%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO029^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n014.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 09:53:10 AM UTC 2026
% Result : Theorem 1.66s 1.45s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 4 unt; 0 typ; 2 def)
% Number of atoms : 165 ( 52 equ; 9 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 180 ( 62 ~; 26 |; 4 &; 79 @)
% ( 7 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 4 usr; 5 con; 0-2 aty)
% Number of variables : 49 ( 24 ^; 17 !; 8 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_3,type,
sK0: ( $o > $o ) > $o ).
thf(func_def_5,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f89,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f62,f82,f85]) ).
thf(f85,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[status(thm)],[f84]) ).
thf(f84,plain,
( $false
| ~ spl1_1 ),
inference(trivial_inequality_removal,[status(thm)],[f83]) ).
thf(f83,plain,
( ( $true = $false )
| ~ spl1_1 ),
inference(forward_demodulation,[status(thm)],[f77,f57]) ).
thf(f57,plain,
( ( ( sK0 @ (~) )
= $false )
| ~ spl1_1 ),
inference(avatar_component_clause,[status(thm)],[f55]) ).
thf(f55,definition,
( spl1_1
<=> ( ( sK0 @ (~) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition]) ).
thf(f77,plain,
( ( sK0 @ (~) )
= $true ),
inference(duplicate_literal_removal,[status(thm)],[f76]) ).
thf(f76,plain,
( ( ( sK0 @ (~) )
= $true )
| ( ( sK0 @ (~) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f63]) ).
thf(f63,plain,
( ( $true
= ( sK0
@ ^ [Y0: $o] :
~ ( ^ [Y1: $o] : Y1
@ Y0 ) ) )
| ( $true
= ( ^ [Y0: $o] : Y0
@ ( sK0
@ ^ [Y0: $o] :
~ ( ^ [Y1: $o] : Y1
@ Y0 ) ) ) ) ),
inference(primitive_instantiation,[status(thm)],[f32]) ).
thf(f32,plain,
! [X3: $o > $o] :
( ( $true
= ( X3
@ ( sK0
@ ^ [Y0: $o] :
~ ( X3 @ Y0 ) ) ) )
| ( $true
= ( sK0
@ ^ [Y0: $o] :
~ ( X3 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X3: $o > $o] :
( ( $true
!= ( ~ ( X3
@ ( sK0
@ ^ [Y0: $o] :
~ ( X3 @ Y0 ) ) ) ) )
| ( $true
= ( sK0
@ ^ [Y0: $o] :
~ ( X3 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
! [X3: $o > $o] :
( ( ( ^ [Y0: $o] :
~ ( X3 @ Y0 )
@ ( sK0
@ ^ [Y0: $o] :
~ ( X3 @ Y0 ) ) )
!= $true )
| ( $true
= ( sK0
@ ^ [Y0: $o] :
~ ( X3 @ Y0 ) ) ) ),
inference(primitive_instantiation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $o > $o] :
( ( $true
!= ( X0 @ ( sK0 @ X0 ) ) )
| ( $true
= ( sK0 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $o > $o] :
( ( ( $true
= ( sK0 @ X0 ) )
| ( $true
!= ( X0 @ ( sK0 @ X0 ) ) ) )
& ( ( $true
!= ( sK0 @ X0 ) )
| ( $true
= ( X0 @ ( sK0 @ X0 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9]) ).
thf(f9,plain,
! [X0: $o > $o] :
( ? [X1: $o] :
( ( ( $true = X1 )
| ( ( X0 @ X1 )
!= $true ) )
& ( ( $true != X1 )
| ( ( X0 @ X1 )
= $true ) ) )
=> ( ( ( $true
= ( sK0 @ X0 ) )
| ( $true
!= ( X0 @ ( sK0 @ X0 ) ) ) )
& ( ( $true
!= ( sK0 @ X0 ) )
| ( $true
= ( X0 @ ( sK0 @ X0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
! [X0: $o > $o] :
? [X1: $o] :
( ( ( $true = X1 )
| ( ( X0 @ X1 )
!= $true ) )
& ( ( $true != X1 )
| ( ( X0 @ X1 )
= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $o > $o] :
? [X1: $o] :
( ( ( X0 @ X1 )
= $true )
<~> ( $true != X1 ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ? [X0: $o > $o] :
! [X1: $o] :
( ( ( X0 @ X1 )
= $true )
<=> ( $true != X1 ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: $o > $o] :
! [X1: $o] :
( ( $true != X1 )
<=> ( ( X0 @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: $o > $o] :
! [X1: $o] :
( ~ X1
<=> ( X0 @ X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: $o > $o] :
! [X1: $o] :
( ~ X1
<=> ( X0 @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: $o > $o] :
! [X1: $o] :
( ~ X1
<=> ( X0 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.rGThpqmC3k/DTF2THF_16989.p',conj) ).
thf(f82,plain,
spl1_2,
inference(avatar_contradiction_clause,[status(thm)],[f81]) ).
thf(f81,plain,
( $false
| spl1_2 ),
inference(subsumption_resolution,[status(thm)],[f77,f61]) ).
thf(f61,plain,
( ( ( sK0 @ (~) )
!= $true )
| spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f59]) ).
thf(f59,definition,
( spl1_2
<=> ( ( sK0 @ (~) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition]) ).
thf(f62,plain,
( spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[status(thm)],[f43,f59,f55]) ).
thf(f43,plain,
( ( ( sK0 @ (~) )
= $false )
| ( ( sK0 @ (~) )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
( ( $true
!= ( sK0
@ ^ [Y0: $o] :
~ ( ^ [Y1: $o] : Y1
@ Y0 ) ) )
| ( ( ^ [Y0: $o] : Y0
@ ( sK0
@ ^ [Y0: $o] :
~ ( ^ [Y1: $o] : Y1
@ Y0 ) ) )
= $false ) ),
inference(primitive_instantiation,[status(thm)],[f22]) ).
thf(f22,plain,
! [X3: $o > $o] :
( ( ( X3
@ ( sK0
@ ^ [Y0: $o] :
~ ( X3 @ Y0 ) ) )
= $false )
| ( $true
!= ( sK0
@ ^ [Y0: $o] :
~ ( X3 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
! [X3: $o > $o] :
( ( $true
= ( ~ ( X3
@ ( sK0
@ ^ [Y0: $o] :
~ ( X3 @ Y0 ) ) ) ) )
| ( $true
!= ( sK0
@ ^ [Y0: $o] :
~ ( X3 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
! [X3: $o > $o] :
( ( ( ^ [Y0: $o] :
~ ( X3 @ Y0 )
@ ( sK0
@ ^ [Y0: $o] :
~ ( X3 @ Y0 ) ) )
= $true )
| ( $true
!= ( sK0
@ ^ [Y0: $o] :
~ ( X3 @ Y0 ) ) ) ),
inference(primitive_instantiation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $o > $o] :
( ( $true
= ( X0 @ ( sK0 @ X0 ) ) )
| ( $true
!= ( sK0 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO029^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n014.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue Feb 24 14:21:42 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
% 0.19/0.48 ---- Original DTF file ---
% 0.19/0.48 thf(spec,logic,$$dhol).
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 % File : SYO029^1 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.48 % Domain : Syntactic
% 0.19/0.48 % Problem : There is an identity unary connective
% 0.19/0.48 % Version : Especial.
% 0.19/0.48 % English :
% 0.19/0.48
% 0.19/0.48 % Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.19/0.48 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.19/0.48 % Source : [Ben09]
% 0.19/0.48 % Names : Example 25 [BB05]
% 0.19/0.48
% 0.19/0.48 % Status : Theorem
% 0.19/0.48 % Rating : 0.08 v9.1.0, 0.00 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.33 v6.1.0, 0.00 v3.7.0
% 0.19/0.48 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.19/0.48 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.19/0.48 % Maximal formula atoms : 0 ( 0 avg)
% 0.19/0.48 % Number of connectives : 3 ( 1 ~; 0 |; 0 &; 1 @)
% 0.19/0.48 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.48 % Maximal formula depth : 5 ( 5 avg)
% 0.19/0.48 % Number of types : 1 ( 0 usr)
% 0.19/0.48 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.19/0.48 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.19/0.48 % Number of variables : 2 ( 0 ^; 1 !; 1 ?; 2 :)
% 0.19/0.48 % SPC : TH0_THM_NEQ_NAR
% 0.19/0.48
% 0.19/0.48 % Comments : Requires set comprehension
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 thf(conj,conjecture,
% 0.19/0.48 ? [N: $o > $o] :
% 0.19/0.48 ! [P: $o] :
% 0.19/0.48 ( ( N @ P )
% 0.19/0.48 <=> ~ P ) ).
% 0.19/0.48
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.32/0.48 ------------------------
% 1.66/1.42 ---- Embedded in THF ---
% 1.66/1.42 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.66/1.42 %%% Generated on Tue Feb 24 14:21:43 EST 2026
% 1.66/1.42 %%% using '$$dhol' embedding, version 1.3.0.
% 1.66/1.42 %%% Logic specification used:
% 1.66/1.42 %%% thf(spec, logic, $$dhol).
% 1.66/1.42
% 1.66/1.42 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.rGThpqmC3k/DTF2DTF16989.p
% See solution above
% 1.66/1.42 ------------------------
% 1.66/1.43 ---- Cleaned THF ---
% 1.66/1.43 thf(conj,conjecture,
% 1.66/1.43 ? [N: $o > $o] :
% 1.66/1.43 ! [P: $o] :
% 1.66/1.43 ( ( N @ P )
% 1.66/1.43 <=> ~ P ) ).
% 1.66/1.43 ------------------------
% 1.66/1.45 % (17098)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_16989 for (3000ds/4Mi)
% 1.66/1.45 % (17101)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_16989 for (3000ds/2Mi)
% 1.66/1.45 % (17097)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_16989 for (3000ds/183Mi)
% 1.66/1.45 % (17100)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_16989 for (3000ds/2Mi)
% 1.66/1.45 % (17103)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_16989 for (3000ds/18Mi)
% 1.66/1.45 % (17102)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_16989 for (3000ds/275Mi)
% 1.66/1.45 % (17099)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_16989 for (3000ds/27Mi)
% 1.66/1.45 % (17100)Instruction limit reached!
% 1.66/1.45 % (17100)------------------------------
% 1.66/1.45 % (17100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.45 % (17099)Refutation not found, incomplete strategy
% 1.66/1.45 % (17099)------------------------------
% 1.66/1.45 % (17099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.45 % (17099)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.45
% 1.66/1.45
% 1.66/1.45 % (17099)Memory used [KB]: 5500
% 1.66/1.45 % (17099)Time elapsed: 0.003 s
% 1.66/1.45 % (17099)Instructions burned: 1 (million)
% 1.66/1.45 % (17099)------------------------------
% 1.66/1.45 % (17099)------------------------------
% 1.66/1.45 % (17101)Instruction limit reached!
% 1.66/1.45 % (17101)------------------------------
% 1.66/1.45 % (17101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.45 % (17101)Termination reason: Unknown
% 1.66/1.45 % (17101)Termination phase: Saturation
% 1.66/1.45
% 1.66/1.45 % (17101)Memory used [KB]: 5500
% 1.66/1.45 % (17101)Time elapsed: 0.003 s
% 1.66/1.45 % (17101)Instructions burned: 2 (million)
% 1.66/1.45 % (17101)------------------------------
% 1.66/1.45 % (17101)------------------------------
% 1.66/1.45 % (17100)Termination reason: Unknown
% 1.66/1.45 % (17100)Termination phase: Saturation
% 1.66/1.45
% 1.66/1.45 % (17100)Memory used [KB]: 5500
% 1.66/1.45 % (17100)Time elapsed: 0.003 s
% 1.66/1.45 % (17100)Instructions burned: 2 (million)
% 1.66/1.45 % (17100)------------------------------
% 1.66/1.45 % (17100)------------------------------
% 1.66/1.45 % (17098)Instruction limit reached!
% 1.66/1.45 % (17098)------------------------------
% 1.66/1.45 % (17098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.45 % (17098)Termination reason: Unknown
% 1.66/1.45 % (17098)Termination phase: Saturation
% 1.66/1.45 % (17102)First to succeed.
% 1.66/1.45
% 1.66/1.45 % (17098)Memory used [KB]: 5500
% 1.66/1.45 % (17098)Time elapsed: 0.005 s
% 1.66/1.45 % (17098)Instructions burned: 5 (million)
% 1.66/1.45 % (17098)------------------------------
% 1.66/1.45 % (17098)------------------------------
% 1.66/1.45 % (17102)Refutation found. Thanks to Tanya!
% 1.66/1.45 % SZS status Theorem for DTF2THF_16989
% 1.66/1.45 % SZS output start Proof for DTF2THF_16989
% 1.66/1.45 thf(func_def_3, type, sK0: ($o > $o) > $o).
% 1.66/1.45 thf(func_def_5, type, ph2: !>[X0: $tType]:(X0)).
% 1.66/1.45 thf(f89,plain,(
% 1.66/1.45 $false),
% 1.66/1.45 inference(avatar_sat_refutation,[status(thm)],[f62,f82,f85])).
% 1.66/1.45 thf(f85,plain,(
% 1.66/1.45 ~spl1_1),
% 1.66/1.45 inference(avatar_contradiction_clause,[status(thm)],[f84])).
% 1.66/1.45 thf(f84,plain,(
% 1.66/1.45 $false | ~spl1_1),
% 1.66/1.45 inference(trivial_inequality_removal,[status(thm)],[f83])).
% 1.66/1.45 thf(f83,plain,(
% 1.66/1.45 ($true = $false) | ~spl1_1),
% 1.66/1.45 inference(forward_demodulation,[status(thm)],[f77,f57])).
% 1.66/1.45 thf(f57,plain,(
% 1.66/1.45 ((sK0 @ ~) = $false) | ~spl1_1),
% 1.66/1.45 inference(avatar_component_clause,[status(thm)],[f55])).
% 1.66/1.45 thf(f55,definition,(
% 1.66/1.45 spl1_1 <=> ((sK0 @ ~) = $false)),
% 1.66/1.45 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 1.66/1.45 thf(f77,plain,(
% 1.66/1.45 ((sK0 @ ~) = $true)),
% 1.66/1.45 inference(duplicate_literal_removal,[status(thm)],[f76])).
% 1.66/1.45 thf(f76,plain,(
% 1.66/1.45 ((sK0 @ ~) = $true) | ((sK0 @ ~) = $true)),
% 1.66/1.45 inference(beta_eta_normalization,[status(thm)],[f63])).
% 1.66/1.45 thf(f63,plain,(
% 1.66/1.45 ($true = (sK0 @ (^[Y0 : $o]: (~ ((^[Y1 : $o]: (Y1)) @ Y0))))) | ($true = ((^[Y0 : $o]: (Y0)) @ (sK0 @ (^[Y0 : $o]: (~ ((^[Y1 : $o]: (Y1)) @ Y0))))))),
% 1.66/1.45 inference(primitive_instantiation,[status(thm)],[f32])).
% 1.66/1.45 thf(f32,plain,(
% 1.66/1.45 ( ! [X3 : $o > $o] : (($true = (X3 @ (sK0 @ (^[Y0 : $o]: (~ (X3 @ Y0)))))) | ($true = (sK0 @ (^[Y0 : $o]: (~ (X3 @ Y0)))))) )),
% 1.66/1.45 inference(not_proxy_clausification,[status(thm)],[f31])).
% 1.66/1.45 thf(f31,plain,(
% 1.66/1.45 ( ! [X3 : $o > $o] : (($true != (~ (X3 @ (sK0 @ (^[Y0 : $o]: (~ (X3 @ Y0))))))) | ($true = (sK0 @ (^[Y0 : $o]: (~ (X3 @ Y0)))))) )),
% 1.66/1.45 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.66/1.45 thf(f26,plain,(
% 1.66/1.45 ( ! [X3 : $o > $o] : ((((^[Y0 : $o]: (~ (X3 @ Y0))) @ (sK0 @ (^[Y0 : $o]: (~ (X3 @ Y0))))) != $true) | ($true = (sK0 @ (^[Y0 : $o]: (~ (X3 @ Y0)))))) )),
% 1.66/1.45 inference(primitive_instantiation,[status(thm)],[f12])).
% 1.66/1.45 thf(f12,plain,(
% 1.66/1.45 ( ! [X0 : $o > $o] : (($true != (X0 @ (sK0 @ X0))) | ($true = (sK0 @ X0))) )),
% 1.66/1.45 inference(cnf_transformation,[status(thm)],[f10])).
% 1.66/1.45 thf(f10,plain,(
% 1.66/1.45 ! [X0 : $o > $o] : ((($true = (sK0 @ X0)) | ($true != (X0 @ (sK0 @ X0)))) & (($true != (sK0 @ X0)) | ($true = (X0 @ (sK0 @ X0)))))),
% 1.66/1.45 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9])).
% 1.66/1.45 thf(f9,plain,(
% 1.66/1.45 ! [X0 : $o > $o] : (? [X1 : $o] : ((($true = X1) | ((X0 @ X1) != $true)) & (($true != X1) | ((X0 @ X1) = $true))) => ((($true = (sK0 @ X0)) | ($true != (X0 @ (sK0 @ X0)))) & (($true != (sK0 @ X0)) | ($true = (X0 @ (sK0 @ X0))))))),
% 1.66/1.45 introduced(definition,[],[choice_axiom])).
% 1.66/1.45 thf(f8,plain,(
% 1.66/1.45 ! [X0 : $o > $o] : ? [X1 : $o] : ((($true = X1) | ((X0 @ X1) != $true)) & (($true != X1) | ((X0 @ X1) = $true)))),
% 1.66/1.45 inference(nnf_transformation,[status(thm)],[f7])).
% 1.66/1.45 thf(f7,plain,(
% 1.66/1.45 ! [X0 : $o > $o] : ? [X1 : $o] : (((X0 @ X1) = $true) <~> ($true != X1))),
% 1.66/1.45 inference(ennf_transformation,[status(thm)],[f6])).
% 1.66/1.45 thf(f6,plain,(
% 1.66/1.45 ~? [X0 : $o > $o] : ! [X1 : $o] : (((X0 @ X1) = $true) <=> ($true != X1))),
% 1.66/1.45 inference(flattening,[status(thm)],[f5])).
% 1.66/1.45 thf(f5,plain,(
% 1.66/1.45 ~? [X0 : $o > $o] : ! [X1 : $o] : (~($true = X1) <=> ((X0 @ X1) = $true))),
% 1.66/1.45 inference(fool_elimination,[status(thm)],[f4])).
% 1.66/1.45 thf(f4,plain,(
% 1.66/1.45 ~? [X0 : $o > $o] : ! [X1 : $o] : (~X1 <=> (X0 @ X1))),
% 1.66/1.45 inference(rectify,[status(thm)],[f2])).
% 1.66/1.45 thf(f2,negated_conjecture,(
% 1.66/1.45 ~? [X0 : $o > $o] : ! [X1 : $o] : (~X1 <=> (X0 @ X1))),
% 1.66/1.45 inference(negated_conjecture,[status(cth)],[f1])).
% 1.66/1.45 thf(f1,conjecture,(
% 1.66/1.45 ? [X0 : $o > $o] : ! [X1 : $o] : (~X1 <=> (X0 @ X1))),
% 1.66/1.45 file('/export/starexec/sandbox/tmp/tmp.rGThpqmC3k/DTF2THF_16989.p',conj)).
% 1.66/1.45 thf(f82,plain,(
% 1.66/1.45 spl1_2),
% 1.66/1.45 inference(avatar_contradiction_clause,[status(thm)],[f81])).
% 1.66/1.45 thf(f81,plain,(
% 1.66/1.45 $false | spl1_2),
% 1.66/1.45 inference(subsumption_resolution,[status(thm)],[f77,f61])).
% 1.66/1.45 thf(f61,plain,(
% 1.66/1.45 ((sK0 @ ~) != $true) | spl1_2),
% 1.66/1.45 inference(avatar_component_clause,[status(thm)],[f59])).
% 1.66/1.45 thf(f59,definition,(
% 1.66/1.45 spl1_2 <=> ((sK0 @ ~) = $true)),
% 1.66/1.45 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 1.66/1.45 thf(f62,plain,(
% 1.66/1.45 spl1_1 | ~spl1_2),
% 1.66/1.45 inference(avatar_split_clause,[status(thm)],[f43,f59,f55])).
% 1.66/1.45 thf(f43,plain,(
% 1.66/1.45 ((sK0 @ ~) = $false) | ((sK0 @ ~) != $true)),
% 1.66/1.45 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.66/1.45 thf(f39,plain,(
% 1.66/1.45 ($true != (sK0 @ (^[Y0 : $o]: (~ ((^[Y1 : $o]: (Y1)) @ Y0))))) | (((^[Y0 : $o]: (Y0)) @ (sK0 @ (^[Y0 : $o]: (~ ((^[Y1 : $o]: (Y1)) @ Y0))))) = $false)),
% 1.66/1.45 inference(primitive_instantiation,[status(thm)],[f22])).
% 1.66/1.45 thf(f22,plain,(
% 1.66/1.45 ( ! [X3 : $o > $o] : (((X3 @ (sK0 @ (^[Y0 : $o]: (~ (X3 @ Y0))))) = $false) | ($true != (sK0 @ (^[Y0 : $o]: (~ (X3 @ Y0)))))) )),
% 1.66/1.45 inference(not_proxy_clausification,[status(thm)],[f21])).
% 1.66/1.45 thf(f21,plain,(
% 1.66/1.45 ( ! [X3 : $o > $o] : (($true = (~ (X3 @ (sK0 @ (^[Y0 : $o]: (~ (X3 @ Y0))))))) | ($true != (sK0 @ (^[Y0 : $o]: (~ (X3 @ Y0)))))) )),
% 1.66/1.45 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.66/1.45 thf(f16,plain,(
% 1.66/1.45 ( ! [X3 : $o > $o] : ((((^[Y0 : $o]: (~ (X3 @ Y0))) @ (sK0 @ (^[Y0 : $o]: (~ (X3 @ Y0))))) = $true) | ($true != (sK0 @ (^[Y0 : $o]: (~ (X3 @ Y0)))))) )),
% 1.66/1.45 inference(primitive_instantiation,[status(thm)],[f11])).
% 1.66/1.45 thf(f11,plain,(
% 1.66/1.45 ( ! [X0 : $o > $o] : (($true = (X0 @ (sK0 @ X0))) | ($true != (sK0 @ X0))) )),
% 1.66/1.45 inference(cnf_transformation,[status(thm)],[f10])).
% 1.66/1.45 % SZS output end Proof for DTF2THF_16989
% 1.66/1.45 % (17102)------------------------------
% 1.66/1.45 % (17102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.45 % (17102)Termination reason: Refutation
% 1.66/1.45
% 1.66/1.45 % (17102)Memory used [KB]: 5500
% 1.66/1.45 % (17102)Time elapsed: 0.005 s
% 1.66/1.45 % (17102)Instructions burned: 4 (million)
% 1.66/1.45 % (17102)------------------------------
% 1.66/1.45 % (17102)------------------------------
% 1.66/1.45 % (17096)Success in time 0.019 s
%------------------------------------------------------------------------------