TSTP Solution File: ALG277^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ALG277^5 : 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 : n028.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 17:57:54 EDT 2022
% Result : Theorem 2.33s 2.54s
% Output : Proof 2.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 26
% Syntax : Number of formulae : 100 ( 40 unt; 0 typ; 4 def)
% Number of atoms : 335 ( 61 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 394 ( 101 ~; 65 |; 6 &; 201 @)
% ( 0 <=>; 18 =>; 3 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 30 usr; 31 con; 0-2 aty)
% Number of variables : 87 ( 7 ^ 80 !; 0 ?; 87 :)
% 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_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_cGROUP3,definition,
( cGROUP3
= ( ^ [X1: g > g > g,X2: g] :
~ ( ~ ( ( cGRP_ASSOC @ X1 )
=> ~ ( cGRP_RIGHT_UNIT @ X1 @ X2 ) )
=> ~ ( cGRP_RIGHT_INVERSE @ X1 @ X2 ) ) ) ) ).
thf(cE13A2,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 @ X3 @ X2 )
= X3 ) )
=> ~ ! [X3: g] :
~ ! [X4: g] :
( ( X1 @ X3 @ X4 )
!= X2 ) )
=> ! [X3: g] :
( ( X1 @ X2 @ X3 )
= X3 ) ) ).
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 @ X3 @ X2 )
= X3 ) )
=> ~ ! [X3: g] :
~ ! [X4: g] :
( ( X1 @ X3 @ X4 )
!= X2 ) )
=> ! [X3: g] :
( ( X1 @ X2 @ X3 )
= X3 ) ),
inference(assume_negation,[status(cth)],[cE13A2]) ).
thf(ax1070,axiom,
( p1
| ~ p2 ),
file('<stdin>',ax1070) ).
thf(ax1071,axiom,
~ p1,
file('<stdin>',ax1071) ).
thf(ax1069,axiom,
( p2
| ~ p3 ),
file('<stdin>',ax1069) ).
thf(ax1068,axiom,
( p3
| ~ p4 ),
file('<stdin>',ax1068) ).
thf(ax1053,axiom,
( ~ p8
| p19 ),
file('<stdin>',ax1053) ).
thf(ax1052,axiom,
( ~ p19
| p20 ),
file('<stdin>',ax1052) ).
thf(ax1065,axiom,
p8,
file('<stdin>',ax1065) ).
thf(ax1055,axiom,
( ~ p14
| ~ p16 ),
file('<stdin>',ax1055) ).
thf(ax1057,axiom,
( p4
| p14 ),
file('<stdin>',ax1057) ).
thf(nax2,axiom,
( p2
<= ! [X1: g] :
( ~ ( ~ ( ! [X2: g,X3: g,X4: g] :
( ( f__0 @ ( f__0 @ X2 @ X3 ) @ X4 )
= ( f__0 @ X2 @ ( f__0 @ X3 @ X4 ) ) )
=> ~ ! [X2: g] :
( ( f__0 @ X2 @ X1 )
= X2 ) )
=> ~ ! [X2: g] :
~ ! [X3: g] :
( ( f__0 @ X2 @ X3 )
!= X1 ) )
=> ! [X2: g] :
( ( f__0 @ X1 @ X2 )
= X2 ) ) ),
file('<stdin>',nax2) ).
thf(ax1051,axiom,
( ~ p20
| ~ p17
| p18 ),
file('<stdin>',ax1051) ).
thf(nax3,axiom,
( p3
<= ( ~ ( ~ ( ! [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 ) )
=> ! [X1: g] :
( ( f__0 @ f__1 @ X1 )
= X1 ) ) ),
file('<stdin>',nax3) ).
thf(ax1054,axiom,
( p16
| p17 ),
file('<stdin>',ax1054) ).
thf(ax1061,axiom,
( ~ p8
| p11 ),
file('<stdin>',ax1061) ).
thf(pax18,axiom,
( p18
=> ( f__1
= ( f__0 @ f__2 @ f__3 ) ) ),
file('<stdin>',pax18) ).
thf(ax1060,axiom,
( ~ p11
| p12 ),
file('<stdin>',ax1060) ).
thf(ax1067,axiom,
( p3
| ~ p5 ),
file('<stdin>',ax1067) ).
thf(ax1059,axiom,
( ~ p12
| ~ p7
| p6 ),
file('<stdin>',ax1059) ).
thf(ax1066,axiom,
( p5
| ~ p6 ),
file('<stdin>',ax1066) ).
thf(nax7,axiom,
( p7
<= ( f__2
= ( f__0 @ f__1 @ f__2 ) ) ),
file('<stdin>',nax7) ).
thf(c_0_20,plain,
( p1
| ~ p2 ),
inference(fof_simplification,[status(thm)],[ax1070]) ).
thf(c_0_21,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax1071]) ).
thf(c_0_22,plain,
( p2
| ~ p3 ),
inference(fof_simplification,[status(thm)],[ax1069]) ).
thf(c_0_23,plain,
( p1
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_24,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_25,plain,
( p3
| ~ p4 ),
inference(fof_simplification,[status(thm)],[ax1068]) ).
thf(c_0_26,plain,
( p2
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_27,plain,
~ p2,
inference(sr,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_28,plain,
( ~ p8
| p19 ),
inference(fof_simplification,[status(thm)],[ax1053]) ).
thf(c_0_29,plain,
( p3
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_30,plain,
~ p3,
inference(sr,[status(thm)],[c_0_26,c_0_27]) ).
thf(c_0_31,plain,
( ~ p19
| p20 ),
inference(fof_simplification,[status(thm)],[ax1052]) ).
thf(c_0_32,plain,
( p19
| ~ p8 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_33,plain,
p8,
inference(split_conjunct,[status(thm)],[ax1065]) ).
thf(c_0_34,plain,
( ~ p14
| ~ p16 ),
inference(fof_simplification,[status(thm)],[ax1055]) ).
thf(c_0_35,plain,
( p4
| p14 ),
inference(split_conjunct,[status(thm)],[ax1057]) ).
thf(c_0_36,plain,
~ p4,
inference(sr,[status(thm)],[c_0_29,c_0_30]) ).
thf(c_0_37,plain,
! [X1522: g,X1523: g,X1524: g,X1525: g,X1526: g] :
( ( ( ( f__0 @ ( f__0 @ X1522 @ X1523 ) @ X1524 )
= ( f__0 @ X1522 @ ( f__0 @ X1523 @ X1524 ) ) )
| p2 )
& ( ( ( f__0 @ X1525 @ esk759_0 )
= X1525 )
| p2 )
& ( ( ( f__0 @ X1526 @ ( esk760_1 @ X1526 ) )
= esk759_0 )
| p2 )
& ( ( ( f__0 @ esk759_0 @ esk761_0 )
!= esk761_0 )
| p2 ) ),
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)],[nax2])])])])])]) ).
thf(c_0_38,plain,
( ~ p20
| ~ p17
| p18 ),
inference(fof_simplification,[status(thm)],[ax1051]) ).
thf(c_0_39,plain,
( p20
| ~ p19 ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_40,plain,
p19,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]) ).
thf(c_0_41,plain,
( ~ p14
| ~ p16 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_42,plain,
p14,
inference(sr,[status(thm)],[c_0_35,c_0_36]) ).
thf(c_0_43,plain,
! [X1: g,X2: g,X3: g] :
( ( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
= ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) )
| p2 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_44,plain,
! [X1: g] :
( ( ( f__0 @ X1 @ esk759_0 )
= X1 )
| p2 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_45,plain,
! [X1506: g,X1507: g,X1508: g,X1509: g,X1510: g] :
( ( ( ( f__0 @ ( f__0 @ X1506 @ X1507 ) @ X1508 )
= ( f__0 @ X1506 @ ( f__0 @ X1507 @ X1508 ) ) )
| p3 )
& ( ( ( f__0 @ X1509 @ f__1 )
= X1509 )
| p3 )
& ( ( ( f__0 @ X1510 @ ( esk752_1 @ X1510 ) )
= f__1 )
| p3 )
& ( ( ( f__0 @ f__1 @ esk753_0 )
!= esk753_0 )
| p3 ) ),
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)],[nax3])])])])])]) ).
thf(c_0_46,plain,
( p18
| ~ p20
| ~ p17 ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
thf(c_0_47,plain,
p20,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40])]) ).
thf(c_0_48,plain,
( p16
| p17 ),
inference(split_conjunct,[status(thm)],[ax1054]) ).
thf(c_0_49,plain,
~ p16,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])]) ).
thf(c_0_50,plain,
! [X1: g,X2: g,X3: g] :
( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
= ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) ),
inference(sr,[status(thm)],[c_0_43,c_0_27]) ).
thf(c_0_51,plain,
! [X1: g] :
( ( f__0 @ X1 @ esk759_0 )
= X1 ),
inference(sr,[status(thm)],[c_0_44,c_0_27]) ).
thf(c_0_52,plain,
! [X1: g] :
( ( ( f__0 @ X1 @ ( esk752_1 @ X1 ) )
= f__1 )
| p3 ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
thf(c_0_53,plain,
! [X1: g] :
( ( ( f__0 @ X1 @ f__1 )
= X1 )
| p3 ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
thf(c_0_54,plain,
( ~ p8
| p11 ),
inference(fof_simplification,[status(thm)],[ax1061]) ).
thf(c_0_55,plain,
( ~ p18
| ( f__1
= ( f__0 @ f__2 @ f__3 ) ) ),
inference(fof_nnf,[status(thm)],[pax18]) ).
thf(c_0_56,plain,
( p18
| ~ p17 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]) ).
thf(c_0_57,plain,
p17,
inference(sr,[status(thm)],[c_0_48,c_0_49]) ).
thf(c_0_58,plain,
! [X1: g,X2: g] :
( ( f__0 @ X1 @ ( f__0 @ esk759_0 @ X2 ) )
= ( f__0 @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
thf(c_0_59,plain,
! [X1: g] :
( ( f__0 @ X1 @ ( esk752_1 @ X1 ) )
= f__1 ),
inference(sr,[status(thm)],[c_0_52,c_0_30]) ).
thf(c_0_60,plain,
! [X1: g] :
( ( f__0 @ X1 @ f__1 )
= X1 ),
inference(sr,[status(thm)],[c_0_53,c_0_30]) ).
thf(c_0_61,plain,
( ~ p11
| p12 ),
inference(fof_simplification,[status(thm)],[ax1060]) ).
thf(c_0_62,plain,
( p11
| ~ p8 ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
thf(c_0_63,plain,
( p3
| ~ p5 ),
inference(fof_simplification,[status(thm)],[ax1067]) ).
thf(c_0_64,plain,
( ( f__1
= ( f__0 @ f__2 @ f__3 ) )
| ~ p18 ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
thf(c_0_65,plain,
p18,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_57])]) ).
thf(c_0_66,plain,
! [X1: g] :
( ( ( f__0 @ X1 @ ( esk760_1 @ X1 ) )
= esk759_0 )
| p2 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_67,plain,
! [X1: g] :
( ( f__0 @ X1 @ ( esk752_1 @ esk759_0 ) )
= X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]) ).
thf(c_0_68,plain,
( ~ p12
| ~ p7
| p6 ),
inference(fof_simplification,[status(thm)],[ax1059]) ).
thf(c_0_69,plain,
( p12
| ~ p11 ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
thf(c_0_70,plain,
p11,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_33])]) ).
thf(c_0_71,plain,
( p5
| ~ p6 ),
inference(fof_simplification,[status(thm)],[ax1066]) ).
thf(c_0_72,plain,
( p3
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
thf(c_0_73,plain,
( ( f__0 @ f__2 @ f__3 )
= f__1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65])]) ).
thf(c_0_74,plain,
! [X1: g] :
( ( f__0 @ X1 @ ( esk760_1 @ X1 ) )
= esk759_0 ),
inference(sr,[status(thm)],[c_0_66,c_0_27]) ).
thf(c_0_75,plain,
esk759_0 = f__1,
inference(spm,[status(thm)],[c_0_59,c_0_67]) ).
thf(c_0_76,plain,
( p6
| ~ p12
| ~ p7 ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
thf(c_0_77,plain,
p12,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70])]) ).
thf(c_0_78,plain,
( p5
| ~ p6 ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
thf(c_0_79,plain,
~ p5,
inference(sr,[status(thm)],[c_0_72,c_0_30]) ).
thf(c_0_80,plain,
! [X1: g] :
( ( f__0 @ f__2 @ ( f__0 @ f__3 @ X1 ) )
= ( f__0 @ f__1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_50,c_0_73]) ).
thf(c_0_81,plain,
! [X1: g] :
( ( f__0 @ X1 @ ( esk760_1 @ X1 ) )
= f__1 ),
inference(rw,[status(thm)],[c_0_74,c_0_75]) ).
thf(c_0_82,plain,
( ( f__2
!= ( f__0 @ f__1 @ f__2 ) )
| p7 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax7])]) ).
thf(c_0_83,plain,
( p6
| ~ p7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_77])]) ).
thf(c_0_84,plain,
~ p6,
inference(sr,[status(thm)],[c_0_78,c_0_79]) ).
thf(c_0_85,plain,
! [X1: g,X2: g] :
( ( f__0 @ X1 @ ( f__0 @ f__1 @ X2 ) )
= ( f__0 @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_50,c_0_60]) ).
thf(c_0_86,plain,
( ( f__0 @ f__1 @ ( esk760_1 @ f__3 ) )
= f__2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_60]) ).
thf(c_0_87,plain,
( p7
| ( f__2
!= ( f__0 @ f__1 @ f__2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
thf(c_0_88,plain,
~ p7,
inference(sr,[status(thm)],[c_0_83,c_0_84]) ).
thf(c_0_89,plain,
! [X1: g] :
( ( f__0 @ X1 @ ( esk760_1 @ f__3 ) )
= ( f__0 @ X1 @ f__2 ) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
thf(c_0_90,plain,
( f__0 @ f__1 @ f__2 )
!= f__2,
inference(sr,[status(thm)],[c_0_87,c_0_88]) ).
thf(c_0_91,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_89]),c_0_90]),
[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 @ X3 @ X2 )
= X3 ) )
=> ~ ! [X3: g] :
~ ! [X4: g] :
( ( X1 @ X3 @ X4 )
!= X2 ) )
=> ! [X3: g] :
( ( X1 @ X2 @ X3 )
= X3 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG277^5 : TPTP v8.1.0. Bugfixed v5.3.0.
% 0.11/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n028.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 : Thu Jun 9 06:15:32 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.33/2.54 % SZS status Theorem
% 2.33/2.54 % Mode: mode506
% 2.33/2.54 % Inferences: 39
% 2.33/2.54 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------