%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV087^5 : 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 : n021.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 09:40:15 AM UTC 2026
% Result : Theorem 0.35s 1.35s
% Output : Refutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 71 ( 2 unt; 0 typ; 7 def)
% Number of atoms : 590 ( 245 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 582 ( 95 ~; 79 |; 57 &; 331 @)
% ( 7 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 324 ( 324 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 9 con; 0-2 aty)
% Number of variables : 283 ( 192 ^; 52 !; 39 ?; 283 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_4,type,
sP0: ( ( $i > $o ) > ( $i > $o ) > $o ) > $o ).
thf(func_def_5,type,
sP1: ( ( $i > $o ) > ( $i > $o ) > $o ) > $o ).
thf(func_def_6,type,
sK2: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_7,type,
sK3: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_8,type,
sK4: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_9,type,
sK5: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_10,type,
sK6: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_11,type,
sK7: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_13,type,
ph9:
!>[X0: $tType] : X0 ).
thf(f117,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f62,f66,f86,f91,f96,f97,f115,f116]) ).
thf(f116,plain,
( ~ spl8_7
| ~ spl8_1 ),
inference(avatar_split_clause,[status(thm)],[f103,f51,f111]) ).
thf(f111,definition,
( spl8_7
<=> ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl8_7])],[avatar_definition]) ).
thf(f51,definition,
( spl8_1
<=> ( ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl8_1])],[avatar_definition]) ).
thf(f103,plain,
( ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl8_1 ),
inference(trivial_inequality_removal,[status(thm)],[f101]) ).
thf(f101,plain,
( ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( $true != $true )
| ~ spl8_1 ),
inference(superposition,[status(thm)],[f25,f53]) ).
thf(f53,plain,
( ( ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= $true )
| ~ spl8_1 ),
inference(avatar_component_clause,[status(thm)],[f51]) ).
thf(f25,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( sP0 @ X0 )
!= $true )
| ( ( sK6 @ X0 )
!= ( sK5 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( ( X0 @ ( sK6 @ X0 ) @ ( sK5 @ X0 ) )
= $true )
& ( ( X0 @ ( sK5 @ X0 ) @ ( sK6 @ X0 ) )
= $true )
& ( ( sK6 @ X0 )
!= ( sK5 @ X0 ) ) )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f17,f18]) ).
thf(f18,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X2 @ X1 )
= $true )
& ( ( X0 @ X1 @ X2 )
= $true )
& ( X1 != X2 ) )
=> ( ( ( X0 @ ( sK6 @ X0 ) @ ( sK5 @ X0 ) )
= $true )
& ( ( X0 @ ( sK5 @ X0 ) @ ( sK6 @ X0 ) )
= $true )
& ( ( sK6 @ X0 )
!= ( sK5 @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X2 @ X1 )
= $true )
& ( ( X0 @ X1 @ X2 )
= $true )
& ( X1 != X2 ) )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X6: $i > $o,X5: $i > $o] :
( ( ( X0 @ X5 @ X6 )
= $true )
& ( ( X0 @ X6 @ X5 )
= $true )
& ( X5 != X6 ) )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X6: $i > $o,X5: $i > $o] :
( ( ( X0 @ X5 @ X6 )
= $true )
& ( ( X0 @ X6 @ X5 )
= $true )
& ( X5 != X6 ) )
| ( ( sP0 @ X0 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f115,plain,
( spl8_7
| ~ spl8_1 ),
inference(avatar_split_clause,[status(thm)],[f106,f51,f111]) ).
thf(f106,plain,
( ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl8_1 ),
inference(equality_proxy_clausification,[status(thm)],[f105]) ).
thf(f105,plain,
( ( ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true )
| ~ spl8_1 ),
inference(beta_eta_normalization,[status(thm)],[f104]) ).
thf(f104,plain,
( ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true )
| ~ spl8_1 ),
inference(trivial_inequality_removal,[status(thm)],[f100]) ).
thf(f100,plain,
( ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true )
| ( $true != $true )
| ~ spl8_1 ),
inference(superposition,[status(thm)],[f27,f53]) ).
thf(f27,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0 @ ( sK6 @ X0 ) @ ( sK5 @ X0 ) )
= $true )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f97,plain,
( ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f96,plain,
( spl8_6
| ~ spl8_3 ),
inference(avatar_split_clause,[status(thm)],[f75,f59,f93]) ).
thf(f93,definition,
( spl8_6
<=> ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl8_6])],[avatar_definition]) ).
thf(f59,definition,
( spl8_3
<=> ( ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl8_3])],[avatar_definition]) ).
thf(f75,plain,
( ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl8_3 ),
inference(equality_proxy_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
( ( ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true )
| ~ spl8_3 ),
inference(beta_eta_normalization,[status(thm)],[f73]) ).
thf(f73,plain,
( ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true )
| ~ spl8_3 ),
inference(trivial_inequality_removal,[status(thm)],[f72]) ).
thf(f72,plain,
( ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true )
| ( $true != $true )
| ~ spl8_3 ),
inference(superposition,[status(thm)],[f24,f61]) ).
thf(f61,plain,
( ( ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= $true )
| ~ spl8_3 ),
inference(avatar_component_clause,[status(thm)],[f59]) ).
thf(f24,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( sP1 @ X0 )
!= $true )
| ( ( X0 @ ( sK4 @ X0 ) @ ( sK2 @ X0 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( ( X0 @ ( sK4 @ X0 ) @ ( sK2 @ X0 ) )
= $true )
& ( ( X0 @ ( sK4 @ X0 ) @ ( sK3 @ X0 ) )
!= $true )
& ( ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) )
= $true ) )
| ( ( sP1 @ X0 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f13,f14]) ).
thf(f14,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ( X0 @ X3 @ X1 )
= $true )
& ( ( X0 @ X3 @ X2 )
!= $true )
& ( ( X0 @ X1 @ X2 )
= $true ) )
=> ( ( ( X0 @ ( sK4 @ X0 ) @ ( sK2 @ X0 ) )
= $true )
& ( ( X0 @ ( sK4 @ X0 ) @ ( sK3 @ X0 ) )
!= $true )
& ( ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ( X0 @ X3 @ X1 )
= $true )
& ( ( X0 @ X3 @ X2 )
!= $true )
& ( ( X0 @ X1 @ X2 )
= $true ) )
| ( ( sP1 @ X0 )
!= $true ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X2: $i > $o,X4: $i > $o,X3: $i > $o] :
( ( ( X0 @ X3 @ X2 )
= $true )
& ( ( X0 @ X3 @ X4 )
!= $true )
& ( ( X0 @ X2 @ X4 )
= $true ) )
| ( ( sP1 @ X0 )
!= $true ) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X2: $i > $o,X4: $i > $o,X3: $i > $o] :
( ( ( X0 @ X3 @ X2 )
= $true )
& ( ( X0 @ X3 @ X4 )
!= $true )
& ( ( X0 @ X2 @ X4 )
= $true ) )
| ( ( sP1 @ X0 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f91,plain,
( spl8_5
| ~ spl8_3 ),
inference(avatar_split_clause,[status(thm)],[f78,f59,f88]) ).
thf(f88,definition,
( spl8_5
<=> ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl8_5])],[avatar_definition]) ).
thf(f78,plain,
( ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl8_3 ),
inference(equality_proxy_clausification,[status(thm)],[f77]) ).
thf(f77,plain,
( ( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true )
| ~ spl8_3 ),
inference(beta_eta_normalization,[status(thm)],[f76]) ).
thf(f76,plain,
( ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true )
| ~ spl8_3 ),
inference(trivial_inequality_removal,[status(thm)],[f71]) ).
thf(f71,plain,
( ( $true != $true )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true )
| ~ spl8_3 ),
inference(superposition,[status(thm)],[f22,f61]) ).
thf(f22,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) )
= $true )
| ( ( sP1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f86,plain,
( ~ spl8_4
| ~ spl8_3 ),
inference(avatar_split_clause,[status(thm)],[f81,f59,f83]) ).
thf(f83,definition,
( spl8_4
<=> ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl8_4])],[avatar_definition]) ).
thf(f81,plain,
( ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl8_3 ),
inference(equality_proxy_clausification,[status(thm)],[f80]) ).
thf(f80,plain,
( ( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= $true )
| ~ spl8_3 ),
inference(beta_eta_normalization,[status(thm)],[f79]) ).
thf(f79,plain,
( ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= $true )
| ~ spl8_3 ),
inference(trivial_inequality_removal,[status(thm)],[f70]) ).
thf(f70,plain,
( ( $true != $true )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= $true )
| ~ spl8_3 ),
inference(superposition,[status(thm)],[f23,f61]) ).
thf(f23,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0 @ ( sK4 @ X0 ) @ ( sK3 @ X0 ) )
!= $true )
| ( ( sP1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f66,plain,
~ spl8_2,
inference(avatar_contradiction_clause,[status(thm)],[f65]) ).
thf(f65,plain,
( $false
| ~ spl8_2 ),
inference(trivial_inequality_removal,[status(thm)],[f64]) ).
thf(f64,plain,
( ( $false = $true )
| ~ spl8_2 ),
inference(beta_eta_normalization,[status(thm)],[f63]) ).
thf(f63,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] : $false
@ X1 )
= ( ^ [Y0: $i] : $true
@ X1 ) )
| ~ spl8_2 ),
inference(argument_congruence,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ( ^ [Y0: $i] : $true )
= ( ^ [Y0: $i] : $false ) )
| ~ spl8_2 ),
inference(avatar_component_clause,[status(thm)],[f55]) ).
thf(f55,definition,
( spl8_2
<=> ( ( ^ [Y0: $i] : $true )
= ( ^ [Y0: $i] : $false ) ) ),
introduced(definition,[new_symbols(naming,[spl8_2])],[avatar_definition]) ).
thf(f62,plain,
( spl8_1
| spl8_2
| spl8_3 ),
inference(avatar_split_clause,[status(thm)],[f38,f59,f55,f51]) ).
thf(f38,plain,
( ( ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= $true )
| ( ( ^ [Y0: $i] : $true )
= ( ^ [Y0: $i] : $false ) )
| ( ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= $true )
| ( ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= $true )
| ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= $true )
| ( $true != $true )
| ( ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= $true )
| ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true ) ),
inference(boolean_simplification,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= $true )
| ( ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= $true )
| ( ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= $true )
| ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= $true )
| ( ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= $true )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false )
= $true )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= $true ) ),
inference(primitive_instantiation,[status(thm)],[f28]) ).
thf(f28,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0 @ ( sK7 @ X0 ) @ ( sK7 @ X0 ) )
!= $true )
| ( ( sP0 @ X0 )
= $true )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false )
= $true )
| ( ( sP1 @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( sP1 @ X0 )
= $true )
| ( ( X0 @ ( sK7 @ X0 ) @ ( sK7 @ X0 ) )
!= $true )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false )
= $true )
| ( ( sP0 @ X0 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f11,f20]) ).
thf(f20,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o] :
( ( X0 @ X1 @ X1 )
!= $true )
=> ( ( X0 @ ( sK7 @ X0 ) @ ( sK7 @ X0 ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( sP1 @ X0 )
= $true )
| ? [X1: $i > $o] :
( ( X0 @ X1 @ X1 )
!= $true )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false )
= $true )
| ( ( sP0 @ X0 )
= $true ) ),
inference(definition_folding,[status(thm)],[f8,f10,f9]) ).
thf(f8,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X2: $i > $o,X4: $i > $o,X3: $i > $o] :
( ( ( X0 @ X3 @ X2 )
= $true )
& ( ( X0 @ X3 @ X4 )
!= $true )
& ( ( X0 @ X2 @ X4 )
= $true ) )
| ? [X1: $i > $o] :
( ( X0 @ X1 @ X1 )
!= $true )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false )
= $true )
| ? [X6: $i > $o,X5: $i > $o] :
( ( ( X0 @ X5 @ X6 )
= $true )
& ( ( X0 @ X6 @ X5 )
= $true )
& ( X5 != X6 ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X6: $i > $o,X5: $i > $o] :
( ( X5 != X6 )
& ( ( X0 @ X5 @ X6 )
= $true )
& ( ( X0 @ X6 @ X5 )
= $true ) )
| ? [X1: $i > $o] :
( ( X0 @ X1 @ X1 )
!= $true )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false )
= $true )
| ? [X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ( ( X0 @ X3 @ X4 )
!= $true )
& ( ( X0 @ X3 @ X2 )
= $true )
& ( ( X0 @ X2 @ X4 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X6: $i > $o,X5: $i > $o] :
( ( ( ( X0 @ X5 @ X6 )
= $true )
& ( ( X0 @ X6 @ X5 )
= $true ) )
=> ( X5 = X6 ) )
& ! [X1: $i > $o] :
( ( X0 @ X1 @ X1 )
= $true )
& ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false )
!= $true )
& ! [X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ( ( ( X0 @ X3 @ X2 )
= $true )
& ( ( X0 @ X2 @ X4 )
= $true ) )
=> ( ( X0 @ X3 @ X4 )
= $true ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X1: $i > $o] :
( ( X0 @ X1 @ X1 )
= $true )
& ! [X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ( ( ( X0 @ X3 @ X2 )
= $true )
& ( ( X0 @ X2 @ X4 )
= $true ) )
=> ( ( X0 @ X3 @ X4 )
= $true ) )
& ! [X6: $i > $o,X5: $i > $o] :
( ( ( ( X0 @ X5 @ X6 )
= $true )
& ( ( X0 @ X6 @ X5 )
= $true ) )
=> ( X5 = X6 ) )
& ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false )
!= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X1: $i > $o] : ( X0 @ X1 @ X1 )
& ! [X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ( ( X0 @ X3 @ X2 )
& ( X0 @ X2 @ X4 ) )
=> ( X0 @ X3 @ X4 ) )
& ! [X5: $i > $o,X6: $i > $o] :
( ( ( X0 @ X5 @ X6 )
& ( X0 @ X6 @ X5 ) )
=> ( X5 = X6 ) )
& ~ ( X0
@ ^ [X7: $i] : $true
@ ^ [X8: $i] : $false ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X1: $i > $o] : ( X0 @ X1 @ X1 )
& ! [X2: $i > $o,X1: $i > $o,X3: $i > $o] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) )
& ! [X5: $i > $o,X4: $i > $o] :
( ( ( X0 @ X5 @ X4 )
& ( X0 @ X4 @ X5 ) )
=> ( X4 = X5 ) )
& ~ ( X0
@ ^ [X1: $i] : $true
@ ^ [X1: $i] : $false ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X1: $i > $o] : ( X0 @ X1 @ X1 )
& ! [X2: $i > $o,X1: $i > $o,X3: $i > $o] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) )
& ! [X5: $i > $o,X4: $i > $o] :
( ( ( X0 @ X5 @ X4 )
& ( X0 @ X4 @ X5 ) )
=> ( X4 = X5 ) )
& ~ ( X0
@ ^ [X1: $i] : $true
@ ^ [X1: $i] : $false ) ),
file('/export/starexec/sandbox/tmp/tmp.uCjYCaZz0V/DTF2THF_22756.p',cTHM120H_pme) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV087^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n021.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:39:54 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.32/0.50 ---- Original DTF file ---
% 0.32/0.50 thf(spec,logic,$$dhol).
% 0.32/0.50 %------------------------------------------------------------------------------
% 0.32/0.50 % File : SEV087^5 : TPTP v9.2.1. Released v4.0.0.
% 0.32/0.50 % Domain : Set Theory (Relations)
% 0.32/0.50 % Problem : TPS problem from RELN-THMS
% 0.32/0.50 % Version : Especial.
% 0.32/0.50 % English :
% 0.32/0.50
% 0.32/0.50 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.32/0.50 % Source : [Bro09]
% 0.32/0.50 % Names : tps_0940 [Bro09]
% 0.32/0.50
% 0.32/0.50 % Status : Theorem
% 0.32/0.50 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.40 v8.2.0, 0.62 v8.1.0, 0.64 v7.5.0, 0.29 v7.4.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.71 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.71 v6.0.0, 0.57 v5.5.0, 0.67 v5.4.0, 0.60 v5.2.0, 0.80 v4.1.0, 0.67 v4.0.0
% 0.32/0.50 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.32/0.50 % Number of atoms : 3 ( 1 equ; 0 cnn)
% 0.32/0.50 % Maximal formula atoms : 3 ( 3 avg)
% 0.32/0.50 % Number of connectives : 22 ( 1 ~; 0 |; 5 &; 14 @)
% 0.32/0.50 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.32/0.50 % Maximal formula depth : 12 ( 12 avg)
% 0.32/0.50 % Number of types : 2 ( 0 usr)
% 0.32/0.50 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.32/0.50 % Number of symbols : 3 ( 0 usr; 2 con; 0-2 aty)
% 0.32/0.50 % Number of variables : 9 ( 2 ^; 6 !; 1 ?; 9 :)
% 0.32/0.50 % SPC : TH0_THM_EQU_NAR
% 0.32/0.50
% 0.32/0.50 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.32/0.50 % project in the Department of Mathematical Sciences at Carnegie
% 0.32/0.50 % Mellon University. Distributed under the Creative Commons copyleft
% 0.32/0.50 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.32/0.50 %------------------------------------------------------------------------------
% 0.32/0.50 thf(cTHM120H_pme,conjecture,
% 0.32/0.50 ? [R: ( $i > $o ) > ( $i > $o ) > $o] :
% 0.32/0.50 ( ~ ( R
% 0.32/0.50 @ ^ [Xx: $i] : $true
% 0.32/0.50 @ ^ [Xx: $i] : $false )
% 0.32/0.50 & ! [Xx: $i > $o] : ( R @ Xx @ Xx )
% 0.32/0.50 & ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
% 0.32/0.50 ( ( ( R @ Xx @ Xy )
% 0.32/0.50 & ( R @ Xy @ Xz ) )
% 0.32/0.50 => ( R @ Xx @ Xz ) )
% 0.32/0.50 & ! [X: $i > $o,Y: $i > $o] :
% 0.32/0.50 ( ( ( R @ X @ Y )
% 0.32/0.50 & ( R @ Y @ X ) )
% 0.32/0.50 => ( X = Y ) ) ) ).
% 0.32/0.50
% 0.32/0.50 %------------------------------------------------------------------------------
% 0.32/0.50 ------------------------
% 0.35/1.30 ---- Embedded in THF ---
% 0.35/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.35/1.30 %%% Generated on Tue Feb 24 12:39:54 EST 2026
% 0.35/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.35/1.30 %%% Logic specification used:
% 0.35/1.30 %%% thf(spec, logic, $$dhol).
% 0.35/1.30
% 0.35/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.uCjYCaZz0V/DTF2DTF22756.p
% See solution above
% 0.35/1.30 ------------------------
% 0.35/1.30 ---- Cleaned THF ---
% 0.35/1.31 thf(cTHM120H_pme,conjecture,
% 0.35/1.31 ? [R: ( $i > $o ) > ( $i > $o ) > $o] :
% 0.35/1.31 ( ~ ( R
% 0.35/1.31 @ ^ [Xx: $i] : $true
% 0.35/1.31 @ ^ [Xx: $i] : $false )
% 0.35/1.31 & ! [Xx: $i > $o] : ( R @ Xx @ Xx )
% 0.35/1.31 & ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
% 0.35/1.31 ( ( ( R @ Xx @ Xy )
% 0.35/1.31 & ( R @ Xy @ Xz ) )
% 0.35/1.31 => ( R @ Xx @ Xz ) )
% 0.35/1.31 & ! [X: $i > $o,Y: $i > $o] :
% 0.35/1.31 ( ( ( R @ X @ Y )
% 0.35/1.31 & ( R @ Y @ X ) )
% 0.35/1.31 => ( X = Y ) ) ) ).
% 0.35/1.31 ------------------------
% 0.35/1.32 % (22863)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22756 for (3000ds/183Mi)
% 0.35/1.32 % (22865)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_22756 for (3000ds/27Mi)
% 0.35/1.32 % (22865)Refutation not found, incomplete strategy
% 0.35/1.32 % (22865)------------------------------
% 0.35/1.32 % (22865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.35/1.32 % (22865)Termination reason: Refutation not found, incomplete strategy
% 0.35/1.32
% 0.35/1.32
% 0.35/1.32 % (22865)Memory used [KB]: 5500
% 0.35/1.32 % (22865)Time elapsed: 0.003 s
% 0.35/1.32 % (22865)Instructions burned: 5 (million)
% 0.35/1.32 % (22865)------------------------------
% 0.35/1.32 % (22865)------------------------------
% 0.35/1.32 % (22866)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22756 for (3000ds/2Mi)
% 0.35/1.32 % (22867)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_22756 for (3000ds/2Mi)
% 0.35/1.32 % (22868)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_22756 for (3000ds/275Mi)
% 0.35/1.32 % (22869)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22756 for (3000ds/18Mi)
% 0.35/1.33 % (22866)Instruction limit reached!
% 0.35/1.33 % (22866)------------------------------
% 0.35/1.33 % (22866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.35/1.33 % (22866)Termination reason: Unknown
% 0.35/1.33 % (22867)Instruction limit reached!
% 0.35/1.33 % (22867)------------------------------
% 0.35/1.33 % (22867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.35/1.33 % (22867)Termination reason: Unknown
% 0.35/1.33 % (22867)Termination phase: Saturation
% 0.35/1.33
% 0.35/1.33 % (22867)Memory used [KB]: 5500
% 0.35/1.33 % (22867)Time elapsed: 0.003 s
% 0.35/1.33 % (22867)Instructions burned: 3 (million)
% 0.35/1.33 % (22867)------------------------------
% 0.35/1.33 % (22867)------------------------------
% 0.35/1.33 % (22866)Termination phase: Saturation
% 0.35/1.33
% 0.35/1.33 % (22866)Memory used [KB]: 5500
% 0.35/1.33 % (22866)Time elapsed: 0.003 s
% 0.35/1.33 % (22866)Instructions burned: 3 (million)
% 0.35/1.33 % (22866)------------------------------
% 0.35/1.33 % (22866)------------------------------
% 0.35/1.33 % (22870)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_22756 for (2999ds/3Mi)
% 0.35/1.33 % (22870)Instruction limit reached!
% 0.35/1.33 % (22870)------------------------------
% 0.35/1.33 % (22870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.35/1.33 % (22870)Termination reason: Unknown
% 0.35/1.33 % (22870)Termination phase: Saturation
% 0.35/1.33
% 0.35/1.33 % (22870)Memory used [KB]: 5500
% 0.35/1.33 % (22870)Time elapsed: 0.002 s
% 0.35/1.33 % (22870)Instructions burned: 3 (million)
% 0.35/1.33 % (22870)------------------------------
% 0.35/1.33 % (22870)------------------------------
% 0.35/1.33 % (22864)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_22756 for (3000ds/4Mi)
% 0.35/1.33 % (22869)Instruction limit reached!
% 0.35/1.33 % (22869)------------------------------
% 0.35/1.33 % (22869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.35/1.33 % (22869)Termination reason: Unknown
% 0.35/1.33 % (22869)Termination phase: Saturation
% 0.35/1.33
% 0.35/1.33 % (22869)Memory used [KB]: 5628
% 0.35/1.33 % (22869)Time elapsed: 0.011 s
% 0.35/1.33 % (22869)Instructions burned: 19 (million)
% 0.35/1.33 % (22869)------------------------------
% 0.35/1.33 % (22869)------------------------------
% 0.35/1.34 % (22864)Instruction limit reached!
% 0.35/1.34 % (22864)------------------------------
% 0.35/1.34 % (22864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.35/1.34 % (22864)Termination reason: Unknown
% 0.35/1.34 % (22864)Termination phase: Saturation
% 0.35/1.34
% 0.35/1.34 % (22864)Memory used [KB]: 5500
% 0.35/1.34 % (22864)Time elapsed: 0.004 s
% 0.35/1.34 % (22864)Instructions burned: 5 (million)
% 0.35/1.34 % (22864)------------------------------
% 0.35/1.34 % (22864)------------------------------
% 0.35/1.34 % (22868)Refutation not found, incomplete strategy
% 0.35/1.34 % (22868)------------------------------
% 0.35/1.34 % (22868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.35/1.34 % (22868)Termination reason: Refutation not found, incomplete strategy
% 0.35/1.34
% 0.35/1.34
% 0.35/1.34 % (22868)Memory used [KB]: 5628
% 0.35/1.34 % (22868)Time elapsed: 0.015 s
% 0.35/1.34 % (22868)Instructions burned: 27 (million)
% 0.35/1.34 % (22868)------------------------------
% 0.35/1.34 % (22868)------------------------------
% 0.35/1.34 % (22872)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_22756 for (2999ds/15Mi)
% 0.35/1.34 % (22873)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_22756 for (2999ds/3Mi)
% 0.35/1.34 % (22873)Instruction limit reached!
% 0.35/1.34 % (22873)------------------------------
% 0.35/1.34 % (22873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.35/1.34 % (22873)Termination reason: Unknown
% 0.35/1.34 % (22873)Termination phase: Saturation
% 0.35/1.34
% 0.35/1.34 % (22873)Memory used [KB]: 5500
% 0.35/1.34 % (22873)Time elapsed: 0.002 s
% 0.35/1.34 % (22873)Instructions burned: 3 (million)
% 0.35/1.34 % (22873)------------------------------
% 0.35/1.34 % (22873)------------------------------
% 0.35/1.35 % (22872)First to succeed.
% 0.35/1.35 % (22874)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_22756 for (2999ds/1041Mi)
% 0.35/1.35 % (22872)Refutation found. Thanks to Tanya!
% 0.35/1.35 % SZS status Theorem for DTF2THF_22756
% 0.35/1.35 % SZS output start Proof for DTF2THF_22756
% 0.35/1.35 thf(func_def_4, type, sP0: (($i > $o) > ($i > $o) > $o) > $o).
% 0.35/1.35 thf(func_def_5, type, sP1: (($i > $o) > ($i > $o) > $o) > $o).
% 0.35/1.35 thf(func_def_6, type, sK2: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 0.35/1.35 thf(func_def_7, type, sK3: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 0.35/1.35 thf(func_def_8, type, sK4: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 0.35/1.35 thf(func_def_9, type, sK5: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 0.35/1.35 thf(func_def_10, type, sK6: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 0.35/1.35 thf(func_def_11, type, sK7: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 0.35/1.35 thf(func_def_13, type, ph9: !>[X0: $tType]:(X0)).
% 0.35/1.35 thf(f117,plain,(
% 0.35/1.35 $false),
% 0.35/1.35 inference(avatar_sat_refutation,[status(thm)],[f62,f66,f86,f91,f96,f97,f115,f116])).
% 0.35/1.35 thf(f116,plain,(
% 0.35/1.35 ~spl8_7 | ~spl8_1),
% 0.35/1.35 inference(avatar_split_clause,[status(thm)],[f103,f51,f111])).
% 0.35/1.35 thf(f111,definition,(
% 0.35/1.35 spl8_7 <=> ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 0.35/1.35 introduced(definition,[new_symbols(naming,[spl8_7])],[avatar_definition])).
% 0.35/1.35 thf(f51,definition,(
% 0.35/1.35 spl8_1 <=> ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true)),
% 0.35/1.35 introduced(definition,[new_symbols(naming,[spl8_1])],[avatar_definition])).
% 0.35/1.35 thf(f103,plain,(
% 0.35/1.35 ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl8_1),
% 0.35/1.35 inference(trivial_inequality_removal,[status(thm)],[f101])).
% 0.35/1.35 thf(f101,plain,(
% 0.35/1.35 ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ($true != $true) | ~spl8_1),
% 0.35/1.35 inference(superposition,[status(thm)],[f25,f53])).
% 0.35/1.35 thf(f53,plain,(
% 0.35/1.35 ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true) | ~spl8_1),
% 0.35/1.35 inference(avatar_component_clause,[status(thm)],[f51])).
% 0.35/1.35 thf(f25,plain,(
% 0.35/1.35 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (((sP0 @ X0) != $true) | ((sK6 @ X0) != (sK5 @ X0))) )),
% 0.35/1.35 inference(cnf_transformation,[status(thm)],[f19])).
% 0.35/1.35 thf(f19,plain,(
% 0.35/1.35 ! [X0 : ($i > $o) > ($i > $o) > $o] : ((((X0 @ (sK6 @ X0) @ (sK5 @ X0)) = $true) & ((X0 @ (sK5 @ X0) @ (sK6 @ X0)) = $true) & ((sK6 @ X0) != (sK5 @ X0))) | ((sP0 @ X0) != $true))),
% 0.35/1.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f17,f18])).
% 0.35/1.35 thf(f18,plain,(
% 0.35/1.35 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o] : (((X0 @ X2 @ X1) = $true) & ((X0 @ X1 @ X2) = $true) & (X1 != X2)) => (((X0 @ (sK6 @ X0) @ (sK5 @ X0)) = $true) & ((X0 @ (sK5 @ X0) @ (sK6 @ X0)) = $true) & ((sK6 @ X0) != (sK5 @ X0))))),
% 0.35/1.35 introduced(definition,[],[choice_axiom])).
% 0.35/1.35 thf(f17,plain,(
% 0.35/1.35 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o] : (((X0 @ X2 @ X1) = $true) & ((X0 @ X1 @ X2) = $true) & (X1 != X2)) | ((sP0 @ X0) != $true))),
% 0.35/1.35 inference(rectify,[status(thm)],[f16])).
% 0.35/1.35 thf(f16,plain,(
% 0.35/1.35 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X6 : $i > $o,X5 : $i > $o] : (((X0 @ X5 @ X6) = $true) & ((X0 @ X6 @ X5) = $true) & (X5 != X6)) | ((sP0 @ X0) != $true))),
% 0.35/1.35 inference(nnf_transformation,[status(thm)],[f9])).
% 0.35/1.35 thf(f9,plain,(
% 0.35/1.35 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X6 : $i > $o,X5 : $i > $o] : (((X0 @ X5 @ X6) = $true) & ((X0 @ X6 @ X5) = $true) & (X5 != X6)) | ~((sP0 @ X0) = $true))),
% 0.35/1.35 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 0.35/1.35 thf(f115,plain,(
% 0.35/1.35 spl8_7 | ~spl8_1),
% 0.35/1.35 inference(avatar_split_clause,[status(thm)],[f106,f51,f111])).
% 0.35/1.35 thf(f106,plain,(
% 0.35/1.35 ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl8_1),
% 0.35/1.35 inference(equality_proxy_clausification,[status(thm)],[f105])).
% 0.35/1.35 thf(f105,plain,(
% 0.35/1.35 (((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ~spl8_1),
% 0.35/1.35 inference(beta_eta_normalization,[status(thm)],[f104])).
% 0.35/1.35 thf(f104,plain,(
% 0.35/1.35 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ~spl8_1),
% 0.35/1.35 inference(trivial_inequality_removal,[status(thm)],[f100])).
% 0.35/1.35 thf(f100,plain,(
% 0.35/1.35 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ($true != $true) | ~spl8_1),
% 0.35/1.35 inference(superposition,[status(thm)],[f27,f53])).
% 0.35/1.35 thf(f27,plain,(
% 0.35/1.35 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (sK6 @ X0) @ (sK5 @ X0)) = $true) | ((sP0 @ X0) != $true)) )),
% 0.35/1.35 inference(cnf_transformation,[status(thm)],[f19])).
% 0.35/1.35 thf(f97,plain,(
% 0.35/1.35 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 0.35/1.35 introduced(definition,[],[theory_tautology_sat_conflict])).
% 0.35/1.35 thf(f96,plain,(
% 0.35/1.35 spl8_6 | ~spl8_3),
% 0.35/1.35 inference(avatar_split_clause,[status(thm)],[f75,f59,f93])).
% 0.35/1.35 thf(f93,definition,(
% 0.35/1.35 spl8_6 <=> ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 0.35/1.35 introduced(definition,[new_symbols(naming,[spl8_6])],[avatar_definition])).
% 0.35/1.35 thf(f59,definition,(
% 0.35/1.35 spl8_3 <=> ((sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true)),
% 0.35/1.35 introduced(definition,[new_symbols(naming,[spl8_3])],[avatar_definition])).
% 0.35/1.35 thf(f75,plain,(
% 0.35/1.35 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl8_3),
% 0.35/1.35 inference(equality_proxy_clausification,[status(thm)],[f74])).
% 0.35/1.35 thf(f74,plain,(
% 0.35/1.35 (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ~spl8_3),
% 0.35/1.35 inference(beta_eta_normalization,[status(thm)],[f73])).
% 0.35/1.35 thf(f73,plain,(
% 0.35/1.35 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ~spl8_3),
% 0.35/1.35 inference(trivial_inequality_removal,[status(thm)],[f72])).
% 0.35/1.35 thf(f72,plain,(
% 0.35/1.35 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ($true != $true) | ~spl8_3),
% 0.35/1.35 inference(superposition,[status(thm)],[f24,f61])).
% 0.35/1.35 thf(f61,plain,(
% 0.35/1.35 ((sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true) | ~spl8_3),
% 0.35/1.35 inference(avatar_component_clause,[status(thm)],[f59])).
% 0.35/1.35 thf(f24,plain,(
% 0.35/1.35 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (((sP1 @ X0) != $true) | ((X0 @ (sK4 @ X0) @ (sK2 @ X0)) = $true)) )),
% 0.35/1.35 inference(cnf_transformation,[status(thm)],[f15])).
% 0.35/1.35 thf(f15,plain,(
% 0.35/1.35 ! [X0 : ($i > $o) > ($i > $o) > $o] : ((((X0 @ (sK4 @ X0) @ (sK2 @ X0)) = $true) & ((X0 @ (sK4 @ X0) @ (sK3 @ X0)) != $true) & ((X0 @ (sK2 @ X0) @ (sK3 @ X0)) = $true)) | ((sP1 @ X0) != $true))),
% 0.35/1.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f13,f14])).
% 0.35/1.35 thf(f14,plain,(
% 0.35/1.35 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (((X0 @ X3 @ X1) = $true) & ((X0 @ X3 @ X2) != $true) & ((X0 @ X1 @ X2) = $true)) => (((X0 @ (sK4 @ X0) @ (sK2 @ X0)) = $true) & ((X0 @ (sK4 @ X0) @ (sK3 @ X0)) != $true) & ((X0 @ (sK2 @ X0) @ (sK3 @ X0)) = $true)))),
% 0.35/1.35 introduced(definition,[],[choice_axiom])).
% 0.35/1.35 thf(f13,plain,(
% 0.35/1.35 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (((X0 @ X3 @ X1) = $true) & ((X0 @ X3 @ X2) != $true) & ((X0 @ X1 @ X2) = $true)) | ((sP1 @ X0) != $true))),
% 0.35/1.35 inference(rectify,[status(thm)],[f12])).
% 0.35/1.35 thf(f12,plain,(
% 0.35/1.35 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X2 : $i > $o,X4 : $i > $o,X3 : $i > $o] : (((X0 @ X3 @ X2) = $true) & ((X0 @ X3 @ X4) != $true) & ((X0 @ X2 @ X4) = $true)) | ((sP1 @ X0) != $true))),
% 0.35/1.35 inference(nnf_transformation,[status(thm)],[f10])).
% 0.35/1.35 thf(f10,plain,(
% 0.35/1.35 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X2 : $i > $o,X4 : $i > $o,X3 : $i > $o] : (((X0 @ X3 @ X2) = $true) & ((X0 @ X3 @ X4) != $true) & ((X0 @ X2 @ X4) = $true)) | ~((sP1 @ X0) = $true))),
% 0.35/1.35 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 0.35/1.35 thf(f91,plain,(
% 0.35/1.35 spl8_5 | ~spl8_3),
% 0.35/1.35 inference(avatar_split_clause,[status(thm)],[f78,f59,f88])).
% 0.35/1.35 thf(f88,definition,(
% 0.35/1.35 spl8_5 <=> ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 0.35/1.35 introduced(definition,[new_symbols(naming,[spl8_5])],[avatar_definition])).
% 0.35/1.35 thf(f78,plain,(
% 0.35/1.35 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl8_3),
% 0.35/1.35 inference(equality_proxy_clausification,[status(thm)],[f77])).
% 0.35/1.35 thf(f77,plain,(
% 0.35/1.35 (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ~spl8_3),
% 0.35/1.35 inference(beta_eta_normalization,[status(thm)],[f76])).
% 0.35/1.35 thf(f76,plain,(
% 0.35/1.35 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ~spl8_3),
% 0.35/1.35 inference(trivial_inequality_removal,[status(thm)],[f71])).
% 0.35/1.35 thf(f71,plain,(
% 0.35/1.35 ($true != $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ~spl8_3),
% 0.35/1.35 inference(superposition,[status(thm)],[f22,f61])).
% 0.35/1.35 thf(f22,plain,(
% 0.35/1.35 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (sK2 @ X0) @ (sK3 @ X0)) = $true) | ((sP1 @ X0) != $true)) )),
% 0.35/1.35 inference(cnf_transformation,[status(thm)],[f15])).
% 0.35/1.35 thf(f86,plain,(
% 0.35/1.35 ~spl8_4 | ~spl8_3),
% 0.35/1.35 inference(avatar_split_clause,[status(thm)],[f81,f59,f83])).
% 0.35/1.35 thf(f83,definition,(
% 0.35/1.35 spl8_4 <=> ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 0.35/1.35 introduced(definition,[new_symbols(naming,[spl8_4])],[avatar_definition])).
% 0.35/1.35 thf(f81,plain,(
% 0.35/1.35 ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl8_3),
% 0.35/1.35 inference(equality_proxy_clausification,[status(thm)],[f80])).
% 0.35/1.35 thf(f80,plain,(
% 0.35/1.35 (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true) | ~spl8_3),
% 0.35/1.35 inference(beta_eta_normalization,[status(thm)],[f79])).
% 0.35/1.35 thf(f79,plain,(
% 0.35/1.35 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true) | ~spl8_3),
% 0.35/1.35 inference(trivial_inequality_removal,[status(thm)],[f70])).
% 0.35/1.35 thf(f70,plain,(
% 0.35/1.35 ($true != $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true) | ~spl8_3),
% 0.35/1.35 inference(superposition,[status(thm)],[f23,f61])).
% 0.35/1.35 thf(f23,plain,(
% 0.35/1.35 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (sK4 @ X0) @ (sK3 @ X0)) != $true) | ((sP1 @ X0) != $true)) )),
% 0.35/1.35 inference(cnf_transformation,[status(thm)],[f15])).
% 0.35/1.35 thf(f66,plain,(
% 0.35/1.35 ~spl8_2),
% 0.35/1.35 inference(avatar_contradiction_clause,[status(thm)],[f65])).
% 0.35/1.35 thf(f65,plain,(
% 0.35/1.35 $false | ~spl8_2),
% 0.35/1.35 inference(trivial_inequality_removal,[status(thm)],[f64])).
% 0.35/1.35 thf(f64,plain,(
% 0.35/1.35 ($false = $true) | ~spl8_2),
% 0.35/1.35 inference(beta_eta_normalization,[status(thm)],[f63])).
% 0.35/1.35 thf(f63,plain,(
% 0.35/1.35 ( ! [X1 : $i] : ((((^[Y0 : $i]: ($false)) @ X1) = ((^[Y0 : $i]: ($true)) @ X1))) ) | ~spl8_2),
% 0.35/1.35 inference(argument_congruence,[status(thm)],[f57])).
% 0.35/1.35 thf(f57,plain,(
% 0.35/1.35 ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ~spl8_2),
% 0.35/1.35 inference(avatar_component_clause,[status(thm)],[f55])).
% 0.35/1.35 thf(f55,definition,(
% 0.35/1.35 spl8_2 <=> ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))),
% 0.35/1.35 introduced(definition,[new_symbols(naming,[spl8_2])],[avatar_definition])).
% 0.35/1.35 thf(f62,plain,(
% 0.35/1.35 spl8_1 | spl8_2 | spl8_3),
% 0.35/1.35 inference(avatar_split_clause,[status(thm)],[f38,f59,f55,f51])).
% 0.35/1.35 thf(f38,plain,(
% 0.35/1.35 ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ((sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true)),
% 0.35/1.35 inference(equality_proxy_clausification,[status(thm)],[f37])).
% 0.35/1.35 thf(f37,plain,(
% 0.35/1.35 ((sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true) | ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true)),
% 0.35/1.35 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 0.35/1.35 thf(f36,plain,(
% 0.35/1.35 ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true) | ($true != $true) | ((sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true)),
% 0.35/1.35 inference(boolean_simplification,[status(thm)],[f35])).
% 0.35/1.35 thf(f35,plain,(
% 0.35/1.35 (((sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true) | ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true) | ((sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true)),
% 0.35/1.35 inference(beta_eta_normalization,[status(thm)],[f30])).
% 0.35/1.35 thf(f30,plain,(
% 0.35/1.35 ((sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true) | ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))) = $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true)),
% 0.35/1.35 inference(primitive_instantiation,[status(thm)],[f28])).
% 0.35/1.35 thf(f28,plain,(
% 0.35/1.35 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (sK7 @ X0) @ (sK7 @ X0)) != $true) | ((sP0 @ X0) = $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))) = $true) | ((sP1 @ X0) = $true)) )),
% 0.35/1.35 inference(cnf_transformation,[status(thm)],[f21])).
% 0.35/1.35 thf(f21,plain,(
% 0.35/1.35 ! [X0 : ($i > $o) > ($i > $o) > $o] : (((sP1 @ X0) = $true) | ((X0 @ (sK7 @ X0) @ (sK7 @ X0)) != $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))) = $true) | ((sP0 @ X0) = $true))),
% 0.35/1.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f11,f20])).
% 0.35/1.35 thf(f20,plain,(
% 0.35/1.35 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o] : ((X0 @ X1 @ X1) != $true) => ((X0 @ (sK7 @ X0) @ (sK7 @ X0)) != $true))),
% 0.35/1.35 introduced(definition,[],[choice_axiom])).
% 0.35/1.35 thf(f11,plain,(
% 0.35/1.35 ! [X0 : ($i > $o) > ($i > $o) > $o] : (((sP1 @ X0) = $true) | ? [X1 : $i > $o] : ((X0 @ X1 @ X1) != $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))) = $true) | ((sP0 @ X0) = $true))),
% 0.35/1.35 inference(definition_folding,[status(thm)],[f8,f10,f9])).
% 0.35/1.35 thf(f8,plain,(
% 0.35/1.35 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X2 : $i > $o,X4 : $i > $o,X3 : $i > $o] : (((X0 @ X3 @ X2) = $true) & ((X0 @ X3 @ X4) != $true) & ((X0 @ X2 @ X4) = $true)) | ? [X1 : $i > $o] : ((X0 @ X1 @ X1) != $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))) = $true) | ? [X6 : $i > $o,X5 : $i > $o] : (((X0 @ X5 @ X6) = $true) & ((X0 @ X6 @ X5) = $true) & (X5 != X6)))),
% 0.35/1.35 inference(flattening,[status(thm)],[f7])).
% 0.35/1.35 thf(f7,plain,(
% 0.35/1.35 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X6 : $i > $o,X5 : $i > $o] : ((X5 != X6) & (((X0 @ X5 @ X6) = $true) & ((X0 @ X6 @ X5) = $true))) | ? [X1 : $i > $o] : ((X0 @ X1 @ X1) != $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))) = $true) | ? [X2 : $i > $o,X3 : $i > $o,X4 : $i > $o] : (((X0 @ X3 @ X4) != $true) & (((X0 @ X3 @ X2) = $true) & ((X0 @ X2 @ X4) = $true))))),
% 0.35/1.35 inference(ennf_transformation,[status(thm)],[f6])).
% 0.35/1.35 thf(f6,plain,(
% 0.35/1.35 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X6 : $i > $o,X5 : $i > $o] : ((((X0 @ X5 @ X6) = $true) & ((X0 @ X6 @ X5) = $true)) => (X5 = X6)) & ! [X1 : $i > $o] : ((X0 @ X1 @ X1) = $true) & ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))) != $true) & ! [X2 : $i > $o,X3 : $i > $o,X4 : $i > $o] : ((((X0 @ X3 @ X2) = $true) & ((X0 @ X2 @ X4) = $true)) => ((X0 @ X3 @ X4) = $true)))),
% 0.35/1.35 inference(flattening,[status(thm)],[f5])).
% 0.35/1.35 thf(f5,plain,(
% 0.35/1.35 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X1 : $i > $o] : ((X0 @ X1 @ X1) = $true) & ! [X2 : $i > $o,X3 : $i > $o,X4 : $i > $o] : ((((X0 @ X3 @ X2) = $true) & ((X0 @ X2 @ X4) = $true)) => ((X0 @ X3 @ X4) = $true)) & ! [X6 : $i > $o,X5 : $i > $o] : ((((X0 @ X5 @ X6) = $true) & ((X0 @ X6 @ X5) = $true)) => (X5 = X6)) & ~((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))) = $true))),
% 0.35/1.35 inference(fool_elimination,[status(thm)],[f4])).
% 0.35/1.35 thf(f4,plain,(
% 0.35/1.35 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X1 : $i > $o] : (X0 @ X1 @ X1) & ! [X2 : $i > $o,X3 : $i > $o,X4 : $i > $o] : (((X0 @ X3 @ X2) & (X0 @ X2 @ X4)) => (X0 @ X3 @ X4)) & ! [X5 : $i > $o,X6 : $i > $o] : (((X0 @ X5 @ X6) & (X0 @ X6 @ X5)) => (X5 = X6)) & ~(X0 @ (^[X7 : $i] : ($true)) @ (^[X8 : $i] : ($false))))),
% 0.35/1.35 inference(rectify,[status(thm)],[f2])).
% 0.35/1.35 thf(f2,negated_conjecture,(
% 0.35/1.35 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X1 : $i > $o] : (X0 @ X1 @ X1) & ! [X2 : $i > $o,X1 : $i > $o,X3 : $i > $o] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X3)) => (X0 @ X1 @ X3)) & ! [X5 : $i > $o,X4 : $i > $o] : (((X0 @ X5 @ X4) & (X0 @ X4 @ X5)) => (X4 = X5)) & ~(X0 @ (^[X1 : $i] : ($true)) @ (^[X1 : $i] : ($false))))),
% 0.35/1.35 inference(negated_conjecture,[status(cth)],[f1])).
% 0.35/1.35 thf(f1,conjecture,(
% 0.35/1.35 ? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X1 : $i > $o] : (X0 @ X1 @ X1) & ! [X2 : $i > $o,X1 : $i > $o,X3 : $i > $o] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X3)) => (X0 @ X1 @ X3)) & ! [X5 : $i > $o,X4 : $i > $o] : (((X0 @ X5 @ X4) & (X0 @ X4 @ X5)) => (X4 = X5)) & ~(X0 @ (^[X1 : $i] : ($true)) @ (^[X1 : $i] : ($false))))),
% 0.35/1.35 file('/export/starexec/sandbox/tmp/tmp.uCjYCaZz0V/DTF2THF_22756.p',cTHM120H_pme)).
% 0.35/1.35 % SZS output end Proof for DTF2THF_22756
% 0.35/1.35 % (22872)------------------------------
% 0.35/1.35 % (22872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.35/1.35 % (22872)Termination reason: Refutation
% 0.35/1.35
% 0.35/1.35 % (22872)Memory used [KB]: 5628
% 0.35/1.35 % (22872)Time elapsed: 0.008 s
% 0.35/1.35 % (22872)Instructions burned: 9 (million)
% 0.35/1.35 % (22872)------------------------------
% 0.35/1.35 % (22872)------------------------------
% 0.35/1.35 % (22862)Success in time 0.036 s
%------------------------------------------------------------------------------