TSTP Solution File: ALG278^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ALG278^5 : 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 : n018.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 2.34s 2.59s
% Output : Proof 2.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 22
% Syntax : Number of formulae : 79 ( 31 unt; 0 typ; 4 def)
% Number of atoms : 284 ( 59 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 351 ( 89 ~; 52 |; 6 &; 182 @)
% ( 0 <=>; 19 =>; 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 : 28 ( 26 usr; 27 con; 0-2 aty)
% Number of variables : 85 ( 7 ^ 78 !; 0 ?; 85 :)
% 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_cGROUP2,definition,
( cGROUP2
= ( ^ [X1: g > g > g,X2: g] :
~ ( ~ ( ( cGRP_ASSOC @ X1 )
=> ~ ( cGRP_LEFT_UNIT @ X1 @ X2 ) )
=> ~ ( cGRP_LEFT_INVERSE @ X1 @ X2 ) ) ) ) ).
thf(cE12A1,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] :
( ( X1 @ X3 @ X2 )
= 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 @ X2 @ X3 )
= X3 ) )
=> ~ ! [X3: g] :
~ ! [X4: g] :
( ( X1 @ X4 @ X3 )
!= X2 ) )
=> ! [X3: g] :
( ( X1 @ X3 @ X2 )
= X3 ) ),
inference(assume_negation,[status(cth)],[cE12A1]) ).
thf(ax1184,axiom,
( p1
| ~ p2 ),
file('<stdin>',ax1184) ).
thf(ax1185,axiom,
~ p1,
file('<stdin>',ax1185) ).
thf(ax1183,axiom,
( p2
| ~ p3 ),
file('<stdin>',ax1183) ).
thf(ax1182,axiom,
( p3
| ~ p4 ),
file('<stdin>',ax1182) ).
thf(ax1124,axiom,
( ~ p36
| p64 ),
file('<stdin>',ax1124) ).
thf(ax1169,axiom,
( ~ p14
| ~ p16 ),
file('<stdin>',ax1169) ).
thf(ax1171,axiom,
( p4
| p14 ),
file('<stdin>',ax1171) ).
thf(ax1050,axiom,
( ~ p64
| p136 ),
file('<stdin>',ax1050) ).
thf(ax1153,axiom,
p36,
file('<stdin>',ax1153) ).
thf(ax1181,axiom,
( p3
| ~ p5 ),
file('<stdin>',ax1181) ).
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 @ X1 @ X2 )
= X2 ) )
=> ~ ! [X2: g] :
~ ! [X3: g] :
( ( f__0 @ X3 @ X2 )
!= X1 ) )
=> ! [X2: g] :
( ( f__0 @ X2 @ X1 )
= X2 ) ) ),
file('<stdin>',nax2) ).
thf(nax16,axiom,
( p16
<= ! [X1: g] :
( ( f__0 @ X1 @ f__2 )
!= f__1 ) ),
file('<stdin>',nax16) ).
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 @ f__1 @ X1 )
= X1 ) )
=> ~ ! [X1: g] :
~ ! [X2: g] :
( ( f__0 @ X2 @ X1 )
!= f__1 ) )
=> ! [X1: g] :
( ( f__0 @ X1 @ f__1 )
= X1 ) ) ),
file('<stdin>',nax3) ).
thf(ax1049,axiom,
( ~ p136
| p6
| p135 ),
file('<stdin>',ax1049) ).
thf(ax1180,axiom,
( p5
| ~ p6 ),
file('<stdin>',ax1180) ).
thf(pax135,axiom,
( p135
=> ! [X1: g] :
( ( X1 = f__2 )
=> ( ( f__0 @ X1 @ f__1 )
!= f__2 ) ) ),
file('<stdin>',pax135) ).
thf(c_0_16,plain,
( p1
| ~ p2 ),
inference(fof_simplification,[status(thm)],[ax1184]) ).
thf(c_0_17,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax1185]) ).
thf(c_0_18,plain,
( p2
| ~ p3 ),
inference(fof_simplification,[status(thm)],[ax1183]) ).
thf(c_0_19,plain,
( p1
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_20,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_21,plain,
( p3
| ~ p4 ),
inference(fof_simplification,[status(thm)],[ax1182]) ).
thf(c_0_22,plain,
( p2
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_23,plain,
~ p2,
inference(sr,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_24,plain,
( p3
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_25,plain,
~ p3,
inference(sr,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_26,plain,
( ~ p36
| p64 ),
inference(fof_simplification,[status(thm)],[ax1124]) ).
thf(c_0_27,plain,
( ~ p14
| ~ p16 ),
inference(fof_simplification,[status(thm)],[ax1169]) ).
thf(c_0_28,plain,
( p4
| p14 ),
inference(split_conjunct,[status(thm)],[ax1171]) ).
thf(c_0_29,plain,
~ p4,
inference(sr,[status(thm)],[c_0_24,c_0_25]) ).
thf(c_0_30,plain,
( ~ p64
| p136 ),
inference(fof_simplification,[status(thm)],[ax1050]) ).
thf(c_0_31,plain,
( p64
| ~ p36 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_32,plain,
p36,
inference(split_conjunct,[status(thm)],[ax1153]) ).
thf(c_0_33,plain,
( p3
| ~ p5 ),
inference(fof_simplification,[status(thm)],[ax1181]) ).
thf(c_0_34,plain,
! [X1672: g,X1673: g,X1674: g,X1675: g,X1676: g] :
( ( ( ( f__0 @ ( f__0 @ X1672 @ X1673 ) @ X1674 )
= ( f__0 @ X1672 @ ( f__0 @ X1673 @ X1674 ) ) )
| p2 )
& ( ( ( f__0 @ esk834_0 @ X1675 )
= X1675 )
| p2 )
& ( ( ( f__0 @ ( esk835_1 @ X1676 ) @ X1676 )
= esk834_0 )
| p2 )
& ( ( ( f__0 @ esk836_0 @ esk834_0 )
!= esk836_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_35,plain,
( ( ( f__0 @ esk803_0 @ f__2 )
= f__1 )
| p16 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax16])])])]) ).
thf(c_0_36,plain,
( ~ p14
| ~ p16 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_37,plain,
p14,
inference(sr,[status(thm)],[c_0_28,c_0_29]) ).
thf(c_0_38,plain,
! [X1656: g,X1657: g,X1658: g,X1659: g,X1660: g] :
( ( ( ( f__0 @ ( f__0 @ X1656 @ X1657 ) @ X1658 )
= ( f__0 @ X1656 @ ( f__0 @ X1657 @ X1658 ) ) )
| p3 )
& ( ( ( f__0 @ f__1 @ X1659 )
= X1659 )
| p3 )
& ( ( ( f__0 @ ( esk827_1 @ X1660 ) @ X1660 )
= f__1 )
| p3 )
& ( ( ( f__0 @ esk828_0 @ f__1 )
!= esk828_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_39,plain,
( ~ p136
| p6
| p135 ),
inference(fof_simplification,[status(thm)],[ax1049]) ).
thf(c_0_40,plain,
( p136
| ~ p64 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_41,plain,
p64,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]) ).
thf(c_0_42,plain,
( p5
| ~ p6 ),
inference(fof_simplification,[status(thm)],[ax1180]) ).
thf(c_0_43,plain,
( p3
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
thf(c_0_44,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_34]) ).
thf(c_0_45,plain,
! [X1: g] :
( ( ( f__0 @ ( esk835_1 @ X1 ) @ X1 )
= esk834_0 )
| p2 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_46,plain,
! [X1: g] :
( ( ( f__0 @ esk834_0 @ X1 )
= X1 )
| p2 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_47,plain,
( ( ( f__0 @ esk803_0 @ f__2 )
= f__1 )
| p16 ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_48,plain,
~ p16,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]) ).
thf(c_0_49,plain,
! [X1: g] :
( ( ( f__0 @ f__1 @ X1 )
= X1 )
| p3 ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
thf(c_0_50,plain,
! [X1257: g] :
( ~ p135
| ( X1257 != f__2 )
| ( ( f__0 @ X1257 @ f__1 )
!= f__2 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax135])])])]) ).
thf(c_0_51,plain,
( p6
| p135
| ~ p136 ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_52,plain,
p136,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41])]) ).
thf(c_0_53,plain,
( p5
| ~ p6 ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
thf(c_0_54,plain,
~ p5,
inference(sr,[status(thm)],[c_0_43,c_0_25]) ).
thf(c_0_55,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_44,c_0_23]) ).
thf(c_0_56,plain,
! [X1: g] :
( ( f__0 @ ( esk835_1 @ X1 ) @ X1 )
= esk834_0 ),
inference(sr,[status(thm)],[c_0_45,c_0_23]) ).
thf(c_0_57,plain,
! [X1: g] :
( ( f__0 @ esk834_0 @ X1 )
= X1 ),
inference(sr,[status(thm)],[c_0_46,c_0_23]) ).
thf(c_0_58,plain,
( ( f__0 @ esk803_0 @ f__2 )
= f__1 ),
inference(sr,[status(thm)],[c_0_47,c_0_48]) ).
thf(c_0_59,plain,
! [X1: g] :
( ( f__0 @ f__1 @ X1 )
= X1 ),
inference(sr,[status(thm)],[c_0_49,c_0_25]) ).
thf(c_0_60,plain,
! [X1: g] :
( ~ p135
| ( X1 != f__2 )
| ( ( f__0 @ X1 @ f__1 )
!= f__2 ) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
thf(c_0_61,plain,
( p135
| p6 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52])]) ).
thf(c_0_62,plain,
~ p6,
inference(sr,[status(thm)],[c_0_53,c_0_54]) ).
thf(c_0_63,plain,
! [X1: g,X2: g] :
( ( f__0 @ ( esk835_1 @ X1 ) @ ( f__0 @ X1 @ X2 ) )
= X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]) ).
thf(c_0_64,plain,
! [X1: g] :
( ( f__0 @ esk803_0 @ ( f__0 @ f__2 @ X1 ) )
= X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_58]),c_0_59]) ).
thf(c_0_65,plain,
( ( ( f__0 @ f__2 @ f__1 )
!= f__2 )
| ~ p135 ),
inference(er,[status(thm)],[c_0_60]) ).
thf(c_0_66,plain,
p135,
inference(sr,[status(thm)],[c_0_61,c_0_62]) ).
thf(c_0_67,plain,
( ( f__0 @ ( esk835_1 @ esk803_0 ) @ f__1 )
= f__2 ),
inference(spm,[status(thm)],[c_0_63,c_0_58]) ).
thf(c_0_68,plain,
! [X1: g] :
( ( f__0 @ ( esk835_1 @ esk803_0 ) @ X1 )
= ( f__0 @ f__2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
thf(c_0_69,plain,
( f__0 @ f__2 @ f__1 )
!= f__2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66])]) ).
thf(c_0_70,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68]),c_0_69]),
[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] :
( ( X1 @ X3 @ X2 )
= X3 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ALG278^5 : TPTP v8.1.0. Bugfixed v5.3.0.
% 0.10/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Thu Jun 9 03:35:52 EDT 2022
% 0.14/0.34 % CPUTime :
% 2.34/2.59 % SZS status Theorem
% 2.34/2.59 % Mode: mode506
% 2.34/2.59 % Inferences: 37
% 2.34/2.59 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------