%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO306^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n001.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 09:53:54 AM UTC 2026
% Result : Theorem 1.61s 1.30s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 5 unt; 0 typ; 2 def)
% Number of atoms : 155 ( 44 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 143 ( 27 ~; 16 |; 20 &; 64 @)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 43 ( 0 ^; 35 !; 8 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cT: $i > $o ).
thf(func_def_1,type,
cS: $i > $o ).
thf(func_def_5,type,
sK0: ( $i > $o ) > $i ).
thf(f29,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f24,f26,f28]) ).
thf(f28,plain,
spl2_2,
inference(avatar_contradiction_clause,[status(thm)],[f27]) ).
thf(f27,plain,
( $false
| spl2_2 ),
inference(subsumption_resolution,[status(thm)],[f23,f12]) ).
thf(f12,plain,
! [X4: $i] :
( $true
= ( cT @ X4 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
= $true )
| ( $true
!= ( X0 @ ( sK0 @ X0 ) ) ) )
& ( ( $true
!= ( cT @ sK1 ) )
| ( ( cS @ sK1 )
!= $true ) )
& ! [X4: $i] :
( ( ( cS @ X4 )
= $true )
& ( $true
= ( cT @ X4 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f10,f9]) ).
thf(f9,plain,
! [X0: $i > $o] :
( ? [X2: $i] :
( $true
!= ( X0 @ X2 ) )
=> ( $true
!= ( X0 @ ( sK0 @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X3: $i] :
( ( $true
!= ( cT @ X3 ) )
| ( ( cS @ X3 )
!= $true ) )
=> ( ( $true
!= ( cT @ sK1 ) )
| ( ( cS @ sK1 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
= $true )
| ? [X2: $i] :
( $true
!= ( X0 @ X2 ) ) )
& ? [X3: $i] :
( ( $true
!= ( cT @ X3 ) )
| ( ( cS @ X3 )
!= $true ) )
& ! [X4: $i] :
( ( ( cS @ X4 )
= $true )
& ( $true
= ( cT @ X4 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X0: $i > $o] :
( ! [X2: $i] :
( $true
= ( X0 @ X2 ) )
| ? [X1: $i] :
( ( X0 @ X1 )
!= $true ) )
& ? [X4: $i] :
( ( $true
!= ( cT @ X4 ) )
| ( ( cS @ X4 )
!= $true ) )
& ! [X3: $i] :
( ( ( cS @ X3 )
= $true )
& ( $true
= ( cT @ X3 ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ? [X4: $i] :
( ( $true
!= ( cT @ X4 ) )
| ( ( cS @ X4 )
!= $true ) )
& ! [X3: $i] :
( ( ( cS @ X3 )
= $true )
& ( $true
= ( cT @ X3 ) ) )
& ! [X0: $i > $o] :
( ! [X2: $i] :
( $true
= ( X0 @ X2 ) )
| ? [X1: $i] :
( ( X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
= $true )
=> ! [X2: $i] :
( $true
= ( X0 @ X2 ) ) )
=> ( ! [X3: $i] :
( ( ( cS @ X3 )
= $true )
& ( $true
= ( cT @ X3 ) ) )
=> ! [X4: $i] :
( ( ( cS @ X4 )
= $true )
& ( $true
= ( cT @ X4 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: $i > $o] :
( ! [X1: $i] : ( X0 @ X1 )
=> ! [X2: $i] : ( X0 @ X2 ) )
=> ( ! [X3: $i] :
( ( cT @ X3 )
& ( cS @ X3 ) )
=> ! [X4: $i] :
( ( cS @ X4 )
& ( cT @ X4 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i > $o] :
( ! [X1: $i] : ( X0 @ X1 )
=> ! [X1: $i] : ( X0 @ X1 ) )
=> ( ! [X1: $i] :
( ( cT @ X1 )
& ( cS @ X1 ) )
=> ! [X1: $i] :
( ( cS @ X1 )
& ( cT @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: $i > $o] :
( ! [X1: $i] : ( X0 @ X1 )
=> ! [X1: $i] : ( X0 @ X1 ) )
=> ( ! [X1: $i] :
( ( cT @ X1 )
& ( cS @ X1 ) )
=> ! [X1: $i] :
( ( cS @ X1 )
& ( cT @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ksQUJ6ZrAK/DTF2THF_17529.p',cDUP_BUG_2) ).
thf(f23,plain,
( ( $true
!= ( cT @ sK1 ) )
| spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f21]) ).
thf(f21,definition,
( spl2_2
<=> ( $true
= ( cT @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f26,plain,
spl2_1,
inference(avatar_contradiction_clause,[status(thm)],[f25]) ).
thf(f25,plain,
( $false
| spl2_1 ),
inference(subsumption_resolution,[status(thm)],[f19,f13]) ).
thf(f13,plain,
! [X4: $i] :
( ( cS @ X4 )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f19,plain,
( ( ( cS @ sK1 )
!= $true )
| spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f17]) ).
thf(f17,definition,
( spl2_1
<=> ( ( cS @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f24,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f14,f21,f17]) ).
thf(f14,plain,
( ( $true
!= ( cT @ sK1 ) )
| ( ( cS @ sK1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO306^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n001.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 14:28:35 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.27/0.47 ---- Original DTF file ---
% 0.27/0.47 thf(spec,logic,$$dhol).
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 % File : SYO306^5 : TPTP v9.2.1. Released v4.0.0.
% 0.27/0.47 % Domain : Syntactic
% 0.27/0.47 % Problem : TPS problem from BASIC-HO-THMS
% 0.27/0.47 % Version : Especial.
% 0.27/0.47 % English :
% 0.27/0.47
% 0.27/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.27/0.47 % Source : [Bro09]
% 0.27/0.47 % Names : tps_0826 [Bro09]
% 0.27/0.47
% 0.27/0.47 % Status : Theorem
% 0.27/0.47 % Rating : 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v4.0.0
% 0.27/0.47 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.27/0.47 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.27/0.47 % Maximal formula atoms : 4 ( 4 avg)
% 0.27/0.47 % Number of connectives : 11 ( 0 ~; 0 |; 2 &; 6 @)
% 0.27/0.47 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.27/0.47 % Maximal formula depth : 6 ( 6 avg)
% 0.27/0.47 % Number of types : 2 ( 0 usr)
% 0.27/0.47 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.27/0.47 % Number of symbols : 2 ( 2 usr; 0 con; 1-1 aty)
% 0.27/0.47 % Number of variables : 5 ( 0 ^; 5 !; 0 ?; 5 :)
% 0.27/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.27/0.47
% 0.27/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.27/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.27/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.27/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 thf(cT,type,
% 0.27/0.47 cT: $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(cS,type,
% 0.27/0.47 cS: $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(cDUP_BUG_2,conjecture,
% 0.27/0.47 ( ! [P: $i > $o] :
% 0.27/0.47 ( ! [Xx: $i] : ( P @ Xx )
% 0.27/0.47 => ! [Xx: $i] : ( P @ Xx ) )
% 0.27/0.47 => ( ! [Xx: $i] :
% 0.27/0.47 ( ( cS @ Xx )
% 0.27/0.47 & ( cT @ Xx ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( cS @ Xx )
% 0.27/0.47 & ( cT @ Xx ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 ------------------------
% 1.47/1.27 ---- Embedded in THF ---
% 1.47/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.27 %%% Generated on Tue Feb 24 14:28:36 EST 2026
% 1.47/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.27 %%% Logic specification used:
% 1.47/1.27 %%% thf(spec, logic, $$dhol).
% 1.47/1.27
% 1.47/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.ksQUJ6ZrAK/DTF2DTF17529.p
% See solution above
% 1.47/1.27 ------------------------
% 1.47/1.28 ---- Cleaned THF ---
% 1.47/1.29 thf(cT,type,
% 1.47/1.29 cT: $i > $o ).
% 1.47/1.29
% 1.47/1.29 thf(cS,type,
% 1.47/1.29 cS: $i > $o ).
% 1.47/1.29
% 1.47/1.29 thf(cDUP_BUG_2,conjecture,
% 1.47/1.29 ( ! [P: $i > $o] :
% 1.47/1.29 ( ! [Xx: $i] : ( P @ Xx )
% 1.47/1.29 => ! [Xx: $i] : ( P @ Xx ) )
% 1.47/1.29 => ( ! [Xx: $i] :
% 1.47/1.29 ( ( cS @ Xx )
% 1.47/1.29 & ( cT @ Xx ) )
% 1.47/1.29 => ! [Xx: $i] :
% 1.47/1.29 ( ( cS @ Xx )
% 1.47/1.29 & ( cT @ Xx ) ) ) ) ).
% 1.47/1.29 ------------------------
% 1.61/1.30 % (17806)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_17529 for (2999ds/275Mi)
% 1.61/1.30 % (17804)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17529 for (2999ds/2Mi)
% 1.61/1.30 % (17806)First to succeed.
% 1.61/1.30 % (17804)Instruction limit reached!
% 1.61/1.30 % (17804)------------------------------
% 1.61/1.30 % (17804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.30 % (17804)Termination reason: Unknown
% 1.61/1.30 % (17804)Termination phase: Saturation
% 1.61/1.30
% 1.61/1.30 % (17804)Memory used [KB]: 5500
% 1.61/1.30 % (17804)Time elapsed: 0.002 s
% 1.61/1.30 % (17804)Instructions burned: 2 (million)
% 1.61/1.30 % (17804)------------------------------
% 1.61/1.30 % (17804)------------------------------
% 1.61/1.30 % (17806)Refutation found. Thanks to Tanya!
% 1.61/1.30 % SZS status Theorem for DTF2THF_17529
% 1.61/1.30 % SZS output start Proof for DTF2THF_17529
% 1.61/1.30 thf(func_def_0, type, cT: $i > $o).
% 1.61/1.30 thf(func_def_1, type, cS: $i > $o).
% 1.61/1.30 thf(func_def_5, type, sK0: ($i > $o) > $i).
% 1.61/1.30 thf(f29,plain,(
% 1.61/1.30 $false),
% 1.61/1.30 inference(avatar_sat_refutation,[status(thm)],[f24,f26,f28])).
% 1.61/1.30 thf(f28,plain,(
% 1.61/1.30 spl2_2),
% 1.61/1.30 inference(avatar_contradiction_clause,[status(thm)],[f27])).
% 1.61/1.30 thf(f27,plain,(
% 1.61/1.30 $false | spl2_2),
% 1.61/1.30 inference(subsumption_resolution,[status(thm)],[f23,f12])).
% 1.61/1.30 thf(f12,plain,(
% 1.61/1.30 ( ! [X4 : $i] : (($true = (cT @ X4))) )),
% 1.61/1.30 inference(cnf_transformation,[status(thm)],[f11])).
% 1.61/1.30 thf(f11,plain,(
% 1.61/1.30 ! [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ X1) = $true) | ($true != (X0 @ (sK0 @ X0)))) & (($true != (cT @ sK1)) | ((cS @ sK1) != $true)) & ! [X4 : $i] : (((cS @ X4) = $true) & ($true = (cT @ X4)))),
% 1.61/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f10,f9])).
% 1.61/1.30 thf(f9,plain,(
% 1.61/1.30 ! [X0 : $i > $o] : (? [X2 : $i] : ($true != (X0 @ X2)) => ($true != (X0 @ (sK0 @ X0))))),
% 1.61/1.30 introduced(definition,[],[choice_axiom])).
% 1.61/1.30 thf(f10,plain,(
% 1.61/1.30 ? [X3 : $i] : (($true != (cT @ X3)) | ((cS @ X3) != $true)) => (($true != (cT @ sK1)) | ((cS @ sK1) != $true))),
% 1.61/1.30 introduced(definition,[],[choice_axiom])).
% 1.61/1.30 thf(f8,plain,(
% 1.61/1.30 ! [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ X1) = $true) | ? [X2 : $i] : ($true != (X0 @ X2))) & ? [X3 : $i] : (($true != (cT @ X3)) | ((cS @ X3) != $true)) & ! [X4 : $i] : (((cS @ X4) = $true) & ($true = (cT @ X4)))),
% 1.61/1.30 inference(rectify,[status(thm)],[f7])).
% 1.61/1.30 thf(f7,plain,(
% 1.61/1.30 ! [X0 : $i > $o] : (! [X2 : $i] : ($true = (X0 @ X2)) | ? [X1 : $i] : ((X0 @ X1) != $true)) & ? [X4 : $i] : (($true != (cT @ X4)) | ((cS @ X4) != $true)) & ! [X3 : $i] : (((cS @ X3) = $true) & ($true = (cT @ X3)))),
% 1.61/1.30 inference(flattening,[status(thm)],[f6])).
% 1.61/1.30 thf(f6,plain,(
% 1.61/1.30 (? [X4 : $i] : (($true != (cT @ X4)) | ((cS @ X4) != $true)) & ! [X3 : $i] : (((cS @ X3) = $true) & ($true = (cT @ X3)))) & ! [X0 : $i > $o] : (! [X2 : $i] : ($true = (X0 @ X2)) | ? [X1 : $i] : ((X0 @ X1) != $true))),
% 1.61/1.30 inference(ennf_transformation,[status(thm)],[f5])).
% 1.61/1.30 thf(f5,plain,(
% 1.61/1.30 ~(! [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ X1) = $true) => ! [X2 : $i] : ($true = (X0 @ X2))) => (! [X3 : $i] : (((cS @ X3) = $true) & ($true = (cT @ X3))) => ! [X4 : $i] : (((cS @ X4) = $true) & ($true = (cT @ X4)))))),
% 1.61/1.30 inference(fool_elimination,[status(thm)],[f4])).
% 1.61/1.30 thf(f4,plain,(
% 1.61/1.30 ~(! [X0 : $i > $o] : (! [X1 : $i] : (X0 @ X1) => ! [X2 : $i] : (X0 @ X2)) => (! [X3 : $i] : ((cT @ X3) & (cS @ X3)) => ! [X4 : $i] : ((cS @ X4) & (cT @ X4))))),
% 1.61/1.30 inference(rectify,[status(thm)],[f2])).
% 1.61/1.30 thf(f2,negated_conjecture,(
% 1.61/1.30 ~(! [X0 : $i > $o] : (! [X1 : $i] : (X0 @ X1) => ! [X1 : $i] : (X0 @ X1)) => (! [X1 : $i] : ((cT @ X1) & (cS @ X1)) => ! [X1 : $i] : ((cS @ X1) & (cT @ X1))))),
% 1.61/1.30 inference(negated_conjecture,[status(cth)],[f1])).
% 1.61/1.30 thf(f1,conjecture,(
% 1.61/1.30 ! [X0 : $i > $o] : (! [X1 : $i] : (X0 @ X1) => ! [X1 : $i] : (X0 @ X1)) => (! [X1 : $i] : ((cT @ X1) & (cS @ X1)) => ! [X1 : $i] : ((cS @ X1) & (cT @ X1)))),
% 1.61/1.30 file('/export/starexec/sandbox2/tmp/tmp.ksQUJ6ZrAK/DTF2THF_17529.p',cDUP_BUG_2)).
% 1.61/1.30 thf(f23,plain,(
% 1.61/1.30 ($true != (cT @ sK1)) | spl2_2),
% 1.61/1.30 inference(avatar_component_clause,[status(thm)],[f21])).
% 1.61/1.30 thf(f21,definition,(
% 1.61/1.30 spl2_2 <=> ($true = (cT @ sK1))),
% 1.61/1.30 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.61/1.30 thf(f26,plain,(
% 1.61/1.30 spl2_1),
% 1.61/1.30 inference(avatar_contradiction_clause,[status(thm)],[f25])).
% 1.61/1.30 thf(f25,plain,(
% 1.61/1.30 $false | spl2_1),
% 1.61/1.30 inference(subsumption_resolution,[status(thm)],[f19,f13])).
% 1.61/1.30 thf(f13,plain,(
% 1.61/1.30 ( ! [X4 : $i] : (((cS @ X4) = $true)) )),
% 1.61/1.30 inference(cnf_transformation,[status(thm)],[f11])).
% 1.61/1.30 thf(f19,plain,(
% 1.61/1.30 ((cS @ sK1) != $true) | spl2_1),
% 1.61/1.30 inference(avatar_component_clause,[status(thm)],[f17])).
% 1.61/1.30 thf(f17,definition,(
% 1.61/1.30 spl2_1 <=> ((cS @ sK1) = $true)),
% 1.61/1.30 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.61/1.30 thf(f24,plain,(
% 1.61/1.30 ~spl2_1 | ~spl2_2),
% 1.61/1.30 inference(avatar_split_clause,[status(thm)],[f14,f21,f17])).
% 1.61/1.30 thf(f14,plain,(
% 1.61/1.30 ($true != (cT @ sK1)) | ((cS @ sK1) != $true)),
% 1.61/1.30 inference(cnf_transformation,[status(thm)],[f11])).
% 1.61/1.30 % SZS output end Proof for DTF2THF_17529
% 1.61/1.30 % (17806)------------------------------
% 1.61/1.30 % (17806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.30 % (17806)Termination reason: Refutation
% 1.61/1.30
% 1.61/1.30 % (17806)Memory used [KB]: 5500
% 1.61/1.30 % (17806)Time elapsed: 0.002 s
% 1.61/1.30 % (17806)Instructions burned: 1 (million)
% 1.61/1.30 % (17806)------------------------------
% 1.61/1.30 % (17806)------------------------------
% 1.61/1.30 % (17800)Success in time 0.012 s
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