%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SET741^4 : TPTP v9.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n029.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 : 300s
% DateTime : Thu Oct 9 02:26:19 PM UTC 2025
% Result : Theorem 108.34s 108.17s
% Output : Proof 108.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 44
% Syntax : Number of formulae : 101 ( 54 unt; 0 typ; 8 def)
% Number of atoms : 359 ( 125 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 527 ( 157 ~; 30 |; 0 &; 277 @)
% ( 0 <=>; 60 =>; 3 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 31 usr; 29 con; 0-2 aty)
% Number of variables : 155 ( 16 ^; 139 !; 0 ?; 155 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i > $i ).
thf(ty_eigen__1,type,
eigen__1: $i > $i ).
thf(ty_eigen__0,type,
eigen__0: $i > $i ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(def_fun_image,definition,
( fun_image
= ( ^ [X1: $i > $i,X2: $i > $o,X3: $i] :
~ ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3
!= ( X1 @ X4 ) ) ) ) ) ).
thf(def_fun_composition,definition,
( fun_composition
= ( ^ [X1: $i > $i,X2: $i > $i,X3: $i] : ( X2 @ ( X1 @ X3 ) ) ) ) ).
thf(def_fun_inv_image,definition,
( fun_inv_image
= ( ^ [X1: $i > $i,X2: $i > $o,X3: $i] :
~ ! [X4: $i] :
( ( X2 @ X4 )
=> ( X4
!= ( X1 @ X3 ) ) ) ) ) ).
thf(def_fun_injective,definition,
( fun_injective
= ( ^ [X1: $i > $i] :
! [X2: $i,X3: $i] :
( ( ( X1 @ X2 )
= ( X1 @ X3 ) )
=> ( X2 = X3 ) ) ) ) ).
thf(def_fun_surjective,definition,
( fun_surjective
= ( ^ [X1: $i > $i] :
! [X2: $i] :
~ ! [X3: $i] :
( X2
!= ( X1 @ X3 ) ) ) ) ).
thf(def_fun_bijective,definition,
( fun_bijective
= ( ^ [X1: $i > $i] :
~ ( ( fun_injective @ X1 )
=> ~ ( fun_surjective @ X1 ) ) ) ) ).
thf(def_fun_decreasing,definition,
( fun_decreasing
= ( ^ [X1: $i > $i,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X2 @ ( X1 @ X4 ) @ ( X1 @ X3 ) ) ) ) ) ).
thf(def_fun_increasing,definition,
( fun_increasing
= ( ^ [X1: $i > $i,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X2 @ ( X1 @ X3 ) @ ( X1 @ X4 ) ) ) ) ) ).
thf(thm,conjecture,
! [X1: $i > $i,X2: $i > $i,X3: $i > $i] :
( ~ ( ~ ( ! [X4: $i,X5: $i] :
( ( ( X3 @ ( X2 @ ( X1 @ X4 ) ) )
= ( X3 @ ( X2 @ ( X1 @ X5 ) ) ) )
=> ( X4 = X5 ) )
=> ~ ! [X4: $i] :
~ ! [X5: $i] :
( X4
!= ( X1 @ ( X3 @ ( X2 @ X5 ) ) ) ) )
=> ~ ! [X4: $i] :
~ ! [X5: $i] :
( X4
!= ( X2 @ ( X1 @ ( X3 @ X5 ) ) ) ) )
=> ~ ( ! [X4: $i,X5: $i] :
( ( ( X3 @ X4 )
= ( X3 @ X5 ) )
=> ( X4 = X5 ) )
=> ~ ! [X4: $i] :
~ ! [X5: $i] :
( X4
!= ( X3 @ X5 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i > $i,X2: $i > $i,X3: $i > $i] :
( ~ ( ~ ( ! [X4: $i,X5: $i] :
( ( ( X3 @ ( X2 @ ( X1 @ X4 ) ) )
= ( X3 @ ( X2 @ ( X1 @ X5 ) ) ) )
=> ( X4 = X5 ) )
=> ~ ! [X4: $i] :
~ ! [X5: $i] :
( X4
!= ( X1 @ ( X3 @ ( X2 @ X5 ) ) ) ) )
=> ~ ! [X4: $i] :
~ ! [X5: $i] :
( X4
!= ( X2 @ ( X1 @ ( X3 @ X5 ) ) ) ) )
=> ~ ( ! [X4: $i,X5: $i] :
( ( ( X3 @ X4 )
= ( X3 @ X5 ) )
=> ( X4 = X5 ) )
=> ~ ! [X4: $i] :
~ ! [X5: $i] :
( X4
!= ( X3 @ X5 ) ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(h1,assumption,
~ ! [X1: $i > $i,X2: $i > $i] :
( ~ ( ~ ( ! [X3: $i,X4: $i] :
( ( ( X2 @ ( X1 @ ( eigen__0 @ X3 ) ) )
= ( X2 @ ( X1 @ ( eigen__0 @ X4 ) ) ) )
=> ( X3 = X4 ) )
=> ~ ! [X3: $i] :
~ ! [X4: $i] :
( X3
!= ( eigen__0 @ ( X2 @ ( X1 @ X4 ) ) ) ) )
=> ~ ! [X3: $i] :
~ ! [X4: $i] :
( X3
!= ( X1 @ ( eigen__0 @ ( X2 @ X4 ) ) ) ) )
=> ~ ( ! [X3: $i,X4: $i] :
( ( ( X2 @ X3 )
= ( X2 @ X4 ) )
=> ( X3 = X4 ) )
=> ~ ! [X3: $i] :
~ ! [X4: $i] :
( X3
!= ( X2 @ X4 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i > $i] :
( ~ ( ~ ( ! [X2: $i,X3: $i] :
( ( ( X1 @ ( eigen__1 @ ( eigen__0 @ X2 ) ) )
= ( X1 @ ( eigen__1 @ ( eigen__0 @ X3 ) ) ) )
=> ( X2 = X3 ) )
=> ~ ! [X2: $i] :
~ ! [X3: $i] :
( X2
!= ( eigen__0 @ ( X1 @ ( eigen__1 @ X3 ) ) ) ) )
=> ~ ! [X2: $i] :
~ ! [X3: $i] :
( X2
!= ( eigen__1 @ ( eigen__0 @ ( X1 @ X3 ) ) ) ) )
=> ~ ( ! [X2: $i,X3: $i] :
( ( ( X1 @ X2 )
= ( X1 @ X3 ) )
=> ( X2 = X3 ) )
=> ~ ! [X2: $i] :
~ ! [X3: $i] :
( X2
!= ( X1 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( ~ ( ! [X1: $i,X2: $i] :
( ( ( eigen__2 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) )
= ( eigen__2 @ ( eigen__1 @ ( eigen__0 @ X2 ) ) ) )
=> ( X1 = X2 ) )
=> ~ ! [X1: $i] :
~ ! [X2: $i] :
( X1
!= ( eigen__0 @ ( eigen__2 @ ( eigen__1 @ X2 ) ) ) ) )
=> ~ ! [X1: $i] :
~ ! [X2: $i] :
( X1
!= ( eigen__1 @ ( eigen__0 @ ( eigen__2 @ X2 ) ) ) ) )
=> ~ ( ! [X1: $i,X2: $i] :
( ( ( eigen__2 @ X1 )
= ( eigen__2 @ X2 ) )
=> ( X1 = X2 ) )
=> ~ ! [X1: $i] :
~ ! [X2: $i] :
( X1
!= ( eigen__2 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ~ ( ! [X1: $i,X2: $i] :
( ( ( eigen__2 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) )
= ( eigen__2 @ ( eigen__1 @ ( eigen__0 @ X2 ) ) ) )
=> ( X1 = X2 ) )
=> ~ ! [X1: $i] :
~ ! [X2: $i] :
( X1
!= ( eigen__0 @ ( eigen__2 @ ( eigen__1 @ X2 ) ) ) ) )
=> ~ ! [X1: $i] :
~ ! [X2: $i] :
( X1
!= ( eigen__1 @ ( eigen__0 @ ( eigen__2 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
( ! [X1: $i,X2: $i] :
( ( ( eigen__2 @ X1 )
= ( eigen__2 @ X2 ) )
=> ( X1 = X2 ) )
=> ~ ! [X1: $i] :
~ ! [X2: $i] :
( X1
!= ( eigen__2 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ! [X1: $i,X2: $i] :
( ( ( eigen__2 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) )
= ( eigen__2 @ ( eigen__1 @ ( eigen__0 @ X2 ) ) ) )
=> ( X1 = X2 ) )
=> ~ ! [X1: $i] :
~ ! [X2: $i] :
( X1
!= ( eigen__0 @ ( eigen__2 @ ( eigen__1 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
! [X1: $i] :
~ ! [X2: $i] :
( X1
!= ( eigen__1 @ ( eigen__0 @ ( eigen__2 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
! [X1: $i,X2: $i] :
( ( ( eigen__2 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) )
= ( eigen__2 @ ( eigen__1 @ ( eigen__0 @ X2 ) ) ) )
=> ( X1 = X2 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
! [X1: $i] :
~ ! [X2: $i] :
( X1
!= ( eigen__0 @ ( eigen__2 @ ( eigen__1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: $i,X2: $i] :
( ( ( eigen__2 @ X1 )
= ( eigen__2 @ X2 ) )
=> ( X1 = X2 ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ! [X1: $i] :
~ ! [X2: $i] :
( X1
!= ( eigen__2 @ X2 ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ! [X1: $i] :
( ( ( eigen__2 @ eigen__3 )
= ( eigen__2 @ X1 ) )
=> ( eigen__3 = X1 ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ( ( eigen__2 @ eigen__3 )
= ( eigen__2 @ eigen__4 ) )
=> ( eigen__3 = eigen__4 ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
( ( eigen__2 @ eigen__3 )
= ( eigen__2 @ eigen__4 ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
eigen__3 != eigen__4,
introduced(assumption,[]) ).
thf(ax84,axiom,
( ~ p3
| ~ p18 ),
file('<stdin>',ax84) ).
thf(pax5,axiom,
( p5
=> ! [X1: $i,X2: $i] :
( ( ( f__2 @ ( f__1 @ ( f__0 @ X1 ) ) )
= ( f__2 @ ( f__1 @ ( f__0 @ X2 ) ) ) )
=> ( X1 = X2 ) ) ),
file('<stdin>',pax5) ).
thf(nax18,axiom,
( p18
<= ! [X1: $i] :
( f__4
!= ( f__1 @ ( f__0 @ ( f__2 @ X1 ) ) ) ) ),
file('<stdin>',nax18) ).
thf(ax101,axiom,
p3,
file('<stdin>',ax101) ).
thf(pax2,axiom,
( p2
=> ( ( f__2 @ f__3 )
= ( f__2 @ f__4 ) ) ),
file('<stdin>',pax2) ).
thf(ax85,axiom,
( ~ p3
| ~ p17 ),
file('<stdin>',ax85) ).
thf(ax99,axiom,
p5,
file('<stdin>',ax99) ).
thf(ax102,axiom,
p2,
file('<stdin>',ax102) ).
thf(nax17,axiom,
( p17
<= ! [X1: $i] :
( f__3
!= ( f__1 @ ( f__0 @ ( f__2 @ X1 ) ) ) ) ),
file('<stdin>',nax17) ).
thf(nax1,axiom,
( p1
<= ( f__3 = f__4 ) ),
file('<stdin>',nax1) ).
thf(ax103,axiom,
~ p1,
file('<stdin>',ax103) ).
thf(c_0_11,plain,
( ~ p3
| ~ p18 ),
inference(fof_simplification,[status(thm)],[ax84]) ).
thf(c_0_12,plain,
! [X111: $i,X112: $i] :
( ~ p5
| ( ( f__2 @ ( f__1 @ ( f__0 @ X111 ) ) )
!= ( f__2 @ ( f__1 @ ( f__0 @ X112 ) ) ) )
| ( X111 = X112 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax5])])]) ).
thf(c_0_13,plain,
( ( f__4
= ( f__1 @ ( f__0 @ ( f__2 @ esk47_0 ) ) ) )
| p18 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax18])])])]) ).
thf(c_0_14,plain,
( ~ p3
| ~ p18 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_15,plain,
p3,
inference(split_conjunct,[status(thm)],[ax101]) ).
thf(c_0_16,plain,
( ~ p2
| ( ( f__2 @ f__3 )
= ( f__2 @ f__4 ) ) ),
inference(fof_nnf,[status(thm)],[pax2]) ).
thf(c_0_17,plain,
( ~ p3
| ~ p17 ),
inference(fof_simplification,[status(thm)],[ax85]) ).
thf(c_0_18,plain,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ p5
| ( ( f__2 @ ( f__1 @ ( f__0 @ X1 ) ) )
!= ( f__2 @ ( f__1 @ ( f__0 @ X2 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_19,plain,
p5,
inference(split_conjunct,[status(thm)],[ax99]) ).
thf(c_0_20,plain,
( ( f__4
= ( f__1 @ ( f__0 @ ( f__2 @ esk47_0 ) ) ) )
| p18 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_21,plain,
~ p18,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]) ).
thf(c_0_22,plain,
( ( ( f__2 @ f__3 )
= ( f__2 @ f__4 ) )
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_23,plain,
p2,
inference(split_conjunct,[status(thm)],[ax102]) ).
thf(c_0_24,plain,
( ( f__3
= ( f__1 @ ( f__0 @ ( f__2 @ esk48_0 ) ) ) )
| p17 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax17])])])]) ).
thf(c_0_25,plain,
( ~ p3
| ~ p17 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_26,plain,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
| ( ( f__2 @ ( f__1 @ ( f__0 @ X1 ) ) )
!= ( f__2 @ ( f__1 @ ( f__0 @ X2 ) ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]) ).
thf(c_0_27,plain,
( ( f__1 @ ( f__0 @ ( f__2 @ esk47_0 ) ) )
= f__4 ),
inference(sr,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_28,plain,
( ( f__2 @ f__4 )
= ( f__2 @ f__3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).
thf(c_0_29,plain,
( ( f__3
= ( f__1 @ ( f__0 @ ( f__2 @ esk48_0 ) ) ) )
| p17 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_30,plain,
~ p17,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_15])]) ).
thf(c_0_31,plain,
( ( f__3 != f__4 )
| p1 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])]) ).
thf(c_0_32,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax103]) ).
thf(c_0_33,plain,
! [X1: $i] :
( ( X1
= ( f__2 @ esk47_0 ) )
| ( ( f__2 @ ( f__1 @ ( f__0 @ X1 ) ) )
!= ( f__2 @ f__3 ) ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
thf(c_0_34,plain,
( ( f__1 @ ( f__0 @ ( f__2 @ esk48_0 ) ) )
= f__3 ),
inference(sr,[status(thm)],[c_0_29,c_0_30]) ).
thf(c_0_35,plain,
( p1
| ( f__3 != f__4 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_36,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_37,plain,
( ( f__2 @ esk47_0 )
= ( f__2 @ esk48_0 ) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
thf(c_0_38,plain,
f__4 != f__3,
inference(sr,[status(thm)],[c_0_35,c_0_36]) ).
thf(c_0_39,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_37]),c_0_34]),c_0_38]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h14,h15,h13,h12,h10,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0])],[]) ).
thf(2,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h12,h10,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[h13,1,h14,h15]) ).
thf(3,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h10,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__4)],[h12,2,h13]) ).
thf(4,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__3)],[h10,3,h12]) ).
thf(h16,assumption,
! [X1: $i] :
( eigen__5
!= ( eigen__2 @ X1 ) ),
introduced(assumption,[]) ).
thf(pax5_001,axiom,
( p5
=> ! [X1: $i,X2: $i] :
( ( ( f__2 @ ( f__1 @ ( f__0 @ X1 ) ) )
= ( f__2 @ ( f__1 @ ( f__0 @ X2 ) ) ) )
=> ( X1 = X2 ) ) ),
file('<stdin>',pax5) ).
thf(pax4,axiom,
( p4
=> ! [X1: $i] :
~ ! [X2: $i] :
( X1
!= ( f__0 @ ( f__2 @ ( f__1 @ X2 ) ) ) ) ),
file('<stdin>',pax4) ).
thf(ax194,axiom,
p5,
file('<stdin>',ax194) ).
thf(ax195,axiom,
p4,
file('<stdin>',ax195) ).
thf(pax101,axiom,
( p101
=> ! [X1: $i] :
( f__5
!= ( f__2 @ X1 ) ) ),
file('<stdin>',pax101) ).
thf(ax197,axiom,
p101,
file('<stdin>',ax197) ).
thf(c_0_6,plain,
! [X203: $i,X204: $i] :
( ~ p5
| ( ( f__2 @ ( f__1 @ ( f__0 @ X203 ) ) )
!= ( f__2 @ ( f__1 @ ( f__0 @ X204 ) ) ) )
| ( X203 = X204 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax5])])]) ).
thf(c_0_7,plain,
! [X207: $i] :
( ~ p4
| ( X207
= ( f__0 @ ( f__2 @ ( f__1 @ ( esk103_1 @ X207 ) ) ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax4])])])])]) ).
thf(c_0_8,plain,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ p5
| ( ( f__2 @ ( f__1 @ ( f__0 @ X1 ) ) )
!= ( f__2 @ ( f__1 @ ( f__0 @ X2 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,plain,
p5,
inference(split_conjunct,[status(thm)],[ax194]) ).
thf(c_0_10,plain,
! [X1: $i] :
( ( X1
= ( f__0 @ ( f__2 @ ( f__1 @ ( esk103_1 @ X1 ) ) ) ) )
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11_002,plain,
p4,
inference(split_conjunct,[status(thm)],[ax195]) ).
thf(c_0_12_003,plain,
! [X93: $i] :
( ~ p101
| ( f__5
!= ( f__2 @ X93 ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax101])])])]) ).
thf(c_0_13_004,plain,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
| ( ( f__2 @ ( f__1 @ ( f__0 @ X1 ) ) )
!= ( f__2 @ ( f__1 @ ( f__0 @ X2 ) ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_9])]) ).
thf(c_0_14_005,plain,
! [X1: $i] :
( ( f__0 @ ( f__2 @ ( f__1 @ ( esk103_1 @ X1 ) ) ) )
= X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11])]) ).
thf(c_0_15_006,plain,
! [X1: $i] :
( ~ p101
| ( f__5
!= ( f__2 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_16_007,plain,
p101,
inference(split_conjunct,[status(thm)],[ax197]) ).
thf(c_0_17_008,plain,
! [X1: $i,X2: $i] :
( ( X1
= ( f__2 @ ( f__1 @ ( esk103_1 @ X2 ) ) ) )
| ( ( f__2 @ ( f__1 @ ( f__0 @ X1 ) ) )
!= ( f__2 @ ( f__1 @ X2 ) ) ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_18_009,plain,
! [X1: $i] :
( ( f__2 @ X1 )
!= f__5 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]) ).
thf(c_0_19_010,plain,
! [X1: $i] :
( ( f__2 @ ( f__1 @ ( esk103_1 @ ( f__0 @ X1 ) ) ) )
= X1 ),
inference(er,[status(thm)],[c_0_17]) ).
thf(c_0_20_011,plain,
$false,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19])]),
[proof] ).
thf(5,plain,
$false,
inference(eprover,[status(thm),assumptions([h16,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0])],[]) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__5)],[h11,5,h16]) ).
thf(7,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h11])],[h5,4,6,h10,h11]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h6,7,h8,h9]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,8,h6,h7]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,9,h4,h5]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,10,h3]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,11,h2]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,12,h1]) ).
thf(0,theorem,
! [X1: $i > $i,X2: $i > $i,X3: $i > $i] :
( ~ ( ~ ( ! [X4: $i,X5: $i] :
( ( ( X3 @ ( X2 @ ( X1 @ X4 ) ) )
= ( X3 @ ( X2 @ ( X1 @ X5 ) ) ) )
=> ( X4 = X5 ) )
=> ~ ! [X4: $i] :
~ ! [X5: $i] :
( X4
!= ( X1 @ ( X3 @ ( X2 @ X5 ) ) ) ) )
=> ~ ! [X4: $i] :
~ ! [X5: $i] :
( X4
!= ( X2 @ ( X1 @ ( X3 @ X5 ) ) ) ) )
=> ~ ( ! [X4: $i,X5: $i] :
( ( ( X3 @ X4 )
= ( X3 @ X5 ) )
=> ( X4 = X5 ) )
=> ~ ! [X4: $i] :
~ ! [X5: $i] :
( X4
!= ( X3 @ X5 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[13,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET741^4 : TPTP v9.2.0. Released v3.6.0.
% 0.10/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 8 14:41:23 EDT 2025
% 0.13/0.34 % CPUTime :
% 108.34/108.17 % SZS status Theorem
% 108.34/108.17 % Mode: mode447
% 108.34/108.17 % Inferences: 48
% 108.34/108.17 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------