%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV175^5 : 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 : 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 09:40:28 AM UTC 2026
% Result : Theorem 1.62s 1.30s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 97 ( 50 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 233 ( 36 ~; 6 |; 25 &; 150 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 59 ( 59 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 4 usr; 3 con; 0-2 aty)
% ( 0 !!; 15 ??; 0 @@+; 0 @@-)
% Number of variables : 54 ( 33 ^; 11 !; 10 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_10,type,
sK0: ( $i > $o ) > $i ).
thf(func_def_12,type,
ph2:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
sK3: $i > $o ).
thf(func_def_14,type,
sK4: $i > $o ).
thf(f47,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f46]) ).
thf(f46,plain,
$false = $true,
inference(superposition,[status(thm)],[f17,f35]) ).
thf(f35,plain,
( ( sK3 @ ( sK0 @ sK3 ) )
= $true ),
inference(equality_resolution,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: $i > $o] :
( ( ( sK0 @ sK3 )
!= ( sK0 @ X0 ) )
| ( ( X0 @ ( sK0 @ X0 ) )
= $true ) ),
inference(superposition,[status(thm)],[f10,f18]) ).
thf(f18,plain,
( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK0 @ Y1 ) ) ) ) )
= ( sK0 @ sK3 ) ),
inference(equality_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( sK0 @ sK3 )
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK0 @ Y1 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ( ( sK0 @ sK3 )
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK0 @ Y1 ) ) ) ) ) )
& ~ ( sK3 @ ( sK0 @ sK3 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ^ [Y0: $i > $o] :
( ( ( sK0 @ Y0 )
= ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( sK0 @ Y2 )
= Y1 )
& ~ ( Y2 @ ( sK0 @ Y2 ) ) ) ) ) )
& ~ ( Y0 @ ( sK0 @ Y0 ) ) )
@ sK3 )
= $true ),
inference(sigma_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( sK0 @ Y0 )
= ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( sK0 @ Y2 )
= Y1 )
& ~ ( Y2 @ ( sK0 @ Y2 ) ) ) ) ) )
& ~ ( Y0 @ ( sK0 @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f11]) ).
thf(f11,plain,
( $true
= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK0 @ Y1 ) ) ) )
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK0 @ Y1 ) ) ) ) ) ) ),
inference(equality_resolution,[status(thm)],[f10]) ).
thf(f10,plain,
! [X1: $i > $o] :
( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK0 @ Y1 ) ) ) ) )
!= ( sK0 @ X1 ) )
| ( ( X1 @ ( sK0 @ X1 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X1: $i > $o] :
( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK0 @ Y1 ) ) ) ) )
!= ( sK0 @ X1 ) )
| ( ( X1 @ ( sK0 @ X1 ) )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8]) ).
thf(f8,plain,
( ? [X0: ( $i > $o ) > $i] :
! [X1: $i > $o] :
( ( ( X0 @ X1 )
!= ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( X0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( X0 @ Y1 ) ) ) ) ) )
| ( ( X1 @ ( X0 @ X1 ) )
= $true ) )
=> ! [X1: $i > $o] :
( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK0 @ Y1 ) ) ) ) )
!= ( sK0 @ X1 ) )
| ( ( X1 @ ( sK0 @ X1 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
? [X0: ( $i > $o ) > $i] :
! [X1: $i > $o] :
( ( ( X0 @ X1 )
!= ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( X0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( X0 @ Y1 ) ) ) ) ) )
| ( ( X1 @ ( X0 @ X1 ) )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: ( $i > $o ) > $i] :
? [X1: $i > $o] :
( ( ( X0 @ X1 )
= ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( X0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( X0 @ Y1 ) ) ) ) ) )
& ( ( X1 @ ( X0 @ X1 ) )
!= $true ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: ( $i > $o ) > $i] :
? [X1: $i > $o] :
( ( ( X0 @ X1 )
= ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( X0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( X0 @ Y1 ) ) ) ) ) )
& ( ( X1 @ ( X0 @ X1 ) )
!= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: ( $i > $o ) > $i] :
? [X1: $i > $o] :
( ( ( X0 @ X1 )
= ( X0
@ ^ [X2: $i] :
? [X3: $i > $o] :
( ~ ( X3 @ ( X0 @ X3 ) )
& ( ( X0 @ X3 )
= X2 ) ) ) )
& ~ ( X1 @ ( X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: ( $i > $o ) > $i] :
? [X1: $i > $o] :
( ( ( X0 @ X1 )
= ( X0
@ ^ [X2: $i] :
? [X3: $i > $o] :
( ~ ( X3 @ ( X0 @ X3 ) )
& ( ( X0 @ X3 )
= X2 ) ) ) )
& ~ ( X1 @ ( X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: ( $i > $o ) > $i] :
? [X1: $i > $o] :
( ( ( X0 @ X1 )
= ( X0
@ ^ [X2: $i] :
? [X3: $i > $o] :
( ~ ( X3 @ ( X0 @ X3 ) )
& ( ( X0 @ X3 )
= X2 ) ) ) )
& ~ ( X1 @ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YrBHLe9XBs/DTF2THF_22948.p',cTHM144A_pme) ).
thf(f17,plain,
( $false
= ( sK3 @ ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( $true
= ( ~ ( sK3 @ ( sK0 @ sK3 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV175^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n022.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:41:21 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.47 ---- Original DTF file ---
% 0.29/0.47 thf(spec,logic,$$dhol).
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 % File : SEV175^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.47 % Domain : Set Theory (Sets of sets)
% 0.29/0.47 % Problem : TPS problem THM144A
% 0.29/0.47 % Version : Especial.
% 0.29/0.47 % English : A lemma for the Injective Cantor Theorem X5309.
% 0.29/0.47
% 0.29/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.47 % Source : [Bro09]
% 0.29/0.47 % Names : tps_0230 [Bro09]
% 0.29/0.47 % : THM144A [TPS]
% 0.29/0.47
% 0.29/0.47 % Status : Theorem
% 0.29/0.47 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.14 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 v5.3.0, 0.60 v5.2.0, 0.80 v5.0.0, 0.60 v4.1.0, 1.00 v4.0.0
% 0.29/0.47 % Syntax : Number of formulae : 1 ( 1 unt; 0 typ; 0 def)
% 0.29/0.47 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.29/0.47 % Maximal formula atoms : 1 ( 2 avg)
% 0.29/0.47 % Number of connectives : 11 ( 2 ~; 0 |; 2 &; 7 @)
% 0.29/0.47 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.29/0.47 % Maximal formula depth : 7 ( 7 avg)
% 0.29/0.47 % Number of types : 2 ( 0 usr)
% 0.29/0.47 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.29/0.47 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.29/0.47 % Number of variables : 4 ( 1 ^; 1 !; 2 ?; 4 :)
% 0.29/0.47 % SPC : TH0_THM_EQU_NAR
% 0.29/0.47
% 0.29/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.47 % : Polymorphic definitions expanded.
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 thf(cTHM144A_pme,conjecture,
% 0.29/0.47 ! [Xh: ( $i > $o ) > $i] :
% 0.29/0.47 ? [Xt: $i > $o] :
% 0.29/0.47 ( ~ ( Xt @ ( Xh @ Xt ) )
% 0.29/0.47 & ( ( Xh
% 0.29/0.47 @ ^ [Xz: $i] :
% 0.29/0.47 ? [Xt0: $i > $o] :
% 0.29/0.47 ( ~ ( Xt0 @ ( Xh @ Xt0 ) )
% 0.29/0.47 & ( Xz
% 0.29/0.47 = ( Xh @ Xt0 ) ) ) )
% 0.29/0.47 = ( Xh @ Xt ) ) ) ).
% 0.29/0.47
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 ------------------------
% 1.43/1.27 ---- Embedded in THF ---
% 1.43/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.43/1.27 %%% Generated on Tue Feb 24 12:41:22 EST 2026
% 1.43/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.43/1.27 %%% Logic specification used:
% 1.43/1.27 %%% thf(spec, logic, $$dhol).
% 1.43/1.27
% 1.43/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.YrBHLe9XBs/DTF2DTF22948.p
% See solution above
% 1.43/1.27 ------------------------
% 1.43/1.28 ---- Cleaned THF ---
% 1.43/1.28 thf(cTHM144A_pme,conjecture,
% 1.43/1.28 ! [Xh: ( $i > $o ) > $i] :
% 1.43/1.28 ? [Xt: $i > $o] :
% 1.43/1.28 ( ~ ( Xt @ ( Xh @ Xt ) )
% 1.43/1.28 & ( ( Xh
% 1.43/1.28 @ ^ [Xz: $i] :
% 1.43/1.28 ? [Xt0: $i > $o] :
% 1.43/1.28 ( ~ ( Xt0 @ ( Xh @ Xt0 ) )
% 1.43/1.28 & ( Xz
% 1.43/1.28 = ( Xh @ Xt0 ) ) ) )
% 1.43/1.28 = ( Xh @ Xt ) ) ) ).
% 1.43/1.28 ------------------------
% 1.43/1.30 % (23241)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_22948 for (2999ds/4Mi)
% 1.62/1.30 % (23241)First to succeed.
% 1.62/1.30 % (23241)Refutation found. Thanks to Tanya!
% 1.62/1.30 % SZS status Theorem for DTF2THF_22948
% 1.62/1.30 % SZS output start Proof for DTF2THF_22948
% 1.62/1.30 thf(func_def_10, type, sK0: ($i > $o) > $i).
% 1.62/1.30 thf(func_def_12, type, ph2: !>[X0: $tType]:(X0)).
% 1.62/1.30 thf(func_def_13, type, sK3: $i > $o).
% 1.62/1.30 thf(func_def_14, type, sK4: $i > $o).
% 1.62/1.30 thf(f47,plain,(
% 1.62/1.30 $false),
% 1.62/1.30 inference(trivial_inequality_removal,[status(thm)],[f46])).
% 1.62/1.30 thf(f46,plain,(
% 1.62/1.30 ($false = $true)),
% 1.62/1.30 inference(superposition,[status(thm)],[f17,f35])).
% 1.62/1.30 thf(f35,plain,(
% 1.62/1.30 ((sK3 @ (sK0 @ sK3)) = $true)),
% 1.62/1.30 inference(equality_resolution,[status(thm)],[f21])).
% 1.62/1.30 thf(f21,plain,(
% 1.62/1.30 ( ! [X0 : $i > $o] : (((sK0 @ sK3) != (sK0 @ X0)) | ((X0 @ (sK0 @ X0)) = $true)) )),
% 1.62/1.30 inference(superposition,[status(thm)],[f10,f18])).
% 1.62/1.30 thf(f18,plain,(
% 1.62/1.30 ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((sK0 @ Y1) = Y0) & (~ (Y1 @ (sK0 @ Y1)))))))) = (sK0 @ sK3))),
% 1.62/1.30 inference(equality_proxy_clausification,[status(thm)],[f16])).
% 1.62/1.30 thf(f16,plain,(
% 1.62/1.30 (((sK0 @ sK3) = (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((sK0 @ Y1) = Y0) & (~ (Y1 @ (sK0 @ Y1))))))))) = $true)),
% 1.62/1.30 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.62/1.30 thf(f14,plain,(
% 1.62/1.30 ((((sK0 @ sK3) = (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((sK0 @ Y1) = Y0) & (~ (Y1 @ (sK0 @ Y1))))))))) & (~ (sK3 @ (sK0 @ sK3)))) = $true)),
% 1.62/1.30 inference(beta_eta_normalization,[status(thm)],[f13])).
% 1.62/1.30 thf(f13,plain,(
% 1.62/1.30 (((^[Y0 : $i > $o]: (((sK0 @ Y0) = (sK0 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: (((sK0 @ Y2) = Y1) & (~ (Y2 @ (sK0 @ Y2))))))))) & (~ (Y0 @ (sK0 @ Y0))))) @ sK3) = $true)),
% 1.62/1.30 inference(sigma_clausification,[status(thm)],[f12])).
% 1.62/1.30 thf(f12,plain,(
% 1.62/1.30 ((?? @ ($i > $o) @ (^[Y0 : $i > $o]: (((sK0 @ Y0) = (sK0 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: (((sK0 @ Y2) = Y1) & (~ (Y2 @ (sK0 @ Y2))))))))) & (~ (Y0 @ (sK0 @ Y0)))))) = $true)),
% 1.62/1.30 inference(beta_eta_normalization,[status(thm)],[f11])).
% 1.62/1.30 thf(f11,plain,(
% 1.62/1.30 ($true = ((^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((sK0 @ Y1) = Y0) & (~ (Y1 @ (sK0 @ Y1))))))) @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((sK0 @ Y1) = Y0) & (~ (Y1 @ (sK0 @ Y1))))))))))),
% 1.62/1.30 inference(equality_resolution,[status(thm)],[f10])).
% 1.62/1.30 thf(f10,plain,(
% 1.62/1.30 ( ! [X1 : $i > $o] : (((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((sK0 @ Y1) = Y0) & (~ (Y1 @ (sK0 @ Y1)))))))) != (sK0 @ X1)) | ((X1 @ (sK0 @ X1)) = $true)) )),
% 1.62/1.30 inference(cnf_transformation,[status(thm)],[f9])).
% 1.62/1.30 thf(f9,plain,(
% 1.62/1.30 ! [X1 : $i > $o] : (((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((sK0 @ Y1) = Y0) & (~ (Y1 @ (sK0 @ Y1)))))))) != (sK0 @ X1)) | ((X1 @ (sK0 @ X1)) = $true))),
% 1.62/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8])).
% 1.62/1.30 thf(f8,plain,(
% 1.62/1.30 ? [X0 : ($i > $o) > $i] : ! [X1 : $i > $o] : (((X0 @ X1) != (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((X0 @ Y1) = Y0) & (~ (Y1 @ (X0 @ Y1))))))))) | ((X1 @ (X0 @ X1)) = $true)) => ! [X1 : $i > $o] : (((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((sK0 @ Y1) = Y0) & (~ (Y1 @ (sK0 @ Y1)))))))) != (sK0 @ X1)) | ((X1 @ (sK0 @ X1)) = $true))),
% 1.62/1.30 introduced(definition,[],[choice_axiom])).
% 1.62/1.30 thf(f7,plain,(
% 1.62/1.30 ? [X0 : ($i > $o) > $i] : ! [X1 : $i > $o] : (((X0 @ X1) != (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((X0 @ Y1) = Y0) & (~ (Y1 @ (X0 @ Y1))))))))) | ((X1 @ (X0 @ X1)) = $true))),
% 1.62/1.30 inference(ennf_transformation,[status(thm)],[f6])).
% 1.62/1.30 thf(f6,plain,(
% 1.62/1.30 ~! [X0 : ($i > $o) > $i] : ? [X1 : $i > $o] : (((X0 @ X1) = (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((X0 @ Y1) = Y0) & (~ (Y1 @ (X0 @ Y1))))))))) & ((X1 @ (X0 @ X1)) != $true))),
% 1.62/1.30 inference(flattening,[status(thm)],[f5])).
% 1.62/1.30 thf(f5,plain,(
% 1.62/1.30 ~! [X0 : ($i > $o) > $i] : ? [X1 : $i > $o] : (((X0 @ X1) = (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((X0 @ Y1) = Y0) & (~ (Y1 @ (X0 @ Y1))))))))) & ~((X1 @ (X0 @ X1)) = $true))),
% 1.62/1.30 inference(fool_elimination,[status(thm)],[f4])).
% 1.62/1.30 thf(f4,plain,(
% 1.62/1.30 ~! [X0 : ($i > $o) > $i] : ? [X1 : $i > $o] : (((X0 @ X1) = (X0 @ (^[X2 : $i] : (? [X3 : $i > $o] : (~(X3 @ (X0 @ X3)) & ((X0 @ X3) = X2)))))) & ~(X1 @ (X0 @ X1)))),
% 1.62/1.30 inference(rectify,[status(thm)],[f2])).
% 1.62/1.30 thf(f2,negated_conjecture,(
% 1.62/1.30 ~! [X0 : ($i > $o) > $i] : ? [X1 : $i > $o] : (((X0 @ X1) = (X0 @ (^[X2 : $i] : (? [X3 : $i > $o] : (~(X3 @ (X0 @ X3)) & ((X0 @ X3) = X2)))))) & ~(X1 @ (X0 @ X1)))),
% 1.62/1.30 inference(negated_conjecture,[status(cth)],[f1])).
% 1.62/1.30 thf(f1,conjecture,(
% 1.62/1.30 ! [X0 : ($i > $o) > $i] : ? [X1 : $i > $o] : (((X0 @ X1) = (X0 @ (^[X2 : $i] : (? [X3 : $i > $o] : (~(X3 @ (X0 @ X3)) & ((X0 @ X3) = X2)))))) & ~(X1 @ (X0 @ X1)))),
% 1.62/1.30 file('/export/starexec/sandbox/tmp/tmp.YrBHLe9XBs/DTF2THF_22948.p',cTHM144A_pme)).
% 1.62/1.30 thf(f17,plain,(
% 1.62/1.30 ($false = (sK3 @ (sK0 @ sK3)))),
% 1.62/1.30 inference(not_proxy_clausification,[status(thm)],[f15])).
% 1.62/1.30 thf(f15,plain,(
% 1.62/1.30 ($true = (~ (sK3 @ (sK0 @ sK3))))),
% 1.62/1.30 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.62/1.30 % SZS output end Proof for DTF2THF_22948
% 1.62/1.30 % (23241)------------------------------
% 1.62/1.30 % (23241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (23241)Termination reason: Refutation
% 1.62/1.30
% 1.62/1.30 % (23241)Memory used [KB]: 5500
% 1.62/1.30 % (23241)Time elapsed: 0.004 s
% 1.62/1.30 % (23241)Instructions burned: 3 (million)
% 1.62/1.30 % (23241)------------------------------
% 1.62/1.30 % (23241)------------------------------
% 1.62/1.30 % (23239)Success in time 0.014 s
%------------------------------------------------------------------------------