%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV408^5 : 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 : n025.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 09:41:11 AM UTC 2026
% Result : Theorem 1.26s 1.12s
% Output : Refutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 74 ( 27 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 95 ( 13 ~; 4 |; 14 &; 54 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 34 ( 2 ^; 18 !; 14 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cF: ( $i > $o ) > $o ).
thf(func_def_4,type,
sK0: ( ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_5,type,
sK1: ( $i > $o ) > ( ( $i > $o ) > $o ) > $i ).
thf(func_def_7,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f19,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f18]) ).
thf(f18,plain,
$true = $false,
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( $true
= ( ^ [Y0: $i > $o] : $false
@ ( sK0
@ ^ [Y0: $i > $o] : $false ) ) ),
inference(primitive_instantiation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: ( $i > $o ) > $o] :
( $true
= ( X0 @ ( sK0 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: ( $i > $o ) > $o] :
( ( $true
= ( X0 @ ( sK0 @ X0 ) ) )
& ! [X2: $i > $o] :
( ( ( $true
= ( sK0 @ X0 @ ( sK1 @ X2 @ X0 ) ) )
& ( $true
!= ( X2 @ ( sK1 @ X2 @ X0 ) ) ) )
| ( ( cF @ X2 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f8,f7]) ).
thf(f7,plain,
! [X0: ( $i > $o ) > $o] :
( ? [X1: $i > $o] :
( ( ( X0 @ X1 )
= $true )
& ! [X2: $i > $o] :
( ? [X3: $i] :
( ( ( X1 @ X3 )
= $true )
& ( ( X2 @ X3 )
!= $true ) )
| ( ( cF @ X2 )
!= $true ) ) )
=> ( ( $true
= ( X0 @ ( sK0 @ X0 ) ) )
& ! [X2: $i > $o] :
( ? [X3: $i] :
( ( $true
= ( sK0 @ X0 @ X3 ) )
& ( ( X2 @ X3 )
!= $true ) )
| ( ( cF @ X2 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
! [X0: ( $i > $o ) > $o,X2: $i > $o] :
( ? [X3: $i] :
( ( $true
= ( sK0 @ X0 @ X3 ) )
& ( ( X2 @ X3 )
!= $true ) )
=> ( ( $true
= ( sK0 @ X0 @ ( sK1 @ X2 @ X0 ) ) )
& ( $true
!= ( X2 @ ( sK1 @ X2 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
! [X0: ( $i > $o ) > $o] :
? [X1: $i > $o] :
( ( ( X0 @ X1 )
= $true )
& ! [X2: $i > $o] :
( ? [X3: $i] :
( ( ( X1 @ X3 )
= $true )
& ( ( X2 @ X3 )
!= $true ) )
| ( ( cF @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: ( $i > $o ) > $o] :
! [X1: $i > $o] :
( ( ( X0 @ X1 )
= $true )
=> ? [X2: $i > $o] :
( ! [X3: $i] :
( ( ( X1 @ X3 )
= $true )
=> ( ( X2 @ X3 )
= $true ) )
& ( ( cF @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: ( $i > $o ) > $o] :
! [X1: $i > $o] :
( ( X0 @ X1 )
=> ? [X2: $i > $o] :
( ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
& ( cF @ X2 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: ( $i > $o ) > $o] :
! [X1: $i > $o] :
( ( X0 @ X1 )
=> ? [X2: $i > $o] :
( ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
& ( cF @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: ( $i > $o ) > $o] :
! [X1: $i > $o] :
( ( X0 @ X1 )
=> ? [X2: $i > $o] :
( ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
& ( cF @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ClYweRtJwQ/DTF2THF_13683.p',cBLEDSOE2_pme) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV408^5 : TPTP v9.2.1. Released v4.0.0.
% 0.10/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Feb 24 12:46:12 EST 2026
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.42 ---- Original DTF file ---
% 0.15/0.42 thf(spec,logic,$$dhol).
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 % File : SEV408^5 : TPTP v9.2.1. Released v4.0.0.
% 0.15/0.42 % Domain : Set Theory
% 0.15/0.42 % Problem : TPS problem from SETS-THMS
% 0.15/0.42 % Version : Especial.
% 0.15/0.42 % English :
% 0.15/0.42
% 0.15/0.42 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.15/0.42 % Source : [Bro09]
% 0.15/0.42 % Names : tps_0772 [Bro09]
% 0.15/0.42
% 0.15/0.42 % Status : Theorem
% 0.15/0.42 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.33 v6.1.0, 0.17 v6.0.0, 0.00 v4.0.0
% 0.15/0.42 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.15/0.42 % Number of atoms : 1 ( 0 equ; 0 cnn)
% 0.15/0.42 % Maximal formula atoms : 1 ( 1 avg)
% 0.15/0.42 % Number of connectives : 7 ( 0 ~; 0 |; 1 &; 4 @)
% 0.15/0.42 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.15/0.42 % Maximal formula depth : 9 ( 9 avg)
% 0.15/0.42 % Number of types : 2 ( 0 usr)
% 0.15/0.42 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.15/0.42 % Number of symbols : 1 ( 1 usr; 0 con; 1-1 aty)
% 0.15/0.42 % Number of variables : 4 ( 0 ^; 2 !; 2 ?; 4 :)
% 0.15/0.42 % SPC : TH0_THM_NEQ_NAR
% 0.15/0.42
% 0.15/0.42 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.15/0.42 % project in the Department of Mathematical Sciences at Carnegie
% 0.15/0.42 % Mellon University. Distributed under the Creative Commons copyleft
% 0.15/0.42 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 thf(cF,type,
% 0.15/0.42 cF: ( $i > $o ) > $o ).
% 0.15/0.42
% 0.15/0.42 thf(cBLEDSOE2_pme,conjecture,
% 0.15/0.42 ? [G: ( $i > $o ) > $o] :
% 0.15/0.42 ! [A: $i > $o] :
% 0.15/0.42 ( ( G @ A )
% 0.15/0.42 => ? [B: $i > $o] :
% 0.15/0.42 ( ( cF @ B )
% 0.15/0.42 & ! [Xx: $i] :
% 0.15/0.42 ( ( A @ Xx )
% 0.15/0.42 => ( B @ Xx ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 ------------------------
% 1.07/1.10 ---- Embedded in THF ---
% 1.07/1.10 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.07/1.10 %%% Generated on Tue Feb 24 12:46:13 EST 2026
% 1.07/1.10 %%% using '$$dhol' embedding, version 1.3.0.
% 1.07/1.10 %%% Logic specification used:
% 1.07/1.10 %%% thf(spec, logic, $$dhol).
% 1.07/1.10
% 1.07/1.10 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ClYweRtJwQ/DTF2DTF13683.p
% See solution above
% 1.07/1.10 ------------------------
% 1.07/1.10 ---- Cleaned THF ---
% 1.07/1.10 thf(cF,type,
% 1.07/1.10 cF: ( $i > $o ) > $o ).
% 1.07/1.10
% 1.07/1.10 thf(cBLEDSOE2_pme,conjecture,
% 1.07/1.10 ? [G: ( $i > $o ) > $o] :
% 1.07/1.10 ! [A: $i > $o] :
% 1.07/1.10 ( ( G @ A )
% 1.07/1.10 => ? [B: $i > $o] :
% 1.07/1.10 ( ( cF @ B )
% 1.07/1.10 & ! [Xx: $i] :
% 1.07/1.10 ( ( A @ Xx )
% 1.07/1.10 => ( B @ Xx ) ) ) ) ).
% 1.07/1.10 ------------------------
% 1.26/1.12 % (13797)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13683 for (3000ds/183Mi)
% 1.26/1.12 % (13799)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_13683 for (3000ds/27Mi)
% 1.26/1.12 % (13800)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13683 for (3000ds/2Mi)
% 1.26/1.12 % (13803)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13683 for (3000ds/18Mi)
% 1.26/1.12 % (13801)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_13683 for (3000ds/2Mi)
% 1.26/1.12 % (13798)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_13683 for (3000ds/4Mi)
% 1.26/1.12 % (13802)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_13683 for (3000ds/275Mi)
% 1.26/1.12 % (13801)Instruction limit reached!
% 1.26/1.12 % (13801)------------------------------
% 1.26/1.12 % (13801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.12 % (13801)Termination reason: Unknown
% 1.26/1.12 % (13801)Termination phase: Saturation
% 1.26/1.12
% 1.26/1.12 % (13801)Memory used [KB]: 5373
% 1.26/1.12 % (13801)Time elapsed: 0.002 s
% 1.26/1.12 % (13801)Instructions burned: 2 (million)
% 1.26/1.12 % (13801)------------------------------
% 1.26/1.12 % (13801)------------------------------
% 1.26/1.12 % (13802)First to succeed.
% 1.26/1.12 % (13800)Also succeeded, but the first one will report.
% 1.26/1.12 % (13797)Also succeeded, but the first one will report.
% 1.26/1.12 % (13802)Refutation found. Thanks to Tanya!
% 1.26/1.12 % SZS status Theorem for DTF2THF_13683
% 1.26/1.12 % SZS output start Proof for DTF2THF_13683
% 1.26/1.12 thf(func_def_0, type, cF: ($i > $o) > $o).
% 1.26/1.12 thf(func_def_4, type, sK0: (($i > $o) > $o) > $i > $o).
% 1.26/1.12 thf(func_def_5, type, sK1: ($i > $o) > (($i > $o) > $o) > $i).
% 1.26/1.12 thf(func_def_7, type, ph3: !>[X0: $tType]:(X0)).
% 1.26/1.12 thf(f19,plain,(
% 1.26/1.12 $false),
% 1.26/1.12 inference(trivial_inequality_removal,[status(thm)],[f18])).
% 1.26/1.12 thf(f18,plain,(
% 1.26/1.12 ($true = $false)),
% 1.26/1.12 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.26/1.12 thf(f14,plain,(
% 1.26/1.12 ($true = ((^[Y0 : $i > $o]: ($false)) @ (sK0 @ (^[Y0 : $i > $o]: ($false)))))),
% 1.26/1.12 inference(primitive_instantiation,[status(thm)],[f12])).
% 1.26/1.12 thf(f12,plain,(
% 1.26/1.12 ( ! [X0 : ($i > $o) > $o] : (($true = (X0 @ (sK0 @ X0)))) )),
% 1.26/1.12 inference(cnf_transformation,[status(thm)],[f9])).
% 1.26/1.12 thf(f9,plain,(
% 1.26/1.12 ! [X0 : ($i > $o) > $o] : (($true = (X0 @ (sK0 @ X0))) & ! [X2 : $i > $o] : ((($true = (sK0 @ X0 @ (sK1 @ X2 @ X0))) & ($true != (X2 @ (sK1 @ X2 @ X0)))) | ((cF @ X2) != $true)))),
% 1.26/1.12 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f8,f7])).
% 1.26/1.12 thf(f7,plain,(
% 1.26/1.12 ! [X0 : ($i > $o) > $o] : (? [X1 : $i > $o] : (((X0 @ X1) = $true) & ! [X2 : $i > $o] : (? [X3 : $i] : (((X1 @ X3) = $true) & ((X2 @ X3) != $true)) | ((cF @ X2) != $true))) => (($true = (X0 @ (sK0 @ X0))) & ! [X2 : $i > $o] : (? [X3 : $i] : (($true = (sK0 @ X0 @ X3)) & ((X2 @ X3) != $true)) | ((cF @ X2) != $true))))),
% 1.26/1.12 introduced(definition,[],[choice_axiom])).
% 1.26/1.12 thf(f8,plain,(
% 1.26/1.12 ! [X0 : ($i > $o) > $o,X2 : $i > $o] : (? [X3 : $i] : (($true = (sK0 @ X0 @ X3)) & ((X2 @ X3) != $true)) => (($true = (sK0 @ X0 @ (sK1 @ X2 @ X0))) & ($true != (X2 @ (sK1 @ X2 @ X0)))))),
% 1.26/1.12 introduced(definition,[],[choice_axiom])).
% 1.26/1.12 thf(f6,plain,(
% 1.26/1.12 ! [X0 : ($i > $o) > $o] : ? [X1 : $i > $o] : (((X0 @ X1) = $true) & ! [X2 : $i > $o] : (? [X3 : $i] : (((X1 @ X3) = $true) & ((X2 @ X3) != $true)) | ((cF @ X2) != $true)))),
% 1.26/1.12 inference(ennf_transformation,[status(thm)],[f5])).
% 1.26/1.12 thf(f5,plain,(
% 1.26/1.12 ~? [X0 : ($i > $o) > $o] : ! [X1 : $i > $o] : (((X0 @ X1) = $true) => ? [X2 : $i > $o] : (! [X3 : $i] : (((X1 @ X3) = $true) => ((X2 @ X3) = $true)) & ((cF @ X2) = $true)))),
% 1.26/1.12 inference(fool_elimination,[status(thm)],[f4])).
% 1.26/1.12 thf(f4,plain,(
% 1.26/1.12 ~? [X0 : ($i > $o) > $o] : ! [X1 : $i > $o] : ((X0 @ X1) => ? [X2 : $i > $o] : (! [X3 : $i] : ((X1 @ X3) => (X2 @ X3)) & (cF @ X2)))),
% 1.26/1.12 inference(rectify,[status(thm)],[f2])).
% 1.26/1.12 thf(f2,negated_conjecture,(
% 1.26/1.12 ~? [X0 : ($i > $o) > $o] : ! [X1 : $i > $o] : ((X0 @ X1) => ? [X2 : $i > $o] : (! [X3 : $i] : ((X1 @ X3) => (X2 @ X3)) & (cF @ X2)))),
% 1.26/1.12 inference(negated_conjecture,[status(cth)],[f1])).
% 1.26/1.12 thf(f1,conjecture,(
% 1.26/1.12 ? [X0 : ($i > $o) > $o] : ! [X1 : $i > $o] : ((X0 @ X1) => ? [X2 : $i > $o] : (! [X3 : $i] : ((X1 @ X3) => (X2 @ X3)) & (cF @ X2)))),
% 1.26/1.12 file('/export/starexec/sandbox/tmp/tmp.ClYweRtJwQ/DTF2THF_13683.p',cBLEDSOE2_pme)).
% 1.26/1.12 % SZS output end Proof for DTF2THF_13683
% 1.26/1.12 % (13802)------------------------------
% 1.26/1.12 % (13802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.12 % (13802)Termination reason: Refutation
% 1.26/1.12
% 1.26/1.12 % (13802)Memory used [KB]: 5500
% 1.26/1.12 % (13802)Time elapsed: 0.002 s
% 1.26/1.12 % (13802)Instructions burned: 1 (million)
% 1.26/1.12 % (13802)------------------------------
% 1.26/1.12 % (13802)------------------------------
% 1.26/1.12 % (13796)Success in time 0.011 s
%------------------------------------------------------------------------------