%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV290^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n002.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 09:40:45 AM UTC 2026
% Result : Theorem 1.50s 1.29s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 11 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 52 ( 13 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 48 ( 7 ~; 0 |; 4 &; 32 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 40 ( 40 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 16 ( 2 ^; 8 !; 6 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
c0: ( $i > $o ) > $o ).
thf(func_def_1,type,
cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
thf(func_def_2,type,
c_less__eq_: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).
thf(func_def_16,type,
sK0: ( ( ( $i > $o ) > $o ) > $o ) > ( $i > $o ) > $o ).
thf(func_def_18,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f24,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f23]) ).
thf(f23,plain,
$false = $true,
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ^ [Y0: ( $i > $o ) > $o] : $false
@ ( sK0
@ ^ [Y0: ( $i > $o ) > $o] : $false ) )
= $true ),
inference(primitive_instantiation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: ( ( $i > $o ) > $o ) > $o] :
( ( X0 @ ( sK0 @ X0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: ( ( $i > $o ) > $o ) > $o] :
( ( $true
!= ( c_less__eq_ @ ( sK0 @ X0 ) @ c0 ) )
& ( ( X0 @ ( sK0 @ X0 ) )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f12,f13]) ).
thf(f13,plain,
! [X0: ( ( $i > $o ) > $o ) > $o] :
( ? [X1: ( $i > $o ) > $o] :
( ( $true
!= ( c_less__eq_ @ X1 @ c0 ) )
& ( ( X0 @ X1 )
= $true ) )
=> ( ( $true
!= ( c_less__eq_ @ ( sK0 @ X0 ) @ c0 ) )
& ( ( X0 @ ( sK0 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X0: ( ( $i > $o ) > $o ) > $o] :
? [X1: ( $i > $o ) > $o] :
( ( $true
!= ( c_less__eq_ @ X1 @ c0 ) )
& ( ( X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ? [X0: ( ( $i > $o ) > $o ) > $o] :
! [X1: ( $i > $o ) > $o] :
( ( ( X0 @ X1 )
= $true )
=> ( $true
= ( c_less__eq_ @ X1 @ c0 ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ? [X0: ( ( $i > $o ) > $o ) > $o] :
! [X1: ( $i > $o ) > $o] :
( ( X0 @ X1 )
=> ( c_less__eq_ @ X1 @ c0 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ? [X6: ( ( $i > $o ) > $o ) > $o] :
! [X2: ( $i > $o ) > $o] :
( ( X6 @ X2 )
=> ( c_less__eq_ @ X2 @ c0 ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
? [X6: ( ( $i > $o ) > $o ) > $o] :
! [X2: ( $i > $o ) > $o] :
( ( X6 @ X2 )
=> ( c_less__eq_ @ X2 @ c0 ) ),
file('/export/starexec/sandbox/tmp/tmp.CkraPjwikw/DTF2THF_14252.p',cBLEDSOE1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV290^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n002.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:43:18 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/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 : SEV290^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.31/0.46 % Domain : Set Theory
% 0.31/0.46 % Problem : TPS problem BLEDSOE1
% 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_0170 [Bro09]
% 0.31/0.46 % : BLEDSOE1 [TPS]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.12 v7.0.0, 0.00 v6.2.0, 0.29 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.2.0
% 0.31/0.46 % Syntax : Number of formulae : 6 ( 2 unt; 3 typ; 2 def)
% 0.31/0.46 % Number of atoms : 8 ( 3 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 2 ( 2 avg)
% 0.31/0.46 % Number of connectives : 18 ( 1 ~; 0 |; 3 &; 11 @)
% 0.31/0.46 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 6 ( 3 avg)
% 0.31/0.46 % Number of types : 2 ( 0 usr)
% 0.31/0.46 % Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 4 ( 3 usr; 0 con; 1-2 aty)
% 0.31/0.46 % Number of variables : 10 ( 5 ^; 3 !; 2 ?; 10 :)
% 0.31/0.46 % SPC : TH0_THM_EQU_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 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(c0_type,type,
% 0.31/0.46 c0: ( $i > $o ) > $o ).
% 0.31/0.46
% 0.31/0.46 thf(cSUCC_type,type,
% 0.31/0.46 cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
% 0.31/0.46
% 0.31/0.46 thf(c_less__eq__type,type,
% 0.31/0.46 c_less__eq_: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).
% 0.31/0.46
% 0.31/0.46 thf(cSUCC_def,definition,
% 0.31/0.46 ( cSUCC
% 0.31/0.46 = ( ^ [Xn: ( $i > $o ) > $o,Xp: $i > $o] :
% 0.31/0.46 ? [Xx: $i] :
% 0.31/0.46 ( ( Xp @ Xx )
% 0.31/0.46 & ( Xn
% 0.31/0.46 @ ^ [Xt: $i] :
% 0.31/0.46 ( ( Xt != Xx )
% 0.31/0.46 & ( Xp @ Xt ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(c_less__eq__def,definition,
% 0.31/0.46 ( c_less__eq_
% 0.31/0.46 = ( ^ [Xx: ( $i > $o ) > $o,Xy: ( $i > $o ) > $o] :
% 0.31/0.46 ! [Xp: ( ( $i > $o ) > $o ) > $o] :
% 0.31/0.46 ( ( ( Xp @ Xx )
% 0.31/0.46 & ! [Xz: ( $i > $o ) > $o] :
% 0.31/0.46 ( ( Xp @ Xz )
% 0.31/0.46 => ( Xp @ ( cSUCC @ Xz ) ) ) )
% 0.31/0.46 => ( Xp @ Xy ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(cBLEDSOE1,conjecture,
% 0.31/0.46 ? [A: ( ( $i > $o ) > $o ) > $o] :
% 0.31/0.46 ! [Xx: ( $i > $o ) > $o] :
% 0.31/0.46 ( ( A @ Xx )
% 0.31/0.46 => ( c_less__eq_ @ Xx @ c0 ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 1.50/1.25 ---- Embedded in THF ---
% 1.50/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.25 %%% Generated on Tue Feb 24 12:43:19 EST 2026
% 1.50/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.25 %%% Logic specification used:
% 1.50/1.25 %%% thf(spec, logic, $$dhol).
% 1.50/1.25
% 1.50/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.CkraPjwikw/DTF2DTF14252.p
% See solution above
% 1.50/1.25 ------------------------
% 1.50/1.26 ---- Cleaned THF ---
% 1.50/1.26 thf(c0_type,type,
% 1.50/1.26 c0: ( $i > $o ) > $o ).
% 1.50/1.26
% 1.50/1.26 thf(cSUCC_type,type,
% 1.50/1.26 cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
% 1.50/1.26
% 1.50/1.26 thf(c_less__eq__type,type,
% 1.50/1.26 c_less__eq_: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).
% 1.50/1.26
% 1.50/1.26 thf(cSUCC_def,definition,
% 1.50/1.26 ( cSUCC
% 1.50/1.26 = ( ^ [Xn: ( $i > $o ) > $o,Xp: $i > $o] :
% 1.50/1.26 ? [Xx: $i] :
% 1.50/1.26 ( ( Xp @ Xx )
% 1.50/1.26 & ( Xn
% 1.50/1.26 @ ^ [Xt: $i] :
% 1.50/1.26 ( ( Xt != Xx )
% 1.50/1.26 & ( Xp @ Xt ) ) ) ) ) ) ).
% 1.50/1.26
% 1.50/1.26 thf(c_less__eq__def,definition,
% 1.50/1.26 ( c_less__eq_
% 1.50/1.26 = ( ^ [Xx: ( $i > $o ) > $o,Xy: ( $i > $o ) > $o] :
% 1.50/1.26 ! [Xp: ( ( $i > $o ) > $o ) > $o] :
% 1.50/1.26 ( ( ( Xp @ Xx )
% 1.50/1.26 & ! [Xz: ( $i > $o ) > $o] :
% 1.50/1.26 ( ( Xp @ Xz )
% 1.50/1.26 => ( Xp @ ( cSUCC @ Xz ) ) ) )
% 1.50/1.26 => ( Xp @ Xy ) ) ) ) ).
% 1.50/1.26
% 1.50/1.26 thf(cBLEDSOE1,conjecture,
% 1.50/1.26 ? [A: ( ( $i > $o ) > $o ) > $o] :
% 1.50/1.26 ! [Xx: ( $i > $o ) > $o] :
% 1.50/1.26 ( ( A @ Xx )
% 1.50/1.26 => ( c_less__eq_ @ Xx @ c0 ) ) ).
% 1.50/1.26 ------------------------
% 1.50/1.27 % (14531)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_14252 for (2999ds/27Mi)
% 1.50/1.27 % (14532)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14252 for (2999ds/2Mi)
% 1.50/1.28 % (14532)Instruction limit reached!
% 1.50/1.28 % (14532)------------------------------
% 1.50/1.28 % (14532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.28 % (14532)Termination reason: Unknown
% 1.50/1.28 % (14532)Termination phase: Saturation
% 1.50/1.28
% 1.50/1.28 % (14532)Memory used [KB]: 5500
% 1.50/1.28 % (14532)Time elapsed: 0.002 s
% 1.50/1.28 % (14532)Instructions burned: 3 (million)
% 1.50/1.28 % (14532)------------------------------
% 1.50/1.28 % (14532)------------------------------
% 1.50/1.28 % (14531)Refutation not found, incomplete strategy
% 1.50/1.28 % (14531)------------------------------
% 1.50/1.28 % (14531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.28 % (14531)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.28
% 1.50/1.28
% 1.50/1.28 % (14531)Memory used [KB]: 5500
% 1.50/1.28 % (14531)Time elapsed: 0.003 s
% 1.50/1.28 % (14531)Instructions burned: 4 (million)
% 1.50/1.28 % (14531)------------------------------
% 1.50/1.28 % (14531)------------------------------
% 1.50/1.28 % (14529)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14252 for (2999ds/183Mi)
% 1.50/1.28 % (14530)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_14252 for (2999ds/4Mi)
% 1.50/1.28 % (14533)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_14252 for (2999ds/2Mi)
% 1.50/1.28 % (14534)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_14252 for (2999ds/275Mi)
% 1.50/1.28 % (14535)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14252 for (2999ds/18Mi)
% 1.50/1.28 % (14533)Instruction limit reached!
% 1.50/1.28 % (14533)------------------------------
% 1.50/1.28 % (14533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.28 % (14533)Termination reason: Unknown
% 1.50/1.28 % (14533)Termination phase: Function definition elimination
% 1.50/1.28
% 1.50/1.28 % (14533)Memory used [KB]: 895
% 1.50/1.28 % (14533)Time elapsed: 0.003 s
% 1.50/1.28 % (14533)Instructions burned: 2 (million)
% 1.50/1.28 % (14533)------------------------------
% 1.50/1.28 % (14533)------------------------------
% 1.50/1.28 % (14534)First to succeed.
% 1.50/1.28 % (14529)Also succeeded, but the first one will report.
% 1.50/1.29 % (14534)Refutation found. Thanks to Tanya!
% 1.50/1.29 % SZS status Theorem for DTF2THF_14252
% 1.50/1.29 % SZS output start Proof for DTF2THF_14252
% 1.50/1.29 thf(func_def_0, type, c0: ($i > $o) > $o).
% 1.50/1.29 thf(func_def_1, type, cSUCC: (($i > $o) > $o) > ($i > $o) > $o).
% 1.50/1.29 thf(func_def_2, type, c_less__eq_: (($i > $o) > $o) > (($i > $o) > $o) > $o).
% 1.50/1.29 thf(func_def_16, type, sK0: ((($i > $o) > $o) > $o) > ($i > $o) > $o).
% 1.50/1.29 thf(func_def_18, type, ph2: !>[X0: $tType]:(X0)).
% 1.50/1.29 thf(f24,plain,(
% 1.50/1.29 $false),
% 1.50/1.29 inference(trivial_inequality_removal,[status(thm)],[f23])).
% 1.50/1.29 thf(f23,plain,(
% 1.50/1.29 ($false = $true)),
% 1.50/1.29 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.50/1.29 thf(f18,plain,(
% 1.50/1.29 (((^[Y0 : ($i > $o) > $o]: ($false)) @ (sK0 @ (^[Y0 : ($i > $o) > $o]: ($false)))) = $true)),
% 1.50/1.29 inference(primitive_instantiation,[status(thm)],[f15])).
% 1.50/1.29 thf(f15,plain,(
% 1.50/1.29 ( ! [X0 : (($i > $o) > $o) > $o] : (((X0 @ (sK0 @ X0)) = $true)) )),
% 1.50/1.29 inference(cnf_transformation,[status(thm)],[f14])).
% 1.50/1.29 thf(f14,plain,(
% 1.50/1.29 ! [X0 : (($i > $o) > $o) > $o] : (($true != (c_less__eq_ @ (sK0 @ X0) @ c0)) & ((X0 @ (sK0 @ X0)) = $true))),
% 1.50/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f12,f13])).
% 1.50/1.29 thf(f13,plain,(
% 1.50/1.29 ! [X0 : (($i > $o) > $o) > $o] : (? [X1 : ($i > $o) > $o] : (($true != (c_less__eq_ @ X1 @ c0)) & ((X0 @ X1) = $true)) => (($true != (c_less__eq_ @ (sK0 @ X0) @ c0)) & ((X0 @ (sK0 @ X0)) = $true)))),
% 1.50/1.29 introduced(definition,[],[choice_axiom])).
% 1.50/1.29 thf(f12,plain,(
% 1.50/1.29 ! [X0 : (($i > $o) > $o) > $o] : ? [X1 : ($i > $o) > $o] : (($true != (c_less__eq_ @ X1 @ c0)) & ((X0 @ X1) = $true))),
% 1.50/1.29 inference(ennf_transformation,[status(thm)],[f7])).
% 1.50/1.29 thf(f7,plain,(
% 1.50/1.29 ~? [X0 : (($i > $o) > $o) > $o] : ! [X1 : ($i > $o) > $o] : (((X0 @ X1) = $true) => ($true = (c_less__eq_ @ X1 @ c0)))),
% 1.50/1.29 inference(fool_elimination,[status(thm)],[f6])).
% 1.50/1.29 thf(f6,plain,(
% 1.50/1.29 ~? [X0 : (($i > $o) > $o) > $o] : ! [X1 : ($i > $o) > $o] : ((X0 @ X1) => (c_less__eq_ @ X1 @ c0))),
% 1.50/1.29 inference(rectify,[status(thm)],[f4])).
% 1.50/1.29 thf(f4,negated_conjecture,(
% 1.50/1.29 ~? [X6 : (($i > $o) > $o) > $o] : ! [X2 : ($i > $o) > $o] : ((X6 @ X2) => (c_less__eq_ @ X2 @ c0))),
% 1.50/1.29 inference(negated_conjecture,[status(cth)],[f3])).
% 1.50/1.29 thf(f3,conjecture,(
% 1.50/1.29 ? [X6 : (($i > $o) > $o) > $o] : ! [X2 : ($i > $o) > $o] : ((X6 @ X2) => (c_less__eq_ @ X2 @ c0))),
% 1.50/1.29 file('/export/starexec/sandbox/tmp/tmp.CkraPjwikw/DTF2THF_14252.p',cBLEDSOE1)).
% 1.50/1.29 % SZS output end Proof for DTF2THF_14252
% 1.50/1.29 % (14534)------------------------------
% 1.50/1.29 % (14534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (14534)Termination reason: Refutation
% 1.50/1.29
% 1.50/1.29 % (14534)Memory used [KB]: 5500
% 1.50/1.29 % (14534)Time elapsed: 0.004 s
% 1.50/1.29 % (14534)Instructions burned: 2 (million)
% 1.50/1.29 % (14534)------------------------------
% 1.50/1.29 % (14534)------------------------------
% 1.50/1.29 % (14528)Success in time 0.02 s
%------------------------------------------------------------------------------