [X1: g] :
( ( ( f__0 @ X1 @ f__1 )
= X1 )
| p12 ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
thf(c_0_100,plain,
! [X1: g,X2: g] :
( ( f__0 @ ( esk237_1 @ X1 ) @ ( f__0 @ X1 @ X2 ) )
= X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_96]),c_0_93]) ).
thf(c_0_101,plain,
! [X1: g,X2: g] :
( p12
| ( ( f__0 @ X1 @ ( f__0 @ X2 @ esk242_0 ) )
!= f__1 )
| ( ( f__0 @ esk242_0 @ ( f__0 @ X1 @ X2 ) )
!= f__1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_99]) ).
thf(c_0_102,plain,
! [X1: g] :
( ( f__0 @ ( esk237_1 @ ( esk237_1 @ X1 ) ) @ f__1 )
= X1 ),
inference(spm,[status(thm)],[c_0_100,c_0_96]) ).
thf(c_0_103,plain,
( ~ p12
| ~ p14
| ~ p15 ),
inference(fof_simplification,[status(thm)],[ax1808]) ).
thf(c_0_104,plain,
! [X1: g] :
( p12
| ( ( f__0 @ X1 @ esk242_0 )
!= f__1 )
| ( ( f__0 @ esk242_0 @ X1 )
!= f__1 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_93]),c_0_93]) ).
thf(c_0_105,plain,
! [X1: g] :
( ( ( esk237_1 @ ( esk237_1 @ X1 ) )
= X1 )
| p12 ),
inference(spm,[status(thm)],[c_0_99,c_0_102]) ).
thf(c_0_106,plain,
( ~ p12
| ~ p14
| ~ p15 ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
thf(c_0_107,plain,
( p12
| ( ( f__0 @ esk242_0 @ ( esk237_1 @ esk242_0 ) )
!= f__1 ) ),
inference(spm,[status(thm)],[c_0_104,c_0_96]) ).
thf(c_0_108,plain,
! [X1: g] :
( ( ( f__0 @ X1 @ ( esk237_1 @ X1 ) )
= f__1 )
| p12 ),
inference(spm,[status(thm)],[c_0_96,c_0_105]) ).
thf(c_0_109,plain,
( ~ p20
| ( ( f__0 @ f__1 @ f__3 )
!= f__3 )
| ( ( f__0 @ f__3 @ f__1 )
!= f__3 ) ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax20])]) ).
thf(c_0_110,plain,
( ~ p12
| ~ p15 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_106,c_0_67])]) ).
thf(c_0_111,plain,
p12,
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
thf(c_0_112,plain,
( ~ p20
| ( ( f__0 @ f__1 @ f__3 )
!= f__3 )
| ( ( f__0 @ f__3 @ f__1 )
!= f__3 ) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
thf(c_0_113,plain,
( p15
| p20 ),
inference(split_conjunct,[status(thm)],[ax1802]) ).
thf(c_0_114,plain,
~ p15,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_111])]) ).
thf(c_0_115,plain,
( ( ( f__0 @ f__3 @ f__1 )
!= f__3 )
| ~ p20 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_112,c_0_93])]) ).
thf(c_0_116,plain,
p20,
inference(sr,[status(thm)],[c_0_113,c_0_114]) ).
thf(c_0_117,plain,
! [X1: g,X2: g] :
( ( f__0 @ ( esk237_1 @ ( esk237_1 @ X1 ) ) @ X2 )
= ( f__0 @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_100,c_0_100]) ).
thf(c_0_118,plain,
( f__0 @ f__3 @ f__1 )
!= f__3,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_115,c_0_116])]) ).
thf(c_0_119,plain,
! [X1: g] :
( ( f__0 @ X1 @ f__1 )
= X1 ),
inference(rw,[status(thm)],[c_0_102,c_0_117]) ).
thf(c_0_120,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_118,c_0_119])]),
[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 )
=> ( ( X1 @ X3 @ X2 )
!= X3 ) ) )
=> ~ ! [X3: g] :
~ ! [X4: g] :
( ( ( X1 @ X3 @ X4 )
= X2 )
=> ( ( X1 @ X4 @ X3 )
!= X2 ) ) ) )
= ( ~ ( ~ ( ! [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 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : ALG272^5 : TPTP v8.1.0. Bugfixed v5.3.0.
% 0.10/0.11 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 7 22:00:36 EDT 2022
% 0.12/0.33 % CPUTime :
% 152.58/152.00 % SZS status Theorem
% 152.58/152.00 % Mode: mode446
% 152.58/152.00 % Inferences: 17386
% 152.58/152.00 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------