%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV177^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 1.13s 1.11s
% Output : Refutation 1.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 2
% Syntax : Number of formulae : 28 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 140 ( 69 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 304 ( 46 ~; 4 |; 34 &; 192 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 75 ( 75 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 6 usr; 3 con; 0-2 aty)
% ( 0 !!; 23 ??; 0 @@+; 0 @@-)
% Number of variables : 70 ( 49 ^; 14 !; 7 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_10,type,
sK0: $i > $o ).
thf(func_def_11,type,
sK1: ( $i > $o ) > $i ).
thf(func_def_13,type,
ph3:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
sK4: $i > $o ).
thf(func_def_15,type,
sK5: $i > $o ).
thf(func_def_16,type,
sK6: $i > $o ).
thf(f63,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f62]) ).
thf(f62,plain,
$true = $false,
inference(superposition,[status(thm)],[f24,f51]) ).
thf(f51,plain,
( ( sK4 @ ( sK1 @ sK4 ) )
= $true ),
inference(equality_resolution,[status(thm)],[f26]) ).
thf(f26,plain,
! [X0: $i > $o] :
( ( ( sK1 @ X0 )
!= ( sK1 @ sK4 ) )
| ( $true
= ( X0 @ ( sK1 @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f17,f25]) ).
thf(f25,plain,
( ( sK1
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK1 @ Y1 ) )
& ( ( sK1 @ Y1 )
= Y0 ) ) ) )
= ( sK1 @ sK4 ) ),
inference(equality_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ( sK1 @ sK4 )
= ( sK1
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK1 @ Y1 ) )
& ( ( sK1 @ Y1 )
= Y0 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( $true
= ( ~ ( sK4 @ ( sK1 @ sK4 ) )
& ( ( sK1 @ sK4 )
= ( sK1
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK1 @ Y1 ) )
& ( ( sK1 @ Y1 )
= Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK1 @ Y0 ) )
& ( ( sK1 @ Y0 )
= ( sK1
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK1 @ Y2 ) )
& ( ( sK1 @ Y2 )
= Y1 ) ) ) ) ) )
@ sK4 )
= $true ),
inference(sigma_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK1 @ Y0 ) )
& ( ( sK1 @ Y0 )
= ( sK1
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK1 @ Y2 ) )
& ( ( sK1 @ Y2 )
= Y1 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK1 @ Y1 ) )
& ( ( sK1 @ Y1 )
= Y0 ) ) )
@ ( sK1
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK1 @ Y1 ) )
& ( ( sK1 @ Y1 )
= Y0 ) ) ) ) )
= $true ),
inference(equality_resolution,[status(thm)],[f17]) ).
thf(f17,plain,
! [X1: $i > $o] :
( ( ( sK1
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK1 @ Y1 ) )
& ( ( sK1 @ Y1 )
= Y0 ) ) ) )
!= ( sK1 @ X1 ) )
| ( ( X1 @ ( sK1 @ X1 ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
! [X1: $i > $o] :
( ( ( sK1
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK1 @ Y1 ) )
& ( ( sK1 @ Y1 )
= Y0 ) ) ) )
!= ( sK1 @ X1 ) )
| ( $false
= ( ~ ( X1 @ ( sK1 @ X1 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
! [X1: $i > $o] :
( ( ( ( sK1 @ X1 )
= ( sK1
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK1 @ Y1 ) )
& ( ( sK1 @ Y1 )
= Y0 ) ) ) ) )
= $false )
| ( $false
= ( ~ ( X1 @ ( sK1 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
! [X1: $i > $o] :
( ( ~ ( X1 @ ( sK1 @ X1 ) )
& ( ( sK1 @ X1 )
= ( sK1
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK1 @ Y1 ) )
& ( ( sK1 @ Y1 )
= Y0 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f13]) ).
thf(f13,plain,
! [X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK1 @ Y0 ) )
& ( ( sK1 @ Y0 )
= ( sK1
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK1 @ Y2 ) )
& ( ( sK1 @ Y2 )
= Y1 ) ) ) ) ) )
@ X1 )
= $false ),
inference(pi_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK1 @ Y0 ) )
& ( ( sK1 @ Y0 )
= ( sK1
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK1 @ Y2 ) )
& ( ( sK1 @ Y2 )
= Y1 ) ) ) ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK1 @ Y1 ) )
& ( ( sK1 @ Y1 )
= Y0 ) ) )
@ ( sK1
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK1 @ Y1 ) )
& ( ( sK1 @ Y1 )
= Y0 ) ) ) ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f10,f9,f9]) ).
thf(f9,plain,
( sK0
= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK1 @ Y1 ) )
& ( ( sK1 @ Y1 )
= Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ( sK0 @ ( sK1 @ sK0 ) )
!= $true )
& ( sK0
= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK1 @ Y1 ) )
& ( ( sK1 @ Y1 )
= Y0 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7]) ).
thf(f7,plain,
( ? [X0: $i > $o,X1: ( $i > $o ) > $i] :
( ( ( X0 @ ( X1 @ X0 ) )
!= $true )
& ( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( X1 @ Y1 ) )
& ( ( X1 @ Y1 )
= Y0 ) ) ) )
= X0 ) )
=> ( ( ( sK0 @ ( sK1 @ sK0 ) )
!= $true )
& ( sK0
= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK1 @ Y1 ) )
& ( ( sK1 @ Y1 )
= Y0 ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: $i > $o,X1: ( $i > $o ) > $i] :
( ( ( X0 @ ( X1 @ X0 ) )
!= $true )
& ( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( X1 @ Y1 ) )
& ( ( X1 @ Y1 )
= Y0 ) ) ) )
= X0 ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: $i > $o,X1: ( $i > $o ) > $i] :
( ( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( X1 @ Y1 ) )
& ( ( X1 @ Y1 )
= Y0 ) ) ) )
= X0 )
=> ( ( X0 @ ( X1 @ X0 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: $i > $o,X1: ( $i > $o ) > $i] :
( ( ( ^ [X2: $i] :
? [X3: $i > $o] :
( ( ( X1 @ X3 )
= X2 )
& ~ ( X3 @ ( X1 @ X3 ) ) ) )
= X0 )
=> ( X0 @ ( X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: $i > $o,X0: ( $i > $o ) > $i] :
( ( ( ^ [X2: $i] :
? [X3: $i > $o] :
( ( ( X0 @ X3 )
= X2 )
& ~ ( X3 @ ( X0 @ X3 ) ) ) )
= X1 )
=> ( X1 @ ( X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: $i > $o,X0: ( $i > $o ) > $i] :
( ( ( ^ [X2: $i] :
? [X3: $i > $o] :
( ( ( X0 @ X3 )
= X2 )
& ~ ( X3 @ ( X0 @ X3 ) ) ) )
= X1 )
=> ( X1 @ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.QwzzbRIYTP/DTF2THF_28229.p',cTHM144_pme) ).
thf(f10,plain,
( ( sK0 @ ( sK1 @ sK0 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f24,plain,
( ( sK4 @ ( sK1 @ sK4 ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( $true
= ( ~ ( sK4 @ ( sK1 @ sK4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEV177^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.31 % Computer : n016.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue Feb 24 12:41:51 EST 2026
% 0.12/0.31 % CPUTime :
% 0.12/0.31 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.41 ---- Original DTF file ---
% 0.15/0.41 thf(spec,logic,$$dhol).
% 0.15/0.41 %------------------------------------------------------------------------------
% 0.15/0.41 % File : SEV177^5 : TPTP v9.2.1. Released v4.0.0.
% 0.15/0.41 % Domain : Set Theory (Sets of sets)
% 0.15/0.41 % Problem : TPS problem THM144
% 0.15/0.41 % Version : Especial.
% 0.15/0.41 % English : A lemma for the Injective Cantor Theorem X5309.
% 0.15/0.41
% 0.15/0.41 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.15/0.41 % Source : [Bro09]
% 0.15/0.41 % Names : tps_0344 [Bro09]
% 0.15/0.41 % : THM144 [TPS]
% 0.15/0.41
% 0.15/0.41 % Status : Theorem
% 0.15/0.41 % 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, 0.12 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, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.33 v4.0.0
% 0.15/0.41 % Syntax : Number of formulae : 1 ( 1 unt; 0 typ; 0 def)
% 0.15/0.41 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.15/0.41 % Maximal formula atoms : 1 ( 2 avg)
% 0.15/0.41 % Number of connectives : 8 ( 1 ~; 0 |; 1 &; 5 @)
% 0.15/0.41 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.15/0.41 % Maximal formula depth : 6 ( 6 avg)
% 0.15/0.41 % Number of types : 2 ( 0 usr)
% 0.15/0.41 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.15/0.41 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.15/0.41 % Number of variables : 4 ( 1 ^; 2 !; 1 ?; 4 :)
% 0.15/0.41 % SPC : TH0_THM_EQU_NAR
% 0.15/0.41
% 0.15/0.41 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.15/0.41 % project in the Department of Mathematical Sciences at Carnegie
% 0.15/0.41 % Mellon University. Distributed under the Creative Commons copyleft
% 0.15/0.41 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.15/0.41 % : Polymorphic definitions expanded.
% 0.15/0.41 %------------------------------------------------------------------------------
% 0.15/0.41 thf(cTHM144_pme,conjecture,
% 0.15/0.41 ! [Xh: ( $i > $o ) > $i,Xd: $i > $o] :
% 0.15/0.41 ( ( Xd
% 0.15/0.41 = ( ^ [Xz: $i] :
% 0.15/0.41 ? [Xt: $i > $o] :
% 0.15/0.41 ( ~ ( Xt @ ( Xh @ Xt ) )
% 0.15/0.41 & ( Xz
% 0.15/0.41 = ( Xh @ Xt ) ) ) ) )
% 0.15/0.41 => ( Xd @ ( Xh @ Xd ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %------------------------------------------------------------------------------
% 0.15/0.41 ------------------------
% 1.13/1.08 ---- Embedded in THF ---
% 1.13/1.08 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.13/1.08 %%% Generated on Tue Feb 24 12:41:51 EST 2026
% 1.13/1.08 %%% using '$$dhol' embedding, version 1.3.0.
% 1.13/1.08 %%% Logic specification used:
% 1.13/1.08 %%% thf(spec, logic, $$dhol).
% 1.13/1.08
% 1.13/1.08 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.QwzzbRIYTP/DTF2DTF28229.p
% See solution above
% 1.13/1.08 ------------------------
% 1.13/1.09 ---- Cleaned THF ---
% 1.13/1.09 thf(cTHM144_pme,conjecture,
% 1.13/1.09 ! [Xh: ( $i > $o ) > $i,Xd: $i > $o] :
% 1.13/1.09 ( ( Xd
% 1.13/1.09 = ( ^ [Xz: $i] :
% 1.13/1.09 ? [Xt: $i > $o] :
% 1.13/1.09 ( ~ ( Xt @ ( Xh @ Xt ) )
% 1.13/1.09 & ( Xz
% 1.13/1.09 = ( Xh @ Xt ) ) ) ) )
% 1.13/1.09 => ( Xd @ ( Xh @ Xd ) ) ) ).
% 1.13/1.09 ------------------------
% 1.13/1.10 % (28330)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28229 for (3000ds/183Mi)
% 1.13/1.11 % (28330)First to succeed.
% 1.13/1.11 % (28330)Refutation found. Thanks to Tanya!
% 1.13/1.11 % SZS status Theorem for DTF2THF_28229
% 1.13/1.11 % SZS output start Proof for DTF2THF_28229
% 1.13/1.11 thf(func_def_10, type, sK0: $i > $o).
% 1.13/1.11 thf(func_def_11, type, sK1: ($i > $o) > $i).
% 1.13/1.11 thf(func_def_13, type, ph3: !>[X0: $tType]:(X0)).
% 1.13/1.11 thf(func_def_14, type, sK4: $i > $o).
% 1.13/1.11 thf(func_def_15, type, sK5: $i > $o).
% 1.13/1.11 thf(func_def_16, type, sK6: $i > $o).
% 1.13/1.11 thf(f63,plain,(
% 1.13/1.11 $false),
% 1.13/1.11 inference(trivial_inequality_removal,[status(thm)],[f62])).
% 1.13/1.11 thf(f62,plain,(
% 1.13/1.11 ($true = $false)),
% 1.13/1.11 inference(superposition,[status(thm)],[f24,f51])).
% 1.13/1.11 thf(f51,plain,(
% 1.13/1.11 ((sK4 @ (sK1 @ sK4)) = $true)),
% 1.13/1.11 inference(equality_resolution,[status(thm)],[f26])).
% 1.13/1.11 thf(f26,plain,(
% 1.13/1.11 ( ! [X0 : $i > $o] : (((sK1 @ X0) != (sK1 @ sK4)) | ($true = (X0 @ (sK1 @ X0)))) )),
% 1.13/1.11 inference(superposition,[status(thm)],[f17,f25])).
% 1.13/1.11 thf(f25,plain,(
% 1.13/1.11 ((sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0)))))) = (sK1 @ sK4))),
% 1.13/1.11 inference(equality_proxy_clausification,[status(thm)],[f22])).
% 1.13/1.11 thf(f22,plain,(
% 1.13/1.11 (((sK1 @ sK4) = (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))))) = $true)),
% 1.13/1.11 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.13/1.11 thf(f21,plain,(
% 1.13/1.11 ($true = ((~ (sK4 @ (sK1 @ sK4))) & ((sK1 @ sK4) = (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0)))))))))),
% 1.13/1.11 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.13/1.11 thf(f20,plain,(
% 1.13/1.11 (((^[Y0 : $i > $o]: ((~ (Y0 @ (sK1 @ Y0))) & ((sK1 @ Y0) = (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ (sK1 @ Y2))) & ((sK1 @ Y2) = Y1))))))))) @ sK4) = $true)),
% 1.13/1.11 inference(sigma_clausification,[status(thm)],[f19])).
% 1.13/1.11 thf(f19,plain,(
% 1.13/1.11 ((?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (Y0 @ (sK1 @ Y0))) & ((sK1 @ Y0) = (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ (sK1 @ Y2))) & ((sK1 @ Y2) = Y1)))))))))) = $true)),
% 1.13/1.11 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.13/1.11 thf(f18,plain,(
% 1.13/1.11 (((^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))) @ (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))))) = $true)),
% 1.13/1.11 inference(equality_resolution,[status(thm)],[f17])).
% 1.13/1.11 thf(f17,plain,(
% 1.13/1.11 ( ! [X1 : $i > $o] : (((sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0)))))) != (sK1 @ X1)) | ((X1 @ (sK1 @ X1)) = $true)) )),
% 1.13/1.11 inference(not_proxy_clausification,[status(thm)],[f16])).
% 1.13/1.11 thf(f16,plain,(
% 1.13/1.11 ( ! [X1 : $i > $o] : (((sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0)))))) != (sK1 @ X1)) | ($false = (~ (X1 @ (sK1 @ X1))))) )),
% 1.13/1.11 inference(equality_proxy_clausification,[status(thm)],[f15])).
% 1.13/1.11 thf(f15,plain,(
% 1.13/1.11 ( ! [X1 : $i > $o] : ((((sK1 @ X1) = (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))))) = $false) | ($false = (~ (X1 @ (sK1 @ X1))))) )),
% 1.13/1.11 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.13/1.11 thf(f14,plain,(
% 1.13/1.11 ( ! [X1 : $i > $o] : ((((~ (X1 @ (sK1 @ X1))) & ((sK1 @ X1) = (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0)))))))) = $false)) )),
% 1.13/1.11 inference(beta_eta_normalization,[status(thm)],[f13])).
% 1.13/1.11 thf(f13,plain,(
% 1.13/1.11 ( ! [X1 : $i > $o] : ((((^[Y0 : $i > $o]: ((~ (Y0 @ (sK1 @ Y0))) & ((sK1 @ Y0) = (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ (sK1 @ Y2))) & ((sK1 @ Y2) = Y1))))))))) @ X1) = $false)) )),
% 1.13/1.11 inference(pi_clausification,[status(thm)],[f12])).
% 1.13/1.11 thf(f12,plain,(
% 1.13/1.11 ((?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (Y0 @ (sK1 @ Y0))) & ((sK1 @ Y0) = (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ (sK1 @ Y2))) & ((sK1 @ Y2) = Y1)))))))))) != $true)),
% 1.13/1.11 inference(beta_eta_normalization,[status(thm)],[f11])).
% 1.13/1.11 thf(f11,plain,(
% 1.13/1.11 (((^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))) @ (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))))) != $true)),
% 1.13/1.11 inference(definition_unfolding,[status(thm)],[f10,f9,f9])).
% 1.13/1.11 thf(f9,plain,(
% 1.13/1.11 (sK0 = (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))))),
% 1.13/1.11 inference(cnf_transformation,[status(thm)],[f8])).
% 1.13/1.11 thf(f8,plain,(
% 1.13/1.11 ((sK0 @ (sK1 @ sK0)) != $true) & (sK0 = (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))))),
% 1.13/1.11 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7])).
% 1.13/1.11 thf(f7,plain,(
% 1.13/1.11 ? [X0 : $i > $o,X1 : ($i > $o) > $i] : (((X0 @ (X1 @ X0)) != $true) & ((^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X1 @ Y1))) & ((X1 @ Y1) = Y0))))) = X0)) => (((sK0 @ (sK1 @ sK0)) != $true) & (sK0 = (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0)))))))),
% 1.13/1.11 introduced(definition,[],[choice_axiom])).
% 1.13/1.11 thf(f6,plain,(
% 1.13/1.11 ? [X0 : $i > $o,X1 : ($i > $o) > $i] : (((X0 @ (X1 @ X0)) != $true) & ((^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X1 @ Y1))) & ((X1 @ Y1) = Y0))))) = X0))),
% 1.13/1.11 inference(ennf_transformation,[status(thm)],[f5])).
% 1.13/1.11 thf(f5,plain,(
% 1.13/1.11 ~! [X0 : $i > $o,X1 : ($i > $o) > $i] : (((^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X1 @ Y1))) & ((X1 @ Y1) = Y0))))) = X0) => ((X0 @ (X1 @ X0)) = $true))),
% 1.13/1.11 inference(fool_elimination,[status(thm)],[f4])).
% 1.13/1.11 thf(f4,plain,(
% 1.13/1.11 ~! [X0 : $i > $o,X1 : ($i > $o) > $i] : (((^[X2 : $i] : (? [X3 : $i > $o] : (((X1 @ X3) = X2) & ~(X3 @ (X1 @ X3))))) = X0) => (X0 @ (X1 @ X0)))),
% 1.13/1.11 inference(rectify,[status(thm)],[f2])).
% 1.13/1.11 thf(f2,negated_conjecture,(
% 1.13/1.11 ~! [X1 : $i > $o,X0 : ($i > $o) > $i] : (((^[X2 : $i] : (? [X3 : $i > $o] : (((X0 @ X3) = X2) & ~(X3 @ (X0 @ X3))))) = X1) => (X1 @ (X0 @ X1)))),
% 1.13/1.11 inference(negated_conjecture,[status(cth)],[f1])).
% 1.13/1.11 thf(f1,conjecture,(
% 1.13/1.11 ! [X1 : $i > $o,X0 : ($i > $o) > $i] : (((^[X2 : $i] : (? [X3 : $i > $o] : (((X0 @ X3) = X2) & ~(X3 @ (X0 @ X3))))) = X1) => (X1 @ (X0 @ X1)))),
% 1.13/1.11 file('/export/starexec/sandbox/tmp/tmp.QwzzbRIYTP/DTF2THF_28229.p',cTHM144_pme)).
% 1.13/1.11 thf(f10,plain,(
% 1.13/1.11 ((sK0 @ (sK1 @ sK0)) != $true)),
% 1.13/1.11 inference(cnf_transformation,[status(thm)],[f8])).
% 1.13/1.11 thf(f24,plain,(
% 1.13/1.11 ((sK4 @ (sK1 @ sK4)) = $false)),
% 1.13/1.11 inference(not_proxy_clausification,[status(thm)],[f23])).
% 1.13/1.11 thf(f23,plain,(
% 1.13/1.11 ($true = (~ (sK4 @ (sK1 @ sK4))))),
% 1.13/1.11 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.13/1.11 % SZS output end Proof for DTF2THF_28229
% 1.13/1.11 % (28330)------------------------------
% 1.13/1.11 % (28330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.13/1.11 % (28330)Termination reason: Refutation
% 1.13/1.11
% 1.13/1.11 % (28330)Memory used [KB]: 5500
% 1.13/1.11 % (28330)Time elapsed: 0.005 s
% 1.13/1.11 % (28330)Instructions burned: 6 (million)
% 1.13/1.11 % (28330)------------------------------
% 1.13/1.11 % (28330)------------------------------
% 1.13/1.11 % (28329)Success in time 0.014 s
%------------------------------------------------------------------------------