%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYN991^1 : 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 : n022.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 : Unsatisfiable 1.50s 1.35s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 17 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 45 ( 14 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 59 ( 0 ~; 0 |; 0 &; 49 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 40 ( 40 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 2 usr; 3 con; 0-2 aty)
% ( 10 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 30 ( 19 ^; 11 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
refl: ( $i > $i > $o ) > $o ).
thf(func_def_10,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f23,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f22]) ).
thf(f22,plain,
$false = $true,
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
! [X2: $i] :
( ( ^ [Y0: $i,Y1: $i] : $false
@ X2
@ X2 )
= $true ),
inference(primitive_instantiation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X2: $i,X1: $i > $i > $o] :
( $true
= ( X1 @ X2 @ X2 ) ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
! [X2: $i,X1: $i > $i > $o] :
( $true
= ( ^ [Y0: $i] : ( X1 @ Y0 @ Y0 )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
! [X1: $i > $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( X1 @ Y0 @ Y0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
! [X1: $i > $i > $o] :
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( $true
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,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,f8]) ).
thf(f8,plain,
( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,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.m5DdPNh2hR/DTF2THF_8608.p',refl) ).
thf(f9,plain,
( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] : ( refl @ Y0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] : ( refl @ Y0 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $i > $i > $o] : ( refl @ X0 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $i > $i > $o] : ( refl @ X0 ),
file('/export/starexec/sandbox/tmp/tmp.m5DdPNh2hR/DTF2THF_8608.p',ax) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYN991^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.30 % Computer : n022.cluster.edu
% 0.13/0.30 % Model : x86_64 x86_64
% 0.13/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.30 % Memory : 8042.1875MB
% 0.13/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.30 % CPULimit : 300
% 0.13/0.30 % WCLimit : 300
% 0.13/0.30 % DateTime : Tue Feb 24 14:21:06 EST 2026
% 0.13/0.30 % CPUTime :
% 0.13/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.40 ---- Original DTF file ---
% 0.17/0.40 thf(spec,logic,$$dhol).
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 % File : SYN991^1 : TPTP v9.2.1. Released v3.7.0.
% 0.17/0.40 % Domain : Syntactic
% 0.17/0.40 % Problem : Inconsistency of axioms that says all relations are reflexive
% 0.17/0.40 % Version : Especial.
% 0.17/0.40 % English :
% 0.17/0.40
% 0.17/0.40 % Refs : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.17/0.40 % Source : [Ben09]
% 0.17/0.40 % Names :
% 0.17/0.40
% 0.17/0.40 % Status : Unsatisfiable
% 0.17/0.40 % Rating : 0.00 v3.7.0
% 0.17/0.40 % Syntax : Number of formulae : 3 ( 2 unt; 1 typ; 1 def)
% 0.17/0.40 % Number of atoms : 3 ( 1 equ; 0 cnn)
% 0.17/0.40 % Maximal formula atoms : 1 ( 1 avg)
% 0.17/0.40 % Number of connectives : 3 ( 0 ~; 0 |; 0 &; 3 @)
% 0.17/0.40 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.17/0.40 % Maximal formula depth : 3 ( 2 avg)
% 0.17/0.40 % Number of types : 2 ( 0 usr)
% 0.17/0.40 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.17/0.40 % Number of symbols : 2 ( 1 usr; 0 con; 1-2 aty)
% 0.17/0.40 % Number of variables : 3 ( 1 ^; 2 !; 0 ?; 3 :)
% 0.17/0.40 % SPC : TH0_UNS_EQU_NAR
% 0.17/0.40
% 0.17/0.40 % Comments : Set instantiation required
% 0.17/0.40 % :
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 thf(refl_type,type,
% 0.17/0.40 refl: ( $i > $i > $o ) > $o ).
% 0.17/0.40
% 0.17/0.40 thf(refl,definition,
% 0.17/0.40 ( refl
% 0.17/0.40 = ( ^ [R: $i > $i > $o] :
% 0.17/0.40 ! [X: $i] : ( R @ X @ X ) ) ) ).
% 0.17/0.40
% 0.17/0.40 thf(ax,axiom,
% 0.17/0.40 ! [R: $i > $i > $o] : ( refl @ R ) ).
% 0.17/0.40
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 ------------------------
% 1.50/1.33 ---- Embedded in THF ---
% 1.50/1.33 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.33 %%% Generated on Tue Feb 24 14:21:07 EST 2026
% 1.50/1.33 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.33 %%% Logic specification used:
% 1.50/1.33 %%% thf(spec, logic, $$dhol).
% 1.50/1.33
% 1.50/1.33 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.m5DdPNh2hR/DTF2DTF8608.p
% See solution above
% 1.50/1.33 ------------------------
% 1.50/1.34 ---- Cleaned THF ---
% 1.50/1.34 thf(refl_type,type,
% 1.50/1.34 refl: ( $i > $i > $o ) > $o ).
% 1.50/1.34
% 1.50/1.34 thf(refl,definition,
% 1.50/1.34 ( refl
% 1.50/1.34 = ( ^ [R: $i > $i > $o] :
% 1.50/1.34 ! [X: $i] : ( R @ X @ X ) ) ) ).
% 1.50/1.34
% 1.50/1.34 thf(ax,axiom,
% 1.50/1.34 ! [R: $i > $i > $o] : ( refl @ R ) ).
% 1.50/1.34 ------------------------
% 1.50/1.35 % (8707)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_8608 for (3000ds/4Mi)
% 1.50/1.35 % (8707)First to succeed.
% 1.50/1.35 % (8707)Refutation found. Thanks to Tanya!
% 1.50/1.35 % SZS status Unsatisfiable for DTF2THF_8608
% 1.50/1.35 % SZS output start Proof for DTF2THF_8608
% 1.50/1.35 thf(func_def_0, type, refl: ($i > $i > $o) > $o).
% 1.50/1.35 thf(func_def_10, type, ph1: !>[X0: $tType]:(X0)).
% 1.50/1.35 thf(f23,plain,(
% 1.50/1.35 $false),
% 1.50/1.35 inference(trivial_inequality_removal,[status(thm)],[f22])).
% 1.50/1.35 thf(f22,plain,(
% 1.50/1.35 ($false = $true)),
% 1.50/1.35 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.50/1.35 thf(f20,plain,(
% 1.50/1.35 ( ! [X2 : $i] : ((((^[Y0 : $i]: ((^[Y1 : $i]: ($false)))) @ X2 @ X2) = $true)) )),
% 1.50/1.35 inference(primitive_instantiation,[status(thm)],[f15])).
% 1.50/1.35 thf(f15,plain,(
% 1.50/1.35 ( ! [X2 : $i,X1 : $i > $i > $o] : (($true = (X1 @ X2 @ X2))) )),
% 1.50/1.35 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.50/1.35 thf(f14,plain,(
% 1.50/1.35 ( ! [X2 : $i,X1 : $i > $i > $o] : (($true = ((^[Y0 : $i]: (X1 @ Y0 @ Y0)) @ X2))) )),
% 1.50/1.35 inference(pi_clausification,[status(thm)],[f13])).
% 1.50/1.35 thf(f13,plain,(
% 1.50/1.35 ( ! [X1 : $i > $i > $o] : (($true = (!! @ $i @ (^[Y0 : $i]: (X1 @ Y0 @ Y0))))) )),
% 1.50/1.35 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.50/1.35 thf(f12,plain,(
% 1.50/1.35 ( ! [X1 : $i > $i > $o] : (($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ X1))) )),
% 1.50/1.35 inference(pi_clausification,[status(thm)],[f11])).
% 1.50/1.35 thf(f11,plain,(
% 1.50/1.35 ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))))),
% 1.50/1.35 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.50/1.35 thf(f10,plain,(
% 1.50/1.35 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (Y1 @ Y2 @ Y2)))) @ Y0))) = $true)),
% 1.50/1.35 inference(definition_unfolding,[status(thm)],[f9,f8])).
% 1.50/1.35 thf(f8,plain,(
% 1.50/1.35 (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 1.50/1.35 inference(cnf_transformation,[status(thm)],[f5])).
% 1.50/1.35 thf(f5,plain,(
% 1.50/1.35 (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 1.50/1.35 inference(fool_elimination,[status(thm)],[f4])).
% 1.50/1.35 thf(f4,plain,(
% 1.50/1.35 ((^[X0 : $i > $i > $o] : (! [X1 : $i] : (X0 @ X1 @ X1))) = refl)),
% 1.50/1.35 inference(rectify,[status(thm)],[f1])).
% 1.50/1.35 thf(f1,axiom,(
% 1.50/1.35 ((^[X0 : $i > $i > $o] : (! [X1 : $i] : (X0 @ X1 @ X1))) = refl)),
% 1.50/1.35 file('/export/starexec/sandbox/tmp/tmp.m5DdPNh2hR/DTF2THF_8608.p',refl)).
% 1.50/1.35 thf(f9,plain,(
% 1.50/1.35 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (refl @ Y0))) = $true)),
% 1.50/1.35 inference(cnf_transformation,[status(thm)],[f7])).
% 1.50/1.35 thf(f7,plain,(
% 1.50/1.35 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (refl @ Y0))) = $true)),
% 1.50/1.35 inference(fool_elimination,[status(thm)],[f6])).
% 1.50/1.35 thf(f6,plain,(
% 1.50/1.35 ! [X0 : $i > $i > $o] : (refl @ X0)),
% 1.50/1.35 inference(rectify,[status(thm)],[f2])).
% 1.50/1.35 thf(f2,axiom,(
% 1.50/1.35 ! [X0 : $i > $i > $o] : (refl @ X0)),
% 1.50/1.35 file('/export/starexec/sandbox/tmp/tmp.m5DdPNh2hR/DTF2THF_8608.p',ax)).
% 1.50/1.35 % SZS output end Proof for DTF2THF_8608
% 1.50/1.35 % (8707)------------------------------
% 1.50/1.35 % (8707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.35 % (8707)Termination reason: Refutation
% 1.50/1.35
% 1.50/1.35 % (8707)Memory used [KB]: 5500
% 1.50/1.35 % (8707)Time elapsed: 0.003 s
% 1.50/1.35 % (8707)Instructions burned: 1 (million)
% 1.50/1.35 % (8707)------------------------------
% 1.50/1.35 % (8707)------------------------------
% 1.50/1.35 % (8705)Success in time 0.002 s
%------------------------------------------------------------------------------