%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU926^5 : 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 : n026.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 09:37:46 AM UTC 2026
% Result : Theorem 1.65s 1.30s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 94 ( 39 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 157 ( 18 ~; 6 |; 19 &; 101 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 52 ( 13 ^; 22 !; 17 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_5,type,
sK0: $i > $o ).
thf(func_def_6,type,
sK1: ( ( $i > $i ) > $o ) > $i > $i ).
thf(func_def_7,type,
sK2: ( ( $i > $i ) > $o ) > $i ).
thf(func_def_10,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f22,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f21]) ).
thf(f21,plain,
$true = $false,
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ^ [Y0: $i > $i] : $false
@ ( sK1
@ ^ [Y0: $i > $i] : $false ) )
= $true ),
inference(primitive_instantiation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X1: ( $i > $i ) > $o] :
( ( X1 @ ( sK1 @ X1 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X1: ( $i > $i ) > $o] :
( ( ( X1 @ ( sK1 @ X1 ) )
= $true )
& ( ( $true
!= ( X1
@ ^ [Y0: $i] : ( sK1 @ X1 @ ( sK1 @ X1 @ Y0 ) ) ) )
| ( ( ( sK0 @ ( sK1 @ X1 @ ( sK2 @ X1 ) ) )
!= $true )
& ( $true
= ( sK0 @ ( sK2 @ X1 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f7,f10,f9,f8]) ).
thf(f8,plain,
( ? [X0: $i > $o] :
! [X1: ( $i > $i ) > $o] :
? [X2: $i > $i] :
( ( ( X1 @ X2 )
= $true )
& ( ( $true
!= ( X1
@ ^ [Y0: $i] : ( X2 @ ( X2 @ Y0 ) ) ) )
| ? [X3: $i] :
( ( $true
!= ( X0 @ ( X2 @ X3 ) ) )
& ( ( X0 @ X3 )
= $true ) ) ) )
=> ! [X1: ( $i > $i ) > $o] :
? [X2: $i > $i] :
( ( ( X1 @ X2 )
= $true )
& ( ( $true
!= ( X1
@ ^ [Y0: $i] : ( X2 @ ( X2 @ Y0 ) ) ) )
| ? [X3: $i] :
( ( ( sK0 @ ( X2 @ X3 ) )
!= $true )
& ( $true
= ( sK0 @ X3 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
! [X1: ( $i > $i ) > $o] :
( ? [X2: $i > $i] :
( ( ( X1 @ X2 )
= $true )
& ( ( $true
!= ( X1
@ ^ [Y0: $i] : ( X2 @ ( X2 @ Y0 ) ) ) )
| ? [X3: $i] :
( ( ( sK0 @ ( X2 @ X3 ) )
!= $true )
& ( $true
= ( sK0 @ X3 ) ) ) ) )
=> ( ( ( X1 @ ( sK1 @ X1 ) )
= $true )
& ( ( $true
!= ( X1
@ ^ [Y0: $i] : ( sK1 @ X1 @ ( sK1 @ X1 @ Y0 ) ) ) )
| ? [X3: $i] :
( ( ( sK0 @ ( sK1 @ X1 @ X3 ) )
!= $true )
& ( $true
= ( sK0 @ X3 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X1: ( $i > $i ) > $o] :
( ? [X3: $i] :
( ( ( sK0 @ ( sK1 @ X1 @ X3 ) )
!= $true )
& ( $true
= ( sK0 @ X3 ) ) )
=> ( ( ( sK0 @ ( sK1 @ X1 @ ( sK2 @ X1 ) ) )
!= $true )
& ( $true
= ( sK0 @ ( sK2 @ X1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
? [X0: $i > $o] :
! [X1: ( $i > $i ) > $o] :
? [X2: $i > $i] :
( ( ( X1 @ X2 )
= $true )
& ( ( $true
!= ( X1
@ ^ [Y0: $i] : ( X2 @ ( X2 @ Y0 ) ) ) )
| ? [X3: $i] :
( ( $true
!= ( X0 @ ( X2 @ X3 ) ) )
& ( ( X0 @ X3 )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: $i > $o] :
? [X1: ( $i > $i ) > $o] :
! [X2: $i > $i] :
( ( ( X1 @ X2 )
= $true )
=> ( ! [X3: $i] :
( ( ( X0 @ X3 )
= $true )
=> ( $true
= ( X0 @ ( X2 @ X3 ) ) ) )
& ( $true
= ( X1
@ ^ [Y0: $i] : ( X2 @ ( X2 @ Y0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: $i > $o] :
? [X1: ( $i > $i ) > $o] :
! [X2: $i > $i] :
( ( ( X1 @ X2 )
= $true )
=> ( ( $true
= ( X1
@ ^ [Y0: $i] : ( X2 @ ( X2 @ Y0 ) ) ) )
& ! [X4: $i] :
( ( ( X0 @ X4 )
= $true )
=> ( ( X0 @ ( X2 @ X4 ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: $i > $o] :
? [X1: ( $i > $i ) > $o] :
! [X2: $i > $i] :
( ( X1 @ X2 )
=> ( ( X1
@ ^ [X3: $i] : ( X2 @ ( X2 @ X3 ) ) )
& ! [X4: $i] :
( ( X0 @ X4 )
=> ( X0 @ ( X2 @ X4 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: $i > $o] :
? [X1: ( $i > $i ) > $o] :
! [X2: $i > $i] :
( ( X1 @ X2 )
=> ( ( X1
@ ^ [X3: $i] : ( X2 @ ( X2 @ X3 ) ) )
& ! [X4: $i] :
( ( X0 @ X4 )
=> ( X0 @ ( X2 @ X4 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: $i > $o] :
? [X1: ( $i > $i ) > $o] :
! [X2: $i > $i] :
( ( X1 @ X2 )
=> ( ( X1
@ ^ [X3: $i] : ( X2 @ ( X2 @ X3 ) ) )
& ! [X4: $i] :
( ( X0 @ X4 )
=> ( X0 @ ( X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ZpJQKmtmZB/DTF2THF_8318.p',cTHM113) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU926^5 : 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 : n026.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 12:37:40 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
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : SEU926^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.46 % Domain : Set Theory
% 0.20/0.46 % Problem : TPS problem THM113
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English : There is a set of functions on P closed under composition.
% 0.20/0.46
% 0.20/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.46 % Source : [Bro09]
% 0.20/0.46 % Names : tps_0214 [Bro09]
% 0.20/0.46 % : THM113 [TPS]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % 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 v5.3.0, 0.50 v5.2.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.20/0.46 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.20/0.46 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 0 ( 0 avg)
% 0.20/0.46 % Number of connectives : 10 ( 0 ~; 0 |; 1 &; 7 @)
% 0.20/0.46 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 10 ( 10 avg)
% 0.20/0.46 % Number of types : 2 ( 0 usr)
% 0.20/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.20/0.46 % Number of variables : 5 ( 1 ^; 3 !; 1 ?; 5 :)
% 0.20/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(cTHM113,conjecture,
% 0.20/0.46 ! [P: $i > $o] :
% 0.20/0.46 ? [M: ( $i > $i ) > $o] :
% 0.20/0.46 ! [G: $i > $i] :
% 0.20/0.46 ( ( M @ G )
% 0.20/0.46 => ( ( M
% 0.20/0.46 @ ^ [Z: $i] : ( G @ ( G @ Z ) ) )
% 0.20/0.46 & ! [Y: $i] :
% 0.20/0.46 ( ( P @ Y )
% 0.20/0.46 => ( P @ ( G @ Y ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 1.50/1.27 ---- Embedded in THF ---
% 1.50/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.27 %%% Generated on Tue Feb 24 12:37:41 EST 2026
% 1.50/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.27 %%% Logic specification used:
% 1.50/1.27 %%% thf(spec, logic, $$dhol).
% 1.50/1.27
% 1.50/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.ZpJQKmtmZB/DTF2DTF8318.p
% See solution above
% 1.50/1.27 ------------------------
% 1.50/1.29 ---- Cleaned THF ---
% 1.50/1.29 thf(cTHM113,conjecture,
% 1.50/1.29 ! [P: $i > $o] :
% 1.50/1.29 ? [M: ( $i > $i ) > $o] :
% 1.50/1.29 ! [G: $i > $i] :
% 1.50/1.29 ( ( M @ G )
% 1.50/1.29 => ( ( M
% 1.50/1.29 @ ^ [Z: $i] : ( G @ ( G @ Z ) ) )
% 1.50/1.29 & ! [Y: $i] :
% 1.50/1.29 ( ( P @ Y )
% 1.50/1.29 => ( P @ ( G @ Y ) ) ) ) ) ).
% 1.50/1.29 ------------------------
% 1.65/1.30 % (8498)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_8318 for (3000ds/183Mi)
% 1.65/1.30 % (8498)First to succeed.
% 1.65/1.30 % (8498)Refutation found. Thanks to Tanya!
% 1.65/1.30 % SZS status Theorem for DTF2THF_8318
% 1.65/1.30 % SZS output start Proof for DTF2THF_8318
% 1.65/1.30 thf(func_def_5, type, sK0: $i > $o).
% 1.65/1.30 thf(func_def_6, type, sK1: (($i > $i) > $o) > $i > $i).
% 1.65/1.30 thf(func_def_7, type, sK2: (($i > $i) > $o) > $i).
% 1.65/1.30 thf(func_def_10, type, ph4: !>[X0: $tType]:(X0)).
% 1.65/1.30 thf(f22,plain,(
% 1.65/1.30 $false),
% 1.65/1.30 inference(trivial_inequality_removal,[status(thm)],[f21])).
% 1.65/1.30 thf(f21,plain,(
% 1.65/1.30 ($true = $false)),
% 1.65/1.30 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.65/1.30 thf(f16,plain,(
% 1.65/1.30 (((^[Y0 : $i > $i]: ($false)) @ (sK1 @ (^[Y0 : $i > $i]: ($false)))) = $true)),
% 1.65/1.30 inference(primitive_instantiation,[status(thm)],[f14])).
% 1.65/1.30 thf(f14,plain,(
% 1.65/1.30 ( ! [X1 : ($i > $i) > $o] : (((X1 @ (sK1 @ X1)) = $true)) )),
% 1.65/1.30 inference(cnf_transformation,[status(thm)],[f11])).
% 1.65/1.30 thf(f11,plain,(
% 1.65/1.30 ! [X1 : ($i > $i) > $o] : (((X1 @ (sK1 @ X1)) = $true) & (($true != (X1 @ (^[Y0 : $i]: (sK1 @ X1 @ (sK1 @ X1 @ Y0))))) | (((sK0 @ (sK1 @ X1 @ (sK2 @ X1))) != $true) & ($true = (sK0 @ (sK2 @ X1))))))),
% 1.65/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f7,f10,f9,f8])).
% 1.65/1.30 thf(f8,plain,(
% 1.65/1.30 ? [X0 : $i > $o] : ! [X1 : ($i > $i) > $o] : ? [X2 : $i > $i] : (((X1 @ X2) = $true) & (($true != (X1 @ (^[Y0 : $i]: (X2 @ (X2 @ Y0))))) | ? [X3 : $i] : (($true != (X0 @ (X2 @ X3))) & ((X0 @ X3) = $true)))) => ! [X1 : ($i > $i) > $o] : ? [X2 : $i > $i] : (((X1 @ X2) = $true) & (($true != (X1 @ (^[Y0 : $i]: (X2 @ (X2 @ Y0))))) | ? [X3 : $i] : (((sK0 @ (X2 @ X3)) != $true) & ($true = (sK0 @ X3)))))),
% 1.65/1.30 introduced(definition,[],[choice_axiom])).
% 1.65/1.30 thf(f9,plain,(
% 1.65/1.30 ! [X1 : ($i > $i) > $o] : (? [X2 : $i > $i] : (((X1 @ X2) = $true) & (($true != (X1 @ (^[Y0 : $i]: (X2 @ (X2 @ Y0))))) | ? [X3 : $i] : (((sK0 @ (X2 @ X3)) != $true) & ($true = (sK0 @ X3))))) => (((X1 @ (sK1 @ X1)) = $true) & (($true != (X1 @ (^[Y0 : $i]: (sK1 @ X1 @ (sK1 @ X1 @ Y0))))) | ? [X3 : $i] : (((sK0 @ (sK1 @ X1 @ X3)) != $true) & ($true = (sK0 @ X3))))))),
% 1.65/1.30 introduced(definition,[],[choice_axiom])).
% 1.65/1.30 thf(f10,plain,(
% 1.65/1.30 ! [X1 : ($i > $i) > $o] : (? [X3 : $i] : (((sK0 @ (sK1 @ X1 @ X3)) != $true) & ($true = (sK0 @ X3))) => (((sK0 @ (sK1 @ X1 @ (sK2 @ X1))) != $true) & ($true = (sK0 @ (sK2 @ X1)))))),
% 1.65/1.30 introduced(definition,[],[choice_axiom])).
% 1.65/1.30 thf(f7,plain,(
% 1.65/1.30 ? [X0 : $i > $o] : ! [X1 : ($i > $i) > $o] : ? [X2 : $i > $i] : (((X1 @ X2) = $true) & (($true != (X1 @ (^[Y0 : $i]: (X2 @ (X2 @ Y0))))) | ? [X3 : $i] : (($true != (X0 @ (X2 @ X3))) & ((X0 @ X3) = $true))))),
% 1.65/1.30 inference(ennf_transformation,[status(thm)],[f6])).
% 1.65/1.30 thf(f6,plain,(
% 1.65/1.30 ~! [X0 : $i > $o] : ? [X1 : ($i > $i) > $o] : ! [X2 : $i > $i] : (((X1 @ X2) = $true) => (! [X3 : $i] : (((X0 @ X3) = $true) => ($true = (X0 @ (X2 @ X3)))) & ($true = (X1 @ (^[Y0 : $i]: (X2 @ (X2 @ Y0)))))))),
% 1.65/1.30 inference(rectify,[status(thm)],[f5])).
% 1.65/1.30 thf(f5,plain,(
% 1.65/1.30 ~! [X0 : $i > $o] : ? [X1 : ($i > $i) > $o] : ! [X2 : $i > $i] : (((X1 @ X2) = $true) => (($true = (X1 @ (^[Y0 : $i]: (X2 @ (X2 @ Y0))))) & ! [X4 : $i] : (((X0 @ X4) = $true) => ((X0 @ (X2 @ X4)) = $true))))),
% 1.65/1.30 inference(fool_elimination,[status(thm)],[f4])).
% 1.65/1.30 thf(f4,plain,(
% 1.65/1.30 ~! [X0 : $i > $o] : ? [X1 : ($i > $i) > $o] : ! [X2 : $i > $i] : ((X1 @ X2) => ((X1 @ (^[X3 : $i] : (X2 @ (X2 @ X3)))) & ! [X4 : $i] : ((X0 @ X4) => (X0 @ (X2 @ X4)))))),
% 1.65/1.30 inference(rectify,[status(thm)],[f2])).
% 1.65/1.30 thf(f2,negated_conjecture,(
% 1.65/1.30 ~! [X0 : $i > $o] : ? [X1 : ($i > $i) > $o] : ! [X2 : $i > $i] : ((X1 @ X2) => ((X1 @ (^[X3 : $i] : (X2 @ (X2 @ X3)))) & ! [X4 : $i] : ((X0 @ X4) => (X0 @ (X2 @ X4)))))),
% 1.65/1.30 inference(negated_conjecture,[status(cth)],[f1])).
% 1.65/1.30 thf(f1,conjecture,(
% 1.65/1.30 ! [X0 : $i > $o] : ? [X1 : ($i > $i) > $o] : ! [X2 : $i > $i] : ((X1 @ X2) => ((X1 @ (^[X3 : $i] : (X2 @ (X2 @ X3)))) & ! [X4 : $i] : ((X0 @ X4) => (X0 @ (X2 @ X4)))))),
% 1.65/1.30 file('/export/starexec/sandbox2/tmp/tmp.ZpJQKmtmZB/DTF2THF_8318.p',cTHM113)).
% 1.65/1.30 % SZS output end Proof for DTF2THF_8318
% 1.65/1.30 % (8498)------------------------------
% 1.65/1.30 % (8498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.30 % (8498)Termination reason: Refutation
% 1.65/1.30
% 1.65/1.30 % (8498)Memory used [KB]: 5500
% 1.65/1.30 % (8498)Time elapsed: 0.003 s
% 1.65/1.30 % (8498)Instructions burned: 1 (million)
% 1.65/1.30 % (8498)------------------------------
% 1.65/1.30 % (8498)------------------------------
% 1.65/1.30 % (8496)Success in time 0.005 s
%------------------------------------------------------------------------------