%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO267^5 : 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 : n014.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 09:53:48 AM UTC 2026
% Result : Theorem 1.64s 1.46s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 110 ( 47 equ; 0 cnn)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 182 ( 19 ~; 7 |; 31 &; 114 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 51 ( 51 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 61 ( 13 ^; 24 !; 24 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_5,type,
sK0: $i > $o ).
thf(func_def_6,type,
sK1: ( ( $i > $i ) > $o ) > $i > $i ).
thf(func_def_7,type,
sK2: ( ( $i > $i ) > $o ) > $i > $i ).
thf(func_def_8,type,
sK3: ( ( $i > $i ) > $o ) > $i ).
thf(func_def_11,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f23,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f22]) ).
thf(f22,plain,
$true = $false,
inference(beta_eta_normalization,[status(thm)],[f17]) ).
thf(f17,plain,
( $true
= ( ^ [Y0: $i > $i] : $false
@ ( sK2
@ ^ [Y0: $i > $i] : $false ) ) ),
inference(primitive_instantiation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X1: ( $i > $i ) > $o] :
( $true
= ( X1 @ ( sK2 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X1: ( $i > $i ) > $o] :
( ( $true
= ( X1 @ ( sK1 @ X1 ) ) )
& ( ( $true
!= ( X1
@ ^ [Y0: $i] : ( sK2 @ X1 @ ( sK1 @ X1 @ Y0 ) ) ) )
| ( ( $true
= ( sK0 @ ( sK3 @ X1 ) ) )
& ( ( sK0 @ ( sK2 @ X1 @ ( sK3 @ X1 ) ) )
!= $true ) ) )
& ( $true
= ( X1 @ ( sK2 @ X1 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f7,f10,f9,f8]) ).
thf(f8,plain,
( ? [X0: $i > $o] :
! [X1: ( $i > $i ) > $o] :
? [X2: $i > $i,X3: $i > $i] :
( ( ( X1 @ X2 )
= $true )
& ( ( $true
!= ( X1
@ ^ [Y0: $i] : ( X3 @ ( X2 @ Y0 ) ) ) )
| ? [X4: $i] :
( ( $true
= ( X0 @ X4 ) )
& ( $true
!= ( X0 @ ( X3 @ X4 ) ) ) ) )
& ( ( X1 @ X3 )
= $true ) )
=> ! [X1: ( $i > $i ) > $o] :
? [X3: $i > $i,X2: $i > $i] :
( ( ( X1 @ X2 )
= $true )
& ( ( $true
!= ( X1
@ ^ [Y0: $i] : ( X3 @ ( X2 @ Y0 ) ) ) )
| ? [X4: $i] :
( ( ( sK0 @ X4 )
= $true )
& ( ( sK0 @ ( X3 @ X4 ) )
!= $true ) ) )
& ( ( X1 @ X3 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
! [X1: ( $i > $i ) > $o] :
( ? [X3: $i > $i,X2: $i > $i] :
( ( ( X1 @ X2 )
= $true )
& ( ( $true
!= ( X1
@ ^ [Y0: $i] : ( X3 @ ( X2 @ Y0 ) ) ) )
| ? [X4: $i] :
( ( ( sK0 @ X4 )
= $true )
& ( ( sK0 @ ( X3 @ X4 ) )
!= $true ) ) )
& ( ( X1 @ X3 )
= $true ) )
=> ( ( $true
= ( X1 @ ( sK1 @ X1 ) ) )
& ( ( $true
!= ( X1
@ ^ [Y0: $i] : ( sK2 @ X1 @ ( sK1 @ X1 @ Y0 ) ) ) )
| ? [X4: $i] :
( ( ( sK0 @ X4 )
= $true )
& ( $true
!= ( sK0 @ ( sK2 @ X1 @ X4 ) ) ) ) )
& ( $true
= ( X1 @ ( sK2 @ X1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X1: ( $i > $i ) > $o] :
( ? [X4: $i] :
( ( ( sK0 @ X4 )
= $true )
& ( $true
!= ( sK0 @ ( sK2 @ X1 @ X4 ) ) ) )
=> ( ( $true
= ( sK0 @ ( sK3 @ X1 ) ) )
& ( ( sK0 @ ( sK2 @ X1 @ ( sK3 @ X1 ) ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
? [X0: $i > $o] :
! [X1: ( $i > $i ) > $o] :
? [X2: $i > $i,X3: $i > $i] :
( ( ( X1 @ X2 )
= $true )
& ( ( $true
!= ( X1
@ ^ [Y0: $i] : ( X3 @ ( X2 @ Y0 ) ) ) )
| ? [X4: $i] :
( ( $true
= ( X0 @ X4 ) )
& ( $true
!= ( X0 @ ( X3 @ X4 ) ) ) ) )
& ( ( X1 @ X3 )
= $true ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: $i > $o] :
! [X1: ( $i > $i ) > $o] :
? [X2: $i > $i,X3: $i > $i] :
( ( ( $true
!= ( X1
@ ^ [Y0: $i] : ( X3 @ ( X2 @ Y0 ) ) ) )
| ? [X4: $i] :
( ( $true
= ( X0 @ X4 ) )
& ( $true
!= ( X0 @ ( X3 @ X4 ) ) ) ) )
& ( ( X1 @ X2 )
= $true )
& ( ( X1 @ X3 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: $i > $o] :
? [X1: ( $i > $i ) > $o] :
! [X2: $i > $i,X3: $i > $i] :
( ( ( ( X1 @ X2 )
= $true )
& ( ( X1 @ X3 )
= $true ) )
=> ( ! [X4: $i] :
( ( $true
= ( X0 @ X4 ) )
=> ( $true
= ( X0 @ ( X3 @ X4 ) ) ) )
& ( $true
= ( X1
@ ^ [Y0: $i] : ( X3 @ ( X2 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: $i > $o] :
? [X1: ( $i > $i ) > $o] :
! [X2: $i > $i,X3: $i > $i] :
( ( ( X1 @ X2 )
& ( X1 @ X3 ) )
=> ( ! [X4: $i] :
( ( X0 @ X4 )
=> ( X0 @ ( X3 @ X4 ) ) )
& ( X1
@ ^ [X5: $i] : ( X3 @ ( X2 @ X5 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: $i > $o] :
? [X1: ( $i > $i ) > $o] :
! [X3: $i > $i,X2: $i > $i] :
( ( ( X1 @ X3 )
& ( X1 @ X2 ) )
=> ( ! [X5: $i] :
( ( X0 @ X5 )
=> ( X0 @ ( X2 @ X5 ) ) )
& ( X1
@ ^ [X4: $i] : ( X2 @ ( X3 @ X4 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: $i > $o] :
? [X1: ( $i > $i ) > $o] :
! [X3: $i > $i,X2: $i > $i] :
( ( ( X1 @ X3 )
& ( X1 @ X2 ) )
=> ( ! [X5: $i] :
( ( X0 @ X5 )
=> ( X0 @ ( X2 @ X5 ) ) )
& ( X1
@ ^ [X4: $i] : ( X2 @ ( X3 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.E3GYKqPh6S/DTF2THF_4512.p',cTHM111) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO267^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n014.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 14:27:12 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.32/0.48 ---- Original DTF file ---
% 0.32/0.48 thf(spec,logic,$$dhol).
% 0.32/0.48 %------------------------------------------------------------------------------
% 0.32/0.48 % File : SYO267^5 : TPTP v9.2.1. Released v4.0.0.
% 0.32/0.48 % Domain : Syntactic
% 0.32/0.48 % Problem : TPS problem THM111
% 0.32/0.48 % Version : Especial.
% 0.32/0.48 % English :
% 0.32/0.48
% 0.32/0.48 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.32/0.48 % Source : [Bro09]
% 0.32/0.48 % Names : tps_0238 [Bro09]
% 0.32/0.48 % : THM111 [TPS]
% 0.32/0.48 % : THM112 [TPS]
% 0.32/0.48
% 0.32/0.48 % Status : Theorem
% 0.32/0.48 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.17 v7.4.0, 0.11 v7.3.0, 0.20 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.2.0, 0.33 v6.1.0, 0.17 v6.0.0, 0.00 v5.5.0, 0.20 v5.4.0, 0.25 v5.3.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.32/0.48 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.32/0.48 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.32/0.48 % Maximal formula atoms : 0 ( 0 avg)
% 0.32/0.48 % Number of connectives : 12 ( 0 ~; 0 |; 2 &; 8 @)
% 0.32/0.48 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.32/0.48 % Maximal formula depth : 11 ( 11 avg)
% 0.32/0.48 % Number of types : 2 ( 0 usr)
% 0.32/0.48 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.32/0.48 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.32/0.48 % Number of variables : 6 ( 1 ^; 4 !; 1 ?; 6 :)
% 0.32/0.48 % SPC : TH0_THM_NEQ_NAR
% 0.32/0.48
% 0.32/0.48 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.32/0.48 % project in the Department of Mathematical Sciences at Carnegie
% 0.32/0.48 % Mellon University. Distributed under the Creative Commons copyleft
% 0.32/0.48 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.32/0.48 %------------------------------------------------------------------------------
% 0.32/0.48 thf(cTHM111,conjecture,
% 0.32/0.48 ! [P: $i > $o] :
% 0.32/0.48 ? [M: ( $i > $i ) > $o] :
% 0.32/0.48 ! [G: $i > $i,H: $i > $i] :
% 0.32/0.48 ( ( ( M @ G )
% 0.32/0.48 & ( M @ H ) )
% 0.32/0.48 => ( ( M
% 0.32/0.48 @ ^ [Z: $i] : ( G @ ( H @ Z ) ) )
% 0.32/0.48 & ! [Y: $i] :
% 0.32/0.48 ( ( P @ Y )
% 0.32/0.48 => ( P @ ( G @ Y ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 %------------------------------------------------------------------------------
% 0.32/0.48 ------------------------
% 1.64/1.43 ---- Embedded in THF ---
% 1.64/1.43 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.64/1.43 %%% Generated on Tue Feb 24 14:27:13 EST 2026
% 1.64/1.43 %%% using '$$dhol' embedding, version 1.3.0.
% 1.64/1.43 %%% Logic specification used:
% 1.64/1.43 %%% thf(spec, logic, $$dhol).
% 1.64/1.43
% 1.64/1.43 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.E3GYKqPh6S/DTF2DTF4512.p
% See solution above
% 1.64/1.43 ------------------------
% 1.64/1.43 ---- Cleaned THF ---
% 1.64/1.44 thf(cTHM111,conjecture,
% 1.64/1.44 ! [P: $i > $o] :
% 1.64/1.44 ? [M: ( $i > $i ) > $o] :
% 1.64/1.44 ! [G: $i > $i,H: $i > $i] :
% 1.64/1.44 ( ( ( M @ G )
% 1.64/1.44 & ( M @ H ) )
% 1.64/1.44 => ( ( M
% 1.64/1.44 @ ^ [Z: $i] : ( G @ ( H @ Z ) ) )
% 1.64/1.44 & ! [Y: $i] :
% 1.64/1.44 ( ( P @ Y )
% 1.64/1.44 => ( P @ ( G @ Y ) ) ) ) ) ).
% 1.64/1.44 ------------------------
% 1.64/1.45 % (4662)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4512 for (3000ds/183Mi)
% 1.64/1.45 % (4663)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_4512 for (3000ds/4Mi)
% 1.64/1.45 % (4665)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4512 for (3000ds/2Mi)
% 1.64/1.45 % (4664)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_4512 for (3000ds/27Mi)
% 1.64/1.45 % (4666)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_4512 for (3000ds/2Mi)
% 1.64/1.45 % (4667)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_4512 for (3000ds/275Mi)
% 1.64/1.45 % (4668)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4512 for (3000ds/18Mi)
% 1.64/1.46 % (4665)Instruction limit reached!
% 1.64/1.46 % (4665)------------------------------
% 1.64/1.46 % (4665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.46 % (4665)Termination reason: Unknown
% 1.64/1.46 % (4665)Termination phase: Saturation
% 1.64/1.46 % (4666)Instruction limit reached!
% 1.64/1.46 % (4666)------------------------------
% 1.64/1.46 % (4666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.46 % (4666)Termination reason: Unknown
% 1.64/1.46 % (4662)First to succeed.
% 1.64/1.46 % (4666)Termination phase: Saturation
% 1.64/1.46
% 1.64/1.46 % (4666)Memory used [KB]: 5500
% 1.64/1.46 % (4666)Time elapsed: 0.003 s
% 1.64/1.46 % (4666)Instructions burned: 3 (million)
% 1.64/1.46 % (4666)------------------------------
% 1.64/1.46 % (4666)------------------------------
% 1.64/1.46
% 1.64/1.46 % (4665)Memory used [KB]: 5500
% 1.64/1.46 % (4665)Time elapsed: 0.003 s
% 1.64/1.46 % (4665)Instructions burned: 2 (million)
% 1.64/1.46 % (4665)------------------------------
% 1.64/1.46 % (4665)------------------------------
% 1.64/1.46 % (4664)Refutation not found, incomplete strategy
% 1.64/1.46 % (4664)------------------------------
% 1.64/1.46 % (4664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.46 % (4664)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.46
% 1.64/1.46
% 1.64/1.46 % (4664)Memory used [KB]: 5500
% 1.64/1.46 % (4664)Time elapsed: 0.003 s
% 1.64/1.46 % (4664)Instructions burned: 2 (million)
% 1.64/1.46 % (4664)------------------------------
% 1.64/1.46 % (4664)------------------------------
% 1.64/1.46 % (4667)Also succeeded, but the first one will report.
% 1.64/1.46 % (4662)Refutation found. Thanks to Tanya!
% 1.64/1.46 % SZS status Theorem for DTF2THF_4512
% 1.64/1.46 % SZS output start Proof for DTF2THF_4512
% 1.64/1.46 thf(func_def_5, type, sK0: $i > $o).
% 1.64/1.46 thf(func_def_6, type, sK1: (($i > $i) > $o) > $i > $i).
% 1.64/1.46 thf(func_def_7, type, sK2: (($i > $i) > $o) > $i > $i).
% 1.64/1.46 thf(func_def_8, type, sK3: (($i > $i) > $o) > $i).
% 1.64/1.46 thf(func_def_11, type, ph5: !>[X0: $tType]:(X0)).
% 1.64/1.46 thf(f23,plain,(
% 1.64/1.46 $false),
% 1.64/1.46 inference(trivial_inequality_removal,[status(thm)],[f22])).
% 1.64/1.46 thf(f22,plain,(
% 1.64/1.46 ($true = $false)),
% 1.64/1.46 inference(beta_eta_normalization,[status(thm)],[f17])).
% 1.64/1.46 thf(f17,plain,(
% 1.64/1.46 ($true = ((^[Y0 : $i > $i]: ($false)) @ (sK2 @ (^[Y0 : $i > $i]: ($false)))))),
% 1.64/1.46 inference(primitive_instantiation,[status(thm)],[f12])).
% 1.64/1.46 thf(f12,plain,(
% 1.64/1.46 ( ! [X1 : ($i > $i) > $o] : (($true = (X1 @ (sK2 @ X1)))) )),
% 1.64/1.46 inference(cnf_transformation,[status(thm)],[f11])).
% 1.64/1.46 thf(f11,plain,(
% 1.64/1.46 ! [X1 : ($i > $i) > $o] : (($true = (X1 @ (sK1 @ X1))) & (($true != (X1 @ (^[Y0 : $i]: (sK2 @ X1 @ (sK1 @ X1 @ Y0))))) | (($true = (sK0 @ (sK3 @ X1))) & ((sK0 @ (sK2 @ X1 @ (sK3 @ X1))) != $true))) & ($true = (X1 @ (sK2 @ X1))))),
% 1.64/1.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f7,f10,f9,f8])).
% 1.64/1.46 thf(f8,plain,(
% 1.64/1.46 ? [X0 : $i > $o] : ! [X1 : ($i > $i) > $o] : ? [X2 : $i > $i,X3 : $i > $i] : (((X1 @ X2) = $true) & (($true != (X1 @ (^[Y0 : $i]: (X3 @ (X2 @ Y0))))) | ? [X4 : $i] : (($true = (X0 @ X4)) & ($true != (X0 @ (X3 @ X4))))) & ((X1 @ X3) = $true)) => ! [X1 : ($i > $i) > $o] : ? [X3 : $i > $i,X2 : $i > $i] : (((X1 @ X2) = $true) & (($true != (X1 @ (^[Y0 : $i]: (X3 @ (X2 @ Y0))))) | ? [X4 : $i] : (((sK0 @ X4) = $true) & ((sK0 @ (X3 @ X4)) != $true))) & ((X1 @ X3) = $true))),
% 1.64/1.46 introduced(definition,[],[choice_axiom])).
% 1.64/1.46 thf(f9,plain,(
% 1.64/1.46 ! [X1 : ($i > $i) > $o] : (? [X3 : $i > $i,X2 : $i > $i] : (((X1 @ X2) = $true) & (($true != (X1 @ (^[Y0 : $i]: (X3 @ (X2 @ Y0))))) | ? [X4 : $i] : (((sK0 @ X4) = $true) & ((sK0 @ (X3 @ X4)) != $true))) & ((X1 @ X3) = $true)) => (($true = (X1 @ (sK1 @ X1))) & (($true != (X1 @ (^[Y0 : $i]: (sK2 @ X1 @ (sK1 @ X1 @ Y0))))) | ? [X4 : $i] : (((sK0 @ X4) = $true) & ($true != (sK0 @ (sK2 @ X1 @ X4))))) & ($true = (X1 @ (sK2 @ X1)))))),
% 1.64/1.46 introduced(definition,[],[choice_axiom])).
% 1.64/1.46 thf(f10,plain,(
% 1.64/1.46 ! [X1 : ($i > $i) > $o] : (? [X4 : $i] : (((sK0 @ X4) = $true) & ($true != (sK0 @ (sK2 @ X1 @ X4)))) => (($true = (sK0 @ (sK3 @ X1))) & ((sK0 @ (sK2 @ X1 @ (sK3 @ X1))) != $true)))),
% 1.64/1.46 introduced(definition,[],[choice_axiom])).
% 1.64/1.46 thf(f7,plain,(
% 1.64/1.46 ? [X0 : $i > $o] : ! [X1 : ($i > $i) > $o] : ? [X2 : $i > $i,X3 : $i > $i] : (((X1 @ X2) = $true) & (($true != (X1 @ (^[Y0 : $i]: (X3 @ (X2 @ Y0))))) | ? [X4 : $i] : (($true = (X0 @ X4)) & ($true != (X0 @ (X3 @ X4))))) & ((X1 @ X3) = $true))),
% 1.64/1.46 inference(flattening,[status(thm)],[f6])).
% 1.64/1.46 thf(f6,plain,(
% 1.64/1.46 ? [X0 : $i > $o] : ! [X1 : ($i > $i) > $o] : ? [X2 : $i > $i,X3 : $i > $i] : ((($true != (X1 @ (^[Y0 : $i]: (X3 @ (X2 @ Y0))))) | ? [X4 : $i] : (($true = (X0 @ X4)) & ($true != (X0 @ (X3 @ X4))))) & (((X1 @ X2) = $true) & ((X1 @ X3) = $true)))),
% 1.64/1.46 inference(ennf_transformation,[status(thm)],[f5])).
% 1.64/1.46 thf(f5,plain,(
% 1.64/1.46 ~! [X0 : $i > $o] : ? [X1 : ($i > $i) > $o] : ! [X2 : $i > $i,X3 : $i > $i] : ((((X1 @ X2) = $true) & ((X1 @ X3) = $true)) => (! [X4 : $i] : (($true = (X0 @ X4)) => ($true = (X0 @ (X3 @ X4)))) & ($true = (X1 @ (^[Y0 : $i]: (X3 @ (X2 @ Y0)))))))),
% 1.64/1.46 inference(fool_elimination,[status(thm)],[f4])).
% 1.64/1.46 thf(f4,plain,(
% 1.64/1.46 ~! [X0 : $i > $o] : ? [X1 : ($i > $i) > $o] : ! [X2 : $i > $i,X3 : $i > $i] : (((X1 @ X2) & (X1 @ X3)) => (! [X4 : $i] : ((X0 @ X4) => (X0 @ (X3 @ X4))) & (X1 @ (^[X5 : $i] : (X3 @ (X2 @ X5))))))),
% 1.64/1.46 inference(rectify,[status(thm)],[f2])).
% 1.64/1.46 thf(f2,negated_conjecture,(
% 1.64/1.46 ~! [X0 : $i > $o] : ? [X1 : ($i > $i) > $o] : ! [X3 : $i > $i,X2 : $i > $i] : (((X1 @ X3) & (X1 @ X2)) => (! [X5 : $i] : ((X0 @ X5) => (X0 @ (X2 @ X5))) & (X1 @ (^[X4 : $i] : (X2 @ (X3 @ X4))))))),
% 1.64/1.46 inference(negated_conjecture,[status(cth)],[f1])).
% 1.64/1.46 thf(f1,conjecture,(
% 1.64/1.46 ! [X0 : $i > $o] : ? [X1 : ($i > $i) > $o] : ! [X3 : $i > $i,X2 : $i > $i] : (((X1 @ X3) & (X1 @ X2)) => (! [X5 : $i] : ((X0 @ X5) => (X0 @ (X2 @ X5))) & (X1 @ (^[X4 : $i] : (X2 @ (X3 @ X4))))))),
% 1.64/1.46 file('/export/starexec/sandbox/tmp/tmp.E3GYKqPh6S/DTF2THF_4512.p',cTHM111)).
% 1.64/1.46 % SZS output end Proof for DTF2THF_4512
% 1.64/1.46 % (4662)------------------------------
% 1.64/1.46 % (4662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.46 % (4662)Termination reason: Refutation
% 1.64/1.46
% 1.64/1.46 % (4662)Memory used [KB]: 5500
% 1.64/1.46 % (4662)Time elapsed: 0.004 s
% 1.64/1.46 % (4662)Instructions burned: 2 (million)
% 1.64/1.46 % (4662)------------------------------
% 1.64/1.46 % (4662)------------------------------
% 1.64/1.46 % (4661)Success in time 0.017 s
%------------------------------------------------------------------------------