%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV384^5 : 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 : n031.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 1.48s 1.23s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 3 unt; 0 typ; 2 def)
% Number of atoms : 391 ( 130 equ; 0 cnn)
% Maximal formula atoms : 10 ( 9 avg)
% Number of connectives : 470 ( 94 ~; 51 |; 47 &; 243 @)
% ( 2 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 123 ( 22 ^; 84 !; 17 ?; 123 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cP: $i > $o ).
thf(func_def_1,type,
s: $i > $o ).
thf(func_def_2,type,
cR: $i > $i > $o ).
thf(func_def_6,type,
sK0: $i > $i ).
thf(func_def_7,type,
sK1: ( $i > $o ) > $i ).
thf(func_def_11,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f299,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f248,f258,f298]) ).
thf(f298,plain,
( spl3_13
| ~ spl3_16 ),
inference(avatar_split_clause,[status(thm)],[f295,f245,f157]) ).
thf(f157,definition,
( spl3_13
<=> ! [X1: $i] :
( $true
= ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_13])],[avatar_definition]) ).
thf(f245,definition,
( spl3_16
<=> ( $true
= ( cP
@ ( sK1
@ ^ [Y0: $i] :
~ ( cP @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_16])],[avatar_definition]) ).
thf(f295,plain,
( ! [X0: $i] :
( $true
= ( cP @ X0 ) )
| ~ spl3_16 ),
inference(trivial_inequality_removal,[status(thm)],[f294]) ).
thf(f294,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( cP @ X0 ) ) )
| ~ spl3_16 ),
inference(superposition,[status(thm)],[f27,f247]) ).
thf(f247,plain,
( ( $true
= ( cP
@ ( sK1
@ ^ [Y0: $i] :
~ ( cP @ Y0 ) ) ) )
| ~ spl3_16 ),
inference(avatar_component_clause,[status(thm)],[f245]) ).
thf(f27,plain,
! [X2: $i,X6: $i > $o] :
( ( ( X6
@ ( sK1
@ ^ [Y0: $i] :
~ ( X6 @ Y0 ) ) )
= $false )
| ( $true
= ( X6 @ X2 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: $i,X6: $i > $o] :
( ( $true
= ( ~ ( X6
@ ( sK1
@ ^ [Y0: $i] :
~ ( X6 @ Y0 ) ) ) ) )
| ( $true
= ( X6 @ X2 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X2: $i,X6: $i > $o] :
( ( $true
!= ( ~ ( X6 @ X2 ) ) )
| ( $true
= ( ~ ( X6
@ ( sK1
@ ^ [Y0: $i] :
~ ( X6 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
! [X2: $i,X6: $i > $o] :
( ( $true
!= ( ^ [Y0: $i] :
~ ( X6 @ Y0 )
@ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
~ ( X6 @ Y0 )
@ ( sK1
@ ^ [Y0: $i] :
~ ( X6 @ Y0 ) ) ) ) ),
inference(primitive_instantiation,[status(thm)],[f16]) ).
thf(f16,plain,
! [X2: $i,X3: $i > $o] :
( ( $true
= ( X3 @ ( sK1 @ X3 ) ) )
| ( $true
!= ( X3 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X0: $i] :
( ( ( ( cR @ X0 @ ( sK0 @ X0 ) )
= $true )
& ( $true
= ( s @ ( sK0 @ X0 ) ) )
& ( $true
!= ( cP @ ( sK0 @ X0 ) ) ) )
| ( $true
= ( cP @ X0 ) ) )
& ! [X2: $i,X3: $i > $o] :
( ( ! [X5: $i] :
( ( $true
!= ( X3 @ X5 ) )
| ( $true
!= ( cR @ ( sK1 @ X3 ) @ X5 ) ) )
& ( $true
= ( X3 @ ( sK1 @ X3 ) ) ) )
| ( $true
!= ( X3 @ X2 ) ) )
& ( ( s @ sK2 )
= $true )
& ( $true
!= ( cP @ sK2 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f12,f11,f10]) ).
thf(f10,plain,
! [X0: $i] :
( ? [X1: $i] :
( ( $true
= ( cR @ X0 @ X1 ) )
& ( $true
= ( s @ X1 ) )
& ( $true
!= ( cP @ X1 ) ) )
=> ( ( ( cR @ X0 @ ( sK0 @ X0 ) )
= $true )
& ( $true
= ( s @ ( sK0 @ X0 ) ) )
& ( $true
!= ( cP @ ( sK0 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X3: $i > $o] :
( ? [X4: $i] :
( ! [X5: $i] :
( ( $true
!= ( X3 @ X5 ) )
| ( ( cR @ X4 @ X5 )
!= $true ) )
& ( $true
= ( X3 @ X4 ) ) )
=> ( ! [X5: $i] :
( ( $true
!= ( X3 @ X5 ) )
| ( $true
!= ( cR @ ( sK1 @ X3 ) @ X5 ) ) )
& ( $true
= ( X3 @ ( sK1 @ X3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X6: $i] :
( ( ( s @ X6 )
= $true )
& ( ( cP @ X6 )
!= $true ) )
=> ( ( ( s @ sK2 )
= $true )
& ( $true
!= ( cP @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ! [X0: $i] :
( ? [X1: $i] :
( ( $true
= ( cR @ X0 @ X1 ) )
& ( $true
= ( s @ X1 ) )
& ( $true
!= ( cP @ X1 ) ) )
| ( $true
= ( cP @ X0 ) ) )
& ! [X2: $i,X3: $i > $o] :
( ? [X4: $i] :
( ! [X5: $i] :
( ( $true
!= ( X3 @ X5 ) )
| ( ( cR @ X4 @ X5 )
!= $true ) )
& ( $true
= ( X3 @ X4 ) ) )
| ( $true
!= ( X3 @ X2 ) ) )
& ? [X6: $i] :
( ( ( s @ X6 )
= $true )
& ( ( cP @ X6 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X0: $i] :
( ? [X1: $i] :
( ( $true
= ( cR @ X0 @ X1 ) )
& ( $true
= ( s @ X1 ) )
& ( $true
!= ( cP @ X1 ) ) )
| ( $true
= ( cP @ X0 ) ) )
& ! [X3: $i,X2: $i > $o] :
( ? [X4: $i] :
( ! [X5: $i] :
( ( $true
!= ( X2 @ X5 ) )
| ( ( cR @ X4 @ X5 )
!= $true ) )
& ( $true
= ( X2 @ X4 ) ) )
| ( ( X2 @ X3 )
!= $true ) )
& ? [X6: $i] :
( ( ( s @ X6 )
= $true )
& ( ( cP @ X6 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ? [X6: $i] :
( ( ( s @ X6 )
= $true )
& ( ( cP @ X6 )
!= $true ) )
& ! [X3: $i,X2: $i > $o] :
( ? [X4: $i] :
( ! [X5: $i] :
( ( $true
!= ( X2 @ X5 ) )
| ( ( cR @ X4 @ X5 )
!= $true ) )
& ( $true
= ( X2 @ X4 ) ) )
| ( ( X2 @ X3 )
!= $true ) )
& ! [X0: $i] :
( ( $true
= ( cP @ X0 ) )
| ? [X1: $i] :
( ( $true
!= ( cP @ X1 ) )
& ( $true
= ( cR @ X0 @ X1 ) )
& ( $true
= ( s @ X1 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( ! [X3: $i,X2: $i > $o] :
( ( ( X2 @ X3 )
= $true )
=> ? [X4: $i] :
( ! [X5: $i] :
( ( ( cR @ X4 @ X5 )
= $true )
=> ( $true
!= ( X2 @ X5 ) ) )
& ( $true
= ( X2 @ X4 ) ) ) )
& ! [X0: $i] :
( ! [X1: $i] :
( ( ( $true
= ( cR @ X0 @ X1 ) )
& ( $true
= ( s @ X1 ) ) )
=> ( $true
= ( cP @ X1 ) ) )
=> ( $true
= ( cP @ X0 ) ) ) )
=> ! [X6: $i] :
( ( ( s @ X6 )
= $true )
=> ( ( cP @ X6 )
= $true ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: $i] :
( ! [X1: $i] :
( ( ( $true
= ( cR @ X0 @ X1 ) )
& ( $true
= ( s @ X1 ) ) )
=> ( $true
= ( cP @ X1 ) ) )
=> ( $true
= ( cP @ X0 ) ) )
& ! [X2: $i > $o,X3: $i] :
( ( ( X2 @ X3 )
= $true )
=> ? [X4: $i] :
( ! [X5: $i] :
( ( ( cR @ X4 @ X5 )
= $true )
=> ( $true
!= ( X2 @ X5 ) ) )
& ( $true
= ( X2 @ X4 ) ) ) ) )
=> ! [X6: $i] :
( ( ( s @ X6 )
= $true )
=> ( ( cP @ X6 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i] :
( ! [X1: $i] :
( ( ( s @ X1 )
& ( cR @ X0 @ X1 ) )
=> ( cP @ X1 ) )
=> ( cP @ X0 ) )
& ! [X2: $i > $o,X3: $i] :
( ( X2 @ X3 )
=> ? [X4: $i] :
( ! [X5: $i] :
( ( cR @ X4 @ X5 )
=> ~ ( X2 @ X5 ) )
& ( X2 @ X4 ) ) ) )
=> ! [X6: $i] :
( ( s @ X6 )
=> ( cP @ X6 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X4: $i] :
( ! [X5: $i] :
( ( ( s @ X5 )
& ( cR @ X4 @ X5 ) )
=> ( cP @ X5 ) )
=> ( cP @ X4 ) )
& ! [X0: $i > $o,X1: $i] :
( ( X0 @ X1 )
=> ? [X2: $i] :
( ! [X3: $i] :
( ( cR @ X2 @ X3 )
=> ~ ( X0 @ X3 ) )
& ( X0 @ X2 ) ) ) )
=> ! [X6: $i] :
( ( s @ X6 )
=> ( cP @ X6 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X4: $i] :
( ! [X5: $i] :
( ( ( s @ X5 )
& ( cR @ X4 @ X5 ) )
=> ( cP @ X5 ) )
=> ( cP @ X4 ) )
& ! [X0: $i > $o,X1: $i] :
( ( X0 @ X1 )
=> ? [X2: $i] :
( ! [X3: $i] :
( ( cR @ X2 @ X3 )
=> ~ ( X0 @ X3 ) )
& ( X0 @ X2 ) ) ) )
=> ! [X6: $i] :
( ( s @ X6 )
=> ( cP @ X6 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.pLXQH6I3bB/DTF2THF_11576.p',cTHM117B) ).
thf(f258,plain,
~ spl3_13,
inference(avatar_contradiction_clause,[status(thm)],[f257]) ).
thf(f257,plain,
( $false
| ~ spl3_13 ),
inference(trivial_inequality_removal,[status(thm)],[f251]) ).
thf(f251,plain,
( ( $true != $true )
| ~ spl3_13 ),
inference(superposition,[status(thm)],[f14,f158]) ).
thf(f158,plain,
( ! [X1: $i] :
( $true
= ( cP @ X1 ) )
| ~ spl3_13 ),
inference(avatar_component_clause,[status(thm)],[f157]) ).
thf(f14,plain,
( $true
!= ( cP @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f248,plain,
( spl3_16
| spl3_13 ),
inference(avatar_split_clause,[status(thm)],[f226,f157,f245]) ).
thf(f226,plain,
! [X0: $i] :
( ( $true
= ( cP
@ ( sK1
@ ^ [Y0: $i] :
~ ( cP @ Y0 ) ) ) )
| ( $true
= ( cP @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f225]) ).
thf(f225,plain,
! [X0: $i] :
( ( $true
= ( cP @ X0 ) )
| ( $true != $true )
| ( $true
= ( cP
@ ( sK1
@ ^ [Y0: $i] :
~ ( cP @ Y0 ) ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f220]) ).
thf(f220,plain,
! [X0: $i] :
( ( $true
= ( cP @ X0 ) )
| ( $true
= ( cP
@ ( sK1
@ ^ [Y0: $i] :
~ ( cP @ Y0 ) ) ) )
| ( $true != $true )
| ( $true
= ( cP
@ ( sK1
@ ^ [Y0: $i] :
~ ( cP @ Y0 ) ) ) ) ),
inference(superposition,[status(thm)],[f18,f83]) ).
thf(f83,plain,
! [X1: $i,X4: $i > $o] :
( ( $true
= ( X4
@ ( sK0
@ ( sK1
@ ^ [Y0: $i] :
~ ( X4 @ Y0 ) ) ) ) )
| ( $true
= ( cP
@ ( sK1
@ ^ [Y0: $i] :
~ ( X4 @ Y0 ) ) ) )
| ( $true
= ( X4 @ X1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f82]) ).
thf(f82,plain,
! [X1: $i,X4: $i > $o] :
( ( $true
= ( cP
@ ( sK1
@ ^ [Y0: $i] :
~ ( X4 @ Y0 ) ) ) )
| ( $true
!= ( ~ ( X4 @ X1 ) ) )
| ( $true
= ( X4
@ ( sK0
@ ( sK1
@ ^ [Y0: $i] :
~ ( X4 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f81]) ).
thf(f81,plain,
! [X1: $i,X4: $i > $o] :
( ( $true
!= ( ~ ( X4
@ ( sK0
@ ( sK1
@ ^ [Y0: $i] :
~ ( X4 @ Y0 ) ) ) ) ) )
| ( $true
!= ( ~ ( X4 @ X1 ) ) )
| ( $true
= ( cP
@ ( sK1
@ ^ [Y0: $i] :
~ ( X4 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f78]) ).
thf(f78,plain,
! [X1: $i,X4: $i > $o] :
( ( $true
!= ( ^ [Y0: $i] :
~ ( X4 @ Y0 )
@ ( sK0
@ ( sK1
@ ^ [Y0: $i] :
~ ( X4 @ Y0 ) ) ) ) )
| ( $true
= ( cP
@ ( sK1
@ ^ [Y0: $i] :
~ ( X4 @ Y0 ) ) ) )
| ( $true
!= ( ^ [Y0: $i] :
~ ( X4 @ Y0 )
@ X1 ) ) ),
inference(primitive_instantiation,[status(thm)],[f37]) ).
thf(f37,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
!= ( X0 @ ( sK0 @ ( sK1 @ X0 ) ) ) )
| ( ( X0 @ X1 )
!= $true )
| ( $true
= ( cP @ ( sK1 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f33]) ).
thf(f33,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
= ( cP @ ( sK1 @ X0 ) ) )
| ( $true
!= ( X0 @ ( sK0 @ ( sK1 @ X0 ) ) ) )
| ( ( X0 @ X1 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f17,f20]) ).
thf(f20,plain,
! [X0: $i] :
( ( ( cR @ X0 @ ( sK0 @ X0 ) )
= $true )
| ( $true
= ( cP @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f17,plain,
! [X2: $i,X3: $i > $o,X5: $i] :
( ( $true
!= ( cR @ ( sK1 @ X3 ) @ X5 ) )
| ( $true
!= ( X3 @ X5 ) )
| ( $true
!= ( X3 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f18,plain,
! [X0: $i] :
( ( $true
!= ( cP @ ( sK0 @ X0 ) ) )
| ( $true
= ( cP @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV384^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n031.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:46:48 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : SEV384^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.45 % Domain : Set Theory
% 0.18/0.45 % Problem : TPS problem THM117B
% 0.18/0.45 % Version : Especial.
% 0.18/0.45 % English : If R is a well-founded relation and P is an inductive property
% 0.18/0.45 % over R restricted to s, then everything in s has property P;
% 0.18/0.45 % here R y w means y > w.
% 0.18/0.45
% 0.18/0.45 % Refs : [BB93] Bailin & Barker-Plummer (1993), L-match: An Inference
% 0.18/0.45 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.45 % Source : [Bro09]
% 0.18/0.45 % Names : tps_0270 [Bro09]
% 0.18/0.45 % : THM117B [TPS]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % 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 v5.4.0, 0.25 v5.1.0, 0.50 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.18/0.45 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.18/0.45 % Number of atoms : 7 ( 0 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 7 ( 7 avg)
% 0.18/0.45 % Number of connectives : 22 ( 1 ~; 0 |; 3 &; 12 @)
% 0.18/0.45 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 12 ( 12 avg)
% 0.18/0.45 % Number of types : 2 ( 0 usr)
% 0.18/0.45 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 3 ( 3 usr; 0 con; 1-2 aty)
% 0.18/0.45 % Number of variables : 7 ( 0 ^; 6 !; 1 ?; 7 :)
% 0.18/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.18/0.45
% 0.18/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(cP,type,
% 0.18/0.45 cP: $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(s,type,
% 0.18/0.45 s: $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(cR,type,
% 0.18/0.45 cR: $i > $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(cTHM117B,conjecture,
% 0.18/0.45 ( ( ! [Xx: $i > $o,Xz: $i] :
% 0.18/0.45 ( ( Xx @ Xz )
% 0.18/0.45 => ? [Xy: $i] :
% 0.18/0.45 ( ( Xx @ Xy )
% 0.18/0.45 & ! [Xw: $i] :
% 0.18/0.45 ( ( cR @ Xy @ Xw )
% 0.18/0.45 => ~ ( Xx @ Xw ) ) ) )
% 0.18/0.45 & ! [Xx1: $i] :
% 0.18/0.45 ( ! [Xy1: $i] :
% 0.18/0.45 ( ( ( s @ Xy1 )
% 0.18/0.45 & ( cR @ Xx1 @ Xy1 ) )
% 0.18/0.45 => ( cP @ Xy1 ) )
% 0.18/0.45 => ( cP @ Xx1 ) ) )
% 0.18/0.45 => ! [Xx2: $i] :
% 0.18/0.45 ( ( s @ Xx2 )
% 0.18/0.45 => ( cP @ Xx2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 ------------------------
% 1.36/1.18 ---- Embedded in THF ---
% 1.36/1.18 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.36/1.18 %%% Generated on Tue Feb 24 12:46:48 EST 2026
% 1.36/1.18 %%% using '$$dhol' embedding, version 1.3.0.
% 1.36/1.18 %%% Logic specification used:
% 1.36/1.18 %%% thf(spec, logic, $$dhol).
% 1.36/1.18
% 1.36/1.18 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.pLXQH6I3bB/DTF2DTF11576.p
% See solution above
% 1.36/1.18 ------------------------
% 1.36/1.19 ---- Cleaned THF ---
% 1.36/1.19 thf(cP,type,
% 1.36/1.19 cP: $i > $o ).
% 1.36/1.19
% 1.36/1.19 thf(s,type,
% 1.36/1.19 s: $i > $o ).
% 1.36/1.19
% 1.36/1.19 thf(cR,type,
% 1.36/1.19 cR: $i > $i > $o ).
% 1.36/1.19
% 1.36/1.19 thf(cTHM117B,conjecture,
% 1.36/1.19 ( ( ! [Xx: $i > $o,Xz: $i] :
% 1.36/1.19 ( ( Xx @ Xz )
% 1.36/1.19 => ? [Xy: $i] :
% 1.36/1.19 ( ( Xx @ Xy )
% 1.36/1.19 & ! [Xw: $i] :
% 1.36/1.19 ( ( cR @ Xy @ Xw )
% 1.36/1.19 => ~ ( Xx @ Xw ) ) ) )
% 1.36/1.19 & ! [Xx1: $i] :
% 1.36/1.19 ( ! [Xy1: $i] :
% 1.36/1.19 ( ( ( s @ Xy1 )
% 1.36/1.19 & ( cR @ Xx1 @ Xy1 ) )
% 1.36/1.19 => ( cP @ Xy1 ) )
% 1.36/1.19 => ( cP @ Xx1 ) ) )
% 1.36/1.19 => ! [Xx2: $i] :
% 1.36/1.19 ( ( s @ Xx2 )
% 1.36/1.19 => ( cP @ Xx2 ) ) ) ).
% 1.36/1.19 ------------------------
% 1.48/1.20 % (11673)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11576 for (3000ds/183Mi)
% 1.48/1.21 % (11676)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11576 for (3000ds/2Mi)
% 1.48/1.21 % (11679)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11576 for (3000ds/18Mi)
% 1.48/1.21 % (11675)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_11576 for (3000ds/27Mi)
% 1.48/1.21 % (11676)Instruction limit reached!
% 1.48/1.21 % (11676)------------------------------
% 1.48/1.21 % (11676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.21 % (11676)Termination reason: Unknown
% 1.48/1.21 % (11676)Termination phase: Saturation
% 1.48/1.21
% 1.48/1.21 % (11676)Memory used [KB]: 5500
% 1.48/1.21 % (11676)Time elapsed: 0.003 s
% 1.48/1.21 % (11676)Instructions burned: 2 (million)
% 1.48/1.21 % (11676)------------------------------
% 1.48/1.21 % (11676)------------------------------
% 1.48/1.21 % (11677)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_11576 for (3000ds/2Mi)
% 1.48/1.21 % (11674)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_11576 for (3000ds/4Mi)
% 1.48/1.21 % (11678)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_11576 for (3000ds/275Mi)
% 1.48/1.21 % (11677)Instruction limit reached!
% 1.48/1.21 % (11677)------------------------------
% 1.48/1.21 % (11677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.21 % (11677)Termination reason: Unknown
% 1.48/1.21 % (11677)Termination phase: Saturation
% 1.48/1.21
% 1.48/1.21 % (11677)Memory used [KB]: 895
% 1.48/1.21 % (11677)Time elapsed: 0.003 s
% 1.48/1.21 % (11677)Instructions burned: 2 (million)
% 1.48/1.21 % (11677)------------------------------
% 1.48/1.21 % (11677)------------------------------
% 1.48/1.21 % (11675)Refutation not found, incomplete strategy
% 1.48/1.21 % (11675)------------------------------
% 1.48/1.21 % (11675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.21 % (11675)Termination reason: Refutation not found, incomplete strategy
% 1.48/1.21
% 1.48/1.21
% 1.48/1.21 % (11675)Memory used [KB]: 5500
% 1.48/1.21 % (11675)Time elapsed: 0.004 s
% 1.48/1.21 % (11675)Instructions burned: 4 (million)
% 1.48/1.21 % (11675)------------------------------
% 1.48/1.21 % (11675)------------------------------
% 1.48/1.21 % (11674)Instruction limit reached!
% 1.48/1.21 % (11674)------------------------------
% 1.48/1.21 % (11674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.21 % (11674)Termination reason: Unknown
% 1.48/1.21 % (11674)Termination phase: Saturation
% 1.48/1.21
% 1.48/1.21 % (11674)Memory used [KB]: 5500
% 1.48/1.21 % (11674)Time elapsed: 0.004 s
% 1.48/1.21 % (11674)Instructions burned: 4 (million)
% 1.48/1.21 % (11674)------------------------------
% 1.48/1.21 % (11674)------------------------------
% 1.48/1.22 % (11679)Instruction limit reached!
% 1.48/1.22 % (11679)------------------------------
% 1.48/1.22 % (11679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.22 % (11679)Termination reason: Unknown
% 1.48/1.22 % (11679)Termination phase: Saturation
% 1.48/1.22
% 1.48/1.22 % (11679)Memory used [KB]: 5628
% 1.48/1.22 % (11679)Time elapsed: 0.013 s
% 1.48/1.22 % (11679)Instructions burned: 18 (million)
% 1.48/1.22 % (11679)------------------------------
% 1.48/1.22 % (11679)------------------------------
% 1.48/1.22 % (11680)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_11576 for (2999ds/3Mi)
% 1.48/1.23 % (11680)Instruction limit reached!
% 1.48/1.23 % (11680)------------------------------
% 1.48/1.23 % (11680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.23 % (11680)Termination reason: Unknown
% 1.48/1.23 % (11680)Termination phase: Saturation
% 1.48/1.23
% 1.48/1.23 % (11680)Memory used [KB]: 5500
% 1.48/1.23 % (11680)Time elapsed: 0.004 s
% 1.48/1.23 % (11680)Instructions burned: 3 (million)
% 1.48/1.23 % (11680)------------------------------
% 1.48/1.23 % (11680)------------------------------
% 1.48/1.23 % (11681)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_11576 for (2999ds/37Mi)
% 1.48/1.23 % (11678)First to succeed.
% 1.48/1.23 % (11683)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_11576 for (2999ds/3Mi)
% 1.48/1.23 % (11682)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_11576 for (2999ds/15Mi)
% 1.48/1.23 % (11683)Instruction limit reached!
% 1.48/1.23 % (11683)------------------------------
% 1.48/1.23 % (11683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.23 % (11683)Termination reason: Unknown
% 1.48/1.23 % (11683)Termination phase: Saturation
% 1.48/1.23
% 1.48/1.23 % (11683)Memory used [KB]: 5500
% 1.48/1.23 % (11683)Time elapsed: 0.003 s
% 1.48/1.23 % (11683)Instructions burned: 3 (million)
% 1.48/1.23 % (11683)------------------------------
% 1.48/1.23 % (11683)------------------------------
% 1.48/1.23 % (11678)Refutation found. Thanks to Tanya!
% 1.48/1.23 % SZS status Theorem for DTF2THF_11576
% 1.48/1.23 % SZS output start Proof for DTF2THF_11576
% 1.48/1.23 thf(func_def_0, type, cP: $i > $o).
% 1.48/1.23 thf(func_def_1, type, s: $i > $o).
% 1.48/1.23 thf(func_def_2, type, cR: $i > $i > $o).
% 1.48/1.23 thf(func_def_6, type, sK0: $i > $i).
% 1.48/1.23 thf(func_def_7, type, sK1: ($i > $o) > $i).
% 1.48/1.23 thf(func_def_11, type, ph4: !>[X0: $tType]:(X0)).
% 1.48/1.23 thf(f299,plain,(
% 1.48/1.23 $false),
% 1.48/1.23 inference(avatar_sat_refutation,[status(thm)],[f248,f258,f298])).
% 1.48/1.23 thf(f298,plain,(
% 1.48/1.23 spl3_13 | ~spl3_16),
% 1.48/1.23 inference(avatar_split_clause,[status(thm)],[f295,f245,f157])).
% 1.48/1.23 thf(f157,definition,(
% 1.48/1.23 spl3_13 <=> ! [X1 : $i] : ($true = (cP @ X1))),
% 1.48/1.23 introduced(definition,[new_symbols(naming,[spl3_13])],[avatar_definition])).
% 1.48/1.23 thf(f245,definition,(
% 1.48/1.23 spl3_16 <=> ($true = (cP @ (sK1 @ (^[Y0 : $i]: (~ (cP @ Y0))))))),
% 1.48/1.23 introduced(definition,[new_symbols(naming,[spl3_16])],[avatar_definition])).
% 1.48/1.23 thf(f295,plain,(
% 1.48/1.23 ( ! [X0 : $i] : (($true = (cP @ X0))) ) | ~spl3_16),
% 1.48/1.23 inference(trivial_inequality_removal,[status(thm)],[f294])).
% 1.48/1.23 thf(f294,plain,(
% 1.48/1.23 ( ! [X0 : $i] : (($true = $false) | ($true = (cP @ X0))) ) | ~spl3_16),
% 1.48/1.23 inference(superposition,[status(thm)],[f27,f247])).
% 1.48/1.23 thf(f247,plain,(
% 1.48/1.23 ($true = (cP @ (sK1 @ (^[Y0 : $i]: (~ (cP @ Y0)))))) | ~spl3_16),
% 1.48/1.23 inference(avatar_component_clause,[status(thm)],[f245])).
% 1.48/1.23 thf(f27,plain,(
% 1.48/1.23 ( ! [X2 : $i,X6 : $i > $o] : (((X6 @ (sK1 @ (^[Y0 : $i]: (~ (X6 @ Y0))))) = $false) | ($true = (X6 @ X2))) )),
% 1.48/1.23 inference(not_proxy_clausification,[status(thm)],[f26])).
% 1.48/1.23 thf(f26,plain,(
% 1.48/1.23 ( ! [X2 : $i,X6 : $i > $o] : (($true = (~ (X6 @ (sK1 @ (^[Y0 : $i]: (~ (X6 @ Y0))))))) | ($true = (X6 @ X2))) )),
% 1.48/1.23 inference(not_proxy_clausification,[status(thm)],[f25])).
% 1.48/1.23 thf(f25,plain,(
% 1.48/1.23 ( ! [X2 : $i,X6 : $i > $o] : (($true != (~ (X6 @ X2))) | ($true = (~ (X6 @ (sK1 @ (^[Y0 : $i]: (~ (X6 @ Y0)))))))) )),
% 1.48/1.23 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.48/1.23 thf(f24,plain,(
% 1.48/1.23 ( ! [X2 : $i,X6 : $i > $o] : (($true != ((^[Y0 : $i]: (~ (X6 @ Y0))) @ X2)) | ($true = ((^[Y0 : $i]: (~ (X6 @ Y0))) @ (sK1 @ (^[Y0 : $i]: (~ (X6 @ Y0))))))) )),
% 1.48/1.23 inference(primitive_instantiation,[status(thm)],[f16])).
% 1.48/1.23 thf(f16,plain,(
% 1.48/1.23 ( ! [X2 : $i,X3 : $i > $o] : (($true = (X3 @ (sK1 @ X3))) | ($true != (X3 @ X2))) )),
% 1.48/1.23 inference(cnf_transformation,[status(thm)],[f13])).
% 1.48/1.23 thf(f13,plain,(
% 1.48/1.23 ! [X0 : $i] : ((((cR @ X0 @ (sK0 @ X0)) = $true) & ($true = (s @ (sK0 @ X0))) & ($true != (cP @ (sK0 @ X0)))) | ($true = (cP @ X0))) & ! [X2 : $i,X3 : $i > $o] : ((! [X5 : $i] : (($true != (X3 @ X5)) | ($true != (cR @ (sK1 @ X3) @ X5))) & ($true = (X3 @ (sK1 @ X3)))) | ($true != (X3 @ X2))) & (((s @ sK2) = $true) & ($true != (cP @ sK2)))),
% 1.48/1.23 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f12,f11,f10])).
% 1.48/1.23 thf(f10,plain,(
% 1.48/1.23 ! [X0 : $i] : (? [X1 : $i] : (($true = (cR @ X0 @ X1)) & ($true = (s @ X1)) & ($true != (cP @ X1))) => (((cR @ X0 @ (sK0 @ X0)) = $true) & ($true = (s @ (sK0 @ X0))) & ($true != (cP @ (sK0 @ X0)))))),
% 1.48/1.23 introduced(definition,[],[choice_axiom])).
% 1.48/1.23 thf(f11,plain,(
% 1.48/1.23 ! [X3 : $i > $o] : (? [X4 : $i] : (! [X5 : $i] : (($true != (X3 @ X5)) | ((cR @ X4 @ X5) != $true)) & ($true = (X3 @ X4))) => (! [X5 : $i] : (($true != (X3 @ X5)) | ($true != (cR @ (sK1 @ X3) @ X5))) & ($true = (X3 @ (sK1 @ X3)))))),
% 1.48/1.23 introduced(definition,[],[choice_axiom])).
% 1.48/1.23 thf(f12,plain,(
% 1.48/1.23 ? [X6 : $i] : (((s @ X6) = $true) & ((cP @ X6) != $true)) => (((s @ sK2) = $true) & ($true != (cP @ sK2)))),
% 1.48/1.23 introduced(definition,[],[choice_axiom])).
% 1.48/1.23 thf(f9,plain,(
% 1.48/1.23 ! [X0 : $i] : (? [X1 : $i] : (($true = (cR @ X0 @ X1)) & ($true = (s @ X1)) & ($true != (cP @ X1))) | ($true = (cP @ X0))) & ! [X2 : $i,X3 : $i > $o] : (? [X4 : $i] : (! [X5 : $i] : (($true != (X3 @ X5)) | ((cR @ X4 @ X5) != $true)) & ($true = (X3 @ X4))) | ($true != (X3 @ X2))) & ? [X6 : $i] : (((s @ X6) = $true) & ((cP @ X6) != $true))),
% 1.48/1.23 inference(rectify,[status(thm)],[f8])).
% 1.48/1.23 thf(f8,plain,(
% 1.48/1.23 ! [X0 : $i] : (? [X1 : $i] : (($true = (cR @ X0 @ X1)) & ($true = (s @ X1)) & ($true != (cP @ X1))) | ($true = (cP @ X0))) & ! [X3 : $i,X2 : $i > $o] : (? [X4 : $i] : (! [X5 : $i] : (($true != (X2 @ X5)) | ((cR @ X4 @ X5) != $true)) & ($true = (X2 @ X4))) | ((X2 @ X3) != $true)) & ? [X6 : $i] : (((s @ X6) = $true) & ((cP @ X6) != $true))),
% 1.48/1.23 inference(flattening,[status(thm)],[f7])).
% 1.48/1.23 thf(f7,plain,(
% 1.48/1.23 ? [X6 : $i] : (((s @ X6) = $true) & ((cP @ X6) != $true)) & (! [X3 : $i,X2 : $i > $o] : (? [X4 : $i] : (! [X5 : $i] : (($true != (X2 @ X5)) | ((cR @ X4 @ X5) != $true)) & ($true = (X2 @ X4))) | ((X2 @ X3) != $true)) & ! [X0 : $i] : (($true = (cP @ X0)) | ? [X1 : $i] : (($true != (cP @ X1)) & (($true = (cR @ X0 @ X1)) & ($true = (s @ X1))))))),
% 1.48/1.23 inference(ennf_transformation,[status(thm)],[f6])).
% 1.48/1.23 thf(f6,plain,(
% 1.48/1.23 ~((! [X3 : $i,X2 : $i > $o] : (((X2 @ X3) = $true) => ? [X4 : $i] : (! [X5 : $i] : (((cR @ X4 @ X5) = $true) => ($true != (X2 @ X5))) & ($true = (X2 @ X4)))) & ! [X0 : $i] : (! [X1 : $i] : ((($true = (cR @ X0 @ X1)) & ($true = (s @ X1))) => ($true = (cP @ X1))) => ($true = (cP @ X0)))) => ! [X6 : $i] : (((s @ X6) = $true) => ((cP @ X6) = $true)))),
% 1.48/1.23 inference(flattening,[status(thm)],[f5])).
% 1.48/1.23 thf(f5,plain,(
% 1.48/1.23 ~((! [X0 : $i] : (! [X1 : $i] : ((($true = (cR @ X0 @ X1)) & ($true = (s @ X1))) => ($true = (cP @ X1))) => ($true = (cP @ X0))) & ! [X2 : $i > $o,X3 : $i] : (((X2 @ X3) = $true) => ? [X4 : $i] : (! [X5 : $i] : (((cR @ X4 @ X5) = $true) => ~($true = (X2 @ X5))) & ($true = (X2 @ X4))))) => ! [X6 : $i] : (((s @ X6) = $true) => ((cP @ X6) = $true)))),
% 1.48/1.23 inference(fool_elimination,[status(thm)],[f4])).
% 1.48/1.23 thf(f4,plain,(
% 1.48/1.23 ~((! [X0 : $i] : (! [X1 : $i] : (((s @ X1) & (cR @ X0 @ X1)) => (cP @ X1)) => (cP @ X0)) & ! [X2 : $i > $o,X3 : $i] : ((X2 @ X3) => ? [X4 : $i] : (! [X5 : $i] : ((cR @ X4 @ X5) => ~(X2 @ X5)) & (X2 @ X4)))) => ! [X6 : $i] : ((s @ X6) => (cP @ X6)))),
% 1.48/1.23 inference(rectify,[status(thm)],[f2])).
% 1.48/1.23 thf(f2,negated_conjecture,(
% 1.48/1.23 ~((! [X4 : $i] : (! [X5 : $i] : (((s @ X5) & (cR @ X4 @ X5)) => (cP @ X5)) => (cP @ X4)) & ! [X0 : $i > $o,X1 : $i] : ((X0 @ X1) => ? [X2 : $i] : (! [X3 : $i] : ((cR @ X2 @ X3) => ~(X0 @ X3)) & (X0 @ X2)))) => ! [X6 : $i] : ((s @ X6) => (cP @ X6)))),
% 1.48/1.23 inference(negated_conjecture,[status(cth)],[f1])).
% 1.48/1.23 thf(f1,conjecture,(
% 1.48/1.23 (! [X4 : $i] : (! [X5 : $i] : (((s @ X5) & (cR @ X4 @ X5)) => (cP @ X5)) => (cP @ X4)) & ! [X0 : $i > $o,X1 : $i] : ((X0 @ X1) => ? [X2 : $i] : (! [X3 : $i] : ((cR @ X2 @ X3) => ~(X0 @ X3)) & (X0 @ X2)))) => ! [X6 : $i] : ((s @ X6) => (cP @ X6))),
% 1.48/1.23 file('/export/starexec/sandbox/tmp/tmp.pLXQH6I3bB/DTF2THF_11576.p',cTHM117B)).
% 1.48/1.23 thf(f258,plain,(
% 1.48/1.23 ~spl3_13),
% 1.48/1.23 inference(avatar_contradiction_clause,[status(thm)],[f257])).
% 1.48/1.23 thf(f257,plain,(
% 1.48/1.23 $false | ~spl3_13),
% 1.48/1.23 inference(trivial_inequality_removal,[status(thm)],[f251])).
% 1.48/1.23 thf(f251,plain,(
% 1.48/1.23 ($true != $true) | ~spl3_13),
% 1.48/1.23 inference(superposition,[status(thm)],[f14,f158])).
% 1.48/1.23 thf(f158,plain,(
% 1.48/1.23 ( ! [X1 : $i] : (($true = (cP @ X1))) ) | ~spl3_13),
% 1.48/1.23 inference(avatar_component_clause,[status(thm)],[f157])).
% 1.48/1.23 thf(f14,plain,(
% 1.48/1.23 ($true != (cP @ sK2))),
% 1.48/1.23 inference(cnf_transformation,[status(thm)],[f13])).
% 1.48/1.23 thf(f248,plain,(
% 1.48/1.23 spl3_16 | spl3_13),
% 1.48/1.23 inference(avatar_split_clause,[status(thm)],[f226,f157,f245])).
% 1.48/1.23 thf(f226,plain,(
% 1.48/1.23 ( ! [X0 : $i] : (($true = (cP @ (sK1 @ (^[Y0 : $i]: (~ (cP @ Y0)))))) | ($true = (cP @ X0))) )),
% 1.48/1.23 inference(trivial_inequality_removal,[status(thm)],[f225])).
% 1.48/1.23 thf(f225,plain,(
% 1.48/1.23 ( ! [X0 : $i] : (($true = (cP @ X0)) | ($true != $true) | ($true = (cP @ (sK1 @ (^[Y0 : $i]: (~ (cP @ Y0))))))) )),
% 1.48/1.23 inference(duplicate_literal_removal,[status(thm)],[f220])).
% 1.48/1.23 thf(f220,plain,(
% 1.48/1.23 ( ! [X0 : $i] : (($true = (cP @ X0)) | ($true = (cP @ (sK1 @ (^[Y0 : $i]: (~ (cP @ Y0)))))) | ($true != $true) | ($true = (cP @ (sK1 @ (^[Y0 : $i]: (~ (cP @ Y0))))))) )),
% 1.48/1.23 inference(superposition,[status(thm)],[f18,f83])).
% 1.48/1.23 thf(f83,plain,(
% 1.48/1.23 ( ! [X1 : $i,X4 : $i > $o] : (($true = (X4 @ (sK0 @ (sK1 @ (^[Y0 : $i]: (~ (X4 @ Y0))))))) | ($true = (cP @ (sK1 @ (^[Y0 : $i]: (~ (X4 @ Y0)))))) | ($true = (X4 @ X1))) )),
% 1.48/1.23 inference(not_proxy_clausification,[status(thm)],[f82])).
% 1.48/1.23 thf(f82,plain,(
% 1.48/1.23 ( ! [X1 : $i,X4 : $i > $o] : (($true = (cP @ (sK1 @ (^[Y0 : $i]: (~ (X4 @ Y0)))))) | ($true != (~ (X4 @ X1))) | ($true = (X4 @ (sK0 @ (sK1 @ (^[Y0 : $i]: (~ (X4 @ Y0)))))))) )),
% 1.48/1.23 inference(not_proxy_clausification,[status(thm)],[f81])).
% 1.48/1.23 thf(f81,plain,(
% 1.48/1.23 ( ! [X1 : $i,X4 : $i > $o] : (($true != (~ (X4 @ (sK0 @ (sK1 @ (^[Y0 : $i]: (~ (X4 @ Y0)))))))) | ($true != (~ (X4 @ X1))) | ($true = (cP @ (sK1 @ (^[Y0 : $i]: (~ (X4 @ Y0))))))) )),
% 1.48/1.23 inference(beta_eta_normalization,[status(thm)],[f78])).
% 1.48/1.23 thf(f78,plain,(
% 1.48/1.23 ( ! [X1 : $i,X4 : $i > $o] : (($true != ((^[Y0 : $i]: (~ (X4 @ Y0))) @ (sK0 @ (sK1 @ (^[Y0 : $i]: (~ (X4 @ Y0))))))) | ($true = (cP @ (sK1 @ (^[Y0 : $i]: (~ (X4 @ Y0)))))) | ($true != ((^[Y0 : $i]: (~ (X4 @ Y0))) @ X1))) )),
% 1.48/1.23 inference(primitive_instantiation,[status(thm)],[f37])).
% 1.48/1.23 thf(f37,plain,(
% 1.48/1.23 ( ! [X0 : $i > $o,X1 : $i] : (($true != (X0 @ (sK0 @ (sK1 @ X0)))) | ((X0 @ X1) != $true) | ($true = (cP @ (sK1 @ X0)))) )),
% 1.48/1.23 inference(trivial_inequality_removal,[status(thm)],[f33])).
% 1.48/1.23 thf(f33,plain,(
% 1.48/1.23 ( ! [X0 : $i > $o,X1 : $i] : (($true = (cP @ (sK1 @ X0))) | ($true != (X0 @ (sK0 @ (sK1 @ X0)))) | ((X0 @ X1) != $true) | ($true != $true)) )),
% 1.48/1.23 inference(superposition,[status(thm)],[f17,f20])).
% 1.48/1.23 thf(f20,plain,(
% 1.48/1.23 ( ! [X0 : $i] : (((cR @ X0 @ (sK0 @ X0)) = $true) | ($true = (cP @ X0))) )),
% 1.48/1.23 inference(cnf_transformation,[status(thm)],[f13])).
% 1.48/1.23 thf(f17,plain,(
% 1.48/1.23 ( ! [X2 : $i,X3 : $i > $o,X5 : $i] : (($true != (cR @ (sK1 @ X3) @ X5)) | ($true != (X3 @ X5)) | ($true != (X3 @ X2))) )),
% 1.48/1.23 inference(cnf_transformation,[status(thm)],[f13])).
% 1.48/1.23 thf(f18,plain,(
% 1.48/1.23 ( ! [X0 : $i] : (($true != (cP @ (sK0 @ X0))) | ($true = (cP @ X0))) )),
% 1.48/1.23 inference(cnf_transformation,[status(thm)],[f13])).
% 1.48/1.23 % SZS output end Proof for DTF2THF_11576
% 1.48/1.23 % (11678)------------------------------
% 1.48/1.23 % (11678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.23 % (11678)Termination reason: Refutation
% 1.48/1.23
% 1.48/1.23 % (11678)Memory used [KB]: 5756
% 1.48/1.23 % (11678)Time elapsed: 0.023 s
% 1.48/1.23 % (11678)Instructions burned: 31 (million)
% 1.48/1.23 % (11678)------------------------------
% 1.48/1.23 % (11678)------------------------------
% 1.48/1.23 % (11672)Success in time 0.037 s
%------------------------------------------------------------------------------