%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV081^5 : 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 : n003.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 09:40:14 AM UTC 2026
% Result : Theorem 1.57s 1.32s
% Output : Refutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 111 ( 40 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 201 ( 26 ~; 11 |; 24 &; 134 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 104 ( 104 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 68 ( 6 ^; 34 !; 28 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_3,type,
sK0: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_4,type,
sK1: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_5,type,
sK2: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_6,type,
sK3: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_9,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f29,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f28]) ).
thf(f28,plain,
$true != $true,
inference(beta_eta_normalization,[status(thm)],[f23]) ).
thf(f23,plain,
( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o] : $true
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : $true )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : $true ) ) ),
inference(equality_resolution,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) )
!= $true )
| ( ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) )
!= $true ) ),
inference(condensation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o,X6: $i > $o,X5: $i > $o] :
( ( ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) )
!= $true )
| ( ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) )
!= $true )
| ( $true
!= ( X0 @ X5 @ X6 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) )
!= $true )
| ( ( ( X0 @ ( sK1 @ X0 ) @ ( sK3 @ X0 ) )
= $true )
& ( $true
= ( X0 @ ( sK2 @ X0 ) @ ( sK1 @ X0 ) ) )
& ( ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) )
!= $true ) )
| ! [X5: $i > $o,X6: $i > $o] :
( $true
!= ( X0 @ X5 @ X6 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f10,f9]) ).
thf(f9,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o] :
( $true
!= ( X0 @ X1 @ X1 ) )
=> ( ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ( ( X0 @ X2 @ X4 )
= $true )
& ( $true
= ( X0 @ X3 @ X2 ) )
& ( ( X0 @ X3 @ X4 )
!= $true ) )
=> ( ( ( X0 @ ( sK1 @ X0 ) @ ( sK3 @ X0 ) )
= $true )
& ( $true
= ( X0 @ ( sK2 @ X0 ) @ ( sK1 @ X0 ) ) )
& ( ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o] :
( $true
!= ( X0 @ X1 @ X1 ) )
| ? [X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ( ( X0 @ X2 @ X4 )
= $true )
& ( $true
= ( X0 @ X3 @ X2 ) )
& ( ( X0 @ X3 @ X4 )
!= $true ) )
| ! [X5: $i > $o,X6: $i > $o] :
( $true
!= ( X0 @ X5 @ X6 ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X3: $i > $o] :
( ( X0 @ X3 @ X3 )
!= $true )
| ? [X4: $i > $o,X5: $i > $o,X6: $i > $o] :
( ( ( X0 @ X4 @ X6 )
= $true )
& ( ( X0 @ X5 @ X4 )
= $true )
& ( $true
!= ( X0 @ X5 @ X6 ) ) )
| ! [X2: $i > $o,X1: $i > $o] :
( ( X0 @ X2 @ X1 )
!= $true ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X2: $i > $o,X1: $i > $o] :
( ( X0 @ X2 @ X1 )
!= $true )
| ? [X3: $i > $o] :
( ( X0 @ X3 @ X3 )
!= $true )
| ? [X6: $i > $o,X5: $i > $o,X4: $i > $o] :
( ( $true
!= ( X0 @ X5 @ X6 ) )
& ( ( X0 @ X5 @ X4 )
= $true )
& ( ( X0 @ X4 @ X6 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o] :
( ( X0 @ X2 @ X1 )
= $true )
& ! [X3: $i > $o] :
( ( X0 @ X3 @ X3 )
= $true )
& ! [X6: $i > $o,X5: $i > $o,X4: $i > $o] :
( ( ( ( X0 @ X5 @ X4 )
= $true )
& ( ( X0 @ X4 @ X6 )
= $true ) )
=> ( $true
= ( X0 @ X5 @ X6 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o] : ( X0 @ X2 @ X1 )
& ! [X3: $i > $o] : ( X0 @ X3 @ X3 )
& ! [X4: $i > $o,X5: $i > $o,X6: $i > $o] :
( ( ( X0 @ X5 @ X4 )
& ( X0 @ X4 @ X6 ) )
=> ( X0 @ X5 @ X6 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X2: $i > $o,X1: $i > $o] : ( X0 @ X1 @ X2 )
& ! [X3: $i > $o] : ( X0 @ X3 @ X3 )
& ! [X4: $i > $o,X3: $i > $o,X5: $i > $o] :
( ( ( X0 @ X3 @ X4 )
& ( X0 @ X4 @ X5 ) )
=> ( X0 @ X3 @ X5 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X2: $i > $o,X1: $i > $o] : ( X0 @ X1 @ X2 )
& ! [X3: $i > $o] : ( X0 @ X3 @ X3 )
& ! [X4: $i > $o,X3: $i > $o,X5: $i > $o] :
( ( ( X0 @ X3 @ X4 )
& ( X0 @ X4 @ X5 ) )
=> ( X0 @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6lBQJyYmNf/DTF2THF_22549.p',cTHM120_1_pme) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEV081^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n003.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 12:39:40 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : SEV081^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.39 % Domain : Set Theory (Relations)
% 0.16/0.39 % Problem : TPS problem from RELN-THMS
% 0.16/0.39 % Version : Especial.
% 0.16/0.39 % English :
% 0.16/0.39
% 0.16/0.39 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.39 % Source : [Bro09]
% 0.16/0.39 % Names : tps_0858 [Bro09]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % 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 v4.0.0
% 0.16/0.39 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.16/0.39 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 0 ( 0 avg)
% 0.16/0.39 % Number of connectives : 14 ( 0 ~; 0 |; 3 &; 10 @)
% 0.16/0.39 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 11 ( 11 avg)
% 0.16/0.39 % Number of types : 2 ( 0 usr)
% 0.16/0.39 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.16/0.39 % Number of variables : 7 ( 0 ^; 4 !; 3 ?; 7 :)
% 0.16/0.39 % SPC : TH0_THM_NEQ_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.39 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.39 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.39 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf(cTHM120_1_pme,conjecture,
% 0.16/0.39 ? [R: ( $i > $o ) > ( $i > $o ) > $o] :
% 0.16/0.39 ( ? [X: $i > $o,Y: $i > $o] : ( R @ X @ Y )
% 0.16/0.39 & ! [Xx: $i > $o] : ( R @ Xx @ Xx )
% 0.16/0.39 & ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
% 0.16/0.39 ( ( ( R @ Xx @ Xy )
% 0.16/0.39 & ( R @ Xy @ Xz ) )
% 0.16/0.39 => ( R @ Xx @ Xz ) ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 1.36/1.29 ---- Embedded in THF ---
% 1.36/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.36/1.29 %%% Generated on Tue Feb 24 12:39:41 EST 2026
% 1.36/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.36/1.29 %%% Logic specification used:
% 1.36/1.29 %%% thf(spec, logic, $$dhol).
% 1.36/1.29
% 1.36/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.6lBQJyYmNf/DTF2DTF22549.p
% See solution above
% 1.36/1.29 ------------------------
% 1.57/1.30 ---- Cleaned THF ---
% 1.57/1.30 thf(cTHM120_1_pme,conjecture,
% 1.57/1.30 ? [R: ( $i > $o ) > ( $i > $o ) > $o] :
% 1.57/1.30 ( ? [X: $i > $o,Y: $i > $o] : ( R @ X @ Y )
% 1.57/1.30 & ! [Xx: $i > $o] : ( R @ Xx @ Xx )
% 1.57/1.30 & ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
% 1.57/1.30 ( ( ( R @ Xx @ Xy )
% 1.57/1.30 & ( R @ Xy @ Xz ) )
% 1.57/1.30 => ( R @ Xx @ Xz ) ) ) ).
% 1.57/1.30 ------------------------
% 1.57/1.32 % (22647)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22549 for (3000ds/183Mi)
% 1.57/1.32 % (22649)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_22549 for (3000ds/27Mi)
% 1.57/1.32 % (22650)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22549 for (3000ds/2Mi)
% 1.57/1.32 % (22652)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_22549 for (3000ds/275Mi)
% 1.57/1.32 % (22648)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_22549 for (3000ds/4Mi)
% 1.57/1.32 % (22653)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22549 for (3000ds/18Mi)
% 1.57/1.32 % (22651)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_22549 for (3000ds/2Mi)
% 1.57/1.32 % (22650)Instruction limit reached!
% 1.57/1.32 % (22650)------------------------------
% 1.57/1.32 % (22650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.32 % (22650)Termination reason: Unknown
% 1.57/1.32 % (22650)Termination phase: Saturation
% 1.57/1.32 % (22651)Instruction limit reached!
% 1.57/1.32 % (22651)------------------------------
% 1.57/1.32 % (22651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.32
% 1.57/1.32 % (22650)Memory used [KB]: 5373
% 1.57/1.32 % (22650)Time elapsed: 0.003 s
% 1.57/1.32 % (22650)Instructions burned: 2 (million)
% 1.57/1.32 % (22650)------------------------------
% 1.57/1.32 % (22650)------------------------------
% 1.57/1.32 % (22651)Termination reason: Unknown
% 1.57/1.32 % (22651)Termination phase: Saturation
% 1.57/1.32
% 1.57/1.32 % (22651)Memory used [KB]: 5500
% 1.57/1.32 % (22651)Time elapsed: 0.003 s
% 1.57/1.32 % (22651)Instructions burned: 2 (million)
% 1.57/1.32 % (22651)------------------------------
% 1.57/1.32 % (22651)------------------------------
% 1.57/1.32 % (22649)Refutation not found, incomplete strategy
% 1.57/1.32 % (22649)------------------------------
% 1.57/1.32 % (22649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.32 % (22649)Termination reason: Refutation not found, incomplete strategy
% 1.57/1.32
% 1.57/1.32
% 1.57/1.32 % (22649)Memory used [KB]: 5500
% 1.57/1.32 % (22649)Time elapsed: 0.003 s
% 1.57/1.32 % (22649)Instructions burned: 2 (million)
% 1.57/1.32 % (22649)------------------------------
% 1.57/1.32 % (22649)------------------------------
% 1.57/1.32 % (22653)First to succeed.
% 1.57/1.32 % (22648)Instruction limit reached!
% 1.57/1.32 % (22648)------------------------------
% 1.57/1.32 % (22648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.32 % (22648)Termination reason: Unknown
% 1.57/1.32 % (22648)Termination phase: Saturation
% 1.57/1.32
% 1.57/1.32 % (22648)Memory used [KB]: 5500
% 1.57/1.32 % (22648)Time elapsed: 0.005 s
% 1.57/1.32 % (22648)Instructions burned: 5 (million)
% 1.57/1.32 % (22648)------------------------------
% 1.57/1.32 % (22648)------------------------------
% 1.57/1.32 % (22647)Also succeeded, but the first one will report.
% 1.57/1.32 % (22653)Refutation found. Thanks to Tanya!
% 1.57/1.32 % SZS status Theorem for DTF2THF_22549
% 1.57/1.32 % SZS output start Proof for DTF2THF_22549
% 1.57/1.32 thf(func_def_3, type, sK0: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.57/1.32 thf(func_def_4, type, sK1: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.57/1.32 thf(func_def_5, type, sK2: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.57/1.32 thf(func_def_6, type, sK3: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.57/1.32 thf(func_def_9, type, ph5: !>[X0: $tType]:(X0)).
% 1.57/1.32 thf(f29,plain,(
% 1.57/1.32 $false),
% 1.57/1.32 inference(trivial_inequality_removal,[status(thm)],[f28])).
% 1.57/1.32 thf(f28,plain,(
% 1.57/1.32 ($true != $true)),
% 1.57/1.32 inference(beta_eta_normalization,[status(thm)],[f23])).
% 1.57/1.32 thf(f23,plain,(
% 1.57/1.32 ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true)))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true)))))))),
% 1.57/1.32 inference(equality_resolution,[status(thm)],[f15])).
% 1.57/1.32 thf(f15,plain,(
% 1.57/1.32 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (sK2 @ X0) @ (sK3 @ X0)) != $true) | ((X0 @ (sK0 @ X0) @ (sK0 @ X0)) != $true)) )),
% 1.57/1.32 inference(condensation,[status(thm)],[f12])).
% 1.57/1.32 thf(f12,plain,(
% 1.57/1.32 ( ! [X0 : ($i > $o) > ($i > $o) > $o,X6 : $i > $o,X5 : $i > $o] : (((X0 @ (sK2 @ X0) @ (sK3 @ X0)) != $true) | ((X0 @ (sK0 @ X0) @ (sK0 @ X0)) != $true) | ($true != (X0 @ X5 @ X6))) )),
% 1.57/1.32 inference(cnf_transformation,[status(thm)],[f11])).
% 1.57/1.32 thf(f11,plain,(
% 1.57/1.32 ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (sK0 @ X0) @ (sK0 @ X0)) != $true) | (((X0 @ (sK1 @ X0) @ (sK3 @ X0)) = $true) & ($true = (X0 @ (sK2 @ X0) @ (sK1 @ X0))) & ((X0 @ (sK2 @ X0) @ (sK3 @ X0)) != $true)) | ! [X5 : $i > $o,X6 : $i > $o] : ($true != (X0 @ X5 @ X6)))),
% 1.57/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f10,f9])).
% 1.57/1.32 thf(f9,plain,(
% 1.57/1.32 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o] : ($true != (X0 @ X1 @ X1)) => ((X0 @ (sK0 @ X0) @ (sK0 @ X0)) != $true))),
% 1.57/1.32 introduced(definition,[],[choice_axiom])).
% 1.57/1.32 thf(f10,plain,(
% 1.57/1.32 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X2 : $i > $o,X3 : $i > $o,X4 : $i > $o] : (((X0 @ X2 @ X4) = $true) & ($true = (X0 @ X3 @ X2)) & ((X0 @ X3 @ X4) != $true)) => (((X0 @ (sK1 @ X0) @ (sK3 @ X0)) = $true) & ($true = (X0 @ (sK2 @ X0) @ (sK1 @ X0))) & ((X0 @ (sK2 @ X0) @ (sK3 @ X0)) != $true)))),
% 1.57/1.32 introduced(definition,[],[choice_axiom])).
% 1.57/1.32 thf(f8,plain,(
% 1.57/1.32 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o] : ($true != (X0 @ X1 @ X1)) | ? [X2 : $i > $o,X3 : $i > $o,X4 : $i > $o] : (((X0 @ X2 @ X4) = $true) & ($true = (X0 @ X3 @ X2)) & ((X0 @ X3 @ X4) != $true)) | ! [X5 : $i > $o,X6 : $i > $o] : ($true != (X0 @ X5 @ X6)))),
% 1.57/1.32 inference(rectify,[status(thm)],[f7])).
% 1.57/1.32 thf(f7,plain,(
% 1.57/1.32 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X3 : $i > $o] : ((X0 @ X3 @ X3) != $true) | ? [X4 : $i > $o,X5 : $i > $o,X6 : $i > $o] : (((X0 @ X4 @ X6) = $true) & ((X0 @ X5 @ X4) = $true) & ($true != (X0 @ X5 @ X6))) | ! [X2 : $i > $o,X1 : $i > $o] : ((X0 @ X2 @ X1) != $true))),
% 1.57/1.32 inference(flattening,[status(thm)],[f6])).
% 1.57/1.32 thf(f6,plain,(
% 1.57/1.32 ! [X0 : ($i > $o) > ($i > $o) > $o] : (! [X2 : $i > $o,X1 : $i > $o] : ((X0 @ X2 @ X1) != $true) | ? [X3 : $i > $o] : ((X0 @ X3 @ X3) != $true) | ? [X6 : $i > $o,X5 : $i > $o,X4 : $i > $o] : (($true != (X0 @ X5 @ X6)) & (((X0 @ X5 @ X4) = $true) & ((X0 @ X4 @ X6) = $true))))),
% 1.57/1.32 inference(ennf_transformation,[status(thm)],[f5])).
% 1.57/1.32 thf(f5,plain,(
% 1.57/1.32 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o] : ((X0 @ X2 @ X1) = $true) & ! [X3 : $i > $o] : ((X0 @ X3 @ X3) = $true) & ! [X6 : $i > $o,X5 : $i > $o,X4 : $i > $o] : ((((X0 @ X5 @ X4) = $true) & ((X0 @ X4 @ X6) = $true)) => ($true = (X0 @ X5 @ X6))))),
% 1.57/1.32 inference(fool_elimination,[status(thm)],[f4])).
% 1.57/1.32 thf(f4,plain,(
% 1.57/1.32 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o] : (X0 @ X2 @ X1) & ! [X3 : $i > $o] : (X0 @ X3 @ X3) & ! [X4 : $i > $o,X5 : $i > $o,X6 : $i > $o] : (((X0 @ X5 @ X4) & (X0 @ X4 @ X6)) => (X0 @ X5 @ X6)))),
% 1.57/1.32 inference(rectify,[status(thm)],[f2])).
% 1.57/1.32 thf(f2,negated_conjecture,(
% 1.57/1.32 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (? [X2 : $i > $o,X1 : $i > $o] : (X0 @ X1 @ X2) & ! [X3 : $i > $o] : (X0 @ X3 @ X3) & ! [X4 : $i > $o,X3 : $i > $o,X5 : $i > $o] : (((X0 @ X3 @ X4) & (X0 @ X4 @ X5)) => (X0 @ X3 @ X5)))),
% 1.57/1.32 inference(negated_conjecture,[status(cth)],[f1])).
% 1.57/1.32 thf(f1,conjecture,(
% 1.57/1.32 ? [X0 : ($i > $o) > ($i > $o) > $o] : (? [X2 : $i > $o,X1 : $i > $o] : (X0 @ X1 @ X2) & ! [X3 : $i > $o] : (X0 @ X3 @ X3) & ! [X4 : $i > $o,X3 : $i > $o,X5 : $i > $o] : (((X0 @ X3 @ X4) & (X0 @ X4 @ X5)) => (X0 @ X3 @ X5)))),
% 1.57/1.32 file('/export/starexec/sandbox/tmp/tmp.6lBQJyYmNf/DTF2THF_22549.p',cTHM120_1_pme)).
% 1.57/1.32 % SZS output end Proof for DTF2THF_22549
% 1.57/1.32 % (22653)------------------------------
% 1.57/1.32 % (22653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.32 % (22653)Termination reason: Refutation
% 1.57/1.32
% 1.57/1.32 % (22653)Memory used [KB]: 5500
% 1.57/1.32 % (22653)Time elapsed: 0.004 s
% 1.57/1.32 % (22653)Instructions burned: 2 (million)
% 1.57/1.32 % (22653)------------------------------
% 1.57/1.32 % (22653)------------------------------
% 1.57/1.32 % (22646)Success in time 0.017 s
%------------------------------------------------------------------------------