%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO258^5 : 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 : 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 09:53:47 AM UTC 2026
% Result : Theorem 1.50s 1.25s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 156 ( 41 equ; 0 cnn)
% Maximal formula atoms : 8 ( 12 avg)
% Number of connectives : 168 ( 21 ~; 12 |; 26 &; 100 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 38 ( 2 ^; 24 !; 12 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
cQ: $i > ( $i > $o ) > $o ).
thf(func_def_2,type,
cP: $i > $i > $o ).
thf(func_def_7,type,
sK0: ( $i > $o ) > $i ).
thf(func_def_10,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f22,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f21]) ).
thf(f21,plain,
$false = $true,
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( $true
= ( ^ [Y0: $i] : $false
@ ( sK0
@ ^ [Y0: $i] : $false ) ) ),
inference(primitive_instantiation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $i > $o] :
( ( X0 @ ( sK0 @ X0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X0: $i > $o] :
( ( ( ( X0 @ a )
!= $true )
| ! [X2: $i] :
( ( ( cQ @ X2 @ X0 )
!= $true )
| ( ( cP @ ( sK0 @ X0 ) @ X2 )
!= $true ) ) )
& ( ( X0 @ ( sK0 @ X0 ) )
= $true ) )
& ( ( cP @ a @ b )
= $true )
& ! [X3: $i > $o] :
( ( cQ @ b @ X3 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9]) ).
thf(f9,plain,
! [X0: $i > $o] :
( ? [X1: $i] :
( ( ( ( X0 @ a )
!= $true )
| ! [X2: $i] :
( ( ( cQ @ X2 @ X0 )
!= $true )
| ( ( cP @ X1 @ X2 )
!= $true ) ) )
& ( ( X0 @ X1 )
= $true ) )
=> ( ( ( ( X0 @ a )
!= $true )
| ! [X2: $i] :
( ( ( cQ @ X2 @ X0 )
!= $true )
| ( ( cP @ ( sK0 @ X0 ) @ X2 )
!= $true ) ) )
& ( ( X0 @ ( sK0 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ! [X0: $i > $o] :
? [X1: $i] :
( ( ( ( X0 @ a )
!= $true )
| ! [X2: $i] :
( ( ( cQ @ X2 @ X0 )
!= $true )
| ( ( cP @ X1 @ X2 )
!= $true ) ) )
& ( ( X0 @ X1 )
= $true ) )
& ( ( cP @ a @ b )
= $true )
& ! [X3: $i > $o] :
( ( cQ @ b @ X3 )
= $true ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X1: $i > $o] :
? [X2: $i] :
( ( ( ( X1 @ a )
!= $true )
| ! [X3: $i] :
( ( ( cQ @ X3 @ X1 )
!= $true )
| ( ( cP @ X2 @ X3 )
!= $true ) ) )
& ( ( X1 @ X2 )
= $true ) )
& ( ( cP @ a @ b )
= $true )
& ! [X0: $i > $o] :
( ( cQ @ b @ X0 )
= $true ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X1: $i > $o] :
? [X2: $i] :
( ( ( ( X1 @ a )
!= $true )
| ! [X3: $i] :
( ( ( cQ @ X3 @ X1 )
!= $true )
| ( ( cP @ X2 @ X3 )
!= $true ) ) )
& ( ( X1 @ X2 )
= $true ) )
& ( ( cP @ a @ b )
= $true )
& ! [X0: $i > $o] :
( ( cQ @ b @ X0 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( ( cP @ a @ b )
= $true )
& ! [X0: $i > $o] :
( ( cQ @ b @ X0 )
= $true ) )
=> ? [X1: $i > $o] :
! [X2: $i] :
( ( ( X1 @ X2 )
= $true )
=> ( ? [X3: $i] :
( ( ( cP @ X2 @ X3 )
= $true )
& ( ( cQ @ X3 @ X1 )
= $true ) )
& ( ( X1 @ a )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ( cP @ a @ b )
& ! [X0: $i > $o] : ( cQ @ b @ X0 ) )
=> ? [X1: $i > $o] :
! [X2: $i] :
( ( X1 @ X2 )
=> ( ? [X3: $i] :
( ( cP @ X2 @ X3 )
& ( cQ @ X3 @ X1 ) )
& ( X1 @ a ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ( cP @ a @ b )
& ! [X0: $i > $o] : ( cQ @ b @ X0 ) )
=> ? [X1: $i > $o] :
! [X2: $i] :
( ( X1 @ X2 )
=> ( ? [X3: $i] :
( ( cP @ X2 @ X3 )
& ( cQ @ X3 @ X1 ) )
& ( X1 @ a ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ( cP @ a @ b )
& ! [X0: $i > $o] : ( cQ @ b @ X0 ) )
=> ? [X1: $i > $o] :
! [X2: $i] :
( ( X1 @ X2 )
=> ( ? [X3: $i] :
( ( cP @ X2 @ X3 )
& ( cQ @ X3 @ X1 ) )
& ( X1 @ a ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.sifMIP0qLI/DTF2THF_30536.p',cBLEDSOE_FENG_6) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO258^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n003.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 15:20:40 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
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : SYO258^5 : TPTP v9.2.1. Released v4.0.0.
% 0.31/0.46 % Domain : Syntactic
% 0.31/0.46 % Problem : TPS problem BLEDSOE-FENG-6
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English :
% 0.31/0.46
% 0.31/0.46 % Refs : [BF93] Bledsoe & Feng (1993), SET-VAR
% 0.31/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.46 % Source : [Bro09]
% 0.31/0.46 % Names : tps_0144 [Bro09]
% 0.31/0.46 % : BLEDSOE-FENG-6 [TPS]
% 0.31/0.46 % : Example 6 [BF93]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % 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 v4.0.1, 0.33 v4.0.0
% 0.31/0.46 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.31/0.46 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 4 ( 4 avg)
% 0.31/0.46 % Number of connectives : 15 ( 0 ~; 0 |; 3 &; 10 @)
% 0.31/0.46 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 10 ( 10 avg)
% 0.31/0.46 % Number of types : 2 ( 0 usr)
% 0.31/0.46 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 4 ( 4 usr; 2 con; 0-2 aty)
% 0.31/0.46 % Number of variables : 4 ( 0 ^; 2 !; 2 ?; 4 :)
% 0.31/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(a,type,
% 0.31/0.46 a: $i ).
% 0.31/0.46
% 0.31/0.46 thf(cQ,type,
% 0.31/0.46 cQ: $i > ( $i > $o ) > $o ).
% 0.31/0.46
% 0.31/0.46 thf(cP,type,
% 0.31/0.46 cP: $i > $i > $o ).
% 0.31/0.46
% 0.31/0.46 thf(b,type,
% 0.31/0.46 b: $i ).
% 0.31/0.46
% 0.31/0.46 thf(cBLEDSOE_FENG_6,conjecture,
% 0.31/0.46 ( ( ( cP @ a @ b )
% 0.31/0.46 & ! [E: $i > $o] : ( cQ @ b @ E ) )
% 0.31/0.46 => ? [A: $i > $o] :
% 0.31/0.46 ! [Xg: $i] :
% 0.31/0.46 ( ( A @ Xg )
% 0.31/0.46 => ( ? [Xx: $i] :
% 0.31/0.46 ( ( cP @ Xg @ Xx )
% 0.31/0.46 & ( cQ @ Xx @ A ) )
% 0.31/0.46 & ( A @ a ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 1.50/1.22 ---- Embedded in THF ---
% 1.50/1.22 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.22 %%% Generated on Tue Feb 24 15:20:41 EST 2026
% 1.50/1.22 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.22 %%% Logic specification used:
% 1.50/1.22 %%% thf(spec, logic, $$dhol).
% 1.50/1.22
% 1.50/1.22 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.sifMIP0qLI/DTF2DTF30536.p
% See solution above
% 1.50/1.22 ------------------------
% 1.50/1.23 ---- Cleaned THF ---
% 1.50/1.23 thf(a,type,
% 1.50/1.23 a: $i ).
% 1.50/1.23
% 1.50/1.23 thf(cQ,type,
% 1.50/1.23 cQ: $i > ( $i > $o ) > $o ).
% 1.50/1.23
% 1.50/1.23 thf(cP,type,
% 1.50/1.23 cP: $i > $i > $o ).
% 1.50/1.23
% 1.50/1.23 thf(b,type,
% 1.50/1.23 b: $i ).
% 1.50/1.23
% 1.50/1.23 thf(cBLEDSOE_FENG_6,conjecture,
% 1.50/1.23 ( ( ( cP @ a @ b )
% 1.50/1.23 & ! [E: $i > $o] : ( cQ @ b @ E ) )
% 1.50/1.23 => ? [A: $i > $o] :
% 1.50/1.23 ! [Xg: $i] :
% 1.50/1.23 ( ( A @ Xg )
% 1.50/1.23 => ( ? [Xx: $i] :
% 1.50/1.23 ( ( cP @ Xg @ Xx )
% 1.50/1.23 & ( cQ @ Xx @ A ) )
% 1.50/1.23 & ( A @ a ) ) ) ) ).
% 1.50/1.23 ------------------------
% 1.50/1.25 % (30633)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30536 for (2999ds/183Mi)
% 1.50/1.25 % (30638)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_30536 for (2999ds/275Mi)
% 1.50/1.25 % (30638)First to succeed.
% 1.50/1.25 % (30638)Refutation found. Thanks to Tanya!
% 1.50/1.25 % SZS status Theorem for DTF2THF_30536
% 1.50/1.25 % SZS output start Proof for DTF2THF_30536
% 1.50/1.25 thf(func_def_1, type, cQ: $i > ($i > $o) > $o).
% 1.50/1.25 thf(func_def_2, type, cP: $i > $i > $o).
% 1.50/1.25 thf(func_def_7, type, sK0: ($i > $o) > $i).
% 1.50/1.25 thf(func_def_10, type, ph2: !>[X0: $tType]:(X0)).
% 1.50/1.25 thf(f22,plain,(
% 1.50/1.25 $false),
% 1.50/1.25 inference(trivial_inequality_removal,[status(thm)],[f21])).
% 1.50/1.25 thf(f21,plain,(
% 1.50/1.25 ($false = $true)),
% 1.50/1.25 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.50/1.25 thf(f16,plain,(
% 1.50/1.25 ($true = ((^[Y0 : $i]: ($false)) @ (sK0 @ (^[Y0 : $i]: ($false)))))),
% 1.50/1.25 inference(primitive_instantiation,[status(thm)],[f13])).
% 1.50/1.25 thf(f13,plain,(
% 1.50/1.25 ( ! [X0 : $i > $o] : (((X0 @ (sK0 @ X0)) = $true)) )),
% 1.50/1.25 inference(cnf_transformation,[status(thm)],[f10])).
% 1.50/1.25 thf(f10,plain,(
% 1.50/1.25 ! [X0 : $i > $o] : ((((X0 @ a) != $true) | ! [X2 : $i] : (((cQ @ X2 @ X0) != $true) | ((cP @ (sK0 @ X0) @ X2) != $true))) & ((X0 @ (sK0 @ X0)) = $true)) & ((cP @ a @ b) = $true) & ! [X3 : $i > $o] : ((cQ @ b @ X3) = $true)),
% 1.50/1.25 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9])).
% 1.50/1.25 thf(f9,plain,(
% 1.50/1.25 ! [X0 : $i > $o] : (? [X1 : $i] : ((((X0 @ a) != $true) | ! [X2 : $i] : (((cQ @ X2 @ X0) != $true) | ((cP @ X1 @ X2) != $true))) & ((X0 @ X1) = $true)) => ((((X0 @ a) != $true) | ! [X2 : $i] : (((cQ @ X2 @ X0) != $true) | ((cP @ (sK0 @ X0) @ X2) != $true))) & ((X0 @ (sK0 @ X0)) = $true)))),
% 1.50/1.25 introduced(definition,[],[choice_axiom])).
% 1.50/1.25 thf(f8,plain,(
% 1.50/1.25 ! [X0 : $i > $o] : ? [X1 : $i] : ((((X0 @ a) != $true) | ! [X2 : $i] : (((cQ @ X2 @ X0) != $true) | ((cP @ X1 @ X2) != $true))) & ((X0 @ X1) = $true)) & ((cP @ a @ b) = $true) & ! [X3 : $i > $o] : ((cQ @ b @ X3) = $true)),
% 1.50/1.25 inference(rectify,[status(thm)],[f7])).
% 1.50/1.25 thf(f7,plain,(
% 1.50/1.25 ! [X1 : $i > $o] : ? [X2 : $i] : ((((X1 @ a) != $true) | ! [X3 : $i] : (((cQ @ X3 @ X1) != $true) | ((cP @ X2 @ X3) != $true))) & ((X1 @ X2) = $true)) & ((cP @ a @ b) = $true) & ! [X0 : $i > $o] : ((cQ @ b @ X0) = $true)),
% 1.50/1.25 inference(flattening,[status(thm)],[f6])).
% 1.50/1.25 thf(f6,plain,(
% 1.50/1.25 ! [X1 : $i > $o] : ? [X2 : $i] : ((((X1 @ a) != $true) | ! [X3 : $i] : (((cQ @ X3 @ X1) != $true) | ((cP @ X2 @ X3) != $true))) & ((X1 @ X2) = $true)) & (((cP @ a @ b) = $true) & ! [X0 : $i > $o] : ((cQ @ b @ X0) = $true))),
% 1.50/1.25 inference(ennf_transformation,[status(thm)],[f5])).
% 1.50/1.25 thf(f5,plain,(
% 1.50/1.25 ~((((cP @ a @ b) = $true) & ! [X0 : $i > $o] : ((cQ @ b @ X0) = $true)) => ? [X1 : $i > $o] : ! [X2 : $i] : (((X1 @ X2) = $true) => (? [X3 : $i] : (((cP @ X2 @ X3) = $true) & ((cQ @ X3 @ X1) = $true)) & ((X1 @ a) = $true))))),
% 1.50/1.25 inference(fool_elimination,[status(thm)],[f4])).
% 1.50/1.25 thf(f4,plain,(
% 1.50/1.25 ~(((cP @ a @ b) & ! [X0 : $i > $o] : (cQ @ b @ X0)) => ? [X1 : $i > $o] : ! [X2 : $i] : ((X1 @ X2) => (? [X3 : $i] : ((cP @ X2 @ X3) & (cQ @ X3 @ X1)) & (X1 @ a))))),
% 1.50/1.25 inference(rectify,[status(thm)],[f2])).
% 1.50/1.25 thf(f2,negated_conjecture,(
% 1.50/1.25 ~(((cP @ a @ b) & ! [X0 : $i > $o] : (cQ @ b @ X0)) => ? [X1 : $i > $o] : ! [X2 : $i] : ((X1 @ X2) => (? [X3 : $i] : ((cP @ X2 @ X3) & (cQ @ X3 @ X1)) & (X1 @ a))))),
% 1.50/1.25 inference(negated_conjecture,[status(cth)],[f1])).
% 1.50/1.25 thf(f1,conjecture,(
% 1.50/1.25 ((cP @ a @ b) & ! [X0 : $i > $o] : (cQ @ b @ X0)) => ? [X1 : $i > $o] : ! [X2 : $i] : ((X1 @ X2) => (? [X3 : $i] : ((cP @ X2 @ X3) & (cQ @ X3 @ X1)) & (X1 @ a)))),
% 1.50/1.25 file('/export/starexec/sandbox2/tmp/tmp.sifMIP0qLI/DTF2THF_30536.p',cBLEDSOE_FENG_6)).
% 1.50/1.25 % SZS output end Proof for DTF2THF_30536
% 1.50/1.25 % (30638)------------------------------
% 1.50/1.25 % (30638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.25 % (30638)Termination reason: Refutation
% 1.50/1.25
% 1.50/1.25 % (30638)Memory used [KB]: 5500
% 1.50/1.25 % (30638)Time elapsed: 0.002 s
% 1.50/1.25 % (30638)Instructions burned: 2 (million)
% 1.50/1.25 % (30638)------------------------------
% 1.50/1.25 % (30638)------------------------------
% 1.50/1.25 % (30632)Success in time 0.002 s
%------------------------------------------------------------------------------