TSTP Solution File: SEU942^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU942^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n010.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 : Tue Jul 19 14:10:57 EDT 2022
% Result : Theorem 73.15s 65.40s
% Output : Proof 73.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 29
% Syntax : Number of formulae : 81 ( 31 unt; 3 typ; 0 def)
% Number of atoms : 681 ( 147 equ; 0 cnn)
% Maximal formula atoms : 32 ( 8 avg)
% Number of connectives : 627 ( 135 ~; 104 |; 10 &; 310 @)
% ( 0 <=>; 68 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 17 con; 0-2 aty)
% Number of variables : 60 ( 7 ^ 53 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $i > $i ).
thf(ty_eigen__0,type,
eigen__0: $i > $i ).
thf(cTHM15B_pme,conjecture,
! [X1: $i > $i] :
( ~ ! [X2: $i > $i] :
( ! [X3: ( $i > $i ) > $o] :
( ~ ( ( X3 @ X1 )
=> ~ ! [X4: $i > $i] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: $i] : ( X1 @ ( X4 @ X5 ) ) ) ) )
=> ( X3 @ X2 ) )
=> ! [X3: $i] :
( ( ( X2 @ X3 )
= X3 )
=> ~ ! [X4: $i] :
( ( ( X2 @ X4 )
= X4 )
=> ( X4 = X3 ) ) ) )
=> ~ ! [X2: $i] :
( ( X1 @ X2 )
!= X2 ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i > $i] :
( ~ ! [X2: $i > $i] :
( ! [X3: ( $i > $i ) > $o] :
( ~ ( ( X3 @ X1 )
=> ~ ! [X4: $i > $i] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: $i] : ( X1 @ ( X4 @ X5 ) ) ) ) )
=> ( X3 @ X2 ) )
=> ! [X3: $i] :
( ( ( X2 @ X3 )
= X3 )
=> ~ ! [X4: $i] :
( ( ( X2 @ X4 )
= X4 )
=> ( X4 = X3 ) ) ) )
=> ~ ! [X2: $i] :
( ( X1 @ X2 )
!= X2 ) ),
inference(assume_negation,[status(cth)],[cTHM15B_pme]) ).
thf(h1,assumption,
~ ( ~ ! [X1: $i > $i] :
( ! [X2: ( $i > $i ) > $o] :
( ~ ( ( X2 @ eigen__0 )
=> ~ ! [X3: $i > $i] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i] : ( eigen__0 @ ( X3 @ X4 ) ) ) ) )
=> ( X2 @ X1 ) )
=> ! [X2: $i] :
( ( ( X1 @ X2 )
= X2 )
=> ~ ! [X3: $i] :
( ( ( X1 @ X3 )
= X3 )
=> ( X3 = X2 ) ) ) )
=> ~ ! [X1: $i] :
( ( eigen__0 @ X1 )
!= X1 ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i > $i] :
( ! [X2: ( $i > $i ) > $o] :
( ~ ( ( X2 @ eigen__0 )
=> ~ ! [X3: $i > $i] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i] : ( eigen__0 @ ( X3 @ X4 ) ) ) ) )
=> ( X2 @ X1 ) )
=> ! [X2: $i] :
( ( ( X1 @ X2 )
= X2 )
=> ~ ! [X3: $i] :
( ( ( X1 @ X3 )
= X3 )
=> ( X3 = X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
! [X1: $i] :
( ( eigen__0 @ X1 )
!= X1 ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ! [X1: ( $i > $i ) > $o] :
( ~ ( ( X1 @ eigen__0 )
=> ~ ! [X2: $i > $i] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i] : ( eigen__0 @ ( X2 @ X3 ) ) ) ) )
=> ( X1 @ eigen__1 ) )
=> ! [X1: $i] :
( ( ( eigen__1 @ X1 )
= X1 )
=> ~ ! [X2: $i] :
( ( ( eigen__1 @ X2 )
= X2 )
=> ( X2 = X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
! [X1: ( $i > $i ) > $o] :
( ~ ( ( X1 @ eigen__0 )
=> ~ ! [X2: $i > $i] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i] : ( eigen__0 @ ( X2 @ X3 ) ) ) ) )
=> ( X1 @ eigen__1 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i] :
( ( ( eigen__1 @ X1 )
= X1 )
=> ~ ! [X2: $i] :
( ( ( eigen__1 @ X2 )
= X2 )
=> ( X2 = X1 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ( ( eigen__1 @ eigen__2 )
= eigen__2 )
=> ~ ! [X1: $i] :
( ( ( eigen__1 @ X1 )
= X1 )
=> ( X1 = eigen__2 ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
( ( eigen__1 @ eigen__2 )
= eigen__2 ),
introduced(assumption,[]) ).
thf(h9,assumption,
! [X1: $i] :
( ( ( eigen__1 @ X1 )
= X1 )
=> ( X1 = eigen__2 ) ),
introduced(assumption,[]) ).
thf(ax995,axiom,
( ~ p6
| p7 ),
file('<stdin>',ax995) ).
thf(ax994,axiom,
( ~ p7
| p8 ),
file('<stdin>',ax994) ).
thf(ax996,axiom,
p6,
file('<stdin>',ax996) ).
thf(ax993,axiom,
( ~ p8
| ~ p3
| p5 ),
file('<stdin>',ax993) ).
thf(pax667,axiom,
( p667
=> ( ~ ( ( ( f__2
= ( f__1 @ f__2 ) )
=> ( ( f__0 @ f__2 )
= ( f__0 @ f__2 ) ) )
=> ~ ! [X1: $i > $i] :
( ( ( f__2
= ( f__1 @ f__2 ) )
=> ( ( X1 @ f__2 )
= ( f__0 @ f__2 ) ) )
=> ( ( f__2
= ( f__1 @ f__2 ) )
=> ( ( f__0 @ ( X1 @ f__2 ) )
= ( f__0 @ f__2 ) ) ) ) )
=> ( ( f__2
= ( f__1 @ f__2 ) )
=> ( ( f__1 @ f__2 )
= ( f__0 @ f__2 ) ) ) ) ),
file('<stdin>',pax667) ).
thf(pax5,axiom,
( p5
=> ( f__2
= ( f__1 @ f__2 ) ) ),
file('<stdin>',pax5) ).
thf(ax998,axiom,
p3,
file('<stdin>',ax998) ).
thf(ax333,axiom,
( ~ p4
| p667 ),
file('<stdin>',ax333) ).
thf(pax1,axiom,
( p1
=> ! [X2: $i] :
( ( f__0 @ X2 )
!= X2 ) ),
file('<stdin>',pax1) ).
thf(pax640,axiom,
( p640
=> ( ~ ( ( ( f__2
= ( f__1 @ f__2 ) )
=> ( ( f__0 @ ( f__0 @ f__2 ) )
= ( f__0 @ ( f__0 @ f__2 ) ) ) )
=> ~ ! [X1: $i > $i] :
( ( ( f__2
= ( f__1 @ f__2 ) )
=> ( ( X1 @ ( f__0 @ f__2 ) )
= ( f__0 @ ( X1 @ f__2 ) ) ) )
=> ( ( f__2
= ( f__1 @ f__2 ) )
=> ( ( f__0 @ ( X1 @ ( f__0 @ f__2 ) ) )
= ( f__0 @ ( f__0 @ ( X1 @ f__2 ) ) ) ) ) ) )
=> ( ( f__2
= ( f__1 @ f__2 ) )
=> ( ( f__1 @ ( f__0 @ f__2 ) )
= ( f__0 @ ( f__1 @ f__2 ) ) ) ) ) ),
file('<stdin>',pax640) ).
thf(ax997,axiom,
p4,
file('<stdin>',ax997) ).
thf(ax1000,axiom,
p1,
file('<stdin>',ax1000) ).
thf(ax360,axiom,
( ~ p4
| p640 ),
file('<stdin>',ax360) ).
thf(pax2,axiom,
( p2
=> ! [X2: $i] :
( ( ( f__1 @ X2 )
= X2 )
=> ( X2 = f__2 ) ) ),
file('<stdin>',pax2) ).
thf(ax999,axiom,
p2,
file('<stdin>',ax999) ).
thf(c_0_15,plain,
( ~ p6
| p7 ),
inference(fof_simplification,[status(thm)],[ax995]) ).
thf(c_0_16,plain,
( ~ p7
| p8 ),
inference(fof_simplification,[status(thm)],[ax994]) ).
thf(c_0_17,plain,
( p7
| ~ p6 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_18,plain,
p6,
inference(split_conjunct,[status(thm)],[ax996]) ).
thf(c_0_19,plain,
( ~ p8
| ~ p3
| p5 ),
inference(fof_simplification,[status(thm)],[ax993]) ).
thf(c_0_20,plain,
( p8
| ~ p7 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_21,plain,
p7,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]) ).
thf(c_0_22,plain,
( ( ( f__2
!= ( f__1 @ f__2 ) )
| ( ( esk285_0 @ f__2 )
= ( f__0 @ f__2 ) )
| ( f__2
= ( f__1 @ f__2 ) )
| ( f__2
!= ( f__1 @ f__2 ) )
| ( ( f__1 @ f__2 )
= ( f__0 @ f__2 ) )
| ~ p667 )
& ( ( f__2
= ( f__1 @ f__2 ) )
| ( f__2
= ( f__1 @ f__2 ) )
| ( f__2
!= ( f__1 @ f__2 ) )
| ( ( f__1 @ f__2 )
= ( f__0 @ f__2 ) )
| ~ p667 )
& ( ( ( f__0 @ ( esk285_0 @ f__2 ) )
!= ( f__0 @ f__2 ) )
| ( f__2
= ( f__1 @ f__2 ) )
| ( f__2
!= ( f__1 @ f__2 ) )
| ( ( f__1 @ f__2 )
= ( f__0 @ f__2 ) )
| ~ p667 )
& ( ( f__2
!= ( f__1 @ f__2 ) )
| ( ( esk285_0 @ f__2 )
= ( f__0 @ f__2 ) )
| ( ( f__0 @ f__2 )
!= ( f__0 @ f__2 ) )
| ( f__2
!= ( f__1 @ f__2 ) )
| ( ( f__1 @ f__2 )
= ( f__0 @ f__2 ) )
| ~ p667 )
& ( ( f__2
= ( f__1 @ f__2 ) )
| ( ( f__0 @ f__2 )
!= ( f__0 @ f__2 ) )
| ( f__2
!= ( f__1 @ f__2 ) )
| ( ( f__1 @ f__2 )
= ( f__0 @ f__2 ) )
| ~ p667 )
& ( ( ( f__0 @ ( esk285_0 @ f__2 ) )
!= ( f__0 @ f__2 ) )
| ( ( f__0 @ f__2 )
!= ( f__0 @ f__2 ) )
| ( f__2
!= ( f__1 @ f__2 ) )
| ( ( f__1 @ f__2 )
= ( f__0 @ f__2 ) )
| ~ p667 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax667])])])]) ).
thf(c_0_23,plain,
( ~ p5
| ( f__2
= ( f__1 @ f__2 ) ) ),
inference(fof_nnf,[status(thm)],[pax5]) ).
thf(c_0_24,plain,
( p5
| ~ p8
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_25,plain,
p3,
inference(split_conjunct,[status(thm)],[ax998]) ).
thf(c_0_26,plain,
p8,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21])]) ).
thf(c_0_27,plain,
( ~ p4
| p667 ),
inference(fof_simplification,[status(thm)],[ax333]) ).
thf(c_0_28,plain,
! [X1602: $i] :
( ~ p1
| ( ( f__0 @ X1602 )
!= X1602 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax1])])])]) ).
thf(c_0_29,plain,
( ( ( f__2
!= ( f__1 @ f__2 ) )
| ( ( esk312_0 @ ( f__0 @ f__2 ) )
= ( f__0 @ ( esk312_0 @ f__2 ) ) )
| ( f__2
= ( f__1 @ f__2 ) )
| ( f__2
!= ( f__1 @ f__2 ) )
| ( ( f__1 @ ( f__0 @ f__2 ) )
= ( f__0 @ ( f__1 @ f__2 ) ) )
| ~ p640 )
& ( ( f__2
= ( f__1 @ f__2 ) )
| ( f__2
= ( f__1 @ f__2 ) )
| ( f__2
!= ( f__1 @ f__2 ) )
| ( ( f__1 @ ( f__0 @ f__2 ) )
= ( f__0 @ ( f__1 @ f__2 ) ) )
| ~ p640 )
& ( ( ( f__0 @ ( esk312_0 @ ( f__0 @ f__2 ) ) )
!= ( f__0 @ ( f__0 @ ( esk312_0 @ f__2 ) ) ) )
| ( f__2
= ( f__1 @ f__2 ) )
| ( f__2
!= ( f__1 @ f__2 ) )
| ( ( f__1 @ ( f__0 @ f__2 ) )
= ( f__0 @ ( f__1 @ f__2 ) ) )
| ~ p640 )
& ( ( f__2
!= ( f__1 @ f__2 ) )
| ( ( esk312_0 @ ( f__0 @ f__2 ) )
= ( f__0 @ ( esk312_0 @ f__2 ) ) )
| ( ( f__0 @ ( f__0 @ f__2 ) )
!= ( f__0 @ ( f__0 @ f__2 ) ) )
| ( f__2
!= ( f__1 @ f__2 ) )
| ( ( f__1 @ ( f__0 @ f__2 ) )
= ( f__0 @ ( f__1 @ f__2 ) ) )
| ~ p640 )
& ( ( f__2
= ( f__1 @ f__2 ) )
| ( ( f__0 @ ( f__0 @ f__2 ) )
!= ( f__0 @ ( f__0 @ f__2 ) ) )
| ( f__2
!= ( f__1 @ f__2 ) )
| ( ( f__1 @ ( f__0 @ f__2 ) )
= ( f__0 @ ( f__1 @ f__2 ) ) )
| ~ p640 )
& ( ( ( f__0 @ ( esk312_0 @ ( f__0 @ f__2 ) ) )
!= ( f__0 @ ( f__0 @ ( esk312_0 @ f__2 ) ) ) )
| ( ( f__0 @ ( f__0 @ f__2 ) )
!= ( f__0 @ ( f__0 @ f__2 ) ) )
| ( f__2
!= ( f__1 @ f__2 ) )
| ( ( f__1 @ ( f__0 @ f__2 ) )
= ( f__0 @ ( f__1 @ f__2 ) ) )
| ~ p640 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax640])])])]) ).
thf(c_0_30,plain,
( ( ( esk285_0 @ f__2 )
= ( f__0 @ f__2 ) )
| ( ( f__1 @ f__2 )
= ( f__0 @ f__2 ) )
| ( f__2
!= ( f__1 @ f__2 ) )
| ( ( f__0 @ f__2 )
!= ( f__0 @ f__2 ) )
| ( f__2
!= ( f__1 @ f__2 ) )
| ~ p667 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_31,plain,
( ( f__2
= ( f__1 @ f__2 ) )
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_32,plain,
p5,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
thf(c_0_33,plain,
( p667
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_34,plain,
p4,
inference(split_conjunct,[status(thm)],[ax997]) ).
thf(c_0_35,plain,
! [X2: $i] :
( ~ p1
| ( ( f__0 @ X2 )
!= X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_36,plain,
p1,
inference(split_conjunct,[status(thm)],[ax1000]) ).
thf(c_0_37,plain,
( ~ p4
| p640 ),
inference(fof_simplification,[status(thm)],[ax360]) ).
thf(c_0_38,plain,
! [X1600: $i] :
( ~ p2
| ( ( f__1 @ X1600 )
!= X1600 )
| ( X1600 = f__2 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax2])])]) ).
thf(c_0_39,plain,
( ( ( esk312_0 @ ( f__0 @ f__2 ) )
= ( f__0 @ ( esk312_0 @ f__2 ) ) )
| ( ( f__1 @ ( f__0 @ f__2 ) )
= ( f__0 @ ( f__1 @ f__2 ) ) )
| ( f__2
!= ( f__1 @ f__2 ) )
| ( ( f__0 @ ( f__0 @ f__2 ) )
!= ( f__0 @ ( f__0 @ f__2 ) ) )
| ( f__2
!= ( f__1 @ f__2 ) )
| ~ p640 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_40,plain,
( ( ( f__0 @ f__2 )
= ( f__1 @ f__2 ) )
| ( ( esk285_0 @ f__2 )
= ( f__0 @ f__2 ) )
| ( f__2
!= ( f__1 @ f__2 ) )
| ~ p667 ),
inference(cn,[status(thm)],[c_0_30]) ).
thf(c_0_41,plain,
( ( f__1 @ f__2 )
= f__2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]) ).
thf(c_0_42,plain,
p667,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]) ).
thf(c_0_43,plain,
! [X2: $i] :
( ( f__0 @ X2 )
!= X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]) ).
thf(c_0_44,plain,
( p640
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_45,plain,
( ( ( f__1 @ ( f__0 @ f__2 ) )
= ( f__0 @ ( f__1 @ f__2 ) ) )
| ( ( f__0 @ ( esk312_0 @ ( f__0 @ f__2 ) ) )
!= ( f__0 @ ( f__0 @ ( esk312_0 @ f__2 ) ) ) )
| ( ( f__0 @ ( f__0 @ f__2 ) )
!= ( f__0 @ ( f__0 @ f__2 ) ) )
| ( f__2
!= ( f__1 @ f__2 ) )
| ~ p640 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_46,plain,
! [X2: $i] :
( ( X2 = f__2 )
| ~ p2
| ( ( f__1 @ X2 )
!= X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
thf(c_0_47,plain,
p2,
inference(split_conjunct,[status(thm)],[ax999]) ).
thf(c_0_48,plain,
( ( ( f__0 @ ( f__1 @ f__2 ) )
= ( f__1 @ ( f__0 @ f__2 ) ) )
| ( ( esk312_0 @ ( f__0 @ f__2 ) )
= ( f__0 @ ( esk312_0 @ f__2 ) ) )
| ( f__2
!= ( f__1 @ f__2 ) )
| ~ p640 ),
inference(cn,[status(thm)],[c_0_39]) ).
thf(c_0_49,plain,
( ( f__0 @ f__2 )
= ( esk285_0 @ f__2 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41]),c_0_41]),c_0_42])]),c_0_43]) ).
thf(c_0_50,plain,
p640,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_34])]) ).
thf(c_0_51,plain,
( ( ( f__0 @ ( f__1 @ f__2 ) )
= ( f__1 @ ( f__0 @ f__2 ) ) )
| ( f__2
!= ( f__1 @ f__2 ) )
| ( ( f__0 @ ( esk312_0 @ ( f__0 @ f__2 ) ) )
!= ( f__0 @ ( f__0 @ ( esk312_0 @ f__2 ) ) ) )
| ~ p640 ),
inference(cn,[status(thm)],[c_0_45]) ).
thf(c_0_52,plain,
! [X2: $i] :
( ( X2 = f__2 )
| ( ( f__1 @ X2 )
!= X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]) ).
thf(c_0_53,plain,
( ( ( f__0 @ ( esk312_0 @ f__2 ) )
= ( esk312_0 @ ( esk285_0 @ f__2 ) ) )
| ( ( f__1 @ ( esk285_0 @ f__2 ) )
= ( esk285_0 @ f__2 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49]),c_0_41]),c_0_49]),c_0_49]),c_0_41]),c_0_50])]) ).
thf(c_0_54,plain,
( esk285_0 @ f__2 )
!= f__2,
inference(spm,[status(thm)],[c_0_43,c_0_49]) ).
thf(c_0_55,plain,
( ( ( f__1 @ ( esk285_0 @ f__2 ) )
= ( esk285_0 @ f__2 ) )
| ( ( f__0 @ ( f__0 @ ( esk312_0 @ f__2 ) ) )
!= ( f__0 @ ( esk312_0 @ ( esk285_0 @ f__2 ) ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_49]),c_0_41]),c_0_49]),c_0_41]),c_0_49]),c_0_50])]) ).
thf(c_0_56,plain,
( ( f__0 @ ( esk312_0 @ f__2 ) )
= ( esk312_0 @ ( esk285_0 @ f__2 ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]) ).
thf(c_0_57,plain,
( ( f__1 @ ( esk285_0 @ f__2 ) )
= ( esk285_0 @ f__2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56])]) ).
thf(c_0_58,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_57]),c_0_54]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h8,h9,h7,h5,h6,h4,h2,h3,h1,h0])],]) ).
thf(2,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,1,h8,h9]) ).
thf(3,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,2,h7]) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,3,h5,h6]) ).
thf(5,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h2,4,h4]) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,5,h2,h3]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,6,h1]) ).
thf(0,theorem,
! [X1: $i > $i] :
( ~ ! [X2: $i > $i] :
( ! [X3: ( $i > $i ) > $o] :
( ~ ( ( X3 @ X1 )
=> ~ ! [X4: $i > $i] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: $i] : ( X1 @ ( X4 @ X5 ) ) ) ) )
=> ( X3 @ X2 ) )
=> ! [X3: $i] :
( ( ( X2 @ X3 )
= X3 )
=> ~ ! [X4: $i] :
( ( ( X2 @ X4 )
= X4 )
=> ( X4 = X3 ) ) ) )
=> ~ ! [X2: $i] :
( ( X1 @ X2 )
!= X2 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[7,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU942^5 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 20 02:21:22 EDT 2022
% 0.13/0.35 % CPUTime :
% 73.15/65.40 % SZS status Theorem
% 73.15/65.40 % Mode: mode453
% 73.15/65.40 % Inferences: 5
% 73.15/65.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------