%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV179^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n029.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 09:40:29 AM UTC 2026
% Result : Theorem 1.63s 1.36s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 139 ( 59 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 279 ( 41 ~; 4 |; 25 &; 189 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 72 ( 72 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 6 usr; 3 con; 0-2 aty)
% ( 0 !!; 19 ??; 0 @@+; 0 @@-)
% Number of variables : 60 ( 46 ^; 10 !; 4 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cD_FOR_X5309: ( ( $i > $o ) > $i ) > $i > $o ).
thf(func_def_12,type,
sK0: ( $i > $o ) > $i ).
thf(func_def_14,type,
ph2:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
sK3: $i > $o ).
thf(func_def_16,type,
sK4: $i > $o ).
thf(func_def_17,type,
sK5: $i > $o ).
thf(f66,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f65]) ).
thf(f65,plain,
$true = $false,
inference(superposition,[status(thm)],[f27,f54]) ).
thf(f54,plain,
( $true
= ( sK3 @ ( sK0 @ sK3 ) ) ),
inference(equality_resolution,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: $i > $o] :
( ( ( sK0 @ X0 )
!= ( sK0 @ sK3 ) )
| ( $true
= ( X0 @ ( sK0 @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f20,f28]) ).
thf(f28,plain,
( ( sK0 @ sK3 )
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( $true
= ( ( sK0 @ sK3 )
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( $true
= ( ~ ( sK3 @ ( sK0 @ sK3 ) )
& ( ( sK0 @ sK3 )
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f23]) ).
thf(f23,plain,
( $true
= ( ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK0 @ Y0 ) )
& ( ( sK0 @ Y0 )
= ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK0 @ Y2 ) )
& ( ( sK0 @ Y2 )
= Y1 ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( $true
= ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK0 @ Y0 ) )
& ( ( sK0 @ Y0 )
= ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK0 @ Y2 ) )
& ( ( sK0 @ Y2 )
= Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f21]) ).
thf(f21,plain,
( $true
= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) )
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ) ),
inference(equality_resolution,[status(thm)],[f20]) ).
thf(f20,plain,
! [X1: $i > $o] :
( ( ( sK0 @ X1 )
!= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) )
| ( $true
= ( X1 @ ( sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
! [X1: $i > $o] :
( ( ( sK0 @ X1 )
!= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) )
| ( $false
= ( ~ ( X1 @ ( sK0 @ X1 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
! [X1: $i > $o] :
( ( $false
= ( ( sK0 @ X1 )
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ) )
| ( $false
= ( ~ ( X1 @ ( sK0 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
! [X1: $i > $o] :
( $false
= ( ~ ( X1 @ ( sK0 @ X1 ) )
& ( ( sK0 @ X1 )
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
! [X1: $i > $o] :
( $false
= ( ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK0 @ Y0 ) )
& ( ( sK0 @ Y0 )
= ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK0 @ Y2 ) )
& ( ( sK0 @ Y2 )
= Y1 ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( $true
!= ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK0 @ Y0 ) )
& ( ( sK0 @ Y0 )
= ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK0 @ Y2 ) )
& ( ( sK0 @ Y2 )
= Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( $true
!= ( ^ [Y0: ( $i > $o ) > $i,Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( Y0 @ Y2 ) )
& ( ( Y0 @ Y2 )
= Y1 ) ) )
@ sK0
@ ( sK0
@ ( ^ [Y0: ( $i > $o ) > $i,Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( Y0 @ Y2 ) )
& ( ( Y0 @ Y2 )
= Y1 ) ) )
@ sK0 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f12,f13,f13]) ).
thf(f13,plain,
( cD_FOR_X5309
= ( ^ [Y0: ( $i > $o ) > $i,Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( Y0 @ Y2 ) )
& ( ( Y0 @ Y2 )
= Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( cD_FOR_X5309
= ( ^ [Y0: ( $i > $o ) > $i,Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( Y0 @ Y2 ) )
& ( ( Y0 @ Y2 )
= Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [X0: ( $i > $o ) > $i,X1: $i] :
? [X2: $i > $o] :
( ( ( X0 @ X2 )
= X1 )
& ~ ( X2 @ ( X0 @ X2 ) ) ) )
= cD_FOR_X5309 ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: ( $i > $o ) > $i,X1: $i] :
? [X2: $i > $o] :
( ( ( X0 @ X2 )
= X1 )
& ~ ( X2 @ ( X0 @ X2 ) ) ) )
= cD_FOR_X5309 ),
file('/export/starexec/sandbox2/tmp/tmp.ZOePTMN8LZ/DTF2THF_15910.p',cD_FOR_X5309_def) ).
thf(f12,plain,
( $true
!= ( cD_FOR_X5309 @ sK0 @ ( sK0 @ ( cD_FOR_X5309 @ sK0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( $true
!= ( cD_FOR_X5309 @ sK0 @ ( sK0 @ ( cD_FOR_X5309 @ sK0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10]) ).
thf(f10,plain,
( ? [X0: ( $i > $o ) > $i] :
( ( cD_FOR_X5309 @ X0 @ ( X0 @ ( cD_FOR_X5309 @ X0 ) ) )
!= $true )
=> ( $true
!= ( cD_FOR_X5309 @ sK0 @ ( sK0 @ ( cD_FOR_X5309 @ sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: ( $i > $o ) > $i] :
( ( cD_FOR_X5309 @ X0 @ ( X0 @ ( cD_FOR_X5309 @ X0 ) ) )
!= $true ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: ( $i > $o ) > $i] :
( ( cD_FOR_X5309 @ X0 @ ( X0 @ ( cD_FOR_X5309 @ X0 ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: ( $i > $o ) > $i] : ( cD_FOR_X5309 @ X0 @ ( X0 @ ( cD_FOR_X5309 @ X0 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X0: ( $i > $o ) > $i] : ( cD_FOR_X5309 @ X0 @ ( X0 @ ( cD_FOR_X5309 @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X0: ( $i > $o ) > $i] : ( cD_FOR_X5309 @ X0 @ ( X0 @ ( cD_FOR_X5309 @ X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ZOePTMN8LZ/DTF2THF_15910.p',cTHM144C_pme) ).
thf(f27,plain,
( $false
= ( sK3 @ ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( $true
= ( ~ ( sK3 @ ( sK0 @ sK3 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV179^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n029.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 12:41:29 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/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 : SEV179^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.19/0.46 % Domain : Set Theory (Sets of sets)
% 0.19/0.46 % Problem : TPS problem from CANTOR-THMS
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English :
% 0.19/0.46
% 0.19/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Bro09]
% 0.19/0.46 % Names : tps_0598 [Bro09]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.40 v5.2.0
% 0.19/0.46 % Syntax : Number of formulae : 3 ( 1 unt; 1 typ; 1 def)
% 0.19/0.46 % Number of atoms : 5 ( 2 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 2 ( 2 avg)
% 0.19/0.46 % Number of connectives : 9 ( 1 ~; 0 |; 1 &; 7 @)
% 0.19/0.46 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 5 ( 3 avg)
% 0.19/0.46 % Number of types : 2 ( 0 usr)
% 0.19/0.46 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 2 ( 1 usr; 0 con; 2-2 aty)
% 0.19/0.46 % Number of variables : 4 ( 2 ^; 1 !; 1 ?; 4 :)
% 0.19/0.46 % SPC : TH0_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.46 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(cD_FOR_X5309_type,type,
% 0.19/0.46 cD_FOR_X5309: ( ( $i > $o ) > $i ) > $i > $o ).
% 0.19/0.46
% 0.19/0.46 thf(cD_FOR_X5309_def,definition,
% 0.19/0.46 ( cD_FOR_X5309
% 0.19/0.46 = ( ^ [Xh: ( $i > $o ) > $i,Xz: $i] :
% 0.19/0.46 ? [Xt: $i > $o] :
% 0.19/0.46 ( ~ ( Xt @ ( Xh @ Xt ) )
% 0.19/0.46 & ( Xz
% 0.19/0.46 = ( Xh @ Xt ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(cTHM144C_pme,conjecture,
% 0.19/0.46 ! [Xh: ( $i > $o ) > $i] : ( cD_FOR_X5309 @ Xh @ ( Xh @ ( cD_FOR_X5309 @ Xh ) ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.63/1.33 ---- Embedded in THF ---
% 1.63/1.33 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.63/1.33 %%% Generated on Tue Feb 24 12:41:30 EST 2026
% 1.63/1.33 %%% using '$$dhol' embedding, version 1.3.0.
% 1.63/1.33 %%% Logic specification used:
% 1.63/1.33 %%% thf(spec, logic, $$dhol).
% 1.63/1.33
% 1.63/1.33 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.ZOePTMN8LZ/DTF2DTF15910.p
% See solution above
% 1.63/1.33 ------------------------
% 1.63/1.34 ---- Cleaned THF ---
% 1.63/1.34 thf(cD_FOR_X5309_type,type,
% 1.63/1.34 cD_FOR_X5309: ( ( $i > $o ) > $i ) > $i > $o ).
% 1.63/1.34
% 1.63/1.34 thf(cD_FOR_X5309_def,definition,
% 1.63/1.34 ( cD_FOR_X5309
% 1.63/1.34 = ( ^ [Xh: ( $i > $o ) > $i,Xz: $i] :
% 1.63/1.34 ? [Xt: $i > $o] :
% 1.63/1.34 ( ~ ( Xt @ ( Xh @ Xt ) )
% 1.63/1.34 & ( Xz
% 1.63/1.34 = ( Xh @ Xt ) ) ) ) ) ).
% 1.63/1.34
% 1.63/1.34 thf(cTHM144C_pme,conjecture,
% 1.63/1.34 ! [Xh: ( $i > $o ) > $i] : ( cD_FOR_X5309 @ Xh @ ( Xh @ ( cD_FOR_X5309 @ Xh ) ) ) ).
% 1.63/1.34 ------------------------
% 1.63/1.35 % (16083)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15910 for (3000ds/183Mi)
% 1.63/1.36 % (16083)First to succeed.
% 1.63/1.36 % (16083)Refutation found. Thanks to Tanya!
% 1.63/1.36 % SZS status Theorem for DTF2THF_15910
% 1.63/1.36 % SZS output start Proof for DTF2THF_15910
% 1.63/1.36 thf(func_def_0, type, cD_FOR_X5309: (($i > $o) > $i) > $i > $o).
% 1.63/1.36 thf(func_def_12, type, sK0: ($i > $o) > $i).
% 1.63/1.36 thf(func_def_14, type, ph2: !>[X0: $tType]:(X0)).
% 1.63/1.36 thf(func_def_15, type, sK3: $i > $o).
% 1.63/1.36 thf(func_def_16, type, sK4: $i > $o).
% 1.63/1.36 thf(func_def_17, type, sK5: $i > $o).
% 1.63/1.36 thf(f66,plain,(
% 1.63/1.36 $false),
% 1.63/1.36 inference(trivial_inequality_removal,[status(thm)],[f65])).
% 1.63/1.36 thf(f65,plain,(
% 1.63/1.36 ($true = $false)),
% 1.63/1.36 inference(superposition,[status(thm)],[f27,f54])).
% 1.63/1.36 thf(f54,plain,(
% 1.63/1.36 ($true = (sK3 @ (sK0 @ sK3)))),
% 1.63/1.36 inference(equality_resolution,[status(thm)],[f30])).
% 1.63/1.36 thf(f30,plain,(
% 1.63/1.36 ( ! [X0 : $i > $o] : (((sK0 @ X0) != (sK0 @ sK3)) | ($true = (X0 @ (sK0 @ X0)))) )),
% 1.63/1.36 inference(superposition,[status(thm)],[f20,f28])).
% 1.63/1.36 thf(f28,plain,(
% 1.63/1.36 ((sK0 @ sK3) = (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK0 @ Y1))) & ((sK0 @ Y1) = Y0)))))))),
% 1.63/1.36 inference(equality_proxy_clausification,[status(thm)],[f25])).
% 1.63/1.36 thf(f25,plain,(
% 1.63/1.36 ($true = ((sK0 @ sK3) = (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK0 @ Y1))) & ((sK0 @ Y1) = Y0))))))))),
% 1.63/1.36 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.63/1.36 thf(f24,plain,(
% 1.63/1.36 ($true = ((~ (sK3 @ (sK0 @ sK3))) & ((sK0 @ sK3) = (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK0 @ Y1))) & ((sK0 @ Y1) = Y0)))))))))),
% 1.63/1.36 inference(beta_eta_normalization,[status(thm)],[f23])).
% 1.63/1.36 thf(f23,plain,(
% 1.63/1.36 ($true = ((^[Y0 : $i > $o]: ((~ (Y0 @ (sK0 @ Y0))) & ((sK0 @ Y0) = (sK0 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ (sK0 @ Y2))) & ((sK0 @ Y2) = Y1))))))))) @ sK3))),
% 1.63/1.36 inference(sigma_clausification,[status(thm)],[f22])).
% 1.63/1.36 thf(f22,plain,(
% 1.63/1.36 ($true = (?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (Y0 @ (sK0 @ Y0))) & ((sK0 @ Y0) = (sK0 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ (sK0 @ Y2))) & ((sK0 @ Y2) = Y1)))))))))))),
% 1.63/1.36 inference(beta_eta_normalization,[status(thm)],[f21])).
% 1.63/1.36 thf(f21,plain,(
% 1.63/1.36 ($true = ((^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK0 @ Y1))) & ((sK0 @ Y1) = Y0))))) @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK0 @ Y1))) & ((sK0 @ Y1) = Y0))))))))),
% 1.63/1.36 inference(equality_resolution,[status(thm)],[f20])).
% 1.63/1.36 thf(f20,plain,(
% 1.63/1.36 ( ! [X1 : $i > $o] : (((sK0 @ X1) != (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK0 @ Y1))) & ((sK0 @ Y1) = Y0))))))) | ($true = (X1 @ (sK0 @ X1)))) )),
% 1.63/1.36 inference(not_proxy_clausification,[status(thm)],[f19])).
% 1.63/1.36 thf(f19,plain,(
% 1.63/1.36 ( ! [X1 : $i > $o] : (((sK0 @ X1) != (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK0 @ Y1))) & ((sK0 @ Y1) = Y0))))))) | ($false = (~ (X1 @ (sK0 @ X1))))) )),
% 1.63/1.36 inference(equality_proxy_clausification,[status(thm)],[f18])).
% 1.63/1.36 thf(f18,plain,(
% 1.63/1.36 ( ! [X1 : $i > $o] : (($false = ((sK0 @ X1) = (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK0 @ Y1))) & ((sK0 @ Y1) = Y0)))))))) | ($false = (~ (X1 @ (sK0 @ X1))))) )),
% 1.63/1.36 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.63/1.36 thf(f17,plain,(
% 1.63/1.36 ( ! [X1 : $i > $o] : (($false = ((~ (X1 @ (sK0 @ X1))) & ((sK0 @ X1) = (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK0 @ Y1))) & ((sK0 @ Y1) = Y0)))))))))) )),
% 1.63/1.36 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.63/1.36 thf(f16,plain,(
% 1.63/1.36 ( ! [X1 : $i > $o] : (($false = ((^[Y0 : $i > $o]: ((~ (Y0 @ (sK0 @ Y0))) & ((sK0 @ Y0) = (sK0 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ (sK0 @ Y2))) & ((sK0 @ Y2) = Y1))))))))) @ X1))) )),
% 1.63/1.36 inference(pi_clausification,[status(thm)],[f15])).
% 1.63/1.36 thf(f15,plain,(
% 1.63/1.36 ($true != (?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (Y0 @ (sK0 @ Y0))) & ((sK0 @ Y0) = (sK0 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ (sK0 @ Y2))) & ((sK0 @ Y2) = Y1)))))))))))),
% 1.63/1.36 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.63/1.36 thf(f14,plain,(
% 1.63/1.36 ($true != ((^[Y0 : ($i > $o) > $i]: ((^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ (Y0 @ Y2))) & ((Y0 @ Y2) = Y1))))))) @ sK0 @ (sK0 @ ((^[Y0 : ($i > $o) > $i]: ((^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ (Y0 @ Y2))) & ((Y0 @ Y2) = Y1))))))) @ sK0))))),
% 1.63/1.36 inference(definition_unfolding,[status(thm)],[f12,f13,f13])).
% 1.63/1.36 thf(f13,plain,(
% 1.63/1.36 (cD_FOR_X5309 = (^[Y0 : ($i > $o) > $i]: ((^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ (Y0 @ Y2))) & ((Y0 @ Y2) = Y1))))))))),
% 1.63/1.36 inference(cnf_transformation,[status(thm)],[f8])).
% 1.63/1.36 thf(f8,plain,(
% 1.63/1.36 (cD_FOR_X5309 = (^[Y0 : ($i > $o) > $i]: ((^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ (Y0 @ Y2))) & ((Y0 @ Y2) = Y1))))))))),
% 1.63/1.36 inference(fool_elimination,[status(thm)],[f7])).
% 1.63/1.36 thf(f7,plain,(
% 1.63/1.36 ((^[X0 : ($i > $o) > $i, X1 : $i] : (? [X2 : $i > $o] : (((X0 @ X2) = X1) & ~(X2 @ (X0 @ X2))))) = cD_FOR_X5309)),
% 1.63/1.36 inference(rectify,[status(thm)],[f1])).
% 1.63/1.36 thf(f1,axiom,(
% 1.63/1.36 ((^[X0 : ($i > $o) > $i, X1 : $i] : (? [X2 : $i > $o] : (((X0 @ X2) = X1) & ~(X2 @ (X0 @ X2))))) = cD_FOR_X5309)),
% 1.63/1.36 file('/export/starexec/sandbox2/tmp/tmp.ZOePTMN8LZ/DTF2THF_15910.p',cD_FOR_X5309_def)).
% 1.63/1.36 thf(f12,plain,(
% 1.63/1.36 ($true != (cD_FOR_X5309 @ sK0 @ (sK0 @ (cD_FOR_X5309 @ sK0))))),
% 1.63/1.36 inference(cnf_transformation,[status(thm)],[f11])).
% 1.63/1.36 thf(f11,plain,(
% 1.63/1.36 ($true != (cD_FOR_X5309 @ sK0 @ (sK0 @ (cD_FOR_X5309 @ sK0))))),
% 1.63/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10])).
% 1.63/1.36 thf(f10,plain,(
% 1.63/1.36 ? [X0 : ($i > $o) > $i] : ((cD_FOR_X5309 @ X0 @ (X0 @ (cD_FOR_X5309 @ X0))) != $true) => ($true != (cD_FOR_X5309 @ sK0 @ (sK0 @ (cD_FOR_X5309 @ sK0))))),
% 1.63/1.36 introduced(definition,[],[choice_axiom])).
% 1.63/1.36 thf(f9,plain,(
% 1.63/1.36 ? [X0 : ($i > $o) > $i] : ((cD_FOR_X5309 @ X0 @ (X0 @ (cD_FOR_X5309 @ X0))) != $true)),
% 1.63/1.36 inference(ennf_transformation,[status(thm)],[f6])).
% 1.63/1.36 thf(f6,plain,(
% 1.63/1.36 ~! [X0 : ($i > $o) > $i] : ((cD_FOR_X5309 @ X0 @ (X0 @ (cD_FOR_X5309 @ X0))) = $true)),
% 1.63/1.36 inference(fool_elimination,[status(thm)],[f5])).
% 1.63/1.36 thf(f5,plain,(
% 1.63/1.36 ~! [X0 : ($i > $o) > $i] : (cD_FOR_X5309 @ X0 @ (X0 @ (cD_FOR_X5309 @ X0)))),
% 1.63/1.36 inference(rectify,[status(thm)],[f3])).
% 1.63/1.36 thf(f3,negated_conjecture,(
% 1.63/1.36 ~! [X0 : ($i > $o) > $i] : (cD_FOR_X5309 @ X0 @ (X0 @ (cD_FOR_X5309 @ X0)))),
% 1.63/1.36 inference(negated_conjecture,[status(cth)],[f2])).
% 1.63/1.36 thf(f2,conjecture,(
% 1.63/1.36 ! [X0 : ($i > $o) > $i] : (cD_FOR_X5309 @ X0 @ (X0 @ (cD_FOR_X5309 @ X0)))),
% 1.63/1.36 file('/export/starexec/sandbox2/tmp/tmp.ZOePTMN8LZ/DTF2THF_15910.p',cTHM144C_pme)).
% 1.63/1.36 thf(f27,plain,(
% 1.63/1.36 ($false = (sK3 @ (sK0 @ sK3)))),
% 1.63/1.36 inference(not_proxy_clausification,[status(thm)],[f26])).
% 1.63/1.36 thf(f26,plain,(
% 1.63/1.36 ($true = (~ (sK3 @ (sK0 @ sK3))))),
% 1.63/1.36 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.63/1.36 % SZS output end Proof for DTF2THF_15910
% 1.63/1.36 % (16083)------------------------------
% 1.63/1.36 % (16083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (16083)Termination reason: Refutation
% 1.63/1.36
% 1.63/1.36 % (16083)Memory used [KB]: 5500
% 1.63/1.36 % (16083)Time elapsed: 0.005 s
% 1.63/1.36 % (16083)Instructions burned: 6 (million)
% 1.63/1.36 % (16083)------------------------------
% 1.63/1.36 % (16083)------------------------------
% 1.63/1.36 % (16082)Success in time 0.015 s
%------------------------------------------------------------------------------