%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU924^5 : 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 : n006.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 09:37:45 AM UTC 2026
% Result : Theorem 1.51s 1.22s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 123 ( 59 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 155 ( 31 ~; 15 |; 19 &; 72 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 48 ( 48 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 85 ( 29 ^; 36 !; 20 ?; 85 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_4,type,
sK0: $i > $i ).
thf(func_def_6,type,
sK2: ( ( $i > $i ) > $o ) > $i > $i ).
thf(func_def_10,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f36,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f35]) ).
thf(f35,plain,
sK1 != sK1,
inference(superposition,[status(thm)],[f14,f34]) ).
thf(f34,plain,
! [X1: $i] :
( sK1
= ( sK0 @ X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: $i] :
( ( ^ [Y0: $i] : sK1
@ X1 )
= ( sK0 @ X1 ) ),
inference(argument_congruence,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ^ [Y0: $i] : sK1 )
= sK0 ),
inference(leibniz_equality_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
! [X2: ( $i > $i ) > $o] :
( ( ( X2
@ ^ [Y0: $i] : sK1 )
!= $true )
| ( ( X2 @ sK0 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f15]) ).
thf(f15,plain,
! [X2: ( $i > $i ) > $o] :
( ( ( X2
@ ^ [Y0: $i] : sK1 )
!= $true )
| ( ( X2
@ ^ [Y0: $i] : sK1 )
!= $true )
| ( ( X2 @ sK0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X2: ( $i > $i ) > $o] :
( ( ( X2
@ ^ [Y0: $i] : sK1 )
!= $true )
| ( ( X2 @ sK0 )
= $true )
| ( ( $true
= ( X2 @ ( sK2 @ X2 ) ) )
& ( ( X2
@ ^ [Y0: $i] : sK1 )
!= $true ) ) )
& ( sK1
!= ( sK0 @ sK3 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f9,f12,f11,f10]) ).
thf(f10,plain,
( ? [X0: $i > $i,X1: $i] :
( ! [X2: ( $i > $i ) > $o] :
( ( ( X2
@ ^ [Y0: $i] : X1 )
!= $true )
| ( ( X2 @ X0 )
= $true )
| ? [X3: $i > $i] :
( ( $true
= ( X2 @ X3 ) )
& ( ( X2
@ ^ [Y0: $i] : X1 )
!= $true ) ) )
& ? [X4: $i] :
( ( X0 @ X4 )
!= X1 ) )
=> ( ! [X2: ( $i > $i ) > $o] :
( ( ( X2
@ ^ [Y0: $i] : sK1 )
!= $true )
| ( ( X2 @ sK0 )
= $true )
| ? [X3: $i > $i] :
( ( $true
= ( X2 @ X3 ) )
& ( ( X2
@ ^ [Y0: $i] : sK1 )
!= $true ) ) )
& ? [X4: $i] :
( sK1
!= ( sK0 @ X4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X2: ( $i > $i ) > $o] :
( ? [X3: $i > $i] :
( ( $true
= ( X2 @ X3 ) )
& ( ( X2
@ ^ [Y0: $i] : sK1 )
!= $true ) )
=> ( ( $true
= ( X2 @ ( sK2 @ X2 ) ) )
& ( ( X2
@ ^ [Y0: $i] : sK1 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X4: $i] :
( sK1
!= ( sK0 @ X4 ) )
=> ( sK1
!= ( sK0 @ sK3 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: $i > $i,X1: $i] :
( ! [X2: ( $i > $i ) > $o] :
( ( ( X2
@ ^ [Y0: $i] : X1 )
!= $true )
| ( ( X2 @ X0 )
= $true )
| ? [X3: $i > $i] :
( ( $true
= ( X2 @ X3 ) )
& ( ( X2
@ ^ [Y0: $i] : X1 )
!= $true ) ) )
& ? [X4: $i] :
( ( X0 @ X4 )
!= X1 ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
? [X1: $i > $i,X0: $i] :
( ! [X2: ( $i > $i ) > $o] :
( ( $true
!= ( X2
@ ^ [Y0: $i] : X0 ) )
| ( ( X2 @ X1 )
= $true )
| ? [X3: $i > $i] :
( ( $true
= ( X2 @ X3 ) )
& ( $true
!= ( X2
@ ^ [Y0: $i] : X0 ) ) ) )
& ? [X4: $i] :
( ( X1 @ X4 )
!= X0 ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
? [X1: $i > $i,X0: $i] :
( ? [X4: $i] :
( ( X1 @ X4 )
!= X0 )
& ! [X2: ( $i > $i ) > $o] :
( ( ( X2 @ X1 )
= $true )
| ? [X3: $i > $i] :
( ( $true
= ( X2 @ X3 ) )
& ( $true
!= ( X2
@ ^ [Y0: $i] : X0 ) ) )
| ( $true
!= ( X2
@ ^ [Y0: $i] : X0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X1: $i > $i,X0: $i] :
( ! [X2: ( $i > $i ) > $o] :
( ( ! [X3: $i > $i] :
( ( $true
= ( X2 @ X3 ) )
=> ( $true
= ( X2
@ ^ [Y0: $i] : X0 ) ) )
& ( $true
= ( X2
@ ^ [Y0: $i] : X0 ) ) )
=> ( ( X2 @ X1 )
= $true ) )
=> ! [X4: $i] :
( ( X1 @ X4 )
= X0 ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: $i,X1: $i > $i] :
( ! [X2: ( $i > $i ) > $o] :
( ( ! [X3: $i > $i] :
( ( $true
= ( X2 @ X3 ) )
=> ( $true
= ( X2
@ ^ [Y0: $i] : X0 ) ) )
& ( $true
= ( X2
@ ^ [Y0: $i] : X0 ) ) )
=> ( ( X2 @ X1 )
= $true ) )
=> ! [X6: $i] :
( ( X1 @ X6 )
= X0 ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: $i,X1: $i > $i] :
( ! [X2: ( $i > $i ) > $o] :
( ( ! [X3: $i > $i] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i] : X0 ) )
& ( X2
@ ^ [X5: $i] : X0 ) )
=> ( X2 @ X1 ) )
=> ! [X6: $i] :
( ( X1 @ X6 )
= X0 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: $i,X1: $i > $i] :
( ! [X2: ( $i > $i ) > $o] :
( ( ! [X4: $i > $i] :
( ( X2 @ X4 )
=> ( X2
@ ^ [X3: $i] : X0 ) )
& ( X2
@ ^ [X3: $i] : X0 ) )
=> ( X2 @ X1 ) )
=> ! [X3: $i] :
( ( X1 @ X3 )
= X0 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: $i,X1: $i > $i] :
( ! [X2: ( $i > $i ) > $o] :
( ( ! [X4: $i > $i] :
( ( X2 @ X4 )
=> ( X2
@ ^ [X3: $i] : X0 ) )
& ( X2
@ ^ [X3: $i] : X0 ) )
=> ( X2 @ X1 ) )
=> ! [X3: $i] :
( ( X1 @ X3 )
= X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.Ja1Qvmftxd/DTF2THF_30015.p',cTHM134_pme) ).
thf(f14,plain,
( sK1
!= ( sK0 @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU924^5 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n006.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:37:15 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.45 ---- Original DTF file ---
% 0.20/0.45 thf(spec,logic,$$dhol).
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 % File : SEU924^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.45 % Domain : Set Theory (Functions)
% 0.20/0.45 % Problem : TPS problem THM134
% 0.20/0.45 % Version : Especial.
% 0.20/0.45 % English : Every positive iterate of a constant function is a constant
% 0.20/0.45 % function.
% 0.20/0.45
% 0.20/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.45 % Source : [Bro09]
% 0.20/0.45 % Names : tps_0145 [Bro09]
% 0.20/0.45 % : THM134 [TPS]
% 0.20/0.45
% 0.20/0.45 % Status : Theorem
% 0.20/0.45 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.54 v8.1.0, 0.45 v7.5.0, 0.14 v7.4.0, 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 v4.0.1, 0.67 v4.0.0
% 0.20/0.45 % Syntax : Number of formulae : 1 ( 1 unt; 0 typ; 0 def)
% 0.20/0.45 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.20/0.45 % Maximal formula atoms : 1 ( 1 avg)
% 0.20/0.45 % Number of connectives : 9 ( 0 ~; 0 |; 1 &; 5 @)
% 0.20/0.45 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.20/0.45 % Maximal formula depth : 11 ( 11 avg)
% 0.20/0.45 % Number of types : 2 ( 0 usr)
% 0.20/0.45 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.20/0.45 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.20/0.45 % Number of variables : 7 ( 2 ^; 5 !; 0 ?; 7 :)
% 0.20/0.45 % SPC : TH0_THM_EQU_NAR
% 0.20/0.45
% 0.20/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.45 % : Polymorphic definitions expanded.
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 thf(cTHM134_pme,conjecture,
% 0.20/0.45 ! [Xz: $i,Xg: $i > $i] :
% 0.20/0.45 ( ! [Xp: ( $i > $i ) > $o] :
% 0.20/0.45 ( ( ( Xp
% 0.20/0.45 @ ^ [Xx: $i] : Xz )
% 0.20/0.45 & ! [Xj: $i > $i] :
% 0.20/0.45 ( ( Xp @ Xj )
% 0.20/0.45 => ( Xp
% 0.20/0.45 @ ^ [Xx: $i] : Xz ) ) )
% 0.20/0.45 => ( Xp @ Xg ) )
% 0.20/0.45 => ! [Xx: $i] :
% 0.20/0.45 ( ( Xg @ Xx )
% 0.20/0.45 = Xz ) ) ).
% 0.20/0.45
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 ------------------------
% 1.37/1.19 ---- Embedded in THF ---
% 1.37/1.19 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.37/1.19 %%% Generated on Tue Feb 24 12:37:16 EST 2026
% 1.37/1.19 %%% using '$$dhol' embedding, version 1.3.0.
% 1.37/1.19 %%% Logic specification used:
% 1.37/1.19 %%% thf(spec, logic, $$dhol).
% 1.37/1.19
% 1.37/1.19 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Ja1Qvmftxd/DTF2DTF30015.p
% See solution above
% 1.37/1.19 ------------------------
% 1.51/1.20 ---- Cleaned THF ---
% 1.51/1.20 thf(cTHM134_pme,conjecture,
% 1.51/1.20 ! [Xz: $i,Xg: $i > $i] :
% 1.51/1.20 ( ! [Xp: ( $i > $i ) > $o] :
% 1.51/1.20 ( ( ( Xp
% 1.51/1.20 @ ^ [Xx: $i] : Xz )
% 1.51/1.20 & ! [Xj: $i > $i] :
% 1.51/1.20 ( ( Xp @ Xj )
% 1.51/1.20 => ( Xp
% 1.51/1.20 @ ^ [Xx: $i] : Xz ) ) )
% 1.51/1.20 => ( Xp @ Xg ) )
% 1.51/1.20 => ! [Xx: $i] :
% 1.51/1.20 ( ( Xg @ Xx )
% 1.51/1.20 = Xz ) ) ).
% 1.51/1.20 ------------------------
% 1.51/1.22 % (30348)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30015 for (2999ds/18Mi)
% 1.51/1.22 % (30346)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_30015 for (2999ds/2Mi)
% 1.51/1.22 % (30346)Instruction limit reached!
% 1.51/1.22 % (30346)------------------------------
% 1.51/1.22 % (30346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.22 % (30346)Termination reason: Unknown
% 1.51/1.22 % (30346)Termination phase: Saturation
% 1.51/1.22
% 1.51/1.22 % (30346)Memory used [KB]: 5500
% 1.51/1.22 % (30346)Time elapsed: 0.002 s
% 1.51/1.22 % (30346)Instructions burned: 2 (million)
% 1.51/1.22 % (30346)------------------------------
% 1.51/1.22 % (30346)------------------------------
% 1.51/1.22 % (30348)First to succeed.
% 1.51/1.22 % (30348)Refutation found. Thanks to Tanya!
% 1.51/1.22 % SZS status Theorem for DTF2THF_30015
% 1.51/1.22 % SZS output start Proof for DTF2THF_30015
% 1.51/1.22 thf(func_def_4, type, sK0: $i > $i).
% 1.51/1.22 thf(func_def_6, type, sK2: (($i > $i) > $o) > $i > $i).
% 1.51/1.22 thf(func_def_10, type, ph5: !>[X0: $tType]:(X0)).
% 1.51/1.22 thf(f36,plain,(
% 1.51/1.22 $false),
% 1.51/1.22 inference(trivial_inequality_removal,[status(thm)],[f35])).
% 1.51/1.22 thf(f35,plain,(
% 1.51/1.22 (sK1 != sK1)),
% 1.51/1.22 inference(superposition,[status(thm)],[f14,f34])).
% 1.51/1.22 thf(f34,plain,(
% 1.51/1.22 ( ! [X1 : $i] : ((sK1 = (sK0 @ X1))) )),
% 1.51/1.22 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.51/1.22 thf(f33,plain,(
% 1.51/1.22 ( ! [X1 : $i] : ((((^[Y0 : $i]: (sK1)) @ X1) = (sK0 @ X1))) )),
% 1.51/1.22 inference(argument_congruence,[status(thm)],[f19])).
% 1.51/1.22 thf(f19,plain,(
% 1.51/1.22 ((^[Y0 : $i]: (sK1)) = sK0)),
% 1.51/1.22 inference(leibniz_equality_elimination,[status(thm)],[f17])).
% 1.51/1.22 thf(f17,plain,(
% 1.51/1.22 ( ! [X2 : ($i > $i) > $o] : (((X2 @ (^[Y0 : $i]: (sK1))) != $true) | ((X2 @ sK0) = $true)) )),
% 1.51/1.22 inference(duplicate_literal_removal,[status(thm)],[f15])).
% 1.51/1.22 thf(f15,plain,(
% 1.51/1.22 ( ! [X2 : ($i > $i) > $o] : (((X2 @ (^[Y0 : $i]: (sK1))) != $true) | ((X2 @ (^[Y0 : $i]: (sK1))) != $true) | ((X2 @ sK0) = $true)) )),
% 1.51/1.22 inference(cnf_transformation,[status(thm)],[f13])).
% 1.51/1.22 thf(f13,plain,(
% 1.51/1.22 ! [X2 : ($i > $i) > $o] : (((X2 @ (^[Y0 : $i]: (sK1))) != $true) | ((X2 @ sK0) = $true) | (($true = (X2 @ (sK2 @ X2))) & ((X2 @ (^[Y0 : $i]: (sK1))) != $true))) & (sK1 != (sK0 @ sK3))),
% 1.51/1.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f9,f12,f11,f10])).
% 1.51/1.22 thf(f10,plain,(
% 1.51/1.22 ? [X0 : $i > $i,X1 : $i] : (! [X2 : ($i > $i) > $o] : (((X2 @ (^[Y0 : $i]: (X1))) != $true) | ((X2 @ X0) = $true) | ? [X3 : $i > $i] : (($true = (X2 @ X3)) & ((X2 @ (^[Y0 : $i]: (X1))) != $true))) & ? [X4 : $i] : ((X0 @ X4) != X1)) => (! [X2 : ($i > $i) > $o] : (((X2 @ (^[Y0 : $i]: (sK1))) != $true) | ((X2 @ sK0) = $true) | ? [X3 : $i > $i] : (($true = (X2 @ X3)) & ((X2 @ (^[Y0 : $i]: (sK1))) != $true))) & ? [X4 : $i] : (sK1 != (sK0 @ X4)))),
% 1.51/1.22 introduced(definition,[],[choice_axiom])).
% 1.51/1.22 thf(f11,plain,(
% 1.51/1.22 ! [X2 : ($i > $i) > $o] : (? [X3 : $i > $i] : (($true = (X2 @ X3)) & ((X2 @ (^[Y0 : $i]: (sK1))) != $true)) => (($true = (X2 @ (sK2 @ X2))) & ((X2 @ (^[Y0 : $i]: (sK1))) != $true)))),
% 1.51/1.22 introduced(definition,[],[choice_axiom])).
% 1.51/1.22 thf(f12,plain,(
% 1.51/1.22 ? [X4 : $i] : (sK1 != (sK0 @ X4)) => (sK1 != (sK0 @ sK3))),
% 1.51/1.22 introduced(definition,[],[choice_axiom])).
% 1.51/1.22 thf(f9,plain,(
% 1.51/1.22 ? [X0 : $i > $i,X1 : $i] : (! [X2 : ($i > $i) > $o] : (((X2 @ (^[Y0 : $i]: (X1))) != $true) | ((X2 @ X0) = $true) | ? [X3 : $i > $i] : (($true = (X2 @ X3)) & ((X2 @ (^[Y0 : $i]: (X1))) != $true))) & ? [X4 : $i] : ((X0 @ X4) != X1))),
% 1.51/1.22 inference(rectify,[status(thm)],[f8])).
% 1.51/1.22 thf(f8,plain,(
% 1.51/1.22 ? [X1 : $i > $i,X0 : $i] : (! [X2 : ($i > $i) > $o] : (($true != (X2 @ (^[Y0 : $i]: (X0)))) | ((X2 @ X1) = $true) | ? [X3 : $i > $i] : (($true = (X2 @ X3)) & ($true != (X2 @ (^[Y0 : $i]: (X0)))))) & ? [X4 : $i] : ((X1 @ X4) != X0))),
% 1.51/1.22 inference(flattening,[status(thm)],[f7])).
% 1.51/1.22 thf(f7,plain,(
% 1.51/1.22 ? [X1 : $i > $i,X0 : $i] : (? [X4 : $i] : ((X1 @ X4) != X0) & ! [X2 : ($i > $i) > $o] : (((X2 @ X1) = $true) | (? [X3 : $i > $i] : (($true = (X2 @ X3)) & ($true != (X2 @ (^[Y0 : $i]: (X0))))) | ($true != (X2 @ (^[Y0 : $i]: (X0)))))))),
% 1.51/1.22 inference(ennf_transformation,[status(thm)],[f6])).
% 1.51/1.22 thf(f6,plain,(
% 1.51/1.22 ~! [X1 : $i > $i,X0 : $i] : (! [X2 : ($i > $i) > $o] : ((! [X3 : $i > $i] : (($true = (X2 @ X3)) => ($true = (X2 @ (^[Y0 : $i]: (X0))))) & ($true = (X2 @ (^[Y0 : $i]: (X0))))) => ((X2 @ X1) = $true)) => ! [X4 : $i] : ((X1 @ X4) = X0))),
% 1.51/1.22 inference(rectify,[status(thm)],[f5])).
% 1.51/1.22 thf(f5,plain,(
% 1.51/1.22 ~! [X0 : $i,X1 : $i > $i] : (! [X2 : ($i > $i) > $o] : ((! [X3 : $i > $i] : (($true = (X2 @ X3)) => ($true = (X2 @ (^[Y0 : $i]: (X0))))) & ($true = (X2 @ (^[Y0 : $i]: (X0))))) => ((X2 @ X1) = $true)) => ! [X6 : $i] : ((X1 @ X6) = X0))),
% 1.51/1.22 inference(fool_elimination,[status(thm)],[f4])).
% 1.51/1.22 thf(f4,plain,(
% 1.51/1.22 ~! [X0 : $i,X1 : $i > $i] : (! [X2 : ($i > $i) > $o] : ((! [X3 : $i > $i] : ((X2 @ X3) => (X2 @ (^[X4 : $i] : (X0)))) & (X2 @ (^[X5 : $i] : (X0)))) => (X2 @ X1)) => ! [X6 : $i] : ((X1 @ X6) = X0))),
% 1.51/1.22 inference(rectify,[status(thm)],[f2])).
% 1.51/1.22 thf(f2,negated_conjecture,(
% 1.51/1.22 ~! [X0 : $i,X1 : $i > $i] : (! [X2 : ($i > $i) > $o] : ((! [X4 : $i > $i] : ((X2 @ X4) => (X2 @ (^[X3 : $i] : (X0)))) & (X2 @ (^[X3 : $i] : (X0)))) => (X2 @ X1)) => ! [X3 : $i] : ((X1 @ X3) = X0))),
% 1.51/1.22 inference(negated_conjecture,[status(cth)],[f1])).
% 1.51/1.22 thf(f1,conjecture,(
% 1.51/1.22 ! [X0 : $i,X1 : $i > $i] : (! [X2 : ($i > $i) > $o] : ((! [X4 : $i > $i] : ((X2 @ X4) => (X2 @ (^[X3 : $i] : (X0)))) & (X2 @ (^[X3 : $i] : (X0)))) => (X2 @ X1)) => ! [X3 : $i] : ((X1 @ X3) = X0))),
% 1.51/1.22 file('/export/starexec/sandbox/tmp/tmp.Ja1Qvmftxd/DTF2THF_30015.p',cTHM134_pme)).
% 1.51/1.22 thf(f14,plain,(
% 1.51/1.22 (sK1 != (sK0 @ sK3))),
% 1.51/1.22 inference(cnf_transformation,[status(thm)],[f13])).
% 1.51/1.22 % SZS output end Proof for DTF2THF_30015
% 1.51/1.22 % (30348)------------------------------
% 1.51/1.22 % (30348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.22 % (30348)Termination reason: Refutation
% 1.51/1.22
% 1.51/1.22 % (30348)Memory used [KB]: 5500
% 1.51/1.22 % (30348)Time elapsed: 0.003 s
% 1.51/1.22 % (30348)Instructions burned: 1 (million)
% 1.51/1.22 % (30348)------------------------------
% 1.51/1.22 % (30348)------------------------------
% 1.51/1.22 % (30341)Success in time 0.013 s
%------------------------------------------------------------------------------