%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO300^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.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 09:53:53 AM UTC 2026
% Result : Theorem 1.59s 1.30s
% Output : Refutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 15 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 79 ( 11 ~; 1 |; 4 &; 58 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 89 ( 89 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 2 con; 0-2 aty)
% Number of variables : 50 ( 24 ^; 20 !; 6 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_5,type,
sK0: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > $i ) > $o ).
thf(func_def_7,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f13,plain,
$false,
inference(flex-flex_simplify,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: ( $i > $i ) > $i] :
( ( ^ [Y0: $i > $i] :
( X0
@ ^ [Y1: $i] : Y1 ) )
!= ( ^ [Y0: $i > $i] : ( X0 @ Y0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: ( $i > $i ) > $i] :
( ( $true != $true )
| ( ( ^ [Y0: $i > $i] :
( X0
@ ^ [Y1: $i] : Y1 ) )
!= ( ^ [Y0: $i > $i] : ( X0 @ Y0 ) ) ) ),
inference(constrained_superposition,[status(thm)],[f9,f10]) ).
thf(f10,plain,
! [X2: ( $i > $i ) > $i] :
( ( sK0 @ X2 @ X2 )
= $true ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X1: ( $i > $i ) > $i] :
( ! [X2: ( $i > $i ) > $i] :
( ( sK0 @ X2 @ X2 )
= $true )
& ( $true
!= ( sK0
@ ^ [Y0: $i > $i] :
( Y0
@ ( X1
@ ^ [Y1: $i] : Y1 ) )
@ X1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7]) ).
thf(f7,plain,
( ? [X0: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > $i ) > $o] :
! [X1: ( $i > $i ) > $i] :
( ! [X2: ( $i > $i ) > $i] :
( ( X0 @ X2 @ X2 )
= $true )
& ( $true
!= ( X0
@ ^ [Y0: $i > $i] :
( Y0
@ ( X1
@ ^ [Y1: $i] : Y1 ) )
@ X1 ) ) )
=> ! [X1: ( $i > $i ) > $i] :
( ! [X2: ( $i > $i ) > $i] :
( ( sK0 @ X2 @ X2 )
= $true )
& ( $true
!= ( sK0
@ ^ [Y0: $i > $i] :
( Y0
@ ( X1
@ ^ [Y1: $i] : Y1 ) )
@ X1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > $i ) > $o] :
! [X1: ( $i > $i ) > $i] :
( ! [X2: ( $i > $i ) > $i] :
( ( X0 @ X2 @ X2 )
= $true )
& ( $true
!= ( X0
@ ^ [Y0: $i > $i] :
( Y0
@ ( X1
@ ^ [Y1: $i] : Y1 ) )
@ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > $i ) > $o] :
? [X1: ( $i > $i ) > $i] :
( ! [X2: ( $i > $i ) > $i] :
( ( X0 @ X2 @ X2 )
= $true )
=> ( $true
= ( X0
@ ^ [Y0: $i > $i] :
( Y0
@ ( X1
@ ^ [Y1: $i] : Y1 ) )
@ X1 ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > $i ) > $o] :
? [X1: ( $i > $i ) > $i] :
( ! [X2: ( $i > $i ) > $i] : ( X0 @ X2 @ X2 )
=> ( X0
@ ^ [X3: $i > $i] :
( X3
@ ( X1
@ ^ [X4: $i] : X4 ) )
@ X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > $i ) > $o] :
? [X1: ( $i > $i ) > $i] :
( ! [X2: ( $i > $i ) > $i] : ( X0 @ X2 @ X2 )
=> ( X0
@ ^ [X3: $i > $i] :
( X3
@ ( X1
@ ^ [X4: $i] : X4 ) )
@ X1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > $i ) > $o] :
? [X1: ( $i > $i ) > $i] :
( ! [X2: ( $i > $i ) > $i] : ( X0 @ X2 @ X2 )
=> ( X0
@ ^ [X3: $i > $i] :
( X3
@ ( X1
@ ^ [X4: $i] : X4 ) )
@ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.6zYX3ZiLmZ/DTF2THF_30331.p',cUNIFTHM1) ).
thf(f9,plain,
! [X1: ( $i > $i ) > $i] :
( $true
!= ( sK0
@ ^ [Y0: $i > $i] :
( Y0
@ ( X1
@ ^ [Y1: $i] : Y1 ) )
@ X1 ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO300^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n017.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 14:26:26 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
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.47 thf(spec,logic,$$dhol).
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % File : SYO300^5 : TPTP v9.2.1. Released v4.0.0.
% 0.28/0.47 % Domain : Syntactic
% 0.28/0.47 % Problem : TPS problem from BASIC-HO-THMS
% 0.28/0.47 % Version : Especial.
% 0.28/0.47 % English :
% 0.28/0.47
% 0.28/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.47 % Source : [Bro09]
% 0.28/0.47 % Names : tps_0770 [Bro09]
% 0.28/0.47
% 0.28/0.47 % Status : Theorem
% 0.28/0.47 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.25 v7.4.0, 0.22 v7.3.0, 0.30 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.25 v6.4.0, 0.29 v6.3.0, 0.33 v6.0.0, 0.17 v5.5.0, 0.00 v4.0.0
% 0.28/0.47 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.28/0.47 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.28/0.47 % Maximal formula atoms : 0 ( 0 avg)
% 0.28/0.47 % Number of connectives : 7 ( 0 ~; 0 |; 0 &; 6 @)
% 0.28/0.47 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.28/0.47 % Maximal formula depth : 10 ( 10 avg)
% 0.28/0.47 % Number of types : 2 ( 0 usr)
% 0.28/0.47 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.28/0.47 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.28/0.47 % Number of variables : 5 ( 2 ^; 2 !; 1 ?; 5 :)
% 0.28/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.28/0.47
% 0.28/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.28/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.28/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.28/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 thf(cUNIFTHM1,conjecture,
% 0.28/0.47 ! [P: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > $i ) > $o] :
% 0.28/0.47 ? [X: ( $i > $i ) > $i] :
% 0.28/0.47 ( ! [Xz: ( $i > $i ) > $i] : ( P @ Xz @ Xz )
% 0.28/0.47 => ( P
% 0.28/0.47 @ ^ [U: $i > $i] :
% 0.28/0.47 ( U
% 0.28/0.47 @ ( X
% 0.28/0.47 @ ^ [V: $i] : V ) )
% 0.28/0.47 @ X ) ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 1.45/1.26 ---- Embedded in THF ---
% 1.45/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.26 %%% Generated on Tue Feb 24 14:26:26 EST 2026
% 1.45/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.26 %%% Logic specification used:
% 1.45/1.26 %%% thf(spec, logic, $$dhol).
% 1.45/1.26
% 1.45/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.6zYX3ZiLmZ/DTF2DTF30331.p
% See solution above
% 1.45/1.26 ------------------------
% 1.45/1.28 ---- Cleaned THF ---
% 1.45/1.28 thf(cUNIFTHM1,conjecture,
% 1.45/1.28 ! [P: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > $i ) > $o] :
% 1.45/1.28 ? [X: ( $i > $i ) > $i] :
% 1.45/1.28 ( ! [Xz: ( $i > $i ) > $i] : ( P @ Xz @ Xz )
% 1.45/1.28 => ( P
% 1.45/1.28 @ ^ [U: $i > $i] :
% 1.45/1.28 ( U
% 1.45/1.28 @ ( X
% 1.45/1.28 @ ^ [V: $i] : V ) )
% 1.45/1.28 @ X ) ) ).
% 1.45/1.28 ------------------------
% 1.45/1.29 % (30616)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_30331 for (2999ds/275Mi)
% 1.45/1.29 % (30613)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_30331 for (2999ds/27Mi)
% 1.45/1.29 % (30616)Refutation not found, incomplete strategy
% 1.45/1.29 % (30616)------------------------------
% 1.45/1.29 % (30616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.29 % (30616)Termination reason: Refutation not found, incomplete strategy
% 1.45/1.29
% 1.45/1.29
% 1.45/1.29 % (30616)Memory used [KB]: 5500
% 1.45/1.29 % (30616)Time elapsed: 0.002 s
% 1.45/1.29 % (30616)Instructions burned: 1 (million)
% 1.45/1.29 % (30616)------------------------------
% 1.45/1.29 % (30616)------------------------------
% 1.45/1.29 % (30613)Refutation not found, incomplete strategy
% 1.45/1.29 % (30613)------------------------------
% 1.45/1.29 % (30613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.29 % (30613)Termination reason: Refutation not found, incomplete strategy
% 1.45/1.29
% 1.45/1.29
% 1.45/1.29 % (30613)Memory used [KB]: 5500
% 1.45/1.29 % (30613)Time elapsed: 0.002 s
% 1.45/1.29 % (30613)Instructions burned: 2 (million)
% 1.45/1.29 % (30613)------------------------------
% 1.45/1.29 % (30613)------------------------------
% 1.59/1.30 % (30611)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30331 for (2999ds/183Mi)
% 1.59/1.30 % (30612)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_30331 for (2999ds/4Mi)
% 1.59/1.30 % (30614)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30331 for (2999ds/2Mi)
% 1.59/1.30 % (30615)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_30331 for (2999ds/2Mi)
% 1.59/1.30 % (30617)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30331 for (2999ds/18Mi)
% 1.59/1.30 % (30611)First to succeed.
% 1.59/1.30 % (30614)Refutation not found, incomplete strategy
% 1.59/1.30 % (30614)------------------------------
% 1.59/1.30 % (30614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.30 % (30614)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.30
% 1.59/1.30
% 1.59/1.30 % (30614)Memory used [KB]: 5500
% 1.59/1.30 % (30614)Time elapsed: 0.003 s
% 1.59/1.30 % (30614)Instructions burned: 1 (million)
% 1.59/1.30 % (30614)------------------------------
% 1.59/1.30 % (30614)------------------------------
% 1.59/1.30 % (30615)Instruction limit reached!
% 1.59/1.30 % (30615)------------------------------
% 1.59/1.30 % (30615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.30 % (30615)Termination reason: Unknown
% 1.59/1.30 % (30615)Termination phase: Saturation
% 1.59/1.30
% 1.59/1.30 % (30615)Memory used [KB]: 5500
% 1.59/1.30 % (30615)Time elapsed: 0.004 s
% 1.59/1.30 % (30615)Instructions burned: 3 (million)
% 1.59/1.30 % (30615)------------------------------
% 1.59/1.30 % (30615)------------------------------
% 1.59/1.30 % (30612)Also succeeded, but the first one will report.
% 1.59/1.30 % (30611)Refutation found. Thanks to Tanya!
% 1.59/1.30 % SZS status Theorem for DTF2THF_30331
% 1.59/1.30 % SZS output start Proof for DTF2THF_30331
% 1.59/1.30 thf(func_def_5, type, sK0: (($i > $i) > $i) > (($i > $i) > $i) > $o).
% 1.59/1.30 thf(func_def_7, type, ph2: !>[X0: $tType]:(X0)).
% 1.59/1.30 thf(f13,plain,(
% 1.59/1.30 $false),
% 1.59/1.30 inference(flex-flex_simplify,[status(thm)],[f12])).
% 1.59/1.30 thf(f12,plain,(
% 1.59/1.30 ( ! [X0 : ($i > $i) > $i] : (((^[Y0 : $i > $i]: (X0 @ (^[Y1 : $i]: (Y1)))) != (^[Y0 : $i > $i]: (X0 @ Y0)))) )),
% 1.59/1.30 inference(trivial_inequality_removal,[status(thm)],[f11])).
% 1.59/1.30 thf(f11,plain,(
% 1.59/1.30 ( ! [X0 : ($i > $i) > $i] : (($true != $true) | ((^[Y0 : $i > $i]: (X0 @ (^[Y1 : $i]: (Y1)))) != (^[Y0 : $i > $i]: (X0 @ Y0)))) )),
% 1.59/1.30 inference(constrained_superposition,[status(thm)],[f9,f10])).
% 1.59/1.30 thf(f10,plain,(
% 1.59/1.30 ( ! [X2 : ($i > $i) > $i] : (((sK0 @ X2 @ X2) = $true)) )),
% 1.59/1.30 inference(cnf_transformation,[status(thm)],[f8])).
% 1.59/1.30 thf(f8,plain,(
% 1.59/1.30 ! [X1 : ($i > $i) > $i] : (! [X2 : ($i > $i) > $i] : ((sK0 @ X2 @ X2) = $true) & ($true != (sK0 @ (^[Y0 : $i > $i]: (Y0 @ (X1 @ (^[Y1 : $i]: (Y1))))) @ X1)))),
% 1.59/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7])).
% 1.59/1.30 thf(f7,plain,(
% 1.59/1.30 ? [X0 : (($i > $i) > $i) > (($i > $i) > $i) > $o] : ! [X1 : ($i > $i) > $i] : (! [X2 : ($i > $i) > $i] : ((X0 @ X2 @ X2) = $true) & ($true != (X0 @ (^[Y0 : $i > $i]: (Y0 @ (X1 @ (^[Y1 : $i]: (Y1))))) @ X1))) => ! [X1 : ($i > $i) > $i] : (! [X2 : ($i > $i) > $i] : ((sK0 @ X2 @ X2) = $true) & ($true != (sK0 @ (^[Y0 : $i > $i]: (Y0 @ (X1 @ (^[Y1 : $i]: (Y1))))) @ X1)))),
% 1.59/1.30 introduced(definition,[],[choice_axiom])).
% 1.59/1.30 thf(f6,plain,(
% 1.59/1.30 ? [X0 : (($i > $i) > $i) > (($i > $i) > $i) > $o] : ! [X1 : ($i > $i) > $i] : (! [X2 : ($i > $i) > $i] : ((X0 @ X2 @ X2) = $true) & ($true != (X0 @ (^[Y0 : $i > $i]: (Y0 @ (X1 @ (^[Y1 : $i]: (Y1))))) @ X1)))),
% 1.59/1.30 inference(ennf_transformation,[status(thm)],[f5])).
% 1.59/1.30 thf(f5,plain,(
% 1.59/1.30 ~! [X0 : (($i > $i) > $i) > (($i > $i) > $i) > $o] : ? [X1 : ($i > $i) > $i] : (! [X2 : ($i > $i) > $i] : ((X0 @ X2 @ X2) = $true) => ($true = (X0 @ (^[Y0 : $i > $i]: (Y0 @ (X1 @ (^[Y1 : $i]: (Y1))))) @ X1)))),
% 1.59/1.30 inference(fool_elimination,[status(thm)],[f4])).
% 1.59/1.30 thf(f4,plain,(
% 1.59/1.30 ~! [X0 : (($i > $i) > $i) > (($i > $i) > $i) > $o] : ? [X1 : ($i > $i) > $i] : (! [X2 : ($i > $i) > $i] : (X0 @ X2 @ X2) => (X0 @ (^[X3 : $i > $i] : (X3 @ (X1 @ (^[X4 : $i] : (X4))))) @ X1))),
% 1.59/1.30 inference(rectify,[status(thm)],[f2])).
% 1.59/1.30 thf(f2,negated_conjecture,(
% 1.59/1.30 ~! [X0 : (($i > $i) > $i) > (($i > $i) > $i) > $o] : ? [X1 : ($i > $i) > $i] : (! [X2 : ($i > $i) > $i] : (X0 @ X2 @ X2) => (X0 @ (^[X3 : $i > $i] : (X3 @ (X1 @ (^[X4 : $i] : (X4))))) @ X1))),
% 1.59/1.30 inference(negated_conjecture,[status(cth)],[f1])).
% 1.59/1.30 thf(f1,conjecture,(
% 1.59/1.30 ! [X0 : (($i > $i) > $i) > (($i > $i) > $i) > $o] : ? [X1 : ($i > $i) > $i] : (! [X2 : ($i > $i) > $i] : (X0 @ X2 @ X2) => (X0 @ (^[X3 : $i > $i] : (X3 @ (X1 @ (^[X4 : $i] : (X4))))) @ X1))),
% 1.59/1.30 file('/export/starexec/sandbox/tmp/tmp.6zYX3ZiLmZ/DTF2THF_30331.p',cUNIFTHM1)).
% 1.59/1.30 thf(f9,plain,(
% 1.59/1.30 ( ! [X1 : ($i > $i) > $i] : (($true != (sK0 @ (^[Y0 : $i > $i]: (Y0 @ (X1 @ (^[Y1 : $i]: (Y1))))) @ X1))) )),
% 1.59/1.30 inference(cnf_transformation,[status(thm)],[f8])).
% 1.59/1.30 % SZS output end Proof for DTF2THF_30331
% 1.59/1.30 % (30611)------------------------------
% 1.59/1.30 % (30611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.30 % (30611)Termination reason: Refutation
% 1.59/1.30
% 1.59/1.30 % (30611)Memory used [KB]: 5500
% 1.59/1.30 % (30611)Time elapsed: 0.004 s
% 1.59/1.30 % (30611)Instructions burned: 1 (million)
% 1.59/1.30 % (30611)------------------------------
% 1.59/1.30 % (30611)------------------------------
% 1.59/1.30 % (30610)Success in time 0.019 s
%------------------------------------------------------------------------------