%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO289^5 : 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 09:53:52 AM UTC 2026
% Result : Theorem 1.29s 1.13s
% Output : Refutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 41 ( 15 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 47 ( 8 ~; 0 |; 5 &; 29 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 1 ^; 23 !; 10 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_3,type,
sK0: $i > $i > $o ).
thf(func_def_7,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f17,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f16]) ).
thf(f16,plain,
$true = $false,
inference(beta_eta_normalization,[status(thm)],[f13]) ).
thf(f13,plain,
( $true
= ( ^ [Y0: $i] : $false
@ sK1 ) ),
inference(primitive_instantiation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X3: $i > $o] :
( $true
= ( X3 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X2: $i] :
( $true
!= ( sK0 @ X2 @ sK1 ) )
& ! [X3: $i > $o] :
( $true
= ( X3 @ sK1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f8]) ).
thf(f8,plain,
( ? [X0: $i > $i > $o,X1: $i] :
( ! [X2: $i] :
( $true
!= ( X0 @ X2 @ X1 ) )
& ! [X3: $i > $o] :
( $true
= ( X3 @ X1 ) ) )
=> ( ! [X2: $i] :
( $true
!= ( sK0 @ X2 @ sK1 ) )
& ! [X3: $i > $o] :
( $true
= ( X3 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
? [X0: $i > $i > $o,X1: $i] :
( ! [X2: $i] :
( $true
!= ( X0 @ X2 @ X1 ) )
& ! [X3: $i > $o] :
( $true
= ( X3 @ X1 ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
? [X1: $i > $i > $o,X0: $i] :
( ! [X3: $i] :
( $true
!= ( X1 @ X3 @ X0 ) )
& ! [X2: $i > $o] :
( $true
= ( X2 @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: $i,X1: $i > $i > $o] :
( ! [X2: $i > $o] :
( $true
= ( X2 @ X0 ) )
=> ? [X3: $i] :
( $true
= ( X1 @ X3 @ X0 ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: $i,X1: $i > $i > $o] :
( ! [X2: $i > $o] : ( X2 @ X0 )
=> ? [X3: $i] : ( X1 @ X3 @ X0 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: $i,X0: $i > $i > $o] :
( ! [X2: $i > $o] : ( X2 @ X1 )
=> ? [X3: $i] : ( X0 @ X3 @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: $i,X0: $i > $i > $o] :
( ! [X2: $i > $o] : ( X2 @ X1 )
=> ? [X3: $i] : ( X0 @ X3 @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.E4KY6oDXXI/DTF2THF_16138.p',cTRIV2) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SYO289^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.31 % Computer : n001.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue Feb 24 14:28:20 EST 2026
% 0.12/0.31 % CPUTime :
% 0.12/0.31 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.41 ---- Original DTF file ---
% 0.18/0.41 thf(spec,logic,$$dhol).
% 0.18/0.41 %------------------------------------------------------------------------------
% 0.18/0.41 % File : SYO289^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.41 % Domain : Syntactic
% 0.18/0.41 % Problem : TPS problem from BASIC-HO-THMS
% 0.18/0.41 % Version : Especial.
% 0.18/0.41 % English :
% 0.18/0.41
% 0.18/0.41 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.41 % Source : [Bro09]
% 0.18/0.41 % Names : tps_0695 [Bro09]
% 0.18/0.41
% 0.18/0.41 % Status : Theorem
% 0.18/0.41 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v4.0.0
% 0.18/0.41 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.18/0.41 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.18/0.41 % Maximal formula atoms : 0 ( 0 avg)
% 0.18/0.41 % Number of connectives : 4 ( 0 ~; 0 |; 0 &; 3 @)
% 0.18/0.41 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.18/0.41 % Maximal formula depth : 7 ( 7 avg)
% 0.18/0.41 % Number of types : 2 ( 0 usr)
% 0.18/0.41 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.18/0.41 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.18/0.41 % Number of variables : 4 ( 0 ^; 3 !; 1 ?; 4 :)
% 0.18/0.41 % SPC : TH0_THM_NEQ_NAR
% 0.18/0.41
% 0.18/0.41 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.41 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.41 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.41 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.41 %------------------------------------------------------------------------------
% 0.18/0.41 thf(cTRIV2,conjecture,
% 0.18/0.41 ! [Xr: $i > $i > $o,Xy: $i] :
% 0.18/0.41 ( ! [Xp: $i > $o] : ( Xp @ Xy )
% 0.18/0.41 => ? [Xx: $i] : ( Xr @ Xx @ Xy ) ) ).
% 0.18/0.41
% 0.18/0.41 %------------------------------------------------------------------------------
% 0.18/0.41 ------------------------
% 1.12/1.10 ---- Embedded in THF ---
% 1.12/1.11 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.12/1.11 %%% Generated on Tue Feb 24 14:28:21 EST 2026
% 1.12/1.11 %%% using '$$dhol' embedding, version 1.3.0.
% 1.12/1.11 %%% Logic specification used:
% 1.12/1.11 %%% thf(spec, logic, $$dhol).
% 1.12/1.11
% 1.12/1.11 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.E4KY6oDXXI/DTF2DTF16138.p
% See solution above
% 1.12/1.11 ------------------------
% 1.12/1.12 ---- Cleaned THF ---
% 1.12/1.12 thf(cTRIV2,conjecture,
% 1.12/1.12 ! [Xr: $i > $i > $o,Xy: $i] :
% 1.12/1.12 ( ! [Xp: $i > $o] : ( Xp @ Xy )
% 1.12/1.12 => ? [Xx: $i] : ( Xr @ Xx @ Xy ) ) ).
% 1.12/1.12 ------------------------
% 1.29/1.13 % (16328)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_16138 for (2999ds/183Mi)
% 1.29/1.13 % (16330)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_16138 for (2999ds/27Mi)
% 1.29/1.13 % (16332)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_16138 for (2999ds/2Mi)
% 1.29/1.13 % (16328)First to succeed.
% 1.29/1.13 % (16332)Instruction limit reached!
% 1.29/1.13 % (16332)------------------------------
% 1.29/1.13 % (16332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.29/1.13 % (16332)Termination reason: Unknown
% 1.29/1.13 % (16332)Termination phase: Saturation
% 1.29/1.13
% 1.29/1.13 % (16332)Memory used [KB]: 5500
% 1.29/1.13 % (16332)Time elapsed: 0.002 s
% 1.29/1.13 % (16332)Instructions burned: 2 (million)
% 1.29/1.13 % (16332)------------------------------
% 1.29/1.13 % (16332)------------------------------
% 1.29/1.13 % (16330)Also succeeded, but the first one will report.
% 1.29/1.13 % (16328)Refutation found. Thanks to Tanya!
% 1.29/1.13 % SZS status Theorem for DTF2THF_16138
% 1.29/1.13 % SZS output start Proof for DTF2THF_16138
% 1.29/1.13 thf(func_def_3, type, sK0: $i > $i > $o).
% 1.29/1.13 thf(func_def_7, type, ph3: !>[X0: $tType]:(X0)).
% 1.29/1.13 thf(f17,plain,(
% 1.29/1.13 $false),
% 1.29/1.13 inference(trivial_inequality_removal,[status(thm)],[f16])).
% 1.29/1.13 thf(f16,plain,(
% 1.29/1.13 ($true = $false)),
% 1.29/1.13 inference(beta_eta_normalization,[status(thm)],[f13])).
% 1.29/1.13 thf(f13,plain,(
% 1.29/1.13 ($true = ((^[Y0 : $i]: ($false)) @ sK1))),
% 1.29/1.13 inference(primitive_instantiation,[status(thm)],[f10])).
% 1.29/1.13 thf(f10,plain,(
% 1.29/1.13 ( ! [X3 : $i > $o] : (($true = (X3 @ sK1))) )),
% 1.29/1.13 inference(cnf_transformation,[status(thm)],[f9])).
% 1.29/1.13 thf(f9,plain,(
% 1.29/1.13 ! [X2 : $i] : ($true != (sK0 @ X2 @ sK1)) & ! [X3 : $i > $o] : ($true = (X3 @ sK1))),
% 1.29/1.13 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f8])).
% 1.29/1.13 thf(f8,plain,(
% 1.29/1.13 ? [X0 : $i > $i > $o,X1 : $i] : (! [X2 : $i] : ($true != (X0 @ X2 @ X1)) & ! [X3 : $i > $o] : ($true = (X3 @ X1))) => (! [X2 : $i] : ($true != (sK0 @ X2 @ sK1)) & ! [X3 : $i > $o] : ($true = (X3 @ sK1)))),
% 1.29/1.13 introduced(definition,[],[choice_axiom])).
% 1.29/1.13 thf(f7,plain,(
% 1.29/1.13 ? [X0 : $i > $i > $o,X1 : $i] : (! [X2 : $i] : ($true != (X0 @ X2 @ X1)) & ! [X3 : $i > $o] : ($true = (X3 @ X1)))),
% 1.29/1.13 inference(rectify,[status(thm)],[f6])).
% 1.29/1.13 thf(f6,plain,(
% 1.29/1.13 ? [X1 : $i > $i > $o,X0 : $i] : (! [X3 : $i] : ($true != (X1 @ X3 @ X0)) & ! [X2 : $i > $o] : ($true = (X2 @ X0)))),
% 1.29/1.13 inference(ennf_transformation,[status(thm)],[f5])).
% 1.29/1.13 thf(f5,plain,(
% 1.29/1.13 ~! [X0 : $i,X1 : $i > $i > $o] : (! [X2 : $i > $o] : ($true = (X2 @ X0)) => ? [X3 : $i] : ($true = (X1 @ X3 @ X0)))),
% 1.29/1.13 inference(fool_elimination,[status(thm)],[f4])).
% 1.29/1.13 thf(f4,plain,(
% 1.29/1.13 ~! [X0 : $i,X1 : $i > $i > $o] : (! [X2 : $i > $o] : (X2 @ X0) => ? [X3 : $i] : (X1 @ X3 @ X0))),
% 1.29/1.13 inference(rectify,[status(thm)],[f2])).
% 1.29/1.13 thf(f2,negated_conjecture,(
% 1.29/1.13 ~! [X1 : $i,X0 : $i > $i > $o] : (! [X2 : $i > $o] : (X2 @ X1) => ? [X3 : $i] : (X0 @ X3 @ X1))),
% 1.29/1.13 inference(negated_conjecture,[status(cth)],[f1])).
% 1.29/1.13 thf(f1,conjecture,(
% 1.29/1.13 ! [X1 : $i,X0 : $i > $i > $o] : (! [X2 : $i > $o] : (X2 @ X1) => ? [X3 : $i] : (X0 @ X3 @ X1))),
% 1.29/1.13 file('/export/starexec/sandbox2/tmp/tmp.E4KY6oDXXI/DTF2THF_16138.p',cTRIV2)).
% 1.29/1.13 % SZS output end Proof for DTF2THF_16138
% 1.29/1.13 % (16328)------------------------------
% 1.29/1.13 % (16328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.29/1.13 % (16328)Termination reason: Refutation
% 1.29/1.13
% 1.29/1.13 % (16328)Memory used [KB]: 5500
% 1.29/1.13 % (16328)Time elapsed: 0.002 s
% 1.29/1.13 % (16328)Instructions burned: 1 (million)
% 1.29/1.13 % (16328)------------------------------
% 1.29/1.13 % (16328)------------------------------
% 1.29/1.13 % (16327)Success in time 0.011 s
%------------------------------------------------------------------------------