%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO238^5 : 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 : n024.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 09:53:44 AM UTC 2026
% Result : Theorem 1.55s 1.31s
% Output : Refutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 5 unt; 0 typ; 2 def)
% Number of atoms : 105 ( 36 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 99 ( 16 ~; 9 |; 6 &; 42 @)
% ( 2 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 30 ( 22 ^; 8 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_2,type,
cP: $i > $o ).
thf(func_def_3,type,
f: $i > $i ).
thf(func_def_10,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f28,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f21,f22,f27]) ).
thf(f27,plain,
spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f26]) ).
thf(f26,plain,
( $false
| spl0_2 ),
inference(subsumption_resolution,[status(thm)],[f25,f11]) ).
thf(f11,plain,
! [X0: $i] :
( ( f @ X0 )
= X0 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( cB != $true )
& ! [X0: $i] :
( ( f @ X0 )
= X0 )
& ( ( cP @ x )
= $true )
& ( ( ( ^ [Y0: $i] : Y0 )
!= ( ^ [Y0: $i] : ( f @ ( f @ Y0 ) ) ) )
| ( cB = $true ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ( cB != $true )
& ( ( cP @ x )
= $true )
& ( ( ( ^ [Y0: $i] : Y0 )
!= ( ^ [Y0: $i] : ( f @ ( f @ Y0 ) ) ) )
| ( cB = $true ) )
& ! [X0: $i] :
( ( f @ X0 )
= X0 ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ! [X0: $i] :
( ( f @ X0 )
= X0 )
=> ( ( ( ( ^ [Y0: $i] : Y0 )
= ( ^ [Y0: $i] : ( f @ ( f @ Y0 ) ) ) )
=> ( cB = $true ) )
=> ( ( ( cP @ x )
= $true )
=> ( cB = $true ) ) ) ),
inference(true_and_false_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( $true
=> ! [X0: $i] :
( ( f @ X0 )
= X0 ) )
=> ( ( ( ( ^ [Y0: $i] : Y0 )
= ( ^ [Y0: $i] : ( f @ ( f @ Y0 ) ) ) )
=> ( cB = $true ) )
=> ( ( ( cP @ x )
= $true )
=> ( cB = $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( $true
=> ! [X0: $i] :
( ( f @ X0 )
= X0 ) )
=> ( ( ( ( ^ [X1: $i] : X1 )
= ( ^ [X2: $i] : ( f @ ( f @ X2 ) ) ) )
=> cB )
=> ( ( cP @ x )
=> cB ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( $true
=> ! [X0: $i] :
( ( f @ X0 )
= X0 ) )
=> ( ( ( ( ^ [X0: $i] : X0 )
= ( ^ [X0: $i] : ( f @ ( f @ X0 ) ) ) )
=> cB )
=> ( ( cP @ x )
=> cB ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( $true
=> ! [X0: $i] :
( ( f @ X0 )
= X0 ) )
=> ( ( ( ( ^ [X0: $i] : X0 )
= ( ^ [X0: $i] : ( f @ ( f @ X0 ) ) ) )
=> cB )
=> ( ( cP @ x )
=> cB ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.rav3TA2xKn/DTF2THF_4409.p',cADDHYP5) ).
thf(f25,plain,
( ( sK2
!= ( f @ sK2 ) )
| spl0_2 ),
inference(forward_demodulation,[status(thm)],[f24,f11]) ).
thf(f24,plain,
( ( sK2
!= ( f @ ( f @ sK2 ) ) )
| spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( ^ [Y0: $i] : Y0
@ sK2 )
!= ( ^ [Y0: $i] : ( f @ ( f @ Y0 ) )
@ sK2 ) )
| spl0_2 ),
inference(negative_extensionality,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( ^ [Y0: $i] : Y0 )
!= ( ^ [Y0: $i] : ( f @ ( f @ Y0 ) ) ) )
| spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f18]) ).
thf(f18,definition,
( spl0_2
<=> ( ( ^ [Y0: $i] : Y0 )
= ( ^ [Y0: $i] : ( f @ ( f @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f22,plain,
~ spl0_1,
inference(avatar_split_clause,[status(thm)],[f12,f14]) ).
thf(f14,definition,
( spl0_1
<=> ( cB = $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f12,plain,
cB != $true,
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f21,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f9,f18,f14]) ).
thf(f9,plain,
( ( ( ^ [Y0: $i] : Y0 )
!= ( ^ [Y0: $i] : ( f @ ( f @ Y0 ) ) ) )
| ( cB = $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO238^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.09 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n024.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 09:26:25 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.38 ---- Original DTF file ---
% 0.17/0.38 thf(spec,logic,$$dhol).
% 0.17/0.38 %------------------------------------------------------------------------------
% 0.17/0.38 % File : SYO238^5 : TPTP v9.2.1. Released v4.0.0.
% 0.17/0.38 % Domain : Syntactic
% 0.17/0.38 % Problem : TPS problem from BASIC-HO-EQ-THMS
% 0.17/0.38 % Version : Especial.
% 0.17/0.38 % English :
% 0.17/0.38
% 0.17/0.38 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.17/0.38 % Source : [Bro09]
% 0.17/0.38 % Names : tps_0822 [Bro09]
% 0.17/0.38
% 0.17/0.38 % Status : Theorem
% 0.17/0.38 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.17/0.38 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.17/0.38 % Number of atoms : 6 ( 2 equ; 0 cnn)
% 0.17/0.38 % Maximal formula atoms : 6 ( 6 avg)
% 0.17/0.38 % Number of connectives : 9 ( 0 ~; 0 |; 0 &; 4 @)
% 0.17/0.38 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.17/0.38 % Maximal formula depth : 5 ( 5 avg)
% 0.17/0.38 % Number of types : 2 ( 0 usr)
% 0.17/0.38 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.17/0.38 % Number of symbols : 6 ( 4 usr; 3 con; 0-2 aty)
% 0.17/0.38 % Number of variables : 3 ( 2 ^; 1 !; 0 ?; 3 :)
% 0.17/0.38 % SPC : TH0_THM_EQU_NAR
% 0.17/0.38
% 0.17/0.38 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.17/0.38 % project in the Department of Mathematical Sciences at Carnegie
% 0.17/0.38 % Mellon University. Distributed under the Creative Commons copyleft
% 0.17/0.38 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.17/0.38 %------------------------------------------------------------------------------
% 0.17/0.38 thf(cB,type,
% 0.17/0.38 cB: $o ).
% 0.17/0.38
% 0.17/0.38 thf(x,type,
% 0.17/0.38 x: $i ).
% 0.17/0.38
% 0.17/0.38 thf(cP,type,
% 0.17/0.38 cP: $i > $o ).
% 0.17/0.38
% 0.17/0.38 thf(f,type,
% 0.17/0.38 f: $i > $i ).
% 0.17/0.38
% 0.17/0.38 thf(cADDHYP5,conjecture,
% 0.17/0.38 ( ( $true
% 0.17/0.38 => ! [Xx0: $i] :
% 0.17/0.38 ( ( f @ Xx0 )
% 0.17/0.38 = Xx0 ) )
% 0.17/0.38 => ( ( ( ( ^ [Xx0: $i] : ( f @ ( f @ Xx0 ) ) )
% 0.17/0.38 = ( ^ [Xx0: $i] : Xx0 ) )
% 0.17/0.38 => cB )
% 0.17/0.38 => ( ( cP @ x )
% 0.17/0.38 => cB ) ) ) ).
% 0.17/0.38
% 0.17/0.38 %------------------------------------------------------------------------------
% 0.17/0.38 ------------------------
% 1.36/1.28 ---- Embedded in THF ---
% 1.36/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.36/1.28 %%% Generated on Tue Feb 24 09:26:26 EST 2026
% 1.36/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.36/1.28 %%% Logic specification used:
% 1.36/1.28 %%% thf(spec, logic, $$dhol).
% 1.36/1.28
% 1.36/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.rav3TA2xKn/DTF2DTF4409.p
% See solution above
% 1.36/1.28 ------------------------
% 1.36/1.29 ---- Cleaned THF ---
% 1.36/1.29 thf(cB,type,
% 1.36/1.29 cB: $o ).
% 1.36/1.29
% 1.36/1.29 thf(x,type,
% 1.36/1.29 x: $i ).
% 1.36/1.29
% 1.36/1.29 thf(cP,type,
% 1.36/1.29 cP: $i > $o ).
% 1.36/1.29
% 1.36/1.29 thf(f,type,
% 1.36/1.29 f: $i > $i ).
% 1.36/1.29
% 1.36/1.29 thf(cADDHYP5,conjecture,
% 1.36/1.29 ( ( $true
% 1.36/1.29 => ! [Xx0: $i] :
% 1.36/1.29 ( ( f @ Xx0 )
% 1.36/1.29 = Xx0 ) )
% 1.36/1.29 => ( ( ( ( ^ [Xx0: $i] : ( f @ ( f @ Xx0 ) ) )
% 1.36/1.29 = ( ^ [Xx0: $i] : Xx0 ) )
% 1.36/1.29 => cB )
% 1.36/1.29 => ( ( cP @ x )
% 1.36/1.29 => cB ) ) ) ).
% 1.36/1.29 ------------------------
% 1.55/1.31 % (4509)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4409 for (3000ds/2Mi)
% 1.55/1.31 % (4508)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_4409 for (3000ds/27Mi)
% 1.55/1.31 % (4511)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_4409 for (3000ds/275Mi)
% 1.55/1.31 % (4507)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_4409 for (3000ds/4Mi)
% 1.55/1.31 % (4510)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_4409 for (3000ds/2Mi)
% 1.55/1.31 % (4512)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4409 for (3000ds/18Mi)
% 1.55/1.31 % (4506)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4409 for (3000ds/183Mi)
% 1.55/1.31 % (4509)Instruction limit reached!
% 1.55/1.31 % (4509)------------------------------
% 1.55/1.31 % (4509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.31 % (4509)Termination reason: Unknown
% 1.55/1.31 % (4509)Termination phase: Saturation
% 1.55/1.31 % (4510)Instruction limit reached!
% 1.55/1.31 % (4510)------------------------------
% 1.55/1.31 % (4510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.31 % (4510)Termination reason: Unknown
% 1.55/1.31 % (4510)Termination phase: Saturation
% 1.55/1.31
% 1.55/1.31 % (4510)Memory used [KB]: 5500
% 1.55/1.31 % (4510)Time elapsed: 0.003 s
% 1.55/1.31 % (4510)Instructions burned: 2 (million)
% 1.55/1.31 % (4510)------------------------------
% 1.55/1.31 % (4510)------------------------------
% 1.55/1.31
% 1.55/1.31 % (4509)Memory used [KB]: 5500
% 1.55/1.31 % (4509)Time elapsed: 0.003 s
% 1.55/1.31 % (4509)Instructions burned: 2 (million)
% 1.55/1.31 % (4509)------------------------------
% 1.55/1.31 % (4509)------------------------------
% 1.55/1.31 % (4511)First to succeed.
% 1.55/1.31 % (4512)Also succeeded, but the first one will report.
% 1.55/1.31 % (4511)Refutation found. Thanks to Tanya!
% 1.55/1.31 % SZS status Theorem for DTF2THF_4409
% 1.55/1.31 % SZS output start Proof for DTF2THF_4409
% 1.55/1.31 thf(func_def_2, type, cP: $i > $o).
% 1.55/1.31 thf(func_def_3, type, f: $i > $i).
% 1.55/1.31 thf(func_def_10, type, ph1: !>[X0: $tType]:(X0)).
% 1.55/1.31 thf(f28,plain,(
% 1.55/1.31 $false),
% 1.55/1.31 inference(avatar_sat_refutation,[status(thm)],[f21,f22,f27])).
% 1.55/1.31 thf(f27,plain,(
% 1.55/1.31 spl0_2),
% 1.55/1.31 inference(avatar_contradiction_clause,[status(thm)],[f26])).
% 1.55/1.31 thf(f26,plain,(
% 1.55/1.31 $false | spl0_2),
% 1.55/1.31 inference(subsumption_resolution,[status(thm)],[f25,f11])).
% 1.55/1.31 thf(f11,plain,(
% 1.55/1.31 ( ! [X0 : $i] : (((f @ X0) = X0)) )),
% 1.55/1.31 inference(cnf_transformation,[status(thm)],[f8])).
% 1.55/1.31 thf(f8,plain,(
% 1.55/1.31 (cB != $true) & ! [X0 : $i] : ((f @ X0) = X0) & ((cP @ x) = $true) & (((^[Y0 : $i]: (Y0)) != (^[Y0 : $i]: (f @ (f @ Y0)))) | (cB = $true))),
% 1.55/1.31 inference(flattening,[status(thm)],[f7])).
% 1.55/1.31 thf(f7,plain,(
% 1.55/1.31 (((cB != $true) & ((cP @ x) = $true)) & (((^[Y0 : $i]: (Y0)) != (^[Y0 : $i]: (f @ (f @ Y0)))) | (cB = $true))) & ! [X0 : $i] : ((f @ X0) = X0)),
% 1.55/1.31 inference(ennf_transformation,[status(thm)],[f6])).
% 1.55/1.31 thf(f6,plain,(
% 1.55/1.31 ~(! [X0 : $i] : ((f @ X0) = X0) => ((((^[Y0 : $i]: (Y0)) = (^[Y0 : $i]: (f @ (f @ Y0)))) => (cB = $true)) => (((cP @ x) = $true) => (cB = $true))))),
% 1.55/1.31 inference(true_and_false_elimination,[status(thm)],[f5])).
% 1.55/1.31 thf(f5,plain,(
% 1.55/1.31 ~(($true => ! [X0 : $i] : ((f @ X0) = X0)) => ((((^[Y0 : $i]: (Y0)) = (^[Y0 : $i]: (f @ (f @ Y0)))) => (cB = $true)) => (((cP @ x) = $true) => (cB = $true))))),
% 1.55/1.31 inference(fool_elimination,[status(thm)],[f4])).
% 1.55/1.31 thf(f4,plain,(
% 1.55/1.31 ~(($true => ! [X0 : $i] : ((f @ X0) = X0)) => ((((^[X1 : $i] : (X1)) = (^[X2 : $i] : (f @ (f @ X2)))) => cB) => ((cP @ x) => cB)))),
% 1.55/1.31 inference(rectify,[status(thm)],[f2])).
% 1.55/1.31 thf(f2,negated_conjecture,(
% 1.55/1.31 ~(($true => ! [X0 : $i] : ((f @ X0) = X0)) => ((((^[X0 : $i] : (X0)) = (^[X0 : $i] : (f @ (f @ X0)))) => cB) => ((cP @ x) => cB)))),
% 1.55/1.31 inference(negated_conjecture,[status(cth)],[f1])).
% 1.55/1.31 thf(f1,conjecture,(
% 1.55/1.31 ($true => ! [X0 : $i] : ((f @ X0) = X0)) => ((((^[X0 : $i] : (X0)) = (^[X0 : $i] : (f @ (f @ X0)))) => cB) => ((cP @ x) => cB))),
% 1.55/1.31 file('/export/starexec/sandbox2/tmp/tmp.rav3TA2xKn/DTF2THF_4409.p',cADDHYP5)).
% 1.55/1.31 thf(f25,plain,(
% 1.55/1.31 (sK2 != (f @ sK2)) | spl0_2),
% 1.55/1.31 inference(forward_demodulation,[status(thm)],[f24,f11])).
% 1.55/1.31 thf(f24,plain,(
% 1.55/1.31 (sK2 != (f @ (f @ sK2))) | spl0_2),
% 1.55/1.31 inference(beta_eta_normalization,[status(thm)],[f23])).
% 1.55/1.31 thf(f23,plain,(
% 1.55/1.31 (((^[Y0 : $i]: (Y0)) @ sK2) != ((^[Y0 : $i]: (f @ (f @ Y0))) @ sK2)) | spl0_2),
% 1.55/1.31 inference(negative_extensionality,[status(thm)],[f20])).
% 1.55/1.31 thf(f20,plain,(
% 1.55/1.31 ((^[Y0 : $i]: (Y0)) != (^[Y0 : $i]: (f @ (f @ Y0)))) | spl0_2),
% 1.55/1.31 inference(avatar_component_clause,[status(thm)],[f18])).
% 1.55/1.31 thf(f18,definition,(
% 1.55/1.31 spl0_2 <=> ((^[Y0 : $i]: (Y0)) = (^[Y0 : $i]: (f @ (f @ Y0))))),
% 1.55/1.31 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.55/1.31 thf(f22,plain,(
% 1.55/1.31 ~spl0_1),
% 1.55/1.31 inference(avatar_split_clause,[status(thm)],[f12,f14])).
% 1.55/1.31 thf(f14,definition,(
% 1.55/1.31 spl0_1 <=> (cB = $true)),
% 1.55/1.31 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.55/1.31 thf(f12,plain,(
% 1.55/1.31 (cB != $true)),
% 1.55/1.31 inference(cnf_transformation,[status(thm)],[f8])).
% 1.55/1.31 thf(f21,plain,(
% 1.55/1.31 spl0_1 | ~spl0_2),
% 1.55/1.31 inference(avatar_split_clause,[status(thm)],[f9,f18,f14])).
% 1.55/1.31 thf(f9,plain,(
% 1.55/1.31 ((^[Y0 : $i]: (Y0)) != (^[Y0 : $i]: (f @ (f @ Y0)))) | (cB = $true)),
% 1.55/1.31 inference(cnf_transformation,[status(thm)],[f8])).
% 1.55/1.31 % SZS output end Proof for DTF2THF_4409
% 1.55/1.31 % (4511)------------------------------
% 1.55/1.31 % (4511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.31 % (4511)Termination reason: Refutation
% 1.55/1.31
% 1.55/1.31 % (4511)Memory used [KB]: 5500
% 1.55/1.31 % (4511)Time elapsed: 0.003 s
% 1.55/1.31 % (4511)Instructions burned: 2 (million)
% 1.55/1.31 % (4511)------------------------------
% 1.55/1.31 % (4511)------------------------------
% 1.55/1.31 % (4505)Success in time 0.015 s
%------------------------------------------------------------------------------