%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV382^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 09:41:08 AM UTC 2026
% Result : Theorem 1.21s 1.07s
% Output : Refutation 1.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 3 unt; 0 typ; 2 def)
% Number of atoms : 329 ( 130 equ; 0 cnn)
% Maximal formula atoms : 16 ( 7 avg)
% Number of connectives : 470 ( 105 ~; 57 |; 38 &; 239 @)
% ( 2 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 51 ( 51 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 155 ( 22 ^; 97 !; 36 ?; 155 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_4,type,
sK0: a > a > $o ).
thf(func_def_5,type,
sK1: a > $o ).
thf(func_def_6,type,
sK2: a > a ).
thf(func_def_7,type,
sK3: ( a > $o ) > a ).
thf(func_def_8,type,
sK4: a ).
thf(func_def_11,type,
ph6:
!>[X0: $tType] : X0 ).
thf(f194,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f175,f184,f193]) ).
thf(f193,plain,
( spl5_8
| ~ spl5_10 ),
inference(avatar_split_clause,[status(thm)],[f190,f172,f120]) ).
thf(f120,definition,
( spl5_8
<=> ! [X1: a] :
( $true
= ( sK1 @ X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_8])],[avatar_definition]) ).
thf(f172,definition,
( spl5_10
<=> ( $true
= ( sK1
@ ( sK3
@ ^ [Y0: a] :
~ ( sK1 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_10])],[avatar_definition]) ).
thf(f190,plain,
( ! [X0: a] :
( $true
= ( sK1 @ X0 ) )
| ~ spl5_10 ),
inference(trivial_inequality_removal,[status(thm)],[f188]) ).
thf(f188,plain,
( ! [X0: a] :
( ( $true
= ( sK1 @ X0 ) )
| ( $true = $false ) )
| ~ spl5_10 ),
inference(superposition,[status(thm)],[f174,f27]) ).
thf(f27,plain,
! [X8: a > $o,X5: a] :
( ( $false
= ( X8
@ ( sK3
@ ^ [Y0: a] :
~ ( X8 @ Y0 ) ) ) )
| ( $true
= ( X8 @ X5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X8: a > $o,X5: a] :
( ( $false
= ( X8
@ ( sK3
@ ^ [Y0: a] :
~ ( X8 @ Y0 ) ) ) )
| ( ( ~ ( X8 @ X5 ) )
!= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X8: a > $o,X5: a] :
( ( $true
= ( ~ ( X8
@ ( sK3
@ ^ [Y0: a] :
~ ( X8 @ Y0 ) ) ) ) )
| ( ( ~ ( X8 @ X5 ) )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f23]) ).
thf(f23,plain,
! [X8: a > $o,X5: a] :
( ( $true
!= ( ^ [Y0: a] :
~ ( X8 @ Y0 )
@ X5 ) )
| ( $true
= ( ^ [Y0: a] :
~ ( X8 @ Y0 )
@ ( sK3
@ ^ [Y0: a] :
~ ( X8 @ Y0 ) ) ) ) ),
inference(primitive_instantiation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X4: a > $o,X5: a] :
( ( $true
= ( X4 @ ( sK3 @ X4 ) ) )
| ( $true
!= ( X4 @ X5 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X2: a] :
( ( ( $true
!= ( sK1 @ ( sK2 @ X2 ) ) )
& ( $true
= ( sK0 @ ( sK2 @ X2 ) @ X2 ) ) )
| ( $true
= ( sK1 @ X2 ) ) )
& ! [X4: a > $o] :
( ! [X5: a] :
( $true
!= ( X4 @ X5 ) )
| ( ( $true
= ( X4 @ ( sK3 @ X4 ) ) )
& ! [X7: a] :
( ( $true
!= ( sK0 @ X7 @ ( sK3 @ X4 ) ) )
| ( ( X4 @ X7 )
!= $true ) ) ) )
& ( $true
!= ( sK1 @ sK4 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f9,f13,f12,f11,f10]) ).
thf(f10,plain,
( ? [X0: a > a > $o,X1: a > $o] :
( ! [X2: a] :
( ? [X3: a] :
( ( $true
!= ( X1 @ X3 ) )
& ( $true
= ( X0 @ X3 @ X2 ) ) )
| ( $true
= ( X1 @ X2 ) ) )
& ! [X4: a > $o] :
( ! [X5: a] :
( $true
!= ( X4 @ X5 ) )
| ? [X6: a] :
( ( $true
= ( X4 @ X6 ) )
& ! [X7: a] :
( ( $true
!= ( X0 @ X7 @ X6 ) )
| ( ( X4 @ X7 )
!= $true ) ) ) )
& ? [X8: a] :
( $true
!= ( X1 @ X8 ) ) )
=> ( ! [X2: a] :
( ? [X3: a] :
( ( $true
!= ( sK1 @ X3 ) )
& ( $true
= ( sK0 @ X3 @ X2 ) ) )
| ( $true
= ( sK1 @ X2 ) ) )
& ! [X4: a > $o] :
( ! [X5: a] :
( $true
!= ( X4 @ X5 ) )
| ? [X6: a] :
( ( $true
= ( X4 @ X6 ) )
& ! [X7: a] :
( ( ( sK0 @ X7 @ X6 )
!= $true )
| ( ( X4 @ X7 )
!= $true ) ) ) )
& ? [X8: a] :
( $true
!= ( sK1 @ X8 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X2: a] :
( ? [X3: a] :
( ( $true
!= ( sK1 @ X3 ) )
& ( $true
= ( sK0 @ X3 @ X2 ) ) )
=> ( ( $true
!= ( sK1 @ ( sK2 @ X2 ) ) )
& ( $true
= ( sK0 @ ( sK2 @ X2 ) @ X2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X4: a > $o] :
( ? [X6: a] :
( ( $true
= ( X4 @ X6 ) )
& ! [X7: a] :
( ( ( sK0 @ X7 @ X6 )
!= $true )
| ( ( X4 @ X7 )
!= $true ) ) )
=> ( ( $true
= ( X4 @ ( sK3 @ X4 ) ) )
& ! [X7: a] :
( ( $true
!= ( sK0 @ X7 @ ( sK3 @ X4 ) ) )
| ( ( X4 @ X7 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X8: a] :
( $true
!= ( sK1 @ X8 ) )
=> ( $true
!= ( sK1 @ sK4 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: a > a > $o,X1: a > $o] :
( ! [X2: a] :
( ? [X3: a] :
( ( $true
!= ( X1 @ X3 ) )
& ( $true
= ( X0 @ X3 @ X2 ) ) )
| ( $true
= ( X1 @ X2 ) ) )
& ! [X4: a > $o] :
( ! [X5: a] :
( $true
!= ( X4 @ X5 ) )
| ? [X6: a] :
( ( $true
= ( X4 @ X6 ) )
& ! [X7: a] :
( ( $true
!= ( X0 @ X7 @ X6 ) )
| ( ( X4 @ X7 )
!= $true ) ) ) )
& ? [X8: a] :
( $true
!= ( X1 @ X8 ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
? [X1: a > a > $o,X0: a > $o] :
( ! [X6: a] :
( ? [X7: a] :
( ( $true
!= ( X0 @ X7 ) )
& ( $true
= ( X1 @ X7 @ X6 ) ) )
| ( $true
= ( X0 @ X6 ) ) )
& ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
!= $true )
| ? [X4: a] :
( ( ( X2 @ X4 )
= $true )
& ! [X5: a] :
( ( $true
!= ( X1 @ X5 @ X4 ) )
| ( ( X2 @ X5 )
!= $true ) ) ) )
& ? [X8: a] :
( $true
!= ( X0 @ X8 ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > a > $o] :
( ? [X8: a] :
( $true
!= ( X0 @ X8 ) )
& ! [X6: a] :
( ? [X7: a] :
( ( $true
!= ( X0 @ X7 ) )
& ( $true
= ( X1 @ X7 @ X6 ) ) )
| ( $true
= ( X0 @ X6 ) ) )
& ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
!= $true )
| ? [X4: a] :
( ( ( X2 @ X4 )
= $true )
& ! [X5: a] :
( ( $true
!= ( X1 @ X5 @ X4 ) )
| ( ( X2 @ X5 )
!= $true ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: a > $o,X1: a > a > $o] :
( ( ! [X6: a] :
( ! [X7: a] :
( ( $true
= ( X1 @ X7 @ X6 ) )
=> ( $true
= ( X0 @ X7 ) ) )
=> ( $true
= ( X0 @ X6 ) ) )
& ! [X2: a > $o] :
( ? [X3: a] :
( ( X2 @ X3 )
= $true )
=> ? [X4: a] :
( ( ( X2 @ X4 )
= $true )
& ! [X5: a] :
( ( $true
= ( X1 @ X5 @ X4 ) )
=> ( ( X2 @ X5 )
!= $true ) ) ) ) )
=> ! [X8: a] :
( $true
= ( X0 @ X8 ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > a > $o] :
( ( ! [X2: a > $o] :
( ? [X3: a] :
( ( X2 @ X3 )
= $true )
=> ? [X4: a] :
( ( ( X2 @ X4 )
= $true )
& ! [X5: a] :
( ( $true
= ( X1 @ X5 @ X4 ) )
=> ( ( X2 @ X5 )
!= $true ) ) ) )
& ! [X6: a] :
( ! [X7: a] :
( ( $true
= ( X1 @ X7 @ X6 ) )
=> ( $true
= ( X0 @ X7 ) ) )
=> ( $true
= ( X0 @ X6 ) ) ) )
=> ! [X8: a] :
( $true
= ( X0 @ X8 ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > a > $o] :
( ( ! [X2: a > $o] :
( ? [X3: a] : ( X2 @ X3 )
=> ? [X4: a] :
( ( X2 @ X4 )
& ! [X5: a] :
( ( X1 @ X5 @ X4 )
=> ~ ( X2 @ X5 ) ) ) )
& ! [X6: a] :
( ! [X7: a] :
( ( X1 @ X7 @ X6 )
=> ( X0 @ X7 ) )
=> ( X0 @ X6 ) ) )
=> ! [X8: a] : ( X0 @ X8 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X0: a > a > $o] :
( ( ! [X2: a > $o] :
( ? [X3: a] : ( X2 @ X3 )
=> ? [X4: a] :
( ( X2 @ X4 )
& ! [X5: a] :
( ( X0 @ X5 @ X4 )
=> ~ ( X2 @ X5 ) ) ) )
& ! [X6: a] :
( ! [X4: a] :
( ( X0 @ X4 @ X6 )
=> ( X1 @ X4 ) )
=> ( X1 @ X6 ) ) )
=> ! [X6: a] : ( X1 @ X6 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > $o,X0: a > a > $o] :
( ( ! [X2: a > $o] :
( ? [X3: a] : ( X2 @ X3 )
=> ? [X4: a] :
( ( X2 @ X4 )
& ! [X5: a] :
( ( X0 @ X5 @ X4 )
=> ~ ( X2 @ X5 ) ) ) )
& ! [X6: a] :
( ! [X4: a] :
( ( X0 @ X4 @ X6 )
=> ( X1 @ X4 ) )
=> ( X1 @ X6 ) ) )
=> ! [X6: a] : ( X1 @ X6 ) ),
file('/export/starexec/sandbox2/tmp/tmp.JG6LrQDiId/DTF2THF_1491.p',cTRANS_IND) ).
thf(f174,plain,
( ( $true
= ( sK1
@ ( sK3
@ ^ [Y0: a] :
~ ( sK1 @ Y0 ) ) ) )
| ~ spl5_10 ),
inference(avatar_component_clause,[status(thm)],[f172]) ).
thf(f184,plain,
~ spl5_8,
inference(avatar_contradiction_clause,[status(thm)],[f183]) ).
thf(f183,plain,
( $false
| ~ spl5_8 ),
inference(trivial_inequality_removal,[status(thm)],[f178]) ).
thf(f178,plain,
( ( $true != $true )
| ~ spl5_8 ),
inference(superposition,[status(thm)],[f15,f121]) ).
thf(f121,plain,
( ! [X1: a] :
( $true
= ( sK1 @ X1 ) )
| ~ spl5_8 ),
inference(avatar_component_clause,[status(thm)],[f120]) ).
thf(f15,plain,
( $true
!= ( sK1 @ sK4 ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f175,plain,
( spl5_8
| spl5_10 ),
inference(avatar_split_clause,[status(thm)],[f170,f172,f120]) ).
thf(f170,plain,
! [X0: a] :
( ( $true
= ( sK1
@ ( sK3
@ ^ [Y0: a] :
~ ( sK1 @ Y0 ) ) ) )
| ( $true
= ( sK1 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f169]) ).
thf(f169,plain,
! [X0: a] :
( ( $true
= ( sK1
@ ( sK3
@ ^ [Y0: a] :
~ ( sK1 @ Y0 ) ) ) )
| ( $true
= ( sK1 @ X0 ) )
| ( $true != $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f149]) ).
thf(f149,plain,
! [X0: a] :
( ( $true
= ( sK1 @ X0 ) )
| ( $true
= ( sK1
@ ( sK3
@ ^ [Y0: a] :
~ ( sK1 @ Y0 ) ) ) )
| ( $true != $true )
| ( $true
= ( sK1
@ ( sK3
@ ^ [Y0: a] :
~ ( sK1 @ Y0 ) ) ) ) ),
inference(superposition,[status(thm)],[f19,f90]) ).
thf(f90,plain,
! [X1: a,X4: a > $o] :
( ( $true
= ( X4
@ ( sK2
@ ( sK3
@ ^ [Y0: a] :
~ ( X4 @ Y0 ) ) ) ) )
| ( $true
= ( sK1
@ ( sK3
@ ^ [Y0: a] :
~ ( X4 @ Y0 ) ) ) )
| ( $true
= ( X4 @ X1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f89]) ).
thf(f89,plain,
! [X1: a,X4: a > $o] :
( ( $true
= ( X4
@ ( sK2
@ ( sK3
@ ^ [Y0: a] :
~ ( X4 @ Y0 ) ) ) ) )
| ( $true
= ( sK1
@ ( sK3
@ ^ [Y0: a] :
~ ( X4 @ Y0 ) ) ) )
| ( $true
!= ( ~ ( X4 @ X1 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f88]) ).
thf(f88,plain,
! [X1: a,X4: a > $o] :
( ( $true
= ( sK1
@ ( sK3
@ ^ [Y0: a] :
~ ( X4 @ Y0 ) ) ) )
| ( $true
!= ( ~ ( X4
@ ( sK2
@ ( sK3
@ ^ [Y0: a] :
~ ( X4 @ Y0 ) ) ) ) ) )
| ( $true
!= ( ~ ( X4 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f81]) ).
thf(f81,plain,
! [X1: a,X4: a > $o] :
( ( $true
= ( sK1
@ ( sK3
@ ^ [Y0: a] :
~ ( X4 @ Y0 ) ) ) )
| ( $true
!= ( ^ [Y0: a] :
~ ( X4 @ Y0 )
@ ( sK2
@ ( sK3
@ ^ [Y0: a] :
~ ( X4 @ Y0 ) ) ) ) )
| ( $true
!= ( ^ [Y0: a] :
~ ( X4 @ Y0 )
@ X1 ) ) ),
inference(primitive_instantiation,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: a > $o,X1: a] :
( ( $true
!= ( X0 @ ( sK2 @ ( sK3 @ X0 ) ) ) )
| ( ( X0 @ X1 )
!= $true )
| ( $true
= ( sK1 @ ( sK3 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f32]) ).
thf(f32,plain,
! [X0: a > $o,X1: a] :
( ( ( X0 @ X1 )
!= $true )
| ( $true
!= ( X0 @ ( sK2 @ ( sK3 @ X0 ) ) ) )
| ( $true
= ( sK1 @ ( sK3 @ X0 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f16,f18]) ).
thf(f18,plain,
! [X2: a] :
( ( $true
= ( sK0 @ ( sK2 @ X2 ) @ X2 ) )
| ( $true
= ( sK1 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f16,plain,
! [X7: a,X4: a > $o,X5: a] :
( ( $true
!= ( sK0 @ X7 @ ( sK3 @ X4 ) ) )
| ( $true
!= ( X4 @ X5 ) )
| ( ( X4 @ X7 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f19,plain,
! [X2: a] :
( ( $true
!= ( sK1 @ ( sK2 @ X2 ) ) )
| ( $true
= ( sK1 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEV382^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n005.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 12:45:44 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.37 ---- Original DTF file ---
% 0.16/0.38 thf(spec,logic,$$dhol).
% 0.16/0.38 %------------------------------------------------------------------------------
% 0.16/0.38 % File : SEV382^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.38 % Domain : Set Theory
% 0.16/0.38 % Problem : TPS problem TRANS-IND
% 0.16/0.38 % Version : Especial.
% 0.16/0.38 % English : Transfinite induction theorem, from [BB93].
% 0.16/0.38
% 0.16/0.38 % Refs : [BB93] Bailin & Barker-Plummer (1993), L-match: An Inference
% 0.16/0.38 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.38 % Source : [Bro09]
% 0.16/0.38 % Names : tps_0328 [Bro09]
% 0.16/0.38 % : TRANS-IND [TPS]
% 0.16/0.38
% 0.16/0.38 % Status : Theorem
% 0.16/0.38 % Rating : 0.25 v9.1.0, 0.12 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.25 v7.4.0, 0.22 v7.3.0, 0.20 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.25 v6.4.0, 0.29 v6.3.0, 0.33 v6.2.0, 0.50 v6.1.0, 0.33 v6.0.0, 0.17 v5.5.0, 0.00 v5.1.0, 0.25 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.16/0.38 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.16/0.38 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.16/0.38 % Maximal formula atoms : 0 ( 0 avg)
% 0.16/0.38 % Number of connectives : 18 ( 1 ~; 0 |; 2 &; 10 @)
% 0.16/0.38 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.16/0.38 % Maximal formula depth : 13 ( 13 avg)
% 0.16/0.38 % Number of types : 2 ( 1 usr)
% 0.16/0.38 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.16/0.38 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.16/0.38 % Number of variables : 9 ( 0 ^; 7 !; 2 ?; 9 :)
% 0.16/0.38 % SPC : TH0_THM_NEQ_NAR
% 0.16/0.38
% 0.16/0.38 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.38 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.38 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.38 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.38 %------------------------------------------------------------------------------
% 0.16/0.38 thf(a_type,type,
% 0.16/0.38 a: $tType ).
% 0.16/0.38
% 0.16/0.38 thf(cTRANS_IND,conjecture,
% 0.16/0.38 ! [Xr: a > a > $o,P: a > $o] :
% 0.16/0.38 ( ( ! [Xs: a > $o] :
% 0.16/0.38 ( ? [Xz: a] : ( Xs @ Xz )
% 0.16/0.38 => ? [Xy: a] :
% 0.16/0.38 ( ( Xs @ Xy )
% 0.16/0.38 & ! [Xw: a] :
% 0.16/0.38 ( ( Xr @ Xw @ Xy )
% 0.16/0.38 => ~ ( Xs @ Xw ) ) ) )
% 0.16/0.38 & ! [Xx: a] :
% 0.16/0.38 ( ! [Xy: a] :
% 0.16/0.38 ( ( Xr @ Xy @ Xx )
% 0.16/0.38 => ( P @ Xy ) )
% 0.16/0.38 => ( P @ Xx ) ) )
% 0.16/0.38 => ! [Xx: a] : ( P @ Xx ) ) ).
% 0.16/0.38
% 0.16/0.38 %------------------------------------------------------------------------------
% 0.16/0.38 ------------------------
% 1.21/1.03 ---- Embedded in THF ---
% 1.21/1.03 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.21/1.03 %%% Generated on Tue Feb 24 12:45:45 EST 2026
% 1.21/1.03 %%% using '$$dhol' embedding, version 1.3.0.
% 1.21/1.03 %%% Logic specification used:
% 1.21/1.03 %%% thf(spec, logic, $$dhol).
% 1.21/1.03
% 1.21/1.03 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.JG6LrQDiId/DTF2DTF1491.p
% See solution above
% 1.21/1.03 ------------------------
% 1.21/1.03 ---- Cleaned THF ---
% 1.21/1.03 thf(a_type,type,
% 1.21/1.03 a: $tType ).
% 1.21/1.03
% 1.21/1.03 thf(cTRANS_IND,conjecture,
% 1.21/1.03 ! [Xr: a > a > $o,P: a > $o] :
% 1.21/1.03 ( ( ! [Xs: a > $o] :
% 1.21/1.03 ( ? [Xz: a] : ( Xs @ Xz )
% 1.21/1.03 => ? [Xy: a] :
% 1.21/1.03 ( ( Xs @ Xy )
% 1.21/1.03 & ! [Xw: a] :
% 1.21/1.03 ( ( Xr @ Xw @ Xy )
% 1.21/1.03 => ~ ( Xs @ Xw ) ) ) )
% 1.21/1.03 & ! [Xx: a] :
% 1.21/1.03 ( ! [Xy: a] :
% 1.21/1.03 ( ( Xr @ Xy @ Xx )
% 1.21/1.03 => ( P @ Xy ) )
% 1.21/1.03 => ( P @ Xx ) ) )
% 1.21/1.03 => ! [Xx: a] : ( P @ Xx ) ) ).
% 1.21/1.03 ------------------------
% 1.21/1.05 % (1604)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1491 for (3000ds/183Mi)
% 1.21/1.05 % (1609)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_1491 for (3000ds/275Mi)
% 1.21/1.05 % (1610)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1491 for (3000ds/18Mi)
% 1.21/1.05 % (1606)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_1491 for (3000ds/27Mi)
% 1.21/1.05 % (1608)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_1491 for (3000ds/2Mi)
% 1.21/1.05 % (1605)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_1491 for (3000ds/4Mi)
% 1.21/1.05 % (1607)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1491 for (3000ds/2Mi)
% 1.21/1.05 % (1608)Instruction limit reached!
% 1.21/1.05 % (1608)------------------------------
% 1.21/1.05 % (1608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.21/1.05 % (1608)Termination reason: Unknown
% 1.21/1.05 % (1608)Termination phase: Clausification
% 1.21/1.05
% 1.21/1.05 % (1608)Memory used [KB]: 895
% 1.21/1.05 % (1608)Time elapsed: 0.002 s
% 1.21/1.05 % (1608)Instructions burned: 2 (million)
% 1.21/1.05 % (1608)------------------------------
% 1.21/1.05 % (1608)------------------------------
% 1.21/1.06 % (1607)Instruction limit reached!
% 1.21/1.06 % (1607)------------------------------
% 1.21/1.06 % (1607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.21/1.06 % (1607)Termination reason: Unknown
% 1.21/1.06 % (1607)Termination phase: Saturation
% 1.21/1.06
% 1.21/1.06 % (1607)Memory used [KB]: 5500
% 1.21/1.06 % (1607)Time elapsed: 0.003 s
% 1.21/1.06 % (1607)Instructions burned: 2 (million)
% 1.21/1.06 % (1607)------------------------------
% 1.21/1.06 % (1607)------------------------------
% 1.21/1.06 % (1606)Refutation not found, incomplete strategy
% 1.21/1.06 % (1606)------------------------------
% 1.21/1.06 % (1606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.21/1.06 % (1606)Termination reason: Refutation not found, incomplete strategy
% 1.21/1.06
% 1.21/1.06
% 1.21/1.06 % (1606)Memory used [KB]: 5500
% 1.21/1.06 % (1606)Time elapsed: 0.003 s
% 1.21/1.06 % (1606)Instructions burned: 3 (million)
% 1.21/1.06 % (1606)------------------------------
% 1.21/1.06 % (1606)------------------------------
% 1.21/1.06 % (1605)Instruction limit reached!
% 1.21/1.06 % (1605)------------------------------
% 1.21/1.06 % (1605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.21/1.06 % (1605)Termination reason: Unknown
% 1.21/1.06 % (1605)Termination phase: Saturation
% 1.21/1.06
% 1.21/1.06 % (1605)Memory used [KB]: 5500
% 1.21/1.06 % (1605)Time elapsed: 0.004 s
% 1.21/1.06 % (1605)Instructions burned: 4 (million)
% 1.21/1.06 % (1605)------------------------------
% 1.21/1.06 % (1605)------------------------------
% 1.21/1.06 % (1610)Instruction limit reached!
% 1.21/1.06 % (1610)------------------------------
% 1.21/1.06 % (1610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.21/1.06 % (1610)Termination reason: Unknown
% 1.21/1.06 % (1610)Termination phase: Saturation
% 1.21/1.06
% 1.21/1.06 % (1610)Memory used [KB]: 5628
% 1.21/1.06 % (1610)Time elapsed: 0.011 s
% 1.21/1.06 % (1610)Instructions burned: 18 (million)
% 1.21/1.06 % (1610)------------------------------
% 1.21/1.06 % (1610)------------------------------
% 1.21/1.06 % (1609)First to succeed.
% 1.21/1.07 % (1609)Refutation found. Thanks to Tanya!
% 1.21/1.07 % SZS status Theorem for DTF2THF_1491
% 1.21/1.07 % SZS output start Proof for DTF2THF_1491
% 1.21/1.07 thf(type_def_5, type, a: $tType).
% 1.21/1.07 thf(func_def_0, type, a: $tType).
% 1.21/1.07 thf(func_def_4, type, sK0: a > a > $o).
% 1.21/1.07 thf(func_def_5, type, sK1: a > $o).
% 1.21/1.07 thf(func_def_6, type, sK2: a > a).
% 1.21/1.07 thf(func_def_7, type, sK3: (a > $o) > a).
% 1.21/1.07 thf(func_def_8, type, sK4: a).
% 1.21/1.07 thf(func_def_11, type, ph6: !>[X0: $tType]:(X0)).
% 1.21/1.07 thf(f194,plain,(
% 1.21/1.07 $false),
% 1.21/1.07 inference(avatar_sat_refutation,[status(thm)],[f175,f184,f193])).
% 1.21/1.07 thf(f193,plain,(
% 1.21/1.07 spl5_8 | ~spl5_10),
% 1.21/1.07 inference(avatar_split_clause,[status(thm)],[f190,f172,f120])).
% 1.21/1.07 thf(f120,definition,(
% 1.21/1.07 spl5_8 <=> ! [X1 : a] : ($true = (sK1 @ X1))),
% 1.21/1.07 introduced(definition,[new_symbols(naming,[spl5_8])],[avatar_definition])).
% 1.21/1.07 thf(f172,definition,(
% 1.21/1.07 spl5_10 <=> ($true = (sK1 @ (sK3 @ (^[Y0 : a]: (~ (sK1 @ Y0))))))),
% 1.21/1.07 introduced(definition,[new_symbols(naming,[spl5_10])],[avatar_definition])).
% 1.21/1.07 thf(f190,plain,(
% 1.21/1.07 ( ! [X0 : a] : (($true = (sK1 @ X0))) ) | ~spl5_10),
% 1.21/1.07 inference(trivial_inequality_removal,[status(thm)],[f188])).
% 1.21/1.07 thf(f188,plain,(
% 1.21/1.07 ( ! [X0 : a] : (($true = (sK1 @ X0)) | ($true = $false)) ) | ~spl5_10),
% 1.21/1.07 inference(superposition,[status(thm)],[f174,f27])).
% 1.21/1.07 thf(f27,plain,(
% 1.21/1.07 ( ! [X8 : a > $o,X5 : a] : (($false = (X8 @ (sK3 @ (^[Y0 : a]: (~ (X8 @ Y0)))))) | ($true = (X8 @ X5))) )),
% 1.21/1.07 inference(not_proxy_clausification,[status(thm)],[f26])).
% 1.21/1.07 thf(f26,plain,(
% 1.21/1.07 ( ! [X8 : a > $o,X5 : a] : (($false = (X8 @ (sK3 @ (^[Y0 : a]: (~ (X8 @ Y0)))))) | ((~ (X8 @ X5)) != $true)) )),
% 1.21/1.07 inference(not_proxy_clausification,[status(thm)],[f25])).
% 1.21/1.07 thf(f25,plain,(
% 1.21/1.07 ( ! [X8 : a > $o,X5 : a] : (($true = (~ (X8 @ (sK3 @ (^[Y0 : a]: (~ (X8 @ Y0))))))) | ((~ (X8 @ X5)) != $true)) )),
% 1.21/1.07 inference(beta_eta_normalization,[status(thm)],[f23])).
% 1.21/1.07 thf(f23,plain,(
% 1.21/1.07 ( ! [X8 : a > $o,X5 : a] : (($true != ((^[Y0 : a]: (~ (X8 @ Y0))) @ X5)) | ($true = ((^[Y0 : a]: (~ (X8 @ Y0))) @ (sK3 @ (^[Y0 : a]: (~ (X8 @ Y0))))))) )),
% 1.21/1.07 inference(primitive_instantiation,[status(thm)],[f17])).
% 1.21/1.07 thf(f17,plain,(
% 1.21/1.07 ( ! [X4 : a > $o,X5 : a] : (($true = (X4 @ (sK3 @ X4))) | ($true != (X4 @ X5))) )),
% 1.21/1.07 inference(cnf_transformation,[status(thm)],[f14])).
% 1.21/1.07 thf(f14,plain,(
% 1.21/1.07 ! [X2 : a] : ((($true != (sK1 @ (sK2 @ X2))) & ($true = (sK0 @ (sK2 @ X2) @ X2))) | ($true = (sK1 @ X2))) & ! [X4 : a > $o] : (! [X5 : a] : ($true != (X4 @ X5)) | (($true = (X4 @ (sK3 @ X4))) & ! [X7 : a] : (($true != (sK0 @ X7 @ (sK3 @ X4))) | ((X4 @ X7) != $true)))) & ($true != (sK1 @ sK4))),
% 1.21/1.07 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f9,f13,f12,f11,f10])).
% 1.21/1.07 thf(f10,plain,(
% 1.21/1.07 ? [X0 : a > a > $o,X1 : a > $o] : (! [X2 : a] : (? [X3 : a] : (($true != (X1 @ X3)) & ($true = (X0 @ X3 @ X2))) | ($true = (X1 @ X2))) & ! [X4 : a > $o] : (! [X5 : a] : ($true != (X4 @ X5)) | ? [X6 : a] : (($true = (X4 @ X6)) & ! [X7 : a] : (($true != (X0 @ X7 @ X6)) | ((X4 @ X7) != $true)))) & ? [X8 : a] : ($true != (X1 @ X8))) => (! [X2 : a] : (? [X3 : a] : (($true != (sK1 @ X3)) & ($true = (sK0 @ X3 @ X2))) | ($true = (sK1 @ X2))) & ! [X4 : a > $o] : (! [X5 : a] : ($true != (X4 @ X5)) | ? [X6 : a] : (($true = (X4 @ X6)) & ! [X7 : a] : (((sK0 @ X7 @ X6) != $true) | ((X4 @ X7) != $true)))) & ? [X8 : a] : ($true != (sK1 @ X8)))),
% 1.21/1.07 introduced(definition,[],[choice_axiom])).
% 1.21/1.07 thf(f11,plain,(
% 1.21/1.07 ! [X2 : a] : (? [X3 : a] : (($true != (sK1 @ X3)) & ($true = (sK0 @ X3 @ X2))) => (($true != (sK1 @ (sK2 @ X2))) & ($true = (sK0 @ (sK2 @ X2) @ X2))))),
% 1.21/1.07 introduced(definition,[],[choice_axiom])).
% 1.21/1.07 thf(f12,plain,(
% 1.21/1.07 ! [X4 : a > $o] : (? [X6 : a] : (($true = (X4 @ X6)) & ! [X7 : a] : (((sK0 @ X7 @ X6) != $true) | ((X4 @ X7) != $true))) => (($true = (X4 @ (sK3 @ X4))) & ! [X7 : a] : (($true != (sK0 @ X7 @ (sK3 @ X4))) | ((X4 @ X7) != $true))))),
% 1.21/1.07 introduced(definition,[],[choice_axiom])).
% 1.21/1.07 thf(f13,plain,(
% 1.21/1.07 ? [X8 : a] : ($true != (sK1 @ X8)) => ($true != (sK1 @ sK4))),
% 1.21/1.07 introduced(definition,[],[choice_axiom])).
% 1.21/1.07 thf(f9,plain,(
% 1.21/1.07 ? [X0 : a > a > $o,X1 : a > $o] : (! [X2 : a] : (? [X3 : a] : (($true != (X1 @ X3)) & ($true = (X0 @ X3 @ X2))) | ($true = (X1 @ X2))) & ! [X4 : a > $o] : (! [X5 : a] : ($true != (X4 @ X5)) | ? [X6 : a] : (($true = (X4 @ X6)) & ! [X7 : a] : (($true != (X0 @ X7 @ X6)) | ((X4 @ X7) != $true)))) & ? [X8 : a] : ($true != (X1 @ X8)))),
% 1.21/1.07 inference(rectify,[status(thm)],[f8])).
% 1.21/1.07 thf(f8,plain,(
% 1.21/1.07 ? [X1 : a > a > $o,X0 : a > $o] : (! [X6 : a] : (? [X7 : a] : (($true != (X0 @ X7)) & ($true = (X1 @ X7 @ X6))) | ($true = (X0 @ X6))) & ! [X2 : a > $o] : (! [X3 : a] : ((X2 @ X3) != $true) | ? [X4 : a] : (((X2 @ X4) = $true) & ! [X5 : a] : (($true != (X1 @ X5 @ X4)) | ((X2 @ X5) != $true)))) & ? [X8 : a] : ($true != (X0 @ X8)))),
% 1.21/1.07 inference(flattening,[status(thm)],[f7])).
% 1.21/1.07 thf(f7,plain,(
% 1.21/1.07 ? [X0 : a > $o,X1 : a > a > $o] : (? [X8 : a] : ($true != (X0 @ X8)) & (! [X6 : a] : (? [X7 : a] : (($true != (X0 @ X7)) & ($true = (X1 @ X7 @ X6))) | ($true = (X0 @ X6))) & ! [X2 : a > $o] : (! [X3 : a] : ((X2 @ X3) != $true) | ? [X4 : a] : (((X2 @ X4) = $true) & ! [X5 : a] : (($true != (X1 @ X5 @ X4)) | ((X2 @ X5) != $true))))))),
% 1.21/1.07 inference(ennf_transformation,[status(thm)],[f6])).
% 1.21/1.07 thf(f6,plain,(
% 1.21/1.07 ~! [X0 : a > $o,X1 : a > a > $o] : ((! [X6 : a] : (! [X7 : a] : (($true = (X1 @ X7 @ X6)) => ($true = (X0 @ X7))) => ($true = (X0 @ X6))) & ! [X2 : a > $o] : (? [X3 : a] : ((X2 @ X3) = $true) => ? [X4 : a] : (((X2 @ X4) = $true) & ! [X5 : a] : (($true = (X1 @ X5 @ X4)) => ((X2 @ X5) != $true))))) => ! [X8 : a] : ($true = (X0 @ X8)))),
% 1.21/1.07 inference(flattening,[status(thm)],[f5])).
% 1.21/1.07 thf(f5,plain,(
% 1.21/1.07 ~! [X0 : a > $o,X1 : a > a > $o] : ((! [X2 : a > $o] : (? [X3 : a] : ((X2 @ X3) = $true) => ? [X4 : a] : (((X2 @ X4) = $true) & ! [X5 : a] : (($true = (X1 @ X5 @ X4)) => ~((X2 @ X5) = $true)))) & ! [X6 : a] : (! [X7 : a] : (($true = (X1 @ X7 @ X6)) => ($true = (X0 @ X7))) => ($true = (X0 @ X6)))) => ! [X8 : a] : ($true = (X0 @ X8)))),
% 1.21/1.07 inference(fool_elimination,[status(thm)],[f4])).
% 1.21/1.07 thf(f4,plain,(
% 1.21/1.07 ~! [X0 : a > $o,X1 : a > a > $o] : ((! [X2 : a > $o] : (? [X3 : a] : (X2 @ X3) => ? [X4 : a] : ((X2 @ X4) & ! [X5 : a] : ((X1 @ X5 @ X4) => ~(X2 @ X5)))) & ! [X6 : a] : (! [X7 : a] : ((X1 @ X7 @ X6) => (X0 @ X7)) => (X0 @ X6))) => ! [X8 : a] : (X0 @ X8))),
% 1.21/1.07 inference(rectify,[status(thm)],[f2])).
% 1.21/1.07 thf(f2,negated_conjecture,(
% 1.21/1.07 ~! [X1 : a > $o,X0 : a > a > $o] : ((! [X2 : a > $o] : (? [X3 : a] : (X2 @ X3) => ? [X4 : a] : ((X2 @ X4) & ! [X5 : a] : ((X0 @ X5 @ X4) => ~(X2 @ X5)))) & ! [X6 : a] : (! [X4 : a] : ((X0 @ X4 @ X6) => (X1 @ X4)) => (X1 @ X6))) => ! [X6 : a] : (X1 @ X6))),
% 1.21/1.07 inference(negated_conjecture,[status(cth)],[f1])).
% 1.21/1.07 thf(f1,conjecture,(
% 1.21/1.07 ! [X1 : a > $o,X0 : a > a > $o] : ((! [X2 : a > $o] : (? [X3 : a] : (X2 @ X3) => ? [X4 : a] : ((X2 @ X4) & ! [X5 : a] : ((X0 @ X5 @ X4) => ~(X2 @ X5)))) & ! [X6 : a] : (! [X4 : a] : ((X0 @ X4 @ X6) => (X1 @ X4)) => (X1 @ X6))) => ! [X6 : a] : (X1 @ X6))),
% 1.21/1.07 file('/export/starexec/sandbox2/tmp/tmp.JG6LrQDiId/DTF2THF_1491.p',cTRANS_IND)).
% 1.21/1.07 thf(f174,plain,(
% 1.21/1.07 ($true = (sK1 @ (sK3 @ (^[Y0 : a]: (~ (sK1 @ Y0)))))) | ~spl5_10),
% 1.21/1.07 inference(avatar_component_clause,[status(thm)],[f172])).
% 1.21/1.07 thf(f184,plain,(
% 1.21/1.07 ~spl5_8),
% 1.21/1.07 inference(avatar_contradiction_clause,[status(thm)],[f183])).
% 1.21/1.07 thf(f183,plain,(
% 1.21/1.07 $false | ~spl5_8),
% 1.21/1.07 inference(trivial_inequality_removal,[status(thm)],[f178])).
% 1.21/1.07 thf(f178,plain,(
% 1.21/1.07 ($true != $true) | ~spl5_8),
% 1.21/1.07 inference(superposition,[status(thm)],[f15,f121])).
% 1.21/1.07 thf(f121,plain,(
% 1.21/1.07 ( ! [X1 : a] : (($true = (sK1 @ X1))) ) | ~spl5_8),
% 1.21/1.07 inference(avatar_component_clause,[status(thm)],[f120])).
% 1.21/1.07 thf(f15,plain,(
% 1.21/1.07 ($true != (sK1 @ sK4))),
% 1.21/1.07 inference(cnf_transformation,[status(thm)],[f14])).
% 1.21/1.07 thf(f175,plain,(
% 1.21/1.07 spl5_8 | spl5_10),
% 1.21/1.07 inference(avatar_split_clause,[status(thm)],[f170,f172,f120])).
% 1.21/1.07 thf(f170,plain,(
% 1.21/1.07 ( ! [X0 : a] : (($true = (sK1 @ (sK3 @ (^[Y0 : a]: (~ (sK1 @ Y0)))))) | ($true = (sK1 @ X0))) )),
% 1.21/1.07 inference(trivial_inequality_removal,[status(thm)],[f169])).
% 1.21/1.07 thf(f169,plain,(
% 1.21/1.07 ( ! [X0 : a] : (($true = (sK1 @ (sK3 @ (^[Y0 : a]: (~ (sK1 @ Y0)))))) | ($true = (sK1 @ X0)) | ($true != $true)) )),
% 1.21/1.07 inference(duplicate_literal_removal,[status(thm)],[f149])).
% 1.21/1.07 thf(f149,plain,(
% 1.21/1.07 ( ! [X0 : a] : (($true = (sK1 @ X0)) | ($true = (sK1 @ (sK3 @ (^[Y0 : a]: (~ (sK1 @ Y0)))))) | ($true != $true) | ($true = (sK1 @ (sK3 @ (^[Y0 : a]: (~ (sK1 @ Y0))))))) )),
% 1.21/1.07 inference(superposition,[status(thm)],[f19,f90])).
% 1.21/1.07 thf(f90,plain,(
% 1.21/1.07 ( ! [X1 : a,X4 : a > $o] : (($true = (X4 @ (sK2 @ (sK3 @ (^[Y0 : a]: (~ (X4 @ Y0))))))) | ($true = (sK1 @ (sK3 @ (^[Y0 : a]: (~ (X4 @ Y0)))))) | ($true = (X4 @ X1))) )),
% 1.21/1.07 inference(not_proxy_clausification,[status(thm)],[f89])).
% 1.21/1.07 thf(f89,plain,(
% 1.21/1.07 ( ! [X1 : a,X4 : a > $o] : (($true = (X4 @ (sK2 @ (sK3 @ (^[Y0 : a]: (~ (X4 @ Y0))))))) | ($true = (sK1 @ (sK3 @ (^[Y0 : a]: (~ (X4 @ Y0)))))) | ($true != (~ (X4 @ X1)))) )),
% 1.21/1.07 inference(not_proxy_clausification,[status(thm)],[f88])).
% 1.21/1.07 thf(f88,plain,(
% 1.21/1.07 ( ! [X1 : a,X4 : a > $o] : (($true = (sK1 @ (sK3 @ (^[Y0 : a]: (~ (X4 @ Y0)))))) | ($true != (~ (X4 @ (sK2 @ (sK3 @ (^[Y0 : a]: (~ (X4 @ Y0)))))))) | ($true != (~ (X4 @ X1)))) )),
% 1.21/1.07 inference(beta_eta_normalization,[status(thm)],[f81])).
% 1.21/1.07 thf(f81,plain,(
% 1.21/1.07 ( ! [X1 : a,X4 : a > $o] : (($true = (sK1 @ (sK3 @ (^[Y0 : a]: (~ (X4 @ Y0)))))) | ($true != ((^[Y0 : a]: (~ (X4 @ Y0))) @ (sK2 @ (sK3 @ (^[Y0 : a]: (~ (X4 @ Y0))))))) | ($true != ((^[Y0 : a]: (~ (X4 @ Y0))) @ X1))) )),
% 1.21/1.07 inference(primitive_instantiation,[status(thm)],[f36])).
% 1.21/1.07 thf(f36,plain,(
% 1.21/1.07 ( ! [X0 : a > $o,X1 : a] : (($true != (X0 @ (sK2 @ (sK3 @ X0)))) | ((X0 @ X1) != $true) | ($true = (sK1 @ (sK3 @ X0)))) )),
% 1.21/1.07 inference(trivial_inequality_removal,[status(thm)],[f32])).
% 1.21/1.07 thf(f32,plain,(
% 1.21/1.07 ( ! [X0 : a > $o,X1 : a] : (((X0 @ X1) != $true) | ($true != (X0 @ (sK2 @ (sK3 @ X0)))) | ($true = (sK1 @ (sK3 @ X0))) | ($true != $true)) )),
% 1.21/1.07 inference(superposition,[status(thm)],[f16,f18])).
% 1.21/1.07 thf(f18,plain,(
% 1.21/1.07 ( ! [X2 : a] : (($true = (sK0 @ (sK2 @ X2) @ X2)) | ($true = (sK1 @ X2))) )),
% 1.21/1.07 inference(cnf_transformation,[status(thm)],[f14])).
% 1.21/1.07 thf(f16,plain,(
% 1.21/1.07 ( ! [X7 : a,X4 : a > $o,X5 : a] : (($true != (sK0 @ X7 @ (sK3 @ X4))) | ($true != (X4 @ X5)) | ((X4 @ X7) != $true)) )),
% 1.21/1.07 inference(cnf_transformation,[status(thm)],[f14])).
% 1.21/1.07 thf(f19,plain,(
% 1.21/1.07 ( ! [X2 : a] : (($true != (sK1 @ (sK2 @ X2))) | ($true = (sK1 @ X2))) )),
% 1.21/1.07 inference(cnf_transformation,[status(thm)],[f14])).
% 1.21/1.07 % SZS output end Proof for DTF2THF_1491
% 1.21/1.07 % (1609)------------------------------
% 1.21/1.07 % (1609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.21/1.07 % (1609)Termination reason: Refutation
% 1.21/1.07
% 1.21/1.07 % (1609)Memory used [KB]: 5628
% 1.21/1.07 % (1609)Time elapsed: 0.014 s
% 1.21/1.07 % (1609)Instructions burned: 19 (million)
% 1.21/1.07 % (1609)------------------------------
% 1.21/1.07 % (1609)------------------------------
% 1.21/1.07 % (1603)Success in time 0.025 s
%------------------------------------------------------------------------------