%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYN992^1 : TPTP v9.2.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:51:41 AM UTC 2026
% Result : Theorem 1.47s 1.30s
% Output : Refutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 20 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 57 ( 22 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 81 ( 6 ~; 0 |; 0 &; 63 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 46 ( 46 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 3 usr; 4 con; 0-2 aty)
% ( 7 !!; 5 ??; 0 @@+; 0 @@-)
% Number of variables : 38 ( 29 ^; 6 !; 3 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
refl: ( $i > $i > $o ) > $o ).
thf(func_def_11,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
sK2: ( $i > $i > $o ) > $i ).
thf(f25,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f24]) ).
thf(f24,plain,
$false = $true,
inference(boolean_simplification,[status(thm)],[f23]) ).
thf(f23,plain,
( $false
= ( ( sK2
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
( $false
= ( ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 )
@ ( sK2
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) )
@ ( sK2
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) ) ) ),
inference(primitive_instantiation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X1: $i > $i > $o] :
( $false
= ( X1 @ ( sK2 @ X1 ) @ ( sK2 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
! [X1: $i > $i > $o] :
( $false
= ( ^ [Y0: $i] : ( X1 @ Y0 @ Y0 )
@ ( sK2 @ X1 ) ) ),
inference(sigma_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
! [X1: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] : ( X1 @ Y0 @ Y0 ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
! [X1: $i > $i > $o] :
( $false
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( $false
= ( ?? @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ~ ( ?? @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ~ ( ?? @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 @ Y2 ) )
@ Y0 ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f9,f10]) ).
thf(f10,plain,
( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= refl ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= refl ),
file('/export/starexec/sandbox/tmp/tmp.9yNtMQBlgc/DTF2THF_15285.p',refl) ).
thf(f9,plain,
( $true
= ( ~ ( ?? @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] : ( refl @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( ?? @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] : ( refl @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: $i > $i > $o] : ( refl @ X0 ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ? [X0: $i > $i > $o] : ( refl @ X0 ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
? [X0: $i > $i > $o] : ( refl @ X0 ),
file('/export/starexec/sandbox/tmp/tmp.9yNtMQBlgc/DTF2THF_15285.p',ax) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN992^1 : TPTP v9.2.1. Bugfixed v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n021.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 14:21:09 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
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : SYN992^1 : TPTP v9.2.1. Bugfixed v4.0.0.
% 0.19/0.46 % Domain : Syntactic
% 0.19/0.46 % Problem : There exists a reflexive relation
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English :
% 0.19/0.46
% 0.19/0.46 % Refs : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Ben09]
% 0.19/0.46 % Names :
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.12 v7.1.0, 0.00 v6.2.0, 0.29 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.19/0.46 % Syntax : Number of formulae : 3 ( 2 unt; 1 typ; 1 def)
% 0.19/0.46 % Number of atoms : 3 ( 1 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.19/0.46 % Number of connectives : 3 ( 0 ~; 0 |; 0 &; 3 @)
% 0.19/0.46 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 3 ( 2 avg)
% 0.19/0.46 % Number of types : 2 ( 0 usr)
% 0.19/0.46 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 2 ( 1 usr; 0 con; 1-2 aty)
% 0.19/0.46 % Number of variables : 3 ( 1 ^; 1 !; 1 ?; 3 :)
% 0.19/0.46 % SPC : TH0_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : Set instantiation required
% 0.19/0.46 % :
% 0.19/0.46 % Bugfixes : v4.0.0 - Fixed conjecture.
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(refl_type,type,
% 0.19/0.46 refl: ( $i > $i > $o ) > $o ).
% 0.19/0.46
% 0.19/0.46 thf(refl,definition,
% 0.19/0.46 ( refl
% 0.19/0.46 = ( ^ [R: $i > $i > $o] :
% 0.19/0.46 ! [X: $i] : ( R @ X @ X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(ax,conjecture,
% 0.19/0.46 ? [R: $i > $i > $o] : ( refl @ R ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.47/1.27 ---- Embedded in THF ---
% 1.47/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.27 %%% Generated on Tue Feb 24 14:21:09 EST 2026
% 1.47/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.27 %%% Logic specification used:
% 1.47/1.27 %%% thf(spec, logic, $$dhol).
% 1.47/1.27
% 1.47/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.9yNtMQBlgc/DTF2DTF15285.p
% See solution above
% 1.47/1.27 ------------------------
% 1.47/1.28 ---- Cleaned THF ---
% 1.47/1.28 thf(refl_type,type,
% 1.47/1.28 refl: ( $i > $i > $o ) > $o ).
% 1.47/1.28
% 1.47/1.28 thf(refl,definition,
% 1.47/1.28 ( refl
% 1.47/1.28 = ( ^ [R: $i > $i > $o] :
% 1.47/1.28 ! [X: $i] : ( R @ X @ X ) ) ) ).
% 1.47/1.28
% 1.47/1.28 thf(ax,conjecture,
% 1.47/1.28 ? [R: $i > $i > $o] : ( refl @ R ) ).
% 1.47/1.28 ------------------------
% 1.47/1.29 % (15475)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_15285 for (2999ds/27Mi)
% 1.47/1.29 % (15477)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_15285 for (2999ds/2Mi)
% 1.47/1.29 % (15475)Refutation not found, incomplete strategy
% 1.47/1.29 % (15475)------------------------------
% 1.47/1.29 % (15475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (15475)Termination reason: Refutation not found, incomplete strategy
% 1.47/1.29
% 1.47/1.29
% 1.47/1.29 % (15475)Memory used [KB]: 5500
% 1.47/1.29 % (15475)Time elapsed: 0.002 s
% 1.47/1.29 % (15475)Instructions burned: 1 (million)
% 1.47/1.29 % (15475)------------------------------
% 1.47/1.29 % (15475)------------------------------
% 1.47/1.29 % (15477)First to succeed.
% 1.47/1.30 % (15477)Refutation found. Thanks to Tanya!
% 1.47/1.30 % SZS status Theorem for DTF2THF_15285
% 1.47/1.30 % SZS output start Proof for DTF2THF_15285
% 1.47/1.30 thf(func_def_0, type, refl: ($i > $i > $o) > $o).
% 1.47/1.30 thf(func_def_11, type, ph1: !>[X0: $tType]:(X0)).
% 1.47/1.30 thf(func_def_12, type, sK2: ($i > $i > $o) > $i).
% 1.47/1.30 thf(f25,plain,(
% 1.47/1.30 $false),
% 1.47/1.30 inference(trivial_inequality_removal,[status(thm)],[f24])).
% 1.47/1.30 thf(f24,plain,(
% 1.47/1.30 ($false = $true)),
% 1.47/1.30 inference(boolean_simplification,[status(thm)],[f23])).
% 1.47/1.30 thf(f23,plain,(
% 1.47/1.30 ($false = ((sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))))))),
% 1.47/1.30 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.47/1.30 thf(f18,plain,(
% 1.47/1.30 ($false = ((^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))) @ (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))) @ (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))))))),
% 1.47/1.30 inference(primitive_instantiation,[status(thm)],[f17])).
% 1.47/1.30 thf(f17,plain,(
% 1.47/1.30 ( ! [X1 : $i > $i > $o] : (($false = (X1 @ (sK2 @ X1) @ (sK2 @ X1)))) )),
% 1.47/1.30 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.47/1.30 thf(f16,plain,(
% 1.47/1.30 ( ! [X1 : $i > $i > $o] : (($false = ((^[Y0 : $i]: (X1 @ Y0 @ Y0)) @ (sK2 @ X1)))) )),
% 1.47/1.30 inference(sigma_clausification,[status(thm)],[f15])).
% 1.47/1.30 thf(f15,plain,(
% 1.47/1.30 ( ! [X1 : $i > $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (X1 @ Y0 @ Y0))) = $false)) )),
% 1.47/1.30 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.47/1.30 thf(f14,plain,(
% 1.47/1.30 ( ! [X1 : $i > $i > $o] : (($false = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ X1))) )),
% 1.47/1.30 inference(pi_clausification,[status(thm)],[f13])).
% 1.47/1.30 thf(f13,plain,(
% 1.47/1.30 ($false = (?? @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))))),
% 1.47/1.30 inference(not_proxy_clausification,[status(thm)],[f12])).
% 1.47/1.30 thf(f12,plain,(
% 1.47/1.30 ((~ (?? @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) = $true)),
% 1.47/1.30 inference(beta_eta_normalization,[status(thm)],[f11])).
% 1.47/1.30 thf(f11,plain,(
% 1.47/1.30 ((~ (?? @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (Y1 @ Y2 @ Y2)))) @ Y0)))) = $true)),
% 1.47/1.30 inference(definition_unfolding,[status(thm)],[f9,f10])).
% 1.47/1.30 thf(f10,plain,(
% 1.47/1.30 (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 1.47/1.30 inference(cnf_transformation,[status(thm)],[f8])).
% 1.47/1.30 thf(f8,plain,(
% 1.47/1.30 (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 1.47/1.30 inference(fool_elimination,[status(thm)],[f7])).
% 1.47/1.30 thf(f7,plain,(
% 1.47/1.30 ((^[X0 : $i > $i > $o] : (! [X1 : $i] : (X0 @ X1 @ X1))) = refl)),
% 1.47/1.30 inference(rectify,[status(thm)],[f1])).
% 1.47/1.30 thf(f1,axiom,(
% 1.47/1.30 ((^[X0 : $i > $i > $o] : (! [X1 : $i] : (X0 @ X1 @ X1))) = refl)),
% 1.47/1.30 file('/export/starexec/sandbox/tmp/tmp.9yNtMQBlgc/DTF2THF_15285.p',refl)).
% 1.47/1.30 thf(f9,plain,(
% 1.47/1.30 ($true = (~ (?? @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (refl @ Y0)))))),
% 1.47/1.30 inference(cnf_transformation,[status(thm)],[f6])).
% 1.47/1.30 thf(f6,plain,(
% 1.47/1.30 ($true = (~ (?? @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (refl @ Y0)))))),
% 1.47/1.30 inference(fool_elimination,[status(thm)],[f5])).
% 1.47/1.30 thf(f5,plain,(
% 1.47/1.30 ~? [X0 : $i > $i > $o] : (refl @ X0)),
% 1.47/1.30 inference(rectify,[status(thm)],[f3])).
% 1.47/1.30 thf(f3,negated_conjecture,(
% 1.47/1.30 ~? [X0 : $i > $i > $o] : (refl @ X0)),
% 1.47/1.30 inference(negated_conjecture,[status(cth)],[f2])).
% 1.47/1.30 thf(f2,conjecture,(
% 1.47/1.30 ? [X0 : $i > $i > $o] : (refl @ X0)),
% 1.47/1.30 file('/export/starexec/sandbox/tmp/tmp.9yNtMQBlgc/DTF2THF_15285.p',ax)).
% 1.47/1.30 % SZS output end Proof for DTF2THF_15285
% 1.47/1.30 % (15477)------------------------------
% 1.47/1.30 % (15477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.30 % (15477)Termination reason: Refutation
% 1.47/1.30
% 1.47/1.30 % (15477)Memory used [KB]: 5500
% 1.47/1.30 % (15477)Time elapsed: 0.002 s
% 1.47/1.30 % (15477)Instructions burned: 1 (million)
% 1.47/1.30 % (15477)------------------------------
% 1.47/1.30 % (15477)------------------------------
% 1.47/1.30 % (15472)Success in time 0.002 s
%------------------------------------------------------------------------------