%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO031^1 : 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 : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:53:11 AM UTC 2026
% Result : Theorem 1.61s 1.31s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 18 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 74 ( 26 equ; 3 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 70 ( 18 ~; 8 |; 0 &; 43 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 2 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 12 ^; 11 !; 4 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_3,type,
sK0: ( $o > $o ) > $o ).
thf(func_def_5,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f94,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f93]) ).
thf(f93,plain,
$true = $false,
inference(boolean_simplification,[status(thm)],[f92]) ).
thf(f92,plain,
( $false = ( ~ $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f90]) ).
thf(f90,plain,
( ( $true = $false )
| ( $false = ( ~ $false ) ) ),
inference(superposition,[status(thm)],[f9,f86]) ).
thf(f86,plain,
( $false
= ( sK0 @ (~) ) ),
inference(duplicate_literal_removal,[status(thm)],[f85]) ).
thf(f85,plain,
( ( $false
= ( sK0 @ (~) ) )
| ( $false
= ( sK0 @ (~) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f70]) ).
thf(f70,plain,
( ( ( ^ [Y0: $o] : Y0
@ ( sK0
@ ^ [Y0: $o] :
~ ( ^ [Y1: $o] : Y1
@ Y0 ) ) )
= $false )
| ( $false
= ( sK0
@ ^ [Y0: $o] :
~ ( ^ [Y1: $o] : Y1
@ Y0 ) ) ) ),
inference(primitive_instantiation,[status(thm)],[f19]) ).
thf(f19,plain,
! [X3: $o > $o] :
( ( $false
= ( X3
@ ( sK0
@ ^ [Y0: $o] :
~ ( X3 @ Y0 ) ) ) )
| ( ( sK0
@ ^ [Y0: $o] :
~ ( X3 @ Y0 ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
! [X3: $o > $o] :
( ( $true
= ( ~ ( X3
@ ( sK0
@ ^ [Y0: $o] :
~ ( X3 @ Y0 ) ) ) ) )
| ( ( sK0
@ ^ [Y0: $o] :
~ ( X3 @ Y0 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f13]) ).
thf(f13,plain,
! [X3: $o > $o] :
( ( $true
= ( ^ [Y0: $o] :
~ ( X3 @ Y0 )
@ ( sK0
@ ^ [Y0: $o] :
~ ( X3 @ Y0 ) ) ) )
| ( ( sK0
@ ^ [Y0: $o] :
~ ( X3 @ Y0 ) )
= $false ) ),
inference(primitive_instantiation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $o > $o] :
( ( ( X0 @ ( sK0 @ X0 ) )
= $true )
| ( $false
= ( sK0 @ X0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $o > $o] :
( ( X0 @ ( sK0 @ X0 ) )
= ( sK0 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $o > $o] :
( ( X0 @ ( sK0 @ X0 ) )
= ( sK0 @ X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f4,f5]) ).
thf(f5,plain,
! [X0: $o > $o] :
( ? [X1: $o] :
( ( X0 @ X1 )
= X1 )
=> ( ( X0 @ ( sK0 @ X0 ) )
= ( sK0 @ X0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f4,plain,
! [X0: $o > $o] :
? [X1: $o] :
( ( X0 @ X1 )
= X1 ),
inference(flattening,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ~ ! [X0: $o > $o] :
? [X1: $o] :
( ( X0 @ X1 )
= X1 ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
~ ! [X0: $o > $o] :
? [X1: $o] :
( ( X0 @ X1 )
= X1 ),
file('/export/starexec/sandbox/tmp/tmp.HAhfTKKXAv/DTF2THF_6400.p',conj) ).
thf(f9,plain,
! [X0: $o > $o] :
( ( ( X0 @ ( sK0 @ X0 ) )
= $false )
| ( $true
= ( sK0 @ X0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO031^1 : TPTP v9.2.1. Released v3.7.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n019.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 14:22:09 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : SYO031^1 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.46 % Domain : Syntactic
% 0.19/0.46 % Problem : Not every unary connective is the identity
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English :
% 0.19/0.46
% 0.19/0.46 % Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.19/0.46 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Ben09]
% 0.19/0.46 % Names : Example 26b [BB05]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.46 v8.1.0, 0.36 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0, 0.00 v3.7.0
% 0.19/0.46 % Syntax : Number of formulae : 1 ( 1 unt; 0 typ; 0 def)
% 0.19/0.46 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.19/0.46 % Number of connectives : 2 ( 1 ~; 0 |; 0 &; 1 @)
% 0.19/0.46 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 4 ( 4 avg)
% 0.19/0.46 % Number of types : 1 ( 0 usr)
% 0.19/0.46 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.19/0.46 % Number of variables : 2 ( 0 ^; 1 !; 1 ?; 2 :)
% 0.19/0.46 % SPC : TH0_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : Requires set comprehension
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(conj,conjecture,
% 0.19/0.46 ~ ! [F: $o > $o] :
% 0.19/0.46 ? [X: $o] :
% 0.19/0.46 ( ( F @ X )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.44/1.28 ---- Embedded in THF ---
% 1.44/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.44/1.28 %%% Generated on Tue Feb 24 14:22:10 EST 2026
% 1.44/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.44/1.28 %%% Logic specification used:
% 1.44/1.28 %%% thf(spec, logic, $$dhol).
% 1.44/1.28
% 1.44/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.HAhfTKKXAv/DTF2DTF6400.p
% See solution above
% 1.44/1.28 ------------------------
% 1.44/1.29 ---- Cleaned THF ---
% 1.44/1.29 thf(conj,conjecture,
% 1.44/1.29 ~ ! [F: $o > $o] :
% 1.44/1.29 ? [X: $o] :
% 1.44/1.29 ( ( F @ X )
% 1.44/1.29 = X ) ).
% 1.44/1.29 ------------------------
% 1.61/1.30 % (6590)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_6400 for (3000ds/4Mi)
% 1.61/1.30 % (6594)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_6400 for (3000ds/275Mi)
% 1.61/1.30 % (6592)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6400 for (3000ds/2Mi)
% 1.61/1.31 % (6590)Instruction limit reached!
% 1.61/1.31 % (6590)------------------------------
% 1.61/1.31 % (6590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (6590)Termination reason: Unknown
% 1.61/1.31 % (6590)Termination phase: Saturation
% 1.61/1.31
% 1.61/1.31 % (6590)Memory used [KB]: 5500
% 1.61/1.31 % (6590)Time elapsed: 0.003 s
% 1.61/1.31 % (6590)Instructions burned: 4 (million)
% 1.61/1.31 % (6590)------------------------------
% 1.61/1.31 % (6590)------------------------------
% 1.61/1.31 % (6592)Instruction limit reached!
% 1.61/1.31 % (6592)------------------------------
% 1.61/1.31 % (6592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (6592)Termination reason: Unknown
% 1.61/1.31 % (6592)Termination phase: Saturation
% 1.61/1.31
% 1.61/1.31 % (6592)Memory used [KB]: 5500
% 1.61/1.31 % (6592)Time elapsed: 0.002 s
% 1.61/1.31 % (6592)Instructions burned: 2 (million)
% 1.61/1.31 % (6592)------------------------------
% 1.61/1.31 % (6592)------------------------------
% 1.61/1.31 % (6594)First to succeed.
% 1.61/1.31 % (6595)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6400 for (3000ds/18Mi)
% 1.61/1.31 % (6594)Refutation found. Thanks to Tanya!
% 1.61/1.31 % SZS status Theorem for DTF2THF_6400
% 1.61/1.31 % SZS output start Proof for DTF2THF_6400
% 1.61/1.31 thf(func_def_3, type, sK0: ($o > $o) > $o).
% 1.61/1.31 thf(func_def_5, type, ph2: !>[X0: $tType]:(X0)).
% 1.61/1.31 thf(f94,plain,(
% 1.61/1.31 $false),
% 1.61/1.31 inference(trivial_inequality_removal,[status(thm)],[f93])).
% 1.61/1.31 thf(f93,plain,(
% 1.61/1.31 ($true = $false)),
% 1.61/1.31 inference(boolean_simplification,[status(thm)],[f92])).
% 1.61/1.31 thf(f92,plain,(
% 1.61/1.31 ($false = (~ $false))),
% 1.61/1.31 inference(trivial_inequality_removal,[status(thm)],[f90])).
% 1.61/1.31 thf(f90,plain,(
% 1.61/1.31 ($true = $false) | ($false = (~ $false))),
% 1.61/1.31 inference(superposition,[status(thm)],[f9,f86])).
% 1.61/1.31 thf(f86,plain,(
% 1.61/1.31 ($false = (sK0 @ ~))),
% 1.61/1.31 inference(duplicate_literal_removal,[status(thm)],[f85])).
% 1.61/1.31 thf(f85,plain,(
% 1.61/1.31 ($false = (sK0 @ ~)) | ($false = (sK0 @ ~))),
% 1.61/1.31 inference(beta_eta_normalization,[status(thm)],[f70])).
% 1.61/1.31 thf(f70,plain,(
% 1.61/1.31 (((^[Y0 : $o]: (Y0)) @ (sK0 @ (^[Y0 : $o]: (~ ((^[Y1 : $o]: (Y1)) @ Y0))))) = $false) | ($false = (sK0 @ (^[Y0 : $o]: (~ ((^[Y1 : $o]: (Y1)) @ Y0)))))),
% 1.61/1.31 inference(primitive_instantiation,[status(thm)],[f19])).
% 1.61/1.31 thf(f19,plain,(
% 1.61/1.31 ( ! [X3 : $o > $o] : (($false = (X3 @ (sK0 @ (^[Y0 : $o]: (~ (X3 @ Y0)))))) | ((sK0 @ (^[Y0 : $o]: (~ (X3 @ Y0)))) = $false)) )),
% 1.61/1.31 inference(not_proxy_clausification,[status(thm)],[f18])).
% 1.61/1.31 thf(f18,plain,(
% 1.61/1.31 ( ! [X3 : $o > $o] : (($true = (~ (X3 @ (sK0 @ (^[Y0 : $o]: (~ (X3 @ Y0))))))) | ((sK0 @ (^[Y0 : $o]: (~ (X3 @ Y0)))) = $false)) )),
% 1.61/1.31 inference(beta_eta_normalization,[status(thm)],[f13])).
% 1.61/1.31 thf(f13,plain,(
% 1.61/1.31 ( ! [X3 : $o > $o] : (($true = ((^[Y0 : $o]: (~ (X3 @ Y0))) @ (sK0 @ (^[Y0 : $o]: (~ (X3 @ Y0)))))) | ((sK0 @ (^[Y0 : $o]: (~ (X3 @ Y0)))) = $false)) )),
% 1.61/1.31 inference(primitive_instantiation,[status(thm)],[f8])).
% 1.61/1.31 thf(f8,plain,(
% 1.61/1.31 ( ! [X0 : $o > $o] : (((X0 @ (sK0 @ X0)) = $true) | ($false = (sK0 @ X0))) )),
% 1.61/1.31 inference(binary_proxy_clausification,[status(thm)],[f7])).
% 1.61/1.31 thf(f7,plain,(
% 1.61/1.31 ( ! [X0 : $o > $o] : (((X0 @ (sK0 @ X0)) = (sK0 @ X0))) )),
% 1.61/1.31 inference(cnf_transformation,[status(thm)],[f6])).
% 1.61/1.31 thf(f6,plain,(
% 1.61/1.31 ! [X0 : $o > $o] : ((X0 @ (sK0 @ X0)) = (sK0 @ X0))),
% 1.61/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f4,f5])).
% 1.61/1.31 thf(f5,plain,(
% 1.61/1.31 ! [X0 : $o > $o] : (? [X1 : $o] : ((X0 @ X1) = X1) => ((X0 @ (sK0 @ X0)) = (sK0 @ X0)))),
% 1.61/1.31 introduced(definition,[],[choice_axiom])).
% 1.61/1.31 thf(f4,plain,(
% 1.61/1.31 ! [X0 : $o > $o] : ? [X1 : $o] : ((X0 @ X1) = X1)),
% 1.61/1.31 inference(flattening,[status(thm)],[f2])).
% 1.61/1.31 thf(f2,negated_conjecture,(
% 1.61/1.31 ~~! [X0 : $o > $o] : ? [X1 : $o] : ((X0 @ X1) = X1)),
% 1.61/1.31 inference(negated_conjecture,[status(cth)],[f1])).
% 1.61/1.31 thf(f1,conjecture,(
% 1.61/1.31 ~! [X0 : $o > $o] : ? [X1 : $o] : ((X0 @ X1) = X1)),
% 1.61/1.31 file('/export/starexec/sandbox/tmp/tmp.HAhfTKKXAv/DTF2THF_6400.p',conj)).
% 1.61/1.31 thf(f9,plain,(
% 1.61/1.31 ( ! [X0 : $o > $o] : (((X0 @ (sK0 @ X0)) = $false) | ($true = (sK0 @ X0))) )),
% 1.61/1.31 inference(binary_proxy_clausification,[status(thm)],[f7])).
% 1.61/1.31 % SZS output end Proof for DTF2THF_6400
% 1.61/1.31 % (6594)------------------------------
% 1.61/1.31 % (6594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (6594)Termination reason: Refutation
% 1.61/1.31
% 1.61/1.31 % (6594)Memory used [KB]: 5500
% 1.61/1.31 % (6594)Time elapsed: 0.004 s
% 1.61/1.31 % (6594)Instructions burned: 3 (million)
% 1.61/1.31 % (6594)------------------------------
% 1.61/1.31 % (6594)------------------------------
% 1.61/1.31 % (6588)Success in time 0.012 s
%------------------------------------------------------------------------------