%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO541^1 : TPTP v9.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n012.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 03:25:59 PM UTC 2025
% Result : Theorem 4.22s 4.42s
% Output : Proof 4.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 20
% Syntax : Number of formulae : 65 ( 22 unt; 0 typ; 1 def)
% Number of atoms : 173 ( 29 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 196 ( 110 ~; 46 |; 0 &; 7 @)
% ( 0 <=>; 31 =>; 2 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 22 con; 0-2 aty)
% Number of variables : 16 ( 10 ^; 6 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(def_if,definition,
( if
= ( ^ [X1: $o,X2: $i > $i,X3: $i > $i] :
( epsii
@ ^ [X4: $i > $i] :
( ( X1
=> ( X4 != X2 ) )
=> ~ ( ~ X1
=> ( X4 != X3 ) ) ) ) ) ) ).
thf(conj,conjecture,
! [X1: $i > $i,X2: $i > $i] :
~ ( ( ( epsii
@ ^ [X3: $i > $i] :
( ( ~ $false
=> ( X3 != X1 ) )
=> ~ ( ~ ~ $false
=> ( X3 != X2 ) ) ) )
= X1 )
=> ( ( epsii
@ ^ [X3: $i > $i] :
( ( $false
=> ( X3 != X1 ) )
=> ~ ( ~ $false
=> ( X3 != X2 ) ) ) )
!= X2 ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i > $i,X2: $i > $i] :
~ ( ( ( epsii
@ ^ [X3: $i > $i] :
( ( ~ $false
=> ( X3 != X1 ) )
=> ~ ( $false
=> ( X3 != X2 ) ) ) )
= X1 )
=> ( ( epsii
@ ^ [X3: $i > $i] :
( ( $false
=> ( X3 != X1 ) )
=> ~ ( ~ $false
=> ( X3 != X2 ) ) ) )
!= X2 ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(nax32,axiom,
( p32
<= ( ( ~ ~ $true
=> ( f__0 != f__0 ) )
=> ~ ( ~ $true
=> ( f__0 != f__1 ) ) ) ),
file('<stdin>',nax32) ).
thf(ax16470,axiom,
( ~ p26
| ~ p32 ),
file('<stdin>',ax16470) ).
thf(ax16501,axiom,
( p1
| ~ p2 ),
file('<stdin>',ax16501) ).
thf(ax16502,axiom,
~ p1,
file('<stdin>',ax16502) ).
thf(pax35,axiom,
( p35
=> ~ $true ),
file('<stdin>',pax35) ).
thf(ax16474,axiom,
( ~ p27
| ~ p28
| ~ p29 ),
file('<stdin>',ax16474) ).
thf(ax16475,axiom,
( p27
| p26 ),
file('<stdin>',ax16475) ).
thf(ax16466,axiom,
( p29
| p35 ),
file('<stdin>',ax16466) ).
thf(nax159,axiom,
( p159
<= ( ( ~ $true
=> ( f__1 != f__0 ) )
=> ~ ( ~ ~ $true
=> ( f__1 != f__1 ) ) ) ),
file('<stdin>',nax159) ).
thf(ax16499,axiom,
( ~ p3
| ~ p4
| ~ p5 ),
file('<stdin>',ax16499) ).
thf(ax16500,axiom,
( p2
| p3 ),
file('<stdin>',ax16500) ).
thf(ax16273,axiom,
( ~ p154
| ~ p159 ),
file('<stdin>',ax16273) ).
thf(ax16407,axiom,
( p28
| p4 ),
file('<stdin>',ax16407) ).
thf(ax16276,axiom,
( ~ p155
| ~ p156
| ~ p157 ),
file('<stdin>',ax16276) ).
thf(ax16277,axiom,
( p155
| p154 ),
file('<stdin>',ax16277) ).
thf(ax13038,axiom,
( p156
| p35 ),
file('<stdin>',ax13038) ).
thf(ax13039,axiom,
( p157
| p5 ),
file('<stdin>',ax13039) ).
thf(c_0_17,plain,
( ( f__0 != f__0 )
| p32 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax32])]) ).
thf(c_0_18,plain,
( ~ p26
| ~ p32 ),
inference(fof_simplification,[status(thm)],[ax16470]) ).
thf(c_0_19,plain,
( p32
| ( f__0 != f__0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_20,plain,
( p1
| ~ p2 ),
inference(fof_simplification,[status(thm)],[ax16501]) ).
thf(c_0_21,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax16502]) ).
thf(c_0_22,plain,
( ~ p26
| ~ p32 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_23,plain,
p32,
inference(cn,[status(thm)],[c_0_19]) ).
thf(c_0_24,plain,
~ p35,
inference(fof_simplification,[status(thm)],[pax35]) ).
thf(c_0_25,plain,
( p1
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_26,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_27,plain,
( ~ p27
| ~ p28
| ~ p29 ),
inference(fof_simplification,[status(thm)],[ax16474]) ).
thf(c_0_28,plain,
( p27
| p26 ),
inference(split_conjunct,[status(thm)],[ax16475]) ).
thf(c_0_29,plain,
~ p26,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).
thf(c_0_30,plain,
( p29
| p35 ),
inference(split_conjunct,[status(thm)],[ax16466]) ).
thf(c_0_31,plain,
~ p35,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_32,plain,
( ( f__1 != f__1 )
| p159 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax159])]) ).
thf(c_0_33,plain,
( ~ p3
| ~ p4
| ~ p5 ),
inference(fof_simplification,[status(thm)],[ax16499]) ).
thf(c_0_34,plain,
( p2
| p3 ),
inference(split_conjunct,[status(thm)],[ax16500]) ).
thf(c_0_35,plain,
~ p2,
inference(sr,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_36,plain,
( ~ p27
| ~ p28
| ~ p29 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_37,plain,
p27,
inference(sr,[status(thm)],[c_0_28,c_0_29]) ).
thf(c_0_38,plain,
p29,
inference(sr,[status(thm)],[c_0_30,c_0_31]) ).
thf(c_0_39,plain,
( ~ p154
| ~ p159 ),
inference(fof_simplification,[status(thm)],[ax16273]) ).
thf(c_0_40,plain,
( p159
| ( f__1 != f__1 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_41,plain,
( ~ p3
| ~ p4
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
thf(c_0_42,plain,
p3,
inference(sr,[status(thm)],[c_0_34,c_0_35]) ).
thf(c_0_43,plain,
( p28
| p4 ),
inference(split_conjunct,[status(thm)],[ax16407]) ).
thf(c_0_44,plain,
~ p28,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_38])]) ).
thf(c_0_45,plain,
( ~ p154
| ~ p159 ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_46,plain,
p159,
inference(cn,[status(thm)],[c_0_40]) ).
thf(c_0_47,plain,
( ~ p4
| ~ p5 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])]) ).
thf(c_0_48,plain,
p4,
inference(sr,[status(thm)],[c_0_43,c_0_44]) ).
thf(c_0_49,plain,
( ~ p155
| ~ p156
| ~ p157 ),
inference(fof_simplification,[status(thm)],[ax16276]) ).
thf(c_0_50,plain,
( p155
| p154 ),
inference(split_conjunct,[status(thm)],[ax16277]) ).
thf(c_0_51,plain,
~ p154,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46])]) ).
thf(c_0_52,plain,
( p156
| p35 ),
inference(split_conjunct,[status(thm)],[ax13038]) ).
thf(c_0_53,plain,
( p157
| p5 ),
inference(split_conjunct,[status(thm)],[ax13039]) ).
thf(c_0_54,plain,
~ p5,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]) ).
thf(c_0_55,plain,
( ~ p155
| ~ p156
| ~ p157 ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
thf(c_0_56,plain,
p155,
inference(sr,[status(thm)],[c_0_50,c_0_51]) ).
thf(c_0_57,plain,
p156,
inference(sr,[status(thm)],[c_0_52,c_0_31]) ).
thf(c_0_58,plain,
p157,
inference(sr,[status(thm)],[c_0_53,c_0_54]) ).
thf(c_0_59,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56]),c_0_57]),c_0_58])]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],[]) ).
thf(0,theorem,
! [X1: $i > $i,X2: $i > $i] :
~ ( ( ( epsii
@ ^ [X3: $i > $i] :
( ( ~ $false
=> ( X3 != X1 ) )
=> ~ ( ~ ~ $false
=> ( X3 != X2 ) ) ) )
= X1 )
=> ( ( epsii
@ ^ [X3: $i > $i] :
( ( $false
=> ( X3 != X1 ) )
=> ~ ( ~ $false
=> ( X3 != X2 ) ) ) )
!= X2 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO541^1 : TPTP v9.2.0. Released v5.2.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Oct 9 00:49:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 4.22/4.42 % SZS status Theorem
% 4.22/4.42 % Mode: mode506
% 4.22/4.42 % Inferences: 67315
% 4.22/4.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------