%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV064^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 : Wed Feb 25 09:40:12 AM UTC 2026
% Result : Theorem 1.50s 1.29s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 5
% Syntax : Number of formulae : 62 ( 3 unt; 0 typ; 1 def)
% Number of atoms : 987 ( 439 equ; 0 cnn)
% Maximal formula atoms : 12 ( 15 avg)
% Number of connectives : 1191 ( 65 ~; 162 |; 38 &; 918 @)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 674 ( 674 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 928 ( 757 ^; 137 !; 34 ?; 928 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_4,type,
sK0: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_5,type,
sK1: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_6,type,
sK2: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_7,type,
sK3: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(func_def_8,type,
sK4: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(func_def_9,type,
sK5: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_11,type,
ph7:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
sK9: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(func_def_19,type,
sK10: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(f344,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f78,f343]) ).
thf(f343,plain,
spl6_2,
inference(avatar_contradiction_clause,[status(thm)],[f342]) ).
thf(f342,plain,
( $false
| spl6_2 ),
inference(subsumption_resolution,[status(thm)],[f341,f259]) ).
thf(f259,plain,
( ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
!= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
| spl6_2 ),
inference(subsumption_resolution,[status(thm)],[f249,f51]) ).
thf(f51,plain,
( ( ( ^ [Y0: $i] : $true )
!= ( ^ [Y0: $i] : $false ) )
| spl6_2 ),
inference(avatar_component_clause,[status(thm)],[f50]) ).
thf(f50,definition,
( spl6_2
<=> ( ( ^ [Y0: $i] : $true )
= ( ^ [Y0: $i] : $false ) ) ),
introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition]) ).
thf(f249,plain,
( ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
!= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
| ( ( ^ [Y0: $i] : $true )
= ( ^ [Y0: $i] : $false ) )
| spl6_2 ),
inference(equality_proxy_clausification,[status(thm)],[f248]) ).
thf(f248,plain,
( ( ( ^ [Y0: $i] : $true )
= ( ^ [Y0: $i] : $false ) )
| ( $true
!= ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) )
| spl6_2 ),
inference(equality_proxy_clausification,[status(thm)],[f247]) ).
thf(f247,plain,
( ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) )
| ( $true
!= ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) )
| spl6_2 ),
inference(beta_eta_normalization,[status(thm)],[f241]) ).
thf(f241,plain,
( ! [X2: $i] :
( ( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
!= $true )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 ) ) )
| spl6_2 ),
inference(primitive_instantiation,[status(thm)],[f79]) ).
thf(f79,plain,
( ! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $true
!= ( X0
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 ) ) )
| ( $true
= ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 ) ) )
| spl6_2 ),
inference(subsumption_resolution,[status(thm)],[f62,f51]) ).
thf(f62,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $true
= ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 ) )
| ( $true
!= ( X0
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 ) ) )
| ( ( ^ [Y0: $i] : $true )
= ( ^ [Y0: $i] : $false ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) )
| ( $true
!= ( X0
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 ) ) )
| ( $true
= ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f60]) ).
thf(f60,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $true != $true )
| ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) )
| ( $true
= ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 ) )
| ( $true
!= ( X0
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f59]) ).
thf(f59,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
= ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 ) )
!= $true )
| ( $true
= ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 ) )
| ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) )
| ( $true
!= ( X0
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f54]) ).
thf(f54,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $true
= ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 ) )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 ) )
| ( $true
!= ( X0
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 ) ) )
| ( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 ) ) ) ),
inference(primitive_instantiation,[status(thm)],[f18]) ).
thf(f18,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( X1 @ ( sK5 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) )
!= $true )
| ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true )
| ( ( X0 @ ( sK2 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) )
!= $true )
| ( $true
= ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [X2: $i] :
( ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true )
| ( $true
= ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 ) ) )
| ( ( ( X1 @ ( sK2 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) )
!= $true )
& ( ( X0 @ ( sK2 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) )
!= $true )
& ! [X7: $i] :
( ( $true
= ( X1 @ ( sK2 @ X1 @ X0 ) @ ( sK1 @ X1 @ X0 ) @ X7 ) )
| ( ( X0 @ ( sK2 @ X1 @ X0 ) @ ( sK1 @ X1 @ X0 ) @ X7 )
= $true ) )
& ! [X8: $i] :
( ( $true
= ( X1 @ ( sK1 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) @ X8 ) )
| ( ( X0 @ ( sK1 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) @ X8 )
= $true ) ) )
| ( ( ( X1 @ ( sK5 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) )
!= $true )
& ( ( X0 @ ( sK5 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f8,f11,f10,f9]) ).
thf(f9,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ? [X3: $i > $o,X4: $i > $o,X5: $i > $o] :
( ? [X6: $i] :
( ( $true
!= ( X1 @ X5 @ X3 @ X6 ) )
& ( $true
!= ( X0 @ X5 @ X3 @ X6 ) ) )
& ! [X7: $i] :
( ( $true
= ( X1 @ X5 @ X4 @ X7 ) )
| ( $true
= ( X0 @ X5 @ X4 @ X7 ) ) )
& ! [X8: $i] :
( ( $true
= ( X1 @ X4 @ X3 @ X8 ) )
| ( $true
= ( X0 @ X4 @ X3 @ X8 ) ) ) )
=> ( ? [X6: $i] :
( ( ( X1 @ ( sK2 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) @ X6 )
!= $true )
& ( $true
!= ( X0 @ ( sK2 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) @ X6 ) ) )
& ! [X7: $i] :
( ( $true
= ( X1 @ ( sK2 @ X1 @ X0 ) @ ( sK1 @ X1 @ X0 ) @ X7 ) )
| ( ( X0 @ ( sK2 @ X1 @ X0 ) @ ( sK1 @ X1 @ X0 ) @ X7 )
= $true ) )
& ! [X8: $i] :
( ( $true
= ( X1 @ ( sK1 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) @ X8 ) )
| ( ( X0 @ ( sK1 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) @ X8 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ? [X6: $i] :
( ( ( X1 @ ( sK2 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) @ X6 )
!= $true )
& ( $true
!= ( X0 @ ( sK2 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) @ X6 ) ) )
=> ( ( ( X1 @ ( sK2 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) )
!= $true )
& ( ( X0 @ ( sK2 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ? [X9: $i,X10: $i > $o] :
( ( ( X1 @ X10 @ X10 @ X9 )
!= $true )
& ( $true
!= ( X0 @ X10 @ X10 @ X9 ) ) )
=> ( ( ( X1 @ ( sK5 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) )
!= $true )
& ( ( X0 @ ( sK5 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [X2: $i] :
( ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true )
| ( $true
= ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 ) ) )
| ? [X3: $i > $o,X4: $i > $o,X5: $i > $o] :
( ? [X6: $i] :
( ( $true
!= ( X1 @ X5 @ X3 @ X6 ) )
& ( $true
!= ( X0 @ X5 @ X3 @ X6 ) ) )
& ! [X7: $i] :
( ( $true
= ( X1 @ X5 @ X4 @ X7 ) )
| ( $true
= ( X0 @ X5 @ X4 @ X7 ) ) )
& ! [X8: $i] :
( ( $true
= ( X1 @ X4 @ X3 @ X8 ) )
| ( $true
= ( X0 @ X4 @ X3 @ X8 ) ) ) )
| ? [X9: $i,X10: $i > $o] :
( ( ( X1 @ X10 @ X10 @ X9 )
!= $true )
& ( $true
!= ( X0 @ X10 @ X10 @ X9 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X0: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [X10: $i] :
( ( $true
= ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 ) )
| ( $true
= ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 ) ) )
| ? [X4: $i > $o,X5: $i > $o,X6: $i > $o] :
( ? [X9: $i] :
( ( $true
!= ( X0 @ X6 @ X4 @ X9 ) )
& ( ( X1 @ X6 @ X4 @ X9 )
!= $true ) )
& ! [X8: $i] :
( ( $true
= ( X0 @ X6 @ X5 @ X8 ) )
| ( $true
= ( X1 @ X6 @ X5 @ X8 ) ) )
& ! [X7: $i] :
( ( $true
= ( X0 @ X5 @ X4 @ X7 ) )
| ( $true
= ( X1 @ X5 @ X4 @ X7 ) ) ) )
| ? [X2: $i,X3: $i > $o] :
( ( ( X0 @ X3 @ X3 @ X2 )
!= $true )
& ( ( X1 @ X3 @ X3 @ X2 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ? [X6: $i > $o,X5: $i > $o,X4: $i > $o] :
( ? [X9: $i] :
( ( $true
!= ( X0 @ X6 @ X4 @ X9 ) )
& ( ( X1 @ X6 @ X4 @ X9 )
!= $true ) )
& ! [X7: $i] :
( ( $true
= ( X0 @ X5 @ X4 @ X7 ) )
| ( $true
= ( X1 @ X5 @ X4 @ X7 ) ) )
& ! [X8: $i] :
( ( $true
= ( X0 @ X6 @ X5 @ X8 ) )
| ( $true
= ( X1 @ X6 @ X5 @ X8 ) ) ) )
| ? [X2: $i,X3: $i > $o] :
( ( ( X0 @ X3 @ X3 @ X2 )
!= $true )
& ( ( X1 @ X3 @ X3 @ X2 )
!= $true ) )
| ! [X10: $i] :
( ( $true
= ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 ) )
| ( $true
= ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [X6: $i > $o,X5: $i > $o,X4: $i > $o] :
( ( ! [X7: $i] :
( ( $true
= ( X0 @ X5 @ X4 @ X7 ) )
| ( $true
= ( X1 @ X5 @ X4 @ X7 ) ) )
& ! [X8: $i] :
( ( $true
= ( X0 @ X6 @ X5 @ X8 ) )
| ( $true
= ( X1 @ X6 @ X5 @ X8 ) ) ) )
=> ! [X9: $i] :
( ( ( X1 @ X6 @ X4 @ X9 )
= $true )
| ( $true
= ( X0 @ X6 @ X4 @ X9 ) ) ) )
& ! [X2: $i,X3: $i > $o] :
( ( ( X1 @ X3 @ X3 @ X2 )
= $true )
| ( ( X0 @ X3 @ X3 @ X2 )
= $true ) )
& ~ ! [X10: $i] :
( ( $true
= ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 ) )
| ( $true
= ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X10 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [X2: $i,X3: $i > $o] :
( ( X0 @ X3 @ X3 @ X2 )
| ( X1 @ X3 @ X3 @ X2 ) )
& ! [X4: $i > $o,X5: $i > $o,X6: $i > $o] :
( ( ! [X7: $i] :
( ( X1 @ X5 @ X4 @ X7 )
| ( X0 @ X5 @ X4 @ X7 ) )
& ! [X8: $i] :
( ( X0 @ X6 @ X5 @ X8 )
| ( X1 @ X6 @ X5 @ X8 ) ) )
=> ! [X9: $i] :
( ( X1 @ X6 @ X4 @ X9 )
| ( X0 @ X6 @ X4 @ X9 ) ) )
& ~ ! [X10: $i] :
( ( X0
@ ^ [X11: $i] : $true
@ ^ [X12: $i] : $false
@ X10 )
| ( X1
@ ^ [X13: $i] : $true
@ ^ [X14: $i] : $false
@ X10 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X0: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [X2: $i,X3: $i > $o] :
( ( X1 @ X3 @ X3 @ X2 )
| ( X0 @ X3 @ X3 @ X2 ) )
& ! [X5: $i > $o,X4: $i > $o,X3: $i > $o] :
( ( ! [X2: $i] :
( ( X0 @ X4 @ X5 @ X2 )
| ( X1 @ X4 @ X5 @ X2 ) )
& ! [X2: $i] :
( ( X1 @ X3 @ X4 @ X2 )
| ( X0 @ X3 @ X4 @ X2 ) ) )
=> ! [X2: $i] :
( ( X0 @ X3 @ X5 @ X2 )
| ( X1 @ X3 @ X5 @ X2 ) ) )
& ~ ! [X2: $i] :
( ( X1
@ ^ [X3: $i] : $true
@ ^ [X3: $i] : $false
@ X2 )
| ( X0
@ ^ [X3: $i] : $true
@ ^ [X3: $i] : $false
@ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X0: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [X2: $i,X3: $i > $o] :
( ( X1 @ X3 @ X3 @ X2 )
| ( X0 @ X3 @ X3 @ X2 ) )
& ! [X5: $i > $o,X4: $i > $o,X3: $i > $o] :
( ( ! [X2: $i] :
( ( X0 @ X4 @ X5 @ X2 )
| ( X1 @ X4 @ X5 @ X2 ) )
& ! [X2: $i] :
( ( X1 @ X3 @ X4 @ X2 )
| ( X0 @ X3 @ X4 @ X2 ) ) )
=> ! [X2: $i] :
( ( X0 @ X3 @ X5 @ X2 )
| ( X1 @ X3 @ X5 @ X2 ) ) )
& ~ ! [X2: $i] :
( ( X1
@ ^ [X3: $i] : $true
@ ^ [X3: $i] : $false
@ X2 )
| ( X0
@ ^ [X3: $i] : $true
@ ^ [X3: $i] : $false
@ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Uht8Zmsw0J/DTF2THF_15271.p',cTHM120C_pme) ).
thf(f341,plain,
( ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
| spl6_2 ),
inference(forward_demodulation,[status(thm)],[f340,f282]) ).
thf(f282,plain,
( ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
| spl6_2 ),
inference(subsumption_resolution,[status(thm)],[f281,f51]) ).
thf(f281,plain,
( ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
| ( ( ^ [Y0: $i] : $true )
= ( ^ [Y0: $i] : $false ) )
| spl6_2 ),
inference(equality_proxy_clausification,[status(thm)],[f280]) ).
thf(f280,plain,
( ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) )
| ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
| spl6_2 ),
inference(duplicate_literal_removal,[status(thm)],[f279]) ).
thf(f279,plain,
( ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
| ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
| ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) )
| spl6_2 ),
inference(equality_proxy_clausification,[status(thm)],[f278]) ).
thf(f278,plain,
( ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
| ( $true
= ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) )
| ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) )
| spl6_2 ),
inference(beta_eta_normalization,[status(thm)],[f260]) ).
thf(f260,plain,
( ! [X2: $i,X8: $i] :
( ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 ) )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X8 )
= $true ) )
| spl6_2 ),
inference(primitive_instantiation,[status(thm)],[f155]) ).
thf(f155,plain,
( ! [X2: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X8: $i] :
( ( $true
= ( X1
@ ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK0 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X8 ) )
| ( ( sK0 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
| ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true ) )
| spl6_2 ),
inference(subsumption_resolution,[status(thm)],[f139,f51]) ).
thf(f139,plain,
! [X2: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X8: $i] :
( ( ( sK0 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
| ( $true
= ( X1
@ ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK0 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X8 ) )
| ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true )
| ( ( ^ [Y0: $i] : $true )
= ( ^ [Y0: $i] : $false ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f138]) ).
thf(f138,plain,
! [X2: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X8: $i] :
( ( $true
= ( X1
@ ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK0 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X8 ) )
| ( $true
= ( ( sK0 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) )
| ( ( ^ [Y0: $i] : $true )
= ( ^ [Y0: $i] : $false ) )
| ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f137]) ).
thf(f137,plain,
! [X2: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X8: $i] :
( ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) )
| ( $true
= ( X1
@ ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK0 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X8 ) )
| ( $true
= ( ( sK0 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) )
| ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f136]) ).
thf(f136,plain,
! [X2: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X8: $i] :
( ( $true
= ( ( sK0 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) )
| ( $true
= ( X1
@ ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK0 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X8 ) )
| ( $true != $true )
| ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true )
| ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) ) ),
inference(boolean_simplification,[status(thm)],[f135]) ).
thf(f135,plain,
! [X2: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X8: $i] :
( ( $true
= ( X1
@ ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK0 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X8 ) )
| ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true )
| ( $true
= ( ( sK0 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) )
| ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) )
| ( ( ( sK5 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK5 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f130]) ).
thf(f130,plain,
! [X2: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X8: $i] :
( ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 ) )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK0 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X8 )
= $true )
| ( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK5 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK5 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK4 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) )
| ( $true
= ( X1
@ ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK0 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X8 ) ) ),
inference(primitive_instantiation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X8: $i] :
( ( ( X0 @ ( sK5 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) )
!= $true )
| ( ( X0 @ ( sK1 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) @ X8 )
= $true )
| ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true )
| ( $true
= ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 ) )
| ( $true
= ( X1 @ ( sK1 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) @ X8 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f340,plain,
( ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
| spl6_2 ),
inference(subsumption_resolution,[status(thm)],[f324,f51]) ).
thf(f324,plain,
( ( ( ^ [Y0: $i] : $true )
= ( ^ [Y0: $i] : $false ) )
| ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
| spl6_2 ),
inference(equality_proxy_clausification,[status(thm)],[f323]) ).
thf(f323,plain,
( ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) )
| ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
| spl6_2 ),
inference(duplicate_literal_removal,[status(thm)],[f322]) ).
thf(f322,plain,
( ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) )
| ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
| ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
| spl6_2 ),
inference(equality_proxy_clausification,[status(thm)],[f321]) ).
thf(f321,plain,
( ( $true
= ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) )
| ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) )
| ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
| spl6_2 ),
inference(beta_eta_normalization,[status(thm)],[f313]) ).
thf(f313,plain,
( ! [X2: $i,X7: $i] :
( ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X7 ) )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 ) )
| ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) )
| spl6_2 ),
inference(primitive_instantiation,[status(thm)],[f210]) ).
thf(f210,plain,
( ! [X2: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X7: $i] :
( ( $true
= ( X1
@ ( sK2 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X7 ) )
| ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true )
| ( ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK2 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) )
| spl6_2 ),
inference(subsumption_resolution,[status(thm)],[f194,f51]) ).
thf(f194,plain,
! [X2: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X7: $i] :
( ( ( ^ [Y0: $i] : $true )
= ( ^ [Y0: $i] : $false ) )
| ( $true
= ( X1
@ ( sK2 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X7 ) )
| ( ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK2 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
| ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f193]) ).
thf(f193,plain,
! [X2: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X7: $i] :
( ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) )
| ( $true
= ( X1
@ ( sK2 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X7 ) )
| ( ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK2 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
| ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f192]) ).
thf(f192,plain,
! [X2: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X7: $i] :
( ( $true
= ( ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK2 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) )
| ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) )
| ( $true
= ( X1
@ ( sK2 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X7 ) )
| ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f191]) ).
thf(f191,plain,
! [X2: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X7: $i] :
( ( $true
= ( ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK2 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) )
| ( $true != $true )
| ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) )
| ( $true
= ( X1
@ ( sK2 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X7 ) )
| ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true ) ),
inference(boolean_simplification,[status(thm)],[f190]) ).
thf(f190,plain,
! [X2: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X7: $i] :
( ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true )
| ( $true
= ( ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK2 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) )
| ( ( ( sK5 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK5 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
!= $true )
| ( $true
= ( X1
@ ( sK2 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X7 ) )
| ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f185]) ).
thf(f185,plain,
! [X2: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X7: $i] :
( ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 ) )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK2 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X7 )
= $true )
| ( $true
= ( X1
@ ( sK2 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X7 ) )
| ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true )
| ( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK5 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK5 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK4 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) ) ),
inference(primitive_instantiation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X7: $i] :
( ( ( X0 @ ( sK5 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) )
!= $true )
| ( $true
= ( X1 @ ( sK2 @ X1 @ X0 ) @ ( sK1 @ X1 @ X0 ) @ X7 ) )
| ( ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true )
| ( $true
= ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 ) )
| ( ( X0 @ ( sK2 @ X1 @ X0 ) @ ( sK1 @ X1 @ X0 ) @ X7 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f78,plain,
~ spl6_2,
inference(avatar_contradiction_clause,[status(thm)],[f77]) ).
thf(f77,plain,
( $false
| ~ spl6_2 ),
inference(trivial_inequality_removal,[status(thm)],[f76]) ).
thf(f76,plain,
( ( $true = $false )
| ~ spl6_2 ),
inference(beta_eta_normalization,[status(thm)],[f75]) ).
thf(f75,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] : $false
@ X1 )
= ( ^ [Y0: $i] : $true
@ X1 ) )
| ~ spl6_2 ),
inference(argument_congruence,[status(thm)],[f52]) ).
thf(f52,plain,
( ( ( ^ [Y0: $i] : $true )
= ( ^ [Y0: $i] : $false ) )
| ~ spl6_2 ),
inference(avatar_component_clause,[status(thm)],[f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEV064^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.36 % Computer : n019.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Tue Feb 24 12:39:24 EST 2026
% 0.16/0.36 % CPUTime :
% 0.16/0.36 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.27/0.48 ---- Original DTF file ---
% 0.27/0.48 thf(spec,logic,$$dhol).
% 0.27/0.48 %------------------------------------------------------------------------------
% 0.27/0.48 % File : SEV064^5 : TPTP v9.2.1. Released v4.0.0.
% 0.27/0.48 % Domain : Set Theory (Relations)
% 0.27/0.48 % Problem : TPS problem THM120C
% 0.27/0.48 % Version : Especial.
% 0.27/0.48 % English :
% 0.27/0.48
% 0.27/0.48 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.27/0.48 % Source : [Bro09]
% 0.27/0.48 % Names : tps_0403 [Bro09]
% 0.27/0.48 % : THM120C [TPS]
% 0.27/0.48
% 0.27/0.48 % Status : Theorem
% 0.27/0.48 % Rating : 0.42 v9.1.0, 0.38 v9.0.0, 0.50 v8.2.0, 0.55 v8.1.0, 0.75 v7.5.0, 0.67 v7.3.0, 0.70 v7.2.0, 0.62 v7.1.0, 0.57 v7.0.0, 0.62 v6.4.0, 0.57 v6.3.0, 0.67 v5.5.0, 0.60 v5.4.0, 0.50 v4.1.0, 0.67 v4.0.0
% 0.27/0.48 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.27/0.48 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.27/0.48 % Maximal formula atoms : 4 ( 4 avg)
% 0.27/0.48 % Number of connectives : 40 ( 1 ~; 5 |; 3 &; 30 @)
% 0.27/0.48 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.27/0.48 % Maximal formula depth : 15 ( 15 avg)
% 0.27/0.48 % Number of types : 2 ( 0 usr)
% 0.27/0.48 % Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% 0.27/0.48 % Number of symbols : 2 ( 0 usr; 2 con; 0-0 aty)
% 0.27/0.48 % Number of variables : 15 ( 4 ^; 9 !; 2 ?; 15 :)
% 0.27/0.48 % SPC : TH0_THM_NEQ_NAR
% 0.27/0.48
% 0.27/0.48 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.27/0.48 % project in the Department of Mathematical Sciences at Carnegie
% 0.27/0.48 % Mellon University. Distributed under the Creative Commons copyleft
% 0.27/0.48 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.27/0.48 % : Polymorphic definitions expanded.
% 0.27/0.48 %------------------------------------------------------------------------------
% 0.27/0.48 thf(cTHM120C_pme,conjecture,
% 0.27/0.48 ? [Xr_28: ( $i > $o ) > ( $i > $o ) > $i > $o,Xr_27: ( $i > $o ) > ( $i > $o ) > $i > $o] :
% 0.27/0.48 ( ~ ! [Xw_2: $i] :
% 0.27/0.48 ( ( Xr_27
% 0.27/0.48 @ ^ [Xx: $i] : $true
% 0.27/0.48 @ ^ [Xx: $i] : $false
% 0.27/0.48 @ Xw_2 )
% 0.27/0.48 | ( Xr_28
% 0.27/0.48 @ ^ [Xx: $i] : $true
% 0.27/0.48 @ ^ [Xx: $i] : $false
% 0.27/0.48 @ Xw_2 ) )
% 0.27/0.48 & ! [Xx: $i > $o,Xw_2: $i] :
% 0.27/0.48 ( ( Xr_27 @ Xx @ Xx @ Xw_2 )
% 0.27/0.48 | ( Xr_28 @ Xx @ Xx @ Xw_2 ) )
% 0.27/0.48 & ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
% 0.27/0.48 ( ( ! [Xw_2: $i] :
% 0.27/0.48 ( ( Xr_27 @ Xx @ Xy @ Xw_2 )
% 0.27/0.48 | ( Xr_28 @ Xx @ Xy @ Xw_2 ) )
% 0.27/0.48 & ! [Xw_2: $i] :
% 0.27/0.48 ( ( Xr_27 @ Xy @ Xz @ Xw_2 )
% 0.27/0.48 | ( Xr_28 @ Xy @ Xz @ Xw_2 ) ) )
% 0.27/0.48 => ! [Xw_2: $i] :
% 0.27/0.48 ( ( Xr_27 @ Xx @ Xz @ Xw_2 )
% 0.27/0.48 | ( Xr_28 @ Xx @ Xz @ Xw_2 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 %------------------------------------------------------------------------------
% 0.27/0.48 ------------------------
% 1.50/1.22 ---- Embedded in THF ---
% 1.50/1.22 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.22 %%% Generated on Tue Feb 24 12:39:25 EST 2026
% 1.50/1.22 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.22 %%% Logic specification used:
% 1.50/1.22 %%% thf(spec, logic, $$dhol).
% 1.50/1.22
% 1.50/1.22 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Uht8Zmsw0J/DTF2DTF15271.p
% See solution above
% 1.50/1.22 ------------------------
% 1.50/1.23 ---- Cleaned THF ---
% 1.50/1.23 thf(cTHM120C_pme,conjecture,
% 1.50/1.23 ? [Xr_28: ( $i > $o ) > ( $i > $o ) > $i > $o,Xr_27: ( $i > $o ) > ( $i > $o ) > $i > $o] :
% 1.50/1.23 ( ~ ! [Xw_2: $i] :
% 1.50/1.23 ( ( Xr_27
% 1.50/1.23 @ ^ [Xx: $i] : $true
% 1.50/1.23 @ ^ [Xx: $i] : $false
% 1.50/1.23 @ Xw_2 )
% 1.50/1.23 | ( Xr_28
% 1.50/1.23 @ ^ [Xx: $i] : $true
% 1.50/1.23 @ ^ [Xx: $i] : $false
% 1.50/1.23 @ Xw_2 ) )
% 1.50/1.23 & ! [Xx: $i > $o,Xw_2: $i] :
% 1.50/1.23 ( ( Xr_27 @ Xx @ Xx @ Xw_2 )
% 1.50/1.23 | ( Xr_28 @ Xx @ Xx @ Xw_2 ) )
% 1.50/1.23 & ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
% 1.50/1.23 ( ( ! [Xw_2: $i] :
% 1.50/1.23 ( ( Xr_27 @ Xx @ Xy @ Xw_2 )
% 1.50/1.23 | ( Xr_28 @ Xx @ Xy @ Xw_2 ) )
% 1.50/1.23 & ! [Xw_2: $i] :
% 1.50/1.23 ( ( Xr_27 @ Xy @ Xz @ Xw_2 )
% 1.50/1.23 | ( Xr_28 @ Xy @ Xz @ Xw_2 ) ) )
% 1.50/1.23 => ! [Xw_2: $i] :
% 1.50/1.23 ( ( Xr_27 @ Xx @ Xz @ Xw_2 )
% 1.50/1.23 | ( Xr_28 @ Xx @ Xz @ Xw_2 ) ) ) ) ).
% 1.50/1.23 ------------------------
% 1.50/1.24 % (15371)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15271 for (3000ds/2Mi)
% 1.50/1.24 % (15368)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15271 for (3000ds/183Mi)
% 1.50/1.24 % (15371)Instruction limit reached!
% 1.50/1.24 % (15371)------------------------------
% 1.50/1.24 % (15371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.24 % (15371)Termination reason: Unknown
% 1.50/1.24 % (15371)Termination phase: Saturation
% 1.50/1.24
% 1.50/1.24 % (15371)Memory used [KB]: 5500
% 1.50/1.24 % (15371)Time elapsed: 0.003 s
% 1.50/1.24 % (15371)Instructions burned: 4 (million)
% 1.50/1.24 % (15371)------------------------------
% 1.50/1.24 % (15371)------------------------------
% 1.50/1.25 % (15374)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15271 for (3000ds/18Mi)
% 1.50/1.25 % (15373)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_15271 for (3000ds/275Mi)
% 1.50/1.25 % (15372)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_15271 for (3000ds/2Mi)
% 1.50/1.25 % (15369)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_15271 for (3000ds/4Mi)
% 1.50/1.25 % (15372)Instruction limit reached!
% 1.50/1.25 % (15372)------------------------------
% 1.50/1.25 % (15372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.25 % (15372)Termination reason: Unknown
% 1.50/1.25 % (15372)Termination phase: Saturation
% 1.50/1.25
% 1.50/1.25 % (15372)Memory used [KB]: 1023
% 1.50/1.25 % (15372)Time elapsed: 0.003 s
% 1.50/1.25 % (15372)Instructions burned: 3 (million)
% 1.50/1.25 % (15372)------------------------------
% 1.50/1.25 % (15372)------------------------------
% 1.50/1.25 % (15370)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_15271 for (3000ds/27Mi)
% 1.50/1.25 % (15369)Instruction limit reached!
% 1.50/1.25 % (15369)------------------------------
% 1.50/1.25 % (15369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.25 % (15369)Termination reason: Unknown
% 1.50/1.25 % (15369)Termination phase: Saturation
% 1.50/1.25
% 1.50/1.25 % (15369)Memory used [KB]: 5500
% 1.50/1.25 % (15369)Time elapsed: 0.004 s
% 1.50/1.25 % (15369)Instructions burned: 4 (million)
% 1.50/1.25 % (15369)------------------------------
% 1.50/1.25 % (15369)------------------------------
% 1.50/1.25 % (15375)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_15271 for (2999ds/3Mi)
% 1.50/1.25 % (15375)Instruction limit reached!
% 1.50/1.25 % (15375)------------------------------
% 1.50/1.25 % (15375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.25 % (15375)Termination reason: Unknown
% 1.50/1.25 % (15375)Termination phase: Property scanning
% 1.50/1.25
% 1.50/1.25 % (15375)Memory used [KB]: 1023
% 1.50/1.25 % (15375)Time elapsed: 0.002 s
% 1.50/1.25 % (15375)Instructions burned: 3 (million)
% 1.50/1.25 % (15375)------------------------------
% 1.50/1.25 % (15375)------------------------------
% 1.50/1.25 % (15370)Refutation not found, incomplete strategy
% 1.50/1.25 % (15370)------------------------------
% 1.50/1.25 % (15370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.25 % (15370)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.25
% 1.50/1.25
% 1.50/1.25 % (15370)Memory used [KB]: 5500
% 1.50/1.25 % (15370)Time elapsed: 0.007 s
% 1.50/1.25 % (15370)Instructions burned: 6 (million)
% 1.50/1.25 % (15370)------------------------------
% 1.50/1.25 % (15370)------------------------------
% 1.50/1.26 % (15374)Instruction limit reached!
% 1.50/1.26 % (15374)------------------------------
% 1.50/1.26 % (15374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.26 % (15374)Termination reason: Unknown
% 1.50/1.26 % (15374)Termination phase: Saturation
% 1.50/1.26
% 1.50/1.26 % (15374)Memory used [KB]: 5628
% 1.50/1.26 % (15374)Time elapsed: 0.011 s
% 1.50/1.26 % (15374)Instructions burned: 19 (million)
% 1.50/1.26 % (15374)------------------------------
% 1.50/1.26 % (15374)------------------------------
% 1.50/1.26 % (15377)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_15271 for (2999ds/15Mi)
% 1.50/1.26 % (15378)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_15271 for (2999ds/3Mi)
% 1.50/1.26 % (15378)Instruction limit reached!
% 1.50/1.26 % (15378)------------------------------
% 1.50/1.26 % (15378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.26 % (15378)Termination reason: Unknown
% 1.50/1.26 % (15378)Termination phase: Saturation
% 1.50/1.26
% 1.50/1.26 % (15378)Memory used [KB]: 1023
% 1.50/1.26 % (15378)Time elapsed: 0.002 s
% 1.50/1.26 % (15378)Instructions burned: 4 (million)
% 1.50/1.26 % (15378)------------------------------
% 1.50/1.26 % (15378)------------------------------
% 1.50/1.27 % (15376)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_15271 for (2999ds/37Mi)
% 1.50/1.27 % (15377)Instruction limit reached!
% 1.50/1.27 % (15377)------------------------------
% 1.50/1.27 % (15377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.27 % (15377)Termination reason: Unknown
% 1.50/1.27 % (15377)Termination phase: Saturation
% 1.50/1.27
% 1.50/1.27 % (15377)Memory used [KB]: 5628
% 1.50/1.27 % (15377)Time elapsed: 0.008 s
% 1.50/1.27 % (15377)Instructions burned: 17 (million)
% 1.50/1.27 % (15377)------------------------------
% 1.50/1.27 % (15377)------------------------------
% 1.50/1.27 % (15380)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_15271 for (2999ds/7Mi)
% 1.50/1.27 % (15381)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_15271 for (2999ds/16Mi)
% 1.50/1.28 % (15380)Instruction limit reached!
% 1.50/1.28 % (15380)------------------------------
% 1.50/1.28 % (15380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.28 % (15380)Termination reason: Unknown
% 1.50/1.28 % (15380)Termination phase: Saturation
% 1.50/1.28
% 1.50/1.28 % (15380)Memory used [KB]: 1023
% 1.50/1.28 % (15380)Time elapsed: 0.005 s
% 1.50/1.28 % (15380)Instructions burned: 7 (million)
% 1.50/1.28 % (15380)------------------------------
% 1.50/1.28 % (15380)------------------------------
% 1.50/1.28 % (15381)Instruction limit reached!
% 1.50/1.28 % (15381)------------------------------
% 1.50/1.28 % (15381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.28 % (15381)Termination reason: Unknown
% 1.50/1.28 % (15381)Termination phase: Saturation
% 1.50/1.28
% 1.50/1.28 % (15381)Memory used [KB]: 5628
% 1.50/1.28 % (15381)Time elapsed: 0.006 s
% 1.50/1.28 % (15381)Instructions burned: 17 (million)
% 1.50/1.28 % (15381)------------------------------
% 1.50/1.28 % (15381)------------------------------
% 1.50/1.28 % (15382)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_15271 for (2999ds/3Mi)
% 1.50/1.28 % (15373)First to succeed.
% 1.50/1.28 % (15382)Instruction limit reached!
% 1.50/1.28 % (15382)------------------------------
% 1.50/1.28 % (15382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.28 % (15382)Termination reason: Unknown
% 1.50/1.28 % (15382)Termination phase: Twee Goal Transformation
% 1.50/1.28
% 1.50/1.28 % (15382)Memory used [KB]: 1023
% 1.50/1.28 % (15382)Time elapsed: 0.003 s
% 1.50/1.28 % (15382)Instructions burned: 6 (million)
% 1.50/1.28 % (15382)------------------------------
% 1.50/1.28 % (15382)------------------------------
% 1.50/1.28 % (15379)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_15271 for (2999ds/1041Mi)
% 1.50/1.29 % (15373)Refutation found. Thanks to Tanya!
% 1.50/1.29 % SZS status Theorem for DTF2THF_15271
% 1.50/1.29 % SZS output start Proof for DTF2THF_15271
% 1.50/1.29 thf(func_def_4, type, sK0: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 1.50/1.29 thf(func_def_5, type, sK1: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 1.50/1.29 thf(func_def_6, type, sK2: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 1.50/1.29 thf(func_def_7, type, sK3: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i).
% 1.50/1.29 thf(func_def_8, type, sK4: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i).
% 1.50/1.29 thf(func_def_9, type, sK5: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 1.50/1.29 thf(func_def_11, type, ph7: !>[X0: $tType]:(X0)).
% 1.50/1.29 thf(func_def_18, type, sK9: (($i > $o) > ($i > $o) > $i > $o) > $i).
% 1.50/1.29 thf(func_def_19, type, sK10: (($i > $o) > ($i > $o) > $i > $o) > $i).
% 1.50/1.29 thf(f344,plain,(
% 1.50/1.29 $false),
% 1.50/1.29 inference(avatar_sat_refutation,[status(thm)],[f78,f343])).
% 1.50/1.29 thf(f343,plain,(
% 1.50/1.29 spl6_2),
% 1.50/1.29 inference(avatar_contradiction_clause,[status(thm)],[f342])).
% 1.50/1.29 thf(f342,plain,(
% 1.50/1.29 $false | spl6_2),
% 1.50/1.29 inference(subsumption_resolution,[status(thm)],[f341,f259])).
% 1.50/1.29 thf(f259,plain,(
% 1.50/1.29 ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) != (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | spl6_2),
% 1.50/1.29 inference(subsumption_resolution,[status(thm)],[f249,f51])).
% 1.50/1.29 thf(f51,plain,(
% 1.50/1.29 ((^[Y0 : $i]: ($true)) != (^[Y0 : $i]: ($false))) | spl6_2),
% 1.50/1.29 inference(avatar_component_clause,[status(thm)],[f50])).
% 1.50/1.29 thf(f50,definition,(
% 1.50/1.29 spl6_2 <=> ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))),
% 1.50/1.29 introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition])).
% 1.50/1.29 thf(f249,plain,(
% 1.50/1.29 ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) != (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | spl6_2),
% 1.50/1.29 inference(equality_proxy_clausification,[status(thm)],[f248])).
% 1.50/1.29 thf(f248,plain,(
% 1.50/1.29 ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ($true != ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) | spl6_2),
% 1.50/1.29 inference(equality_proxy_clausification,[status(thm)],[f247])).
% 1.50/1.29 thf(f247,plain,(
% 1.50/1.29 ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | ($true != ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) | spl6_2),
% 1.50/1.29 inference(beta_eta_normalization,[status(thm)],[f241])).
% 1.50/1.29 thf(f241,plain,(
% 1.50/1.29 ( ! [X2 : $i] : ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) != $true) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) ) | spl6_2),
% 1.50/1.29 inference(primitive_instantiation,[status(thm)],[f79])).
% 1.50/1.29 thf(f79,plain,(
% 1.50/1.29 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o] : (($true != (X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0))) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) ) | spl6_2),
% 1.50/1.29 inference(subsumption_resolution,[status(thm)],[f62,f51])).
% 1.50/1.29 thf(f62,plain,(
% 1.50/1.29 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o] : (($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ($true != (X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) )),
% 1.50/1.29 inference(equality_proxy_clausification,[status(thm)],[f61])).
% 1.50/1.29 thf(f61,plain,(
% 1.50/1.29 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o] : (($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | ($true != (X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0))) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) )),
% 1.50/1.29 inference(trivial_inequality_removal,[status(thm)],[f60])).
% 1.50/1.29 thf(f60,plain,(
% 1.50/1.29 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o] : (($true != $true) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ($true != (X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)))) )),
% 1.50/1.29 inference(boolean_simplification,[status(thm)],[f59])).
% 1.50/1.29 thf(f59,plain,(
% 1.50/1.29 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o] : ((((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) != $true) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | ($true != (X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)))) )),
% 1.50/1.29 inference(beta_eta_normalization,[status(thm)],[f54])).
% 1.50/1.29 thf(f54,plain,(
% 1.50/1.29 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o] : (($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ($true != (X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0))) | ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)))) )),
% 1.50/1.29 inference(primitive_instantiation,[status(thm)],[f18])).
% 1.50/1.29 thf(f18,plain,(
% 1.50/1.29 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)) != $true) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ((X0 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK3 @ X1 @ X0)) != $true) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) )),
% 1.50/1.29 inference(cnf_transformation,[status(thm)],[f12])).
% 1.50/1.29 thf(f12,plain,(
% 1.50/1.29 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (! [X2 : $i] : (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ((((X1 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK3 @ X1 @ X0)) != $true) & ((X0 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK3 @ X1 @ X0)) != $true)) & ! [X7 : $i] : (($true = (X1 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7)) | ((X0 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7) = $true)) & ! [X8 : $i] : (($true = (X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X8)) | ((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X8) = $true))) | (((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)) != $true) & ((X0 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)) != $true)))),
% 1.50/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f8,f11,f10,f9])).
% 1.50/1.29 thf(f9,plain,(
% 1.50/1.29 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X3 : $i > $o,X4 : $i > $o,X5 : $i > $o] : (? [X6 : $i] : (($true != (X1 @ X5 @ X3 @ X6)) & ($true != (X0 @ X5 @ X3 @ X6))) & ! [X7 : $i] : (($true = (X1 @ X5 @ X4 @ X7)) | ($true = (X0 @ X5 @ X4 @ X7))) & ! [X8 : $i] : (($true = (X1 @ X4 @ X3 @ X8)) | ($true = (X0 @ X4 @ X3 @ X8)))) => (? [X6 : $i] : (((X1 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6) != $true) & ($true != (X0 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6))) & ! [X7 : $i] : (($true = (X1 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7)) | ((X0 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7) = $true)) & ! [X8 : $i] : (($true = (X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X8)) | ((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X8) = $true))))),
% 1.50/1.29 introduced(definition,[],[choice_axiom])).
% 1.50/1.29 thf(f10,plain,(
% 1.50/1.29 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X6 : $i] : (((X1 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6) != $true) & ($true != (X0 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6))) => (((X1 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK3 @ X1 @ X0)) != $true) & ((X0 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK3 @ X1 @ X0)) != $true)))),
% 1.50/1.29 introduced(definition,[],[choice_axiom])).
% 1.50/1.29 thf(f11,plain,(
% 1.50/1.29 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X9 : $i,X10 : $i > $o] : (((X1 @ X10 @ X10 @ X9) != $true) & ($true != (X0 @ X10 @ X10 @ X9))) => (((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)) != $true) & ((X0 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)) != $true)))),
% 1.50/1.29 introduced(definition,[],[choice_axiom])).
% 1.50/1.29 thf(f8,plain,(
% 1.50/1.29 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (! [X2 : $i] : (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ? [X3 : $i > $o,X4 : $i > $o,X5 : $i > $o] : (? [X6 : $i] : (($true != (X1 @ X5 @ X3 @ X6)) & ($true != (X0 @ X5 @ X3 @ X6))) & ! [X7 : $i] : (($true = (X1 @ X5 @ X4 @ X7)) | ($true = (X0 @ X5 @ X4 @ X7))) & ! [X8 : $i] : (($true = (X1 @ X4 @ X3 @ X8)) | ($true = (X0 @ X4 @ X3 @ X8)))) | ? [X9 : $i,X10 : $i > $o] : (((X1 @ X10 @ X10 @ X9) != $true) & ($true != (X0 @ X10 @ X10 @ X9))))),
% 1.50/1.29 inference(rectify,[status(thm)],[f7])).
% 1.50/1.29 thf(f7,plain,(
% 1.50/1.29 ! [X1 : ($i > $o) > ($i > $o) > $i > $o,X0 : ($i > $o) > ($i > $o) > $i > $o] : (! [X10 : $i] : (($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ? [X4 : $i > $o,X5 : $i > $o,X6 : $i > $o] : (? [X9 : $i] : (($true != (X0 @ X6 @ X4 @ X9)) & ((X1 @ X6 @ X4 @ X9) != $true)) & ! [X8 : $i] : (($true = (X0 @ X6 @ X5 @ X8)) | ($true = (X1 @ X6 @ X5 @ X8))) & ! [X7 : $i] : (($true = (X0 @ X5 @ X4 @ X7)) | ($true = (X1 @ X5 @ X4 @ X7)))) | ? [X2 : $i,X3 : $i > $o] : (((X0 @ X3 @ X3 @ X2) != $true) & ((X1 @ X3 @ X3 @ X2) != $true)))),
% 1.50/1.29 inference(flattening,[status(thm)],[f6])).
% 1.50/1.29 thf(f6,plain,(
% 1.50/1.29 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X6 : $i > $o,X5 : $i > $o,X4 : $i > $o] : (? [X9 : $i] : (($true != (X0 @ X6 @ X4 @ X9)) & ((X1 @ X6 @ X4 @ X9) != $true)) & (! [X7 : $i] : (($true = (X0 @ X5 @ X4 @ X7)) | ($true = (X1 @ X5 @ X4 @ X7))) & ! [X8 : $i] : (($true = (X0 @ X6 @ X5 @ X8)) | ($true = (X1 @ X6 @ X5 @ X8))))) | ? [X2 : $i,X3 : $i > $o] : (((X0 @ X3 @ X3 @ X2) != $true) & ((X1 @ X3 @ X3 @ X2) != $true)) | ! [X10 : $i] : (($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))))),
% 1.50/1.29 inference(ennf_transformation,[status(thm)],[f5])).
% 1.50/1.29 thf(f5,plain,(
% 1.50/1.29 ~? [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (! [X6 : $i > $o,X5 : $i > $o,X4 : $i > $o] : ((! [X7 : $i] : (($true = (X0 @ X5 @ X4 @ X7)) | ($true = (X1 @ X5 @ X4 @ X7))) & ! [X8 : $i] : (($true = (X0 @ X6 @ X5 @ X8)) | ($true = (X1 @ X6 @ X5 @ X8)))) => ! [X9 : $i] : (((X1 @ X6 @ X4 @ X9) = $true) | ($true = (X0 @ X6 @ X4 @ X9)))) & ! [X2 : $i,X3 : $i > $o] : (((X1 @ X3 @ X3 @ X2) = $true) | ((X0 @ X3 @ X3 @ X2) = $true)) & ~! [X10 : $i] : (($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))))),
% 1.50/1.29 inference(fool_elimination,[status(thm)],[f4])).
% 1.50/1.29 thf(f4,plain,(
% 1.50/1.29 ~? [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (! [X2 : $i,X3 : $i > $o] : ((X0 @ X3 @ X3 @ X2) | (X1 @ X3 @ X3 @ X2)) & ! [X4 : $i > $o,X5 : $i > $o,X6 : $i > $o] : ((! [X7 : $i] : ((X1 @ X5 @ X4 @ X7) | (X0 @ X5 @ X4 @ X7)) & ! [X8 : $i] : ((X0 @ X6 @ X5 @ X8) | (X1 @ X6 @ X5 @ X8))) => ! [X9 : $i] : ((X1 @ X6 @ X4 @ X9) | (X0 @ X6 @ X4 @ X9))) & ~! [X10 : $i] : ((X0 @ (^[X11 : $i] : ($true)) @ (^[X12 : $i] : ($false)) @ X10) | (X1 @ (^[X13 : $i] : ($true)) @ (^[X14 : $i] : ($false)) @ X10)))),
% 1.50/1.29 inference(rectify,[status(thm)],[f2])).
% 1.50/1.29 thf(f2,negated_conjecture,(
% 1.50/1.29 ~? [X1 : ($i > $o) > ($i > $o) > $i > $o,X0 : ($i > $o) > ($i > $o) > $i > $o] : (! [X2 : $i,X3 : $i > $o] : ((X1 @ X3 @ X3 @ X2) | (X0 @ X3 @ X3 @ X2)) & ! [X5 : $i > $o,X4 : $i > $o,X3 : $i > $o] : ((! [X2 : $i] : ((X0 @ X4 @ X5 @ X2) | (X1 @ X4 @ X5 @ X2)) & ! [X2 : $i] : ((X1 @ X3 @ X4 @ X2) | (X0 @ X3 @ X4 @ X2))) => ! [X2 : $i] : ((X0 @ X3 @ X5 @ X2) | (X1 @ X3 @ X5 @ X2))) & ~! [X2 : $i] : ((X1 @ (^[X3 : $i] : ($true)) @ (^[X3 : $i] : ($false)) @ X2) | (X0 @ (^[X3 : $i] : ($true)) @ (^[X3 : $i] : ($false)) @ X2)))),
% 1.50/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.50/1.29 thf(f1,conjecture,(
% 1.50/1.29 ? [X1 : ($i > $o) > ($i > $o) > $i > $o,X0 : ($i > $o) > ($i > $o) > $i > $o] : (! [X2 : $i,X3 : $i > $o] : ((X1 @ X3 @ X3 @ X2) | (X0 @ X3 @ X3 @ X2)) & ! [X5 : $i > $o,X4 : $i > $o,X3 : $i > $o] : ((! [X2 : $i] : ((X0 @ X4 @ X5 @ X2) | (X1 @ X4 @ X5 @ X2)) & ! [X2 : $i] : ((X1 @ X3 @ X4 @ X2) | (X0 @ X3 @ X4 @ X2))) => ! [X2 : $i] : ((X0 @ X3 @ X5 @ X2) | (X1 @ X3 @ X5 @ X2))) & ~! [X2 : $i] : ((X1 @ (^[X3 : $i] : ($true)) @ (^[X3 : $i] : ($false)) @ X2) | (X0 @ (^[X3 : $i] : ($true)) @ (^[X3 : $i] : ($false)) @ X2)))),
% 1.50/1.29 file('/export/starexec/sandbox/tmp/tmp.Uht8Zmsw0J/DTF2THF_15271.p',cTHM120C_pme)).
% 1.50/1.29 thf(f341,plain,(
% 1.50/1.29 ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | spl6_2),
% 1.50/1.29 inference(forward_demodulation,[status(thm)],[f340,f282])).
% 1.50/1.29 thf(f282,plain,(
% 1.50/1.29 ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | spl6_2),
% 1.50/1.29 inference(subsumption_resolution,[status(thm)],[f281,f51])).
% 1.50/1.29 thf(f281,plain,(
% 1.50/1.29 ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | spl6_2),
% 1.50/1.29 inference(equality_proxy_clausification,[status(thm)],[f280])).
% 1.50/1.29 thf(f280,plain,(
% 1.50/1.29 ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | spl6_2),
% 1.50/1.29 inference(duplicate_literal_removal,[status(thm)],[f279])).
% 1.50/1.29 thf(f279,plain,(
% 1.50/1.29 ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | spl6_2),
% 1.50/1.29 inference(equality_proxy_clausification,[status(thm)],[f278])).
% 1.50/1.29 thf(f278,plain,(
% 1.50/1.29 ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ($true = ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | spl6_2),
% 1.50/1.29 inference(beta_eta_normalization,[status(thm)],[f260])).
% 1.50/1.29 thf(f260,plain,(
% 1.50/1.29 ( ! [X2 : $i,X8 : $i] : (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X8) = $true)) ) | spl6_2),
% 1.50/1.29 inference(primitive_instantiation,[status(thm)],[f155])).
% 1.50/1.29 thf(f155,plain,(
% 1.50/1.29 ( ! [X2 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (($true = (X1 @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X8)) | ((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true)) ) | spl6_2),
% 1.50/1.29 inference(subsumption_resolution,[status(thm)],[f139,f51])).
% 1.50/1.29 thf(f139,plain,(
% 1.50/1.29 ( ! [X2 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ($true = (X1 @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X8)) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) )),
% 1.50/1.29 inference(equality_proxy_clausification,[status(thm)],[f138])).
% 1.50/1.29 thf(f138,plain,(
% 1.50/1.29 ( ! [X2 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (($true = (X1 @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X8)) | ($true = ((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true)) )),
% 1.50/1.29 inference(equality_proxy_clausification,[status(thm)],[f137])).
% 1.50/1.29 thf(f137,plain,(
% 1.50/1.29 ( ! [X2 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | ($true = (X1 @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X8)) | ($true = ((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true)) )),
% 1.50/1.29 inference(trivial_inequality_removal,[status(thm)],[f136])).
% 1.50/1.29 thf(f136,plain,(
% 1.50/1.29 ( ! [X2 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (($true = ((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) | ($true = (X1 @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X8)) | ($true != $true) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))))) )),
% 1.50/1.29 inference(boolean_simplification,[status(thm)],[f135])).
% 1.50/1.29 thf(f135,plain,(
% 1.50/1.29 ( ! [X2 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (($true = (X1 @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X8)) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ($true = ((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | (((sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) != $true)) )),
% 1.50/1.29 inference(beta_eta_normalization,[status(thm)],[f130])).
% 1.50/1.29 thf(f130,plain,(
% 1.50/1.29 ( ! [X2 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X8) = $true) | ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) | ($true = (X1 @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X8))) )),
% 1.50/1.29 inference(primitive_instantiation,[status(thm)],[f13])).
% 1.50/1.29 thf(f13,plain,(
% 1.50/1.29 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((X0 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)) != $true) | ((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X8) = $true) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ($true = (X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X8))) )),
% 1.50/1.29 inference(cnf_transformation,[status(thm)],[f12])).
% 1.50/1.29 thf(f340,plain,(
% 1.50/1.29 ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | spl6_2),
% 1.50/1.29 inference(subsumption_resolution,[status(thm)],[f324,f51])).
% 1.50/1.29 thf(f324,plain,(
% 1.50/1.29 ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | spl6_2),
% 1.50/1.29 inference(equality_proxy_clausification,[status(thm)],[f323])).
% 1.50/1.29 thf(f323,plain,(
% 1.50/1.29 ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | spl6_2),
% 1.50/1.29 inference(duplicate_literal_removal,[status(thm)],[f322])).
% 1.50/1.29 thf(f322,plain,(
% 1.50/1.29 ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | spl6_2),
% 1.50/1.29 inference(equality_proxy_clausification,[status(thm)],[f321])).
% 1.50/1.29 thf(f321,plain,(
% 1.50/1.29 ($true = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | spl6_2),
% 1.50/1.29 inference(beta_eta_normalization,[status(thm)],[f313])).
% 1.50/1.29 thf(f313,plain,(
% 1.50/1.29 ( ! [X2 : $i,X7 : $i] : (($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X7)) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) ) | spl6_2),
% 1.50/1.29 inference(primitive_instantiation,[status(thm)],[f210])).
% 1.50/1.29 thf(f210,plain,(
% 1.50/1.29 ( ! [X2 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X7 : $i] : (($true = (X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X7)) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ((sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) ) | spl6_2),
% 1.50/1.29 inference(subsumption_resolution,[status(thm)],[f194,f51])).
% 1.50/1.29 thf(f194,plain,(
% 1.50/1.29 ( ! [X2 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X7 : $i] : (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ($true = (X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X7)) | ((sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true)) )),
% 1.50/1.29 inference(equality_proxy_clausification,[status(thm)],[f193])).
% 1.50/1.29 thf(f193,plain,(
% 1.50/1.29 ( ! [X2 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X7 : $i] : (($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | ($true = (X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X7)) | ((sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true)) )),
% 1.50/1.29 inference(equality_proxy_clausification,[status(thm)],[f192])).
% 1.50/1.29 thf(f192,plain,(
% 1.50/1.29 ( ! [X2 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X7 : $i] : (($true = ((sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | ($true = (X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X7)) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true)) )),
% 1.50/1.29 inference(trivial_inequality_removal,[status(thm)],[f191])).
% 1.50/1.29 thf(f191,plain,(
% 1.50/1.29 ( ! [X2 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X7 : $i] : (($true = ((sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) | ($true != $true) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | ($true = (X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X7)) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true)) )),
% 1.50/1.29 inference(boolean_simplification,[status(thm)],[f190])).
% 1.50/1.29 thf(f190,plain,(
% 1.50/1.29 ( ! [X2 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X7 : $i] : (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ($true = ((sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) | (((sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) != $true) | ($true = (X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X7)) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))))) )),
% 1.50/1.29 inference(beta_eta_normalization,[status(thm)],[f185])).
% 1.50/1.29 thf(f185,plain,(
% 1.50/1.29 ( ! [X2 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X7 : $i] : (($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X7) = $true) | ($true = (X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X7)) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))))) )),
% 1.50/1.29 inference(primitive_instantiation,[status(thm)],[f15])).
% 1.50/1.29 thf(f15,plain,(
% 1.50/1.29 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X7 : $i] : (((X0 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)) != $true) | ($true = (X1 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7)) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ((X0 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7) = $true)) )),
% 1.50/1.29 inference(cnf_transformation,[status(thm)],[f12])).
% 1.50/1.29 thf(f78,plain,(
% 1.50/1.29 ~spl6_2),
% 1.50/1.29 inference(avatar_contradiction_clause,[status(thm)],[f77])).
% 1.50/1.29 thf(f77,plain,(
% 1.50/1.29 $false | ~spl6_2),
% 1.50/1.29 inference(trivial_inequality_removal,[status(thm)],[f76])).
% 1.50/1.29 thf(f76,plain,(
% 1.50/1.29 ($true = $false) | ~spl6_2),
% 1.50/1.29 inference(beta_eta_normalization,[status(thm)],[f75])).
% 1.50/1.29 thf(f75,plain,(
% 1.50/1.29 ( ! [X1 : $i] : ((((^[Y0 : $i]: ($false)) @ X1) = ((^[Y0 : $i]: ($true)) @ X1))) ) | ~spl6_2),
% 1.50/1.29 inference(argument_congruence,[status(thm)],[f52])).
% 1.50/1.29 thf(f52,plain,(
% 1.50/1.29 ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ~spl6_2),
% 1.50/1.29 inference(avatar_component_clause,[status(thm)],[f50])).
% 1.50/1.29 % SZS output end Proof for DTF2THF_15271
% 1.50/1.29 % (15373)------------------------------
% 1.50/1.29 % (15373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (15373)Termination reason: Refutation
% 1.50/1.29
% 1.50/1.29 % (15373)Memory used [KB]: 6012
% 1.50/1.29 % (15373)Time elapsed: 0.038 s
% 1.50/1.29 % (15373)Instructions burned: 67 (million)
% 1.50/1.29 % (15373)------------------------------
% 1.50/1.29 % (15373)------------------------------
% 1.50/1.29 % (15367)Success in time 0.047 s
%------------------------------------------------------------------------------